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Mechanical Properties
of Polymers and Composites
(IN
TWO
VOLUME
VOLUMES)
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Mechanical Properties
of Polymers and Composites
(IN
TWO
VOLUMES)
VOLUME
2
LAWRENCE
E. NIELSEN
Monsanto Company
St. Louis, Missouri
MARCEL
DEKKER,INC.
New York
COPYRIGHT
©
ALL
RESERVED
RIGHTS
1974
by MARCEL
DEKKER,
INC.
Neither this book nor any part may be reproduced or
transmitted in any form or by any means, electronic
or mechanical, including photocopying, microfilming,
and recording, or by any information storage and
retrieval system, without permission in writing from
the publisher.
MARCEL
DEKKER,
270 Madison
LIBRARY
ISBN:
INC.
Avenue,
OF CONGRESS
New York,
CATALOG
New York
CARD
NUMBER:
0-8247-6208-8
Current printing (last digit);
10 9
7 CGS a es
PRINTED
IN THE UNITED
STATES
OF AMERICA
10016
74-80758
Atte)
Deanne
and
My
Mother
y
CONTENTS
Contents
of
Volume
1
ix
Preface
Chapter
xi
5
STRESS-STRAIN
le
Stress
A.
BEHAVIOR
Strain
AND
25)
Introduction
Zoi)
Models
258
Effect
of
Effect
Shear
Versus
260
262
Temperature
Rate of Testing
Envelope
of
and
the
Failure
265
Hydrostatic
Pressure
Weight
270
Effect of
Branching
Molecular
Effect
of
Crosslinking
PUD
Effect
of
Crystallinity
280
Effects
and
Bafa
of
Plasticization
and
Copolymerization
283
Molecular
285
Orientation
Polyblends,
Polymers
AAEAE
2597)
Behavior
Compression and
Tensile Tests
Tie
STRENGTH
Brittle
Block,
Fracture
and
Graft
Dey
and
Stress
Concentrators
294
A.
Stress
294
B.
Fracture
Theories
Concentrators
of
296
Theory
Yielding
and
Cold-Drawing
299
CONTENTS
vi
Vic
Impact
Strength
and
Tearing
308
Tests
308
A.
Nature
of
Impact
B.
Effect
of
Notches
309
C.
Effect
of
Temperature
Sys}
D.
Effects
E.
Other
of
314
Orientation
Factors
Affecting
Impact
Syi7/
Strength
Chapter
6
OTHER
F.
Impact
Strength
G.
Tearing
of
Polyblends
320
Summary
S22
Problems
323
References
328
MECHANICAL
Heat
PROPERTIES
Distortion
341
Temperature
341
Fatigue
348
Friction
353
Abrasion,
Wear,
and
Scratch
Resistance
Hardness
WATE
Chapter
7
318
BD
and
Indentation
Tests
363
Summary
369
Problems
370
References
si7/al
PARTICULATE-FILLED
POLYMERS
Ie
Introduction
to
ADE
Rheology
of
Composite
37/8)
Systems
Suspensions
Relation Between
Sheer Modulus
Viscosity
379
380
and
386
CONTENTS
vii
TV.
Moduli
of
Filled
Polymers
A.
Regular
B.
Inverted Systems
Inversion
Systems
C.
Errors
in
D.
Experimental
and
Phase
394
Moduli
401
Examples
and
A.
Fillers
B.
387
Composite
Strength
Rigid
387
405
Stress-Strain
Polyblends,
Behavior
405
Block
Polymers,
and
415
Foams
Chapter
8
VI.
Creep
VIL.
Dynamic
Vit.
Other
405
and
Stress
Relaxation
Mechanical
Mechanical
A.
Impact
B.
Heat
C.
Hardness
D.
Coefficients
Expansion
Properties
Properties
and
Temperature
430
431
433
Wear
of
422
430
Strength
Distortion
418
Thermal
434
Summary
437
Problems
438
References
442
FIBER-FILLED
COMPOSITES
COMPOSITES
ie
Introduction
ities
Moduli
III.
Strength
of
AND
OTHER
453
Fiber-Filled
of
453
Composites
Fiber-Filled
A.
Uniaxially
Oriented
B.
Strength of Randomly
Fiber Composites and
Composites
Fibers
Oriented
Laminates
454
465
465
474
viii
CONTENTS
TVie
Other
479
Properties
A.
Creep
479
B.
Fatigue
480
C.
Heat
D.
Impact
E.
Distortion
Temperature
481
483
Strength
Coefficients
of
Thermal
Expansion
487
Vv.
Ribbon-Filled
Valitse
Other
Types
Composites
of
Composites
496
Polymers
496
A.
Flake-Filled
B.
Composites
C.
Interpenetrating
Composites
with
Thick
500
VIII.
Problems
501
exes
References
503
CONVERSION FACTORS
AND VISCOSITY
Appendix
GLASS TRANSITION TEMPERATURE
OF POLYMERS
POINTS
Author
Subject
499
Summary
Appendix
STRUCTURE
OF
FOR
COMMON
MODULI,
POLYMERS
Index
Index
LIST
OF
SYMBOLS
511
STRESS
53
AND
MELTING
RELATIONS
BETWEEN ENGINEERING MODULI
TENSOR MODULI AND TENSOR COMPLIANCES
ANISOTROPIC MATERIALS
Vv
497
VII.
CHEMICAL
Appendix
Interlayers
Network
Appendix
Appendix
490
5:5
AND
FOR
Bug
525
537
553
CONTENTS
Mechanical
Creep
and
Tests
Stress
and
Polymer
Relaxation.
OF
VOLUME
1
Transitions.
Dynamic
slpre
Elastic
Mechanical
Moduli.
Properties.
PREFACE
Polymers
materials
use
and
rapid
rigid
cal
mechanical
an
but
which
those
working
departments
more
courses
sections
on
on
ial
in
this
ton
University.
mechanical
in
recent
knowledge
many
and
to
by
polymer
has
properties
years.
of
already
Design
This
of
been
engineers
viscoelasticity
on
and
and
xi
are
the
with
on
specialist
in
the
useful
on
of
putting
applications
synthesis
being
forced
mechanical
includes
semester
courses
are
offering
which
one
for
established
are
Much
in
the
be
have
a
a
to
be
book,
widely
enough
and
for
tested
emphasis
less
to
polymers.
laboratories
behavior
and
depth
suitable
properties
a
sciences
technology.
be
not
mechani-
about
simple
universities
material
should
been
elastomers
of
workers
published
is
is
and
Many
Industrial
mechanical
on
or
who
soft
knowledge
has
been
widespread
versatile
from
of
It
which
detail
polymers.
a
groups
has
polymers
enough
mechanical
book
book
a scientist
polymers
for
structural
Their
their
range
interests.
date
of
problems,
course
emphasis
by
has
in
the
polymers
with
in
cover
volume
metals.
from
a need
properties
field
largely
is
up
understood
to
There
backgrounds
since
large
importance
which
materials.
of
cheap,
result
properties
different
easily
in
growth
properties
decade
relatively
comparable
mechanical
to
are
the
at
mater-
Washing-
more
involving
of
to
polymers
gain
properties
of
reals
PREFACE
polymers
as
more
more
of
and
the
heat
the
these
importance
performance
for
polymers
purpose
as
of
many
and
of
their
elementary
to
the
mechanical
materials
are
concerned.
book
outlines
This
polymers
mental
to
factors
magnitude
lar
both
of
weight,
zation,
is
placed
upon
the
both
years
and
general
behavior
experimental
and
are
given
Composite
development
and
useful
area
for
structural
polymer
A
and
Structural
most
unified
these
and
factors
principles,
empirical
many
extensive
common
polymers.
which
have
Environ-
and
molecu-
plastici-
molecular
In
of
the
pressure,
copolymerization.
is
of
of
include
all
a
people
factors.
morphology,
there
is
behavior
external
useful
is
composite
copolymerization,
crystallite
cases,
emphasis
rules,
and
reference
also
Developments,
occurred
in
recent
attention.
are
now
a major
Composites
are
materials,
applications
second
It
all
polymers
temperature,
affect
properties
structural
theoretical,
materials
activity.
materials.
complete
the
and
However,
specific
there
of
aware
weight,
Thus,
level.
in
more
that
mechanical
crosslinking,
block
equations.
of
general
time,
branching,
needs
properties
loads.
crystallinity
practical
to
include
and
the
glass
etc.)
mechanical
intermediate
environmental
applied
Orientation,
to
the
molecular
objects.
the
fulfill
as
as
and
becoming
orientation,
discusses
book
metals
are
(such
finished
at
this
Fabricators
molecular
which
the
displace
factors
a book
of
far
materials
applications.
treatments,
need
newer
is
objective
picture
and
of
in
of
rapidly
probably
the
this
the
field
field
book
is
mechanical
of
research
and
becoming
important
the
major
of
to
next
composite
present
properties
a
PREFACE
of
xiii
composites
in
an
comparable
book
mechanical
behavior
exists
ticulate-filled
high
impact
aspects
cal
most
ledge
of
of
the
anisotropy,
different
in
discusses
anisotropy
scientists
field
their
different
Other
the
detail
at
because
an
this
engineers
are
familiar
only
Extensive
reference
is
made
to
the
most
important
only
mathemati-
of
entirely
their
may
be
entirely
this
level
with
know-
are
reason,
elementary
and
and
a working
properties
For
par-
too
materials
no
the
cover
are
need
past
mechanical
directions.
in
who
of
foams,
books
or
composite
in
field
materials,
engineers
used
present,
including
composites
Many
At
entire
materials,
of
and
materials
is,
the
polyblends.
materials.
that
manner.
fiber-filled
and
scientists
from
covers
composite
polymers,
these
different
understood
which
of
polymers
certain
for
easily
book
since
most
isotropic
materials.
has
been
made
to
that
illustrate
have
been
service
‘really
but
culling
add
very
it
should
himself
a point.
missed,
by
topic,
select
with
the
out
be
what
to
easy
a
author
he
of
our
for
been
has
literature.
Undoubtedly,
tens
little
the
hopes
thousands
references
few
of
done
by
references
to
looking
for
quickly
up
the
those
references
performed
Thus,
reader
attempt
and
important
has
knowledge.
the
An
a
useful
which
any
given
acquaint
listed
references.
The
the
author
preparation
numerous
include
cannot
of
suggestions
Joseph
acknowledge
this
book.
after
Bergomi,
Colleagues
reading
Rolf
everyone
the
Buchdahl,
who
who
has
have
original
Melvin
helped
in
offered
manuscript
Hedrick,
Myron
Holm,
xiv
PREFACE
Allen
Kenyon,
Woodbrey.
the
Mrs.
manuscript.
reading,
author
write
James
the
and
this
Kurz,
Bobbie
his
Kaplan
Deanne,
literature,
mass
of
Thomas
my
and
papers
Lewis,
Eli
Perry,
had
the
formidable
wife,
not
only
the
for
indexes,
the
helped
but
she
three
years
Lawrence
E.
and
task
James
of
with
typing
the
tolerated
required
book.
Nielsen
proof
the
to
Mechanical Properties
of Polymers and Composites
(IN
TWO
VOLUME
VOLUMES)
2
se
OMe
ot 7
| Jimeoee
:
hae
:
ee
Chapter
Stress-Strain
I.
Stress-Strain
Introduction
The
mechanics
discussed
most
widely
practical
test
the
as
as
clear
nature
in
used
However,
of
curve
of
or
rates
and
it
of
datum
is,
at
in
a
tests.
to
test
Because
only
finished
give
of
the
and
other
conditions;
to
data
in
addition
obvious
that
in
using
must
do
tensile
have
to
the
a
lot
or
one
tests
guessing
257
is
important
factors,
guide
and
to
not
the
how
only
or
a
a
single
and
designer
many
data
speed
the
temperatures,
much
requires
are
shear
time
but
known,
data
Thus,
data.
is
viscoelastic
many
at
based
the
for.
temperature
data
have
a very
the
this
uniaxial
of
applications
flexural
stress-strain
of
test
Often
compression
the
polymers
engineer
requires
desirable
rough
types
feeling
of
object.
characteristic
To
a
a
to
the
is
use
sensitivity
best,
only
It
this
needs
Often
high
have
their
and
stress-strain
really
testing,
engineer
of
of
engineers
assumed.
biaxial
the
The
which
published.
he
Strength
test
typical
mechanical
with
point
is
be
one
behave
material.
would
all
1.
generally
test
will
information
are
relationship
is
and
stress-strain
which
of
polymers
testing
the
Chapter
and
stress-strain
polymer
of
curves
been
Behavior
Tests
A.
stress-strain
5
it
and
also
is
usually
available,
past
experience
on
258
5.
and
often
FUd fw
overdesign
aes
of
toughness
terms
the
therefore,
before
should
be
under
the
an
aid
it
is
simple
is,
Hooke's
is
large
to
of
sure
STRENGTH
that
indication
ways,
the
it will
manner.
which
and
concept
which
a
is
of
in
material
impact
draw
can
strength
materials
cold
the
Toughness,
that
Brittle
to
of
curve.
energy
of
The
one
toughness
elongations
the
have
are
low
very
tough
break.
hand,
1.
The
given
understanding
to
are
for
two
at
in
K is
shape
curves
of
1 along
elongation
independent
of
the
initial
speed
slope
of
the
modulus.
modulus,
but
the
force
speed
testing,
or
of
Kelvin
model
as
(case
models.
their
(1).
of
A
spring
testing,
the
that
stress-strain
A dashpot,
resisting
shown
C)
stress-strain
with
of
the
of
simple
to
the
Voigt
the
the
rates
and
no
of
Figure
proportional
has
to
look
shown
holds,
has
in
a
on
motion
case
B of
stress-strain
by
the
speed
dashpot,
and
E is
dashpot,
the
stress
the
an
stress-strain
o = Kn
as
be
toughness.
several
materials
modulus
law
proportional
where
to
give
its
Thus,
ductile
a constant
other
curve
a
some
curves
a constant
Figure
in
models
has
is
also
indication
helpful
stress-strain
the
order
AND
Models
curves,
curve
in
only
in
breaking.
while
of
As
Four
area
related
toughness
B.
defined
an
not
but
be
is
absorb
because
tests
a material
may
of
object
BEHAVIOR
purpose.
Stress-strain
strength
an
STRESS-STRAIN
spring
of
the
testing
modulus
starts
stretches,
+ Ee
at
the
of
(1)
de/dt,
the
some
stress
n is
the
spring.
value
Because
greater
increases.
viscosity
of
than
The
of
the
zero,
slope
the
and
of
I.
STRESS-STRAIN
TESTS
259
10°°(N/m2)
STRESS
x
10°(N/m2)
STRESS
x
iaers
The
of
the
stress-strain
testing,
line
The
curve,
is
K,
the
Maxwell
which
is
o =
behavior
and
Kz
=
of
2K,.
modulus
of
unit
(case
given
Kn[1l
by
-
al
simple
K =
the
D)
models
at
two
speeds
de/dt.
spring.
has
a more
complex
stress-strain
(1):
exp(Ee/Kn)].
(2)
260
5.
The
initial
the
speed
slope
of
corresponds
the
upon
the
part
of
all
speed
the
the
to
the
materials
models.
However,
(case
brittle
polymers
None
the
of
ductile
A)
very
up
models
from
to
give
the
different.
show
and
to
depends
relax
out
stretching,
complex
behavior
have
the
curves
and
than
similar
and
many
less
Maxwell
unit
(case
characteristic
flexural,
and
compression
same
results,
but
in
Even
the
first
compression
determined
in
tension.
Comparison
for
in
a
while
in
with
determined
such
of
Young's
the
fairly
Figure
tensile
of
D).
many
2.
In
by
are
flaws
important
is
polymer
of
the
and
the
curves
curves
such
in
as
type
of
expected
be
quite
are
The
than
be
will
which
higher
moduli
those
compression
polystyrene
and
is
fails
in
a brittle
behaves
as
a ductile
elongation
to
break
materials
submicroscopic
in
the
the
might
different.
material
brittle
role
tests
polymer
higher
upon
curves
generally
tension
point
and
the
stress-strain
compression
a yield
of
modulus
Tests
dependent
general
part
brittle
properties
an
Tensile
very
in
tension
Versus
are
determined
play
to
curve
dashpot.
failure,
curves
the
The
points
Shear
by
polymer
similar
of
elongations
stops
the
of
the
begins
more
STRENGTH
magnitude
polymers
point
yield
determined
Manner
the
their
in
show
brittle
curves
Compression
Tensile,
shown
motion
of
higher
spring
AND
independent
part
dashpot
the
generally
show
Stress-strain
to
the
is
At
and
BEHAVIOR
polymers.
C.
test.
when
comes
Actual
springs
spring.
Eventually
elongation
first
decrease,
testing
stress.
which
the
the
curves
of
modulus,
since
stretching
of
the
the
deformation
to
slopes
gives
STRESS-STRAIN
are
cracks.
compression
(2).
largely
The
because
cracks
the
do
not
stresses
I.
STRESS-STRAIN
TESTS
261
POLYSTYRENE
1079)
(PSI
STRESS
x
Oi
45-6800
15
20
25
30
STRAIN (%)
IQaWep
2
The stress-strain behavior of a normally brittle polymer
such as polystyrene under tension and compression.
tend
to
close
Canty
tend
tests
are
theory
the
to
be
more
should
polymers
this
be
the
six
factor
of
of
open
the
the
twelve
less——a
tend
to
pure
its
ratio
Thus,
polymer
in
the
strength
times
much
them.
flaws
compressive
to
is
than
of
while
tension
material.
One
a brittle
tensile
of
compression
strength;
1.5
to
4 is
in
more
(3).
Flexural
curve
characteristic
that
material
This
rather
characteristic
predicts
common
cracks
is
largely
and
strength.
strengths
the
In
a result
compressive
flexural
of
the
be
nonlinearity
strength
tests
greater
part
being
of
the
than
of
tensile
the
greater
specimen
strengths.
stress-strain
than
the
is
under
tensile
tension
a polymer
When
test
theoretically
the
shear
strength.
tensile
or
if
it
manner.
D.
Effect
properties.
transition
region
from
Over
wide
well
below
behavior
low
a
Ty
is
Ep may
at
again
illustrated
Yield
the
with
and
is
prominent
going
T,
or
g
just
1,
The
is
Figure
the
melting
yield
a
more
point.
the
material
3
temperature
from
following
is
low
higher
the
the
secondary
appear
speed
yielding
glass
near
greatly
increases.
is
temperature
of
to
the
glass
testing
occur.
transitions
the
extremely
are
transition
higher
Some
become
at
higher
(5).
generally
for
of
be
ep
At
where
effects
3,can
the
temperatures
These
glass
types
to break
B
the
temperature
ce,
be
in
the
the
point,
elongation
no
All
changing
increasing
the
there
discussed.
in Chapter
by
through
and
The
of
stress-strain
point
Figure
temperature
in
been
the
a yield
points
temperature.
the
state
behaves
material
modulus
When
decrease.
in
the
actual
twice
triaxial
a
tensile
a
In
than
less
tension,
in
strength
tensile
strength.
under
is
polymer
above
high
the
all
given
there
in
on
curves
characteristic:
temperatures
even
effect
already
temperatures,
Finally,
on
range.
to
shear
generally
have
single
enough
fails
shear
notch,
a great
effects
stress-strain
obtained
a
it
Temperature
has
The
is
specimen
a
contains
Temperature
the
manner,
in
fail
assumptions,
strength
of
a brittle
twice
curve.
stress-strain
generally
be
If
brittle
of
in
should
cases
stress
fails
certain
Under
(4).
linear
materials
tough
while
a
assume
them
calculate
to
used
equations
classical
the
because
error
in
somewhat
generally
are
strengths
Flexural
compression.
under
part
and
STRENGTH
AND
BEHAVIOR
STRESS-STRAIN
5.
262
must
polymers
ductile
and
soft,
I.
STRESS-STRAIN
TESTS
263
PSI
STRESS,
STRAIN,
inalepa,
The
stress-strain
behavior
temperatures.
[Reprinted
Modern
21,
Plast.,
show
yield
than
at
121
points
see
at
Yield
of
(June
ey generally
temperature
for
amorphous
found
on
the
4 and
as
and
have
of
(6).
much
that
the
of
T.
as
crystalline
(T-Tg)
In
Figures
105°C
since
curve
near
is
g
different
but
of
oxide
Ty when
as
increase
opposite
are
shown
effect
in
brought
variable
Ty of
in
Typical
ey are
rather
temperature
(6,7).
the
5 the
an
the
polymers
used
temperature
the
with
Oy and
all
4 and
T,
as
polymers
on
for
if
polyphenylene
same
decreases
materials,
curves
at
Nason,
transition
Oy decrease
temperature
The
together
temperature
by
some
effect
5
closer
with
and
1944).]
strengths
The
acetate
Carswell
secondary
increases.
be
cellulose
from
the
PERCENT
6}
the
can
results
Figures
much
rather
than
polymers
the
differ
polymethyl
methacrylate
is
is
Yet,
polymers
210°C.
plotted
ona
all
(T-T,)
the
scale.
105°C
5.
264
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
1400
1200
<E
S 1000 $c
&
=
© 800
>
co
oCc
M
&
600
2
@
=
400
200
0
-250
-200
-150
-100
T-Tg (°C)
Fig.
-50
0 25
4
Yield strength as a function of temperature
methacrylate,
polycarbonate of bisphenol-A,
oxide,
and
Trachte,
The
polysulfone.
J.
Appl.
elongation
temperatures
appears.
is
At
for
these
The
temperatures
in
cryogenic
show
general
However,
film
Figure
in
few
and
elongations
at which
of
relation
is
large
at
a yleld
point
first
Ep often
the
to
decreases
stress-strain
the
nearly
all
all
with
curves
modulus-temperature
polymers
such
as
biaxially
fibers
of
polyethylene
to
and
6.
temperatures
a
polymers
materials,
behavior
DiBenedetto
ZA Sel S57:0))
rend
ductile
However,
terephthalate
nylon
of
temperature
shown
brittle.
break
from
14,
the
different
curve
to
Sci.,
above
temperature.
at
[Reprinted
Polymer
for polymethyl
polyphenylene
break
of
ten
are
oriented
percent
very
polyethylene
terephthalate
or
more
even
and
at
-
STRESS-STRAIN
TESTS
265
O10
008
€y
,
[e)(e)D
004
Yield
Tensile
Strain
0.02
-250
-200
-150
-100
-50
0
T-Tg (°C)
Balquae5
Tensile yield strain as a function of temperature for
polymethyl methacrylate,
bisphenol-A polycarbonate,
polyphenylene oxide,
and polysulfone.
[Reprinted from
DiBenedetto
(1970) .]
and
these
very
these
polymers
strain
test
capacity
The
effects
modulus
and
rate
speed
for
of
0°K
Testing
of
the
to
large
near
of
the
quite
a
The
of
elongation
the
tough
Rate
basis
Polymer
appear
low
7(11).
Appl.
(8-10).
causes
is
J.
temperatures
E.
Figure
the
low
Trachte,
rise
and
of
behavior
the
temperature
the
since
testing
is
about
ultimate
are
illustrated
what
one
the
heat
superposition
strength
increase,
for
rigid
testing
increases
(11-18).
The
Ep, May
For
expect
very
on
principle.
decreases
(19-21).
in
would
generally
however
stress-
Envelope
break
rubbers,
2249
temperatures
because
Failure
time-temperature
or
cryogenic
partly
in
14,
icine
(10).
speed
yield
At
Sci.,
but
The
the
polymers
increase
brittle
as
with
polymers
266
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
STRESS - STRAIN
=
8000+
Se
©
——
)
/om
=S
ELASTIC
(Dynes
MODULUS
20
— Ou
STRAIN
(%)
10
20
ioe
TEMPERATURE
Fig.
Stress-strain
temperatures
curves
shown
temperature
curve.
the
are
effects
elastomers
varied
over
linearly
to
the
the
typical
for
effects
can
be
the
polymer
superimposed
but
logarithm
rigid
large
decades.
The
of
ductile
if
the
yield
the
taken
at
modulus
materials
speed
stress
strain
the
versus
rate
of
Oy
and
testing
oF is
temperature,
the
and
yield
K
is
oF +K
de/dt
stress
a
log (de/dt)
when
constant
de/dt
according
at
(3)
=
fixed
1 at
the
is
increases
equation
Jy =
where
a
the
small,
several
with
of
on
6
specified
temperatures.
I.
STRESS-STRAIN
TESTS
267
Pass
€
2
7)
a)
*20
at
SS
~810=V(mm/min)
“As
“2
300
7
a
Ww
== 05
an
n
Poe
i
Zi
i
“a2
-=a1
rai
|
6
STRAIN
1askeps
8
(%)
7
Tensile stress-strain curves up to the yield point taken
at the strain rates shown on the curves.
The polymer is
an epoxy resin.
[Reprinted from Ishai, J. Appl. Polymer
di; 963°
Attempts
strain
to
have
parameters
produce
master
obtained
on
tests
different
the
at
same
scale
Sci.,
(1967)=)
rigid
shift
(17).
been
made
obtained
curves
over
(17,
polymers
factors
from
along
E,
versus
reciprocal
be
used
to
predict
results
of
superposition
stress
of
a
range
time
relaxation,
are
shown
or
of
different
speeds
and
and
be
yield
strengths
and
superimposed
speed
of
used
testing,
E,(t),
in Figures
stress-
temperatures
compression,
factors
rate
the
Moduli
all
shift
the
of
tensile,
can
the
the
superimpose
21-26).
temperatures
Furthermore,
the
to
flexure
by
using
testing
for
the
modulus,
(devdeyney
versus
8 and
time.
9
(24).
can
Typical
The
268
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
14
18
22
Factor
A
TEMP.°C
4
230
180
130
90
55
in
o,,/T
273
psi
log
—10
—6
—2
2
6
10
A + log t,/azin min
Bulicieens
Log
2730p/T
vulcanizates.
versus
log
tp/@p
tp = time
for
to break.
fluorinated
@p = 1 at
rubber
90°C.
is used to displace curves along the abscissa for
amount of shift is shown in tables in upper right
{Reprinted
from
Smith
Master
curves
for
manner
as
rate
the
elongation
is
to
Chu,
tensile
of
break
J.
strength
testing
go
Polymer
decreases
(1/ty)
through
Sci.,
A2,
in
a
decreases.
a maximum
as
10,
sigmoidal
The
the
curves
speed
of
for
the
testing
changed.
Another
speed
and
and
(972)
13355
elanuiry:
corner.
of
is
testing
called
compresses
typical
strength
type
of
has
the
a great
failure
is
scheme
been
by
proposed
failure
deal
to
a
op obtained
is
The
information
shown
common
at
in
for
Smith
envelope.
of
envelope
reduced
by multiplying
superposition
Figure
temperature
(21-24)
failure
into
reference
temperature
a
for
The
temperature
T by
elastomers
envelope
Single
10.
and
the
curve.
A
tensile
ae
factor
(°K)
Srey ake
I.
STRESS-STRAIN
TESTS
269
8
-10
ag
=
G
6
LOG ty /ay in min
Whe
Plots of elongation to
for fluorinated rubber
Qn = 1 at 90°C.
shown in Figure
SCi.,
A2i,
10,
Lowering
moves
the
the
might
points
OA,
of
OB,
are
basis
of
the
actual
for
a material
in
the
the
area
the
the
bottom
part
is
The
obtained
stress-strain
the
of
tensile
the
in
occurs.
constant
tests
in
of
failure
Figure
In
10
the
the
is
while
rigid
calculated
rather
same
failure
the
se
envelope.
area
load
which
OA
the
curves,
curve
strength
The
testing
decreased.
failure
cross-sectional
failure
is
stress-strain
on
original
when
typical
of
around
curve
temperature
points
top.
speed
stress-strain
the
are
being
the
counter-clockwise
when
OC
along
increasing
data
OB
and
at
the
or
instance,
curve
are
polymers
as
(1972).]
fracture
Elastomers
tests
133
For
versus log tp/%m
tp = time to break.
Symbols for different temperatures are
8.
[Modified from Smith and Chu, J. Polymer
temperature
become
figure,
break
(ig - 1)
vulcanizates.
experimental
envelope.
&
than
upon
envelope
creep-rupture
load
on
constantly
270
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
STRESS
1)
STRAIN
janie,
Alo)
Failure envelope for schematically
dependence of stress-strain curves
temperature.
[Reprinted
3597 (1963).]
This
will
occur
creep
until
F.
the
Effect
SS
Within
stress-strain
Smith,
J.
Polymer
sSCi.)
Ad:
<
increases.
always
from
representing the
on strain rate and
implies
if
that
enough
elongation
above
time
some
is
reaches
critical
allowed
a critical
for
load,
the
failure
material
to
value.
of
HydrosSE
tatic
ES
recent
Pressu
ES
I re
years
behavior
the
has
effect
been
of
quite
hydrostatic
clearly
pressure
established
on
(27=38) .
I. STRESS-STRAIN
In
all
cases
pressure.
the
The
pressure
but
increase
or
tendency
for
with
increase
271
modulus
not
in
all
decrease
or
and
elongation
op
decrease
The
depending
upon
the
with
but
it
effect
of
pressure
volume
in
reduce
the
packing.
of
the
The
tend
result
by
of
G.
sted Ty is
weights
weights
become
term
order
the
the
and
(of
increased
the
low
deformations,
of
1000
enough
and
percent.
the
the
increase
some
the
modulus
with
is
the
Ep:
The
beneficial
for
brittle
is
a
yield
free
density
cracks
defects
and
either
any
and
11
results
keep
are
temperature.
At
cheesy
to
10°
to
of
pressure
polymers
become
of
either
to
of
closed;
this
effect
counter-
behavior
as
a
volume.
weight
ambient
can
Weight
and Branching
elongation
entangled
cracks
free
Molecular
order
op and
tendency
in
polymers
the
of
to
decrease
Figure
associated
the
to
on
a
polyethylene,
polymers.
effect
of
of
either
to
with
cases
with
is
and
break
typical
are
or
tends
increase
molecular
below
volume
effects
of
effect
also
decrease
low
these
strength
to
the
Effect
Very
free
are
phenomena
The
pressure
minimizing
balanced
of
brittle
The
to
increases
the
can
there
polymer;
materials
B
which
(30).
the
polymer.
amount
would
if
¢€,
in
most
polypropylene
expected
the
with
increases
strength
elongation
decreases
on
are
tensile
pressure;
and
increase
generally
ductile
The
data
stress
effect
for
stress
also
cases.
polytetrafluoroethylene,
on
yield
yield
materials.
polymers,
presents
the
at
increase
to
brittle
some
ductile
TESTS
break.
and
show
elongation
liquids
higher
molecular
elastomers
At
higher),
true
viscous
still
the
rubbery
to
with
higher
polymer
behavior
break
low
becomes
molecular
molecules
to
of
short
the
272
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
24
P=100,000 psi
20
P=80,000 PSI
|
16
l2
\\
~
STRESS
(X1073
PS|)
Z
P=60,000 PSI
Ss
P=30,000 PSI
2
(0)
4
6
8
"0
(2
14
16
18
2.0
(IN/IN)
STRAIN
1atkej,
lal
The stress-strain behavior of polypropylene
at different
pressures.
[Reprinted from Mears, et al., J. Appl.
Phys.,
40,
4229
(1969)
.]
Polymers
transition
be
extremely
forces
Chain
such
in
into
the
effect
on
Above
act
as
It
weight
ambient
may
be
because
a
of
be
strong
imperfections
properties,
low
but
glass
Carry
ends
test
shrinkage
to
For
shatter
such
entanglements
structure
chain
to
prepare
strength.
to
tend
enough
molecular
the
to
and
great
enough
in
have
temperature
thermal
are
very
some
which
impossible
the
specimen
must
becomes
minimum
and
the
pieces
there
elastic
the
strength
(39).
small
strength
the
molecular
above
making
polymer
ends
the
low
materials
materials
affect
the
of
polymer
before
brittle
involved
brittle
very
temperatures
Specimens
the
of
any
which
have
load
(40).
adversely
Venyadastele
moduli.
molecular
elongation
weight
increase
needed
toward
a
to
form
limiting
a
specimen,
value
I.
STRESS-STRAIN
at
very
TESTS
high
polymers
molecular
with
maximum
PRIS}
weight
hydrogen
properties
(39,41-48).
bonding
at
lower
between
Polar
chains
molecular
polymers
reach
weights
and
their
than
do
nonpolar
polymers.
The
early
work
indicated
that
important
variable
the
Mo:
effect
to
the
molecular
just
The
(43).
the
number
average
average
upon
rigid
some
than
molecular
weight
where
an
has
of
equation
shown
has
some
between
seems
Lei and
fractions
molecular
the
that
than
strength
of
of
the
function
tensile
mixtures
polymers
was
also
function
distributions
follows
work
complex
the
weight
cases
broad
strength
a more
of
weight
Later
polystyrene,
in most
rather
is
molecular
behavior
molecular
(39,41,42,45-47).
weight
For
tensile
stress-strain
variable
However,
studied
the
weight
(43).
depend
on
M
were
weight,
form:
C5= Sn9 7
(4)
M
where
TRO
is
the
limiting
molecular
weight,
and
Igeyilels)
& B°
other
snopes?
molecular
An
In
weight
indication
type
of
molecular
(51),
Goppel
strength
viscosity;
is
of
and
K is
the
seems
to
se
the
importance
weight
by
more
would
similar
viscosity
be
of
the
very
important
entanglements
determining
works
of
Toggenburger
Goppel
increased
indicate
than
that
number
that
found
linearly
weight
than
also
the
variable.
and
of
the
stress-strain
(49),
the
with
average
average
high
equation
rather
in
(52).
important
A
for
average
the
Wyman
strength
constant.
cases
polypropylene
this
a
per
given
is
properties
weight
of
tensile
Boyer
tensile
the
inherent
molecular
molecular
weight.
(50),
274
5.
Boyer
found
the
viscosity.
styrene
with
strength
Toggenburger
copolymers.
molecular
polymers
was
Similar
and
Thus,
viscosity
also
but
given
the
general
the
simple
properties
over
into
Yanko
the
(47)
rubbers
of
weight
vulcanized
that
with
elongation
to
break
first,
at
very
crosslinking,
of
initial
is
a result
in
the
as
molecular
of
network
The
Ep
tensile
polymer
but
up
initial
weight
on
the
properties
polypropylene
that
complex.
effects
Flory
of
are
and
crosslinked
weights
of
of
the
The
weight
at
before
somewhat.
as
carried
(45,46)
molecular
properties
such
break
accurate,
value.
decrease
weight
not
limiting
molecular
imperfections,
is
weight
with
to
The
effect
vulcanizates
dangling
chain
ends
increases.
of
crystalline
depend
a
4 between
molecular
a
for
appears
equation
the
strength
to
branched
stress-strain
well.
average
increased
molecular
and
as
by
the
the
melt
polymers
thus,
more
to
stress-strain
polyethylene
is
affect
elongation
weight
tended
fewer
as
shown
viscosity.
branched
Since
the
all
tensile
melt
and
linear
It,
affects
rubbers
the
when
strongly
the
well
However,
linear
and
rubbers,
number
also
high
the
than
melt
correlate
curve
polymers.
STRENGTH
branched
not
of
Only
molecular
only
the
uncrosslinked
but
not
dependence
not
on
polymers.
uncrosslinked
found
Wyman
strength
and
weight
same
logarithm
of
and
did
AND
with
branching.
the
relationship
properties
increased
starting
the
branched
molecular
Molecular
the
by
linear
the
gave
strength
weight,
the
the
of
entanglements
for
and
strength
entanglements
lower
stress-strain
tensile
reported
fewer
molecular
were
in
had
both
because
BEHAVIOR
increased
studied
against
are
polystyrene.
polystyrene
branched)
plotted
results
polymers
The
weights
(linear
strength
of
STRESS-STRAIN
upon
polymers
molecular
such
weight
I.
STRESS-STRAIN
in
a
manner
TESTS
similar
However,
the
apparent
because
in much
weight
same
there
the
the
other
the
boundary
polymer
weight
The
also
as
a
low
of
crystal
crystalline
variable
to
be
do.
is
(54).
Thus,
"tie
brittle
and
is
at
affected
degree
of
crystallinity
H.
Effect
of
Crosslinking
The
effects
The
increase
and
low
have
extent
of
Thus,
both
which
as
to
low
Tye
collect
change
at
weight
molecular
spherulitic
the
On
strengths
weight
with
(55).
structure
behavior
molecular
may
above
molecular
so
to
in
toughness.
molecules,"
by
molecular
because
tends
low
less
together
temperatures
this
weight.
be
material
confused
polymer
and
to
crystallinity
to
weight
of
of
tends
molecular
polymers
further
degree
morphology
with
tends
entanglements
weight
number
tend
change
help
spherulites,
the
weight
the
in
molecular
between
polymers
may
decrease
(44,48,53,54).
hold
properties
molecular
reduces
type
chain
increases
hand,
molecular
way
of
is
upon
polymers
crystallites
weight
increasing
amorphous
the
dependence
molecular
to
dependence
the
general
275
of
and
a
molecular
weight.
understood
of
strain
properties
tests
o
the
specimen
rough
be
used
important
and
approximation,
as
a guide
theory
This
to
best
the
kinetic
the
stress-
predicts
for
that
M
stress
most
(56,57).
rubbers
of
o = ORE
The
can
elasticity
rubber
of
are
a
As
elastomers.
for
theory
tensile
crosslinking
fa - —)/2
-( <7) J-
(5)
Cc
is
based
in
the
upon
the
unstretched
original
state.
cross-sectional
In
this
equation
area
p is
of
276
5.
the density,
degrees
the
is
Kelvin,
polymer
molecular
is
R
the
strain
is
given
—<
such
is
takes
as
shear
ue is
the
number
of
before
polymer
For
the
the
square
first
into
the
chain
the
at
flaws
ends.
according
to
was
a
the
weight
of
is
the
Le
stretched
definition
strain
is
of
three
deformations.
correction
network
stress-strain
kinetic
in
average
L
proper
this
of
STRENGTH
crosslinked,
and
small
in
The
the
number
it
brackets;
approximation
account
the
AND
temperature
molecular
the
strain
BEHAVIOR
the
specimen,
rubbers
engineering
dangling
tests
the
of
is
average
M, is
length
in
T
crosslinks,
polymer.
ene usual
which
constant,
unstretched
the
term
gas
weight
of
pines
the
between
length
STRESS-STRAIN
theory
of
The
factor
structure
curve
for
rubber
simple
elasticity
is
where
the
deformed
defined
moduli
shear
Ge
oRT
e
M
stress
specimen
in
in
Figure
=
o, is
this
2 of
G
tan
06
(6)
c
based
case,
Chapter
upon
and
1.
the
6 is
From
the
dimensions
of
shearing
angle
equations
5 and
M
B=
the
stress-strain
is
directions,
(7)
Cc
3o0RT
_
M
Material
6,
as
are:
wD
G = SR?
The
the
(8)
(o)
curve
for
simultaneously
as
a
biaxial
stretched
-@))
predicted
_E|/u
by
\2
the
tensile
equal
kinetic
tn
test,
amounts
theory
of
in
in
which
the
two
rubber
elasticwcy.
I.
STRESS-STRAIN
This
equation
required
biaxial
is
as
does
that
than
for
the
since
the
only
the
thickness
test
is
kinetic
a
rubber
theory
increases
as
not
correctly
Figure
12
linked
rubber
with
elongation
crosslinking
stress
a
amount
is
greater
tensile
is
correctly
of
directions
to
2
large
shape
curve
predicted
to
break
of
a
predicts
contract
the
curve
by
rubber
tensile
that
increases,
deformations
of
the
3
4
a
This
the
in
of
the
a
typical
kinetic
decreases
strength
as
goes
5
6
7
the
that
theory
stress-strain
curve.
cross-
theory.
the
degree
through
10°’
DYNES/Cm?)
(X
STRESS
|
for
test.
free
crosslinking
stress-strain
The
two
that
the
increases.
of
dimension.
at
the
each
uniaxial
rubber
However,
in
given
dimension
degree
predict
compares
by
usual
of
the
MS decreases.
The
the
test
The
is,
predicts
stretch
expected
modulus
277
to
a biaxial
of
TESTS
8
EXTENSION RATIO,L/L,
IMBCfy LW72
The stress-strain curve of a typical vulcanized natural
rubber compared to the stress-strain curve predicted by
the kinetic theory of rubber elasticity.
a
278
5.
pronounced
maximum
rapidly
decreases
Both
these
of
undesirable
least
network
and
their
a
due
to
loads
of
found
with
most
of
then
the
highly
STRENGTH
and
then
(24,58-62).
in
13
in
Figure
M. or
on
stressed
to
(58).
crosslinking
stress
distributed
AND
increases
increasing
a heterogeneity
BEHAVIOR
crosslinking
illustrated
These
are
degree
crosslinking
are
puts
chains.
low
the
effects
which
the
as
effects
partly
crosslinks
at
STRESS-STRAIN
the
a
other
are
spacing
relatively
chains
break
chains,
The
at
between
few
of
Lies,
forcing
3000
1000
2000
800
600
1000-4
400
/in2)
TENSILE
STRENGTH
(ib
ELONG
TO
BREAK
(%)
200
1.0
20
30
40
CONCENTRATION
OF
5.0
60
CROSS-LINKING
jraleis
70
AGENT
I}
Stress-strain properties of rubber
as a function of the
percent of crosslinking agent.
[Reprinted from Nielsen,
J. Macromol.
Sci., ¢3, 69 (1969)
from the data of BLO,
As
ulGh Gs
POlymexns
Give
4
egos
(1949)
.]
8.0
I.
STRESS-STRAIN
them
to
Case
(63,64)
a
TESTS
either
break
has
regularly
spaced
to
crosslinks
varies
out
by
uniformity
impose
be
A
explain
The
proportional
density
of
special
the
x
The
is
effective
related
number
approximate
to
L/L,
of
crosslinks
than
tetra-
theories
properties
Ve,
of
at
(59,66)
vulcanized
break,
the
have
Ape
reciprocal
that
of
is,
(10)
2
crosslinked
approximately
crosslinks
the
chains
molecular
per
unit
weight
volume
ve
between
M. by
H
where
of
the
networks
motions
root
been
be
than
of
crosslinks
yA
B
chain
square
between
trifunctional
e€,
ratio
that
has
Trifunctional
ultimate
them.
higher
spacing
could
on
extension
a
in which
crosslinks
number
the
have
on
show
prediction
rubbers
a greater
stress
which
the
This
crosslinks.
to
effective
which
containing
have
the
should
manner.
restrictions
(59,66-68).
in
between
should
relieve
calculations
networks
crosslinks.
to
network
on
Also,
to
as
network
a random
spacing
drastic
developed
should
the
the
points
less
rubbers
a
tetrafunctional
functional
been
than
experiments
crosslinking
so
theoretical
in
(65).
containing
slip
crosslinked
break
of
controlled
or
made
elongation
borne
279
Nis
(24)
The
tensile
(as)
Avogadro's
experimental
Chu
oe
results
find
that
number.
but
the
strength
o,
not
Equation
for
exponent
B
10
others
on
according
vg
to
holds
(24,69).
is
some
not
0.50
theories
for
some
Smith
but
and
0.40.
should
be
280
5.
proportional
before
the
however,
to
ve2F or
maximum
some
Ped
rather
found
in
is
data
to ve
experimental
structures
average
parameter
However,
weight
are
that
crosslinked.
largely
by
through-going
together
for
There
UB
and
of
an
the
break
strain
materials
covalent
empirical
to
to
0.5
v
e
variations
differences
by
an
on
and
resins
rigid
a
the
(or
to
energy
are
so
of
Van
Waals'
der
are
high
in
molecular
of
producing
low
essentially
in
no
rigid
the
strength.
molecular
strength
polymers
unless
is
determined
intermolecular
needed
to
tie
the
correlation
of
the
energy
below
the
area
break
H,
under
that
by
required
is
given
its
(71,72).
B
dissipated
correlation
bonds,
structure
by
stress-strain
The
damping
to
break
the
to
hysteresis
for
the
an
may
be
I.
K varies
related
to
the
break
curve)
to
amplitude
elastomer.
of
The
equation
Up, = kHy!
constant
in
single
interpenetration
modulus
interesting
elastomer
The
or
strength.
is
just
Experimentally,
The wide
due
STRENGTH
crosslinking
proportional
crosslinks
chains
AND
v.-
have
of
of
described
effect
as
the
strength
hysteresis
is
Me or
effective
is
B
be
BEHAVIOR
(59,67,68).
B
probably
cannot
little
Although
the
o,
degrees
v, (24,70).
thermosetting
the
that
entanglements
as
many
o
are
as
has
materials;
molecules
data
such
in
or
which
Crosslinking
low
reached
indicate
than
network
weight
Vv, for
STRESS-STRAIN
(12)
Slightly
from
cohesive
energy
polymer
density
to
polymer,
of
the
and
it
rubber.
Effect
of Crysta
llinit
y
Se E
S
EN
Unoriented
crystallites
at
temperatures
below
T,
g
tend
to
I.
STRESS-STRAIN
make
TESTS
polymers
result
from
brittle
strains
crystallites,
by
crystallization
by
made
up
held
together
of
to
material
of
a
of
in
molecules."
For
elastomeric
behavior.
In
or
phase
going
crystallinity,
the
rubber
to
At very
high
spherulites
curve
of
a
crystallinity
to
but
break
It
of
of
a
that
is
similar
material
effects
polymer
in
rather
polypropylene
(78).
about
decreases
in
from
a
degree
that
of
of
an
a
yield
if
point.
large
stress-strain
(53,
78-84).
limited
An
presence
crosslinked
showing
cases
a
brings
over
many
from
stress-strain
a high
the
brittle
primarily
the
to
a
and
especially
has
imperfections
crystallite
different
crystallinity,
the
crystalline
materials,
changes
are
one
comes
to
are
lamellae
exist,
Strength
curve
rigid
material
for
may
produced
The
between
portion
quite
the
important
molecular
and
may
the
polymers
from
crystallinity
one
present,
these
crystallinities
strength
that
brittle
illustrates
to
degrees
are
no
go
ends
ductile
stress-strain
rubber
on
which
produces
another
chains.
folded
by
during
Crystalline
molecules"
very
phase
concentrations
still
results.
from
uncrosslinked
and
be
Chain
"tie
few
"tie
crystalline
may
brittleness
produced
stress
from
amorphous
the
This
amorphous
voids
molecules"
strength
low
of
containing
(73-77).
very
so
the
brittleness.
"tie
collect
to
or
There
lamellae
strengths.
on
presence
process,
another
lamellae,
the
the
by
low
imposed
produces
which
factor
tend
with
crystallites.
the
layer
281
range
increase
increases
in
modulus
elongation
to
yield
Figure
and
and
of
in
yield
elongation
(80).
is
difficult
crystallinity
from
to
those
separate
of
the
morphology
effects
of
degree
since
it
often
of
is
found
14
282
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
0.015
original film
quench
— 0.010
N
F
€
(3
2 min cryst.
esse
Pa
=
.
2
0.005 £ :
10 min cryst.
eens
lan
STRESS
O
100
200
300
400
ELONGATION
(%)
Bag.
The
stress-strain
properties
of
14
isotactic
polypropylene
after different thermal histories:
- the original film may
have been oriented.
--- Quench-cooled
from the melt
(no
Spherulites).
--+-2 minutes crystallization at 125°C
(partial spherulization).
....
10 minutes crystallization
at 125°C
(completely spherulitic).
[Reprinted from Barish,
J.
Appl.
that
Polymer
a more
brought
an
break
along
place
at
"tie
the
by
in
lites
their
temperature,
drawing
structure
is
a
polymer
an
and
At
(79).
is
an
times,
morphology
changes
the
folded
unfolded
chain
chains
accompanies
or
there
are
and
below
of
structure
into
highly
few
low
spheru-
the
test
cold-
spherulite
become
takes
imperfect
probability
the
often
impurities
yaace ue is
of
be
fracture
where
of
small
increased
the
the
other
Guetea ale
can
spherulites
spherulites
which
in which
Large
With
which
annealing,
concentration
increased
there
or
(79).
between
high
structure,
cooling
(73).
boundaries
during
Cold-drawing
slow
radii
but
(CUES
AV 5||
spherulitic
either
weight
there
Gaby
crystallinity
molecules"
molecular
6,
pronounced
about
increase
Sci.,
is
a
destroyed.
fibrillar
aligned
in
I.
STRESS-STRAIN
the
of
TESTS
direction
of
crystalline
Horio
(74),
before
has
shown
that
Zaukelies
as
planes
in
a manner
of
the
cooling
melting
of
a
morphology
and
determined
by
temperature
properties
initial
annealing
process
temperature
continue
at
secondary
reorganization
or
a
of
occur
temperature
recrystallization
of
part
J.
Effects
of
For
amorphous
increase
of
of
the
polymers,
the
the
slip
as
or
annealing
by
an
long
This
many
agents
benzoate
The
are
largely
a high
aging
or
of
change,
days,
process
(81).
periods
slow
and
spherulitic
sodium
polymer
or
alpha
size
the
instance,
However,
and
treatments,
nucleating
spherulites
over
spherulitic
Heat
affects
is
in which
crystallites
Plasticization
along
spherulite
cooling
for
polymers,
crystalline
particles
(81,93).
partial
point
the
crystalline
rate
may
below
room
of
treatment.
also
near
For
size
and
melting
(81,89-92).
the
(85-87)
by motion
history.
also
reduces
Stein
even
metals.
crystallites
polymer
the
the
fine
However,
crystalline
deform
(especially
of
(75-77),
components.
ductile
to
Peterlin
crystalline
thermal
tend
cold-drawing
of
may
above
of
combination
ductile
its
from
of
starts,
crystallinity
addition
polypropylene
a
is
temperature),
The
process
in
to
the
point
nucleation
annealing
to
a polymer
slow
that
similar
related
others.
and
crystallites
the
may
amorphous
by
and
a complex
the
structure
be
the
is
mechanism
discussed
(73),
nylon,
brittleness.
room
Padden
shown
transition
in
been
has
as
for
has
detailed
(88)
structure
below
The
cold-drawing
there
of
Closely
such
and
actual
orientations
such
polymers
Keith
the
283
stretch.
a
slow
time
at
which
believed
there
is
to
a
(94-96).
Copolymerization
effects
of
plasticization
and
284
5.
copolymerization
shift
in
the
are
glass
primarily
(T-T,)
between
important
variable
which
a
common
curve
liquids
be
the
and
polymer
coiled
in
whether
poor
has
a
in
intensity
chloride
amount
plasticizer
of
Material
to
The
and
decrease
phase.
from
the
plasticized
greatly
effect
while
of
each
a material
of
these
spherulitic
complex
produce
of
the
has
with
degree
and
effects
the
of
factors
already
been
and
yield
to
tightly
if
or
a
and
small
a ductile
or
lower
the
by
on
entirely
T g’
the
stress
for
in
data
As
tend
a
hand,
decreases
The
by
amorphous
other
spherulitic
temperature.
stress-strain
(105).
slightly
increase
the
down
the
destroyed
polymers,
breaking
may
discussed.
copolymers
are
or
are
dilute
break
up
on
illustrated
structure
which
crystallinity,
Ty either
these
acetate
from
of
crystalline
Copolymerization,
is
addition
Plasticizers
elongation
shifts
of
for
Polycarbonate
polymer
crystallinity,
modulus
the
variables
ethylene-vinyl
more
may
polymer.
and
of
and
the
the
the
Ty:
to
a polymer
eliminated
(100-104).
where
change
is
appear
more
of
in
one.
is
degree
reduces
morphology,
can
which
shift
solvent
be
brittleness
liquid
plasticization.
Thus,
decrease
the
the
approximately
a good
solvent.
good
Ty is
which
in
a
and
the
to
the
temperature
to
tend
transition
the
is
from
to
effects
STRENGTH
The
data
molecules
examples
a brittle
copolymerization
different
to
are
situation
liquid
the
Ty:
addition
not
increase
by
polyvinyl
in
AND
expected
most
other
than
glass
be
BEHAVIOR
temperature
produce
Polymer
may
secondary
reduced
or
solvent
Plasticizers
it
However,
(97-99).
a
test
superimposes
(6,25).
to
to
temperature
the
plasticizers
related
those
transition
difference
STRESS-STRAIN
behavior
combined
in
the
Table
effects
1 for
crystallinity
increasing
The
amounts
I.
STRESS-STRAIN
TESTS
285
Table
Stress-Strain
Properties
1
of —Ethylene-Vinyl
Acetate
Copolymers
Property
Yield
Stress
Tensile
of
Strength
to
Yield
(%)
Elongation
to
Break
(%)
acetate,
material
all
contents
the
of
rubber
long
oy decreases
becomes
elongation
until
is
as
so
to
break
percent
found.
The
is
then
any
Molecular
The
strength
and
by
followed
polymer
by
or
polymers
increases
parallel
to
the
direction
with
gone;
above,
tensile
no
vinyl
then
a very
strength
to
longer
the
a yield
acetate
at
vinyl
weak
point.
content
acetate
uncrosslinked
changes
only
effectively
slowly
as
crosslink
the
decreases.
ductility
of
orientation
produced
rapidly
by
(sometimes
uniaxial
polymers
the
of
either
of
cooling
cold-rolling.
drawing,
the
and
is
until
Orientation
be
can
there
increases
is
ey increases
crystallinity
by molecular
orientation
and
that
op dramatically
K.
modified
rubbery
crystallinity
45
there
polymer,
in
(psi)
Elongation
vinyl
The
(psi)
The
perpendicular
hot
the
dramatically)
to
the
but
be
greatly
chains.
polymer
tensile
orientation,
can
of
stretching
or
melt,
strength
in
the
the
by
of
a molten
cold-
rigid
direction
strength
orientation
The
decreases
(106-125).
286
The
5. STRESS-STRAIN
tensile
and
as
but
strength,
the
in
decrease
great
the
the
the
case
Figure
15
illustrates
May
become
ductile
but
in
perpendicular
brittle
the
with
low
stress-strain
to
and
of
the
the
behavior
a yield
direction
strength
and
behavior
of
point
of
often
oriented
and
very
the
high
polymer
elongation.
BRITTLE
polymer
elongation,
becomes
Figure
ductile,
16
more
illustrates
especially
POLYMER
(psi)
STRESS
5,000
2
4
6
8
STRAIN
lnskep
The
stress-strain
brittle
in
the
behavior
unoriented
parallel to direction of
dicular to the direction
of
state.
10
l2
(%)
ALG
typical
|| =
not
brittle
10,000
0
the
orientation
are
direction,
the
many
as
strength.
orientation
have
trends
the
to
direction
tensile
typical
same
the
parallel
perpendicular
in
Parallel
the
increase
as
polymers.
show
modulus
Young's
and
stress
yield
BEHAVIOR AND STRENGTH
polymers
tensile
which
stress
are
orientation.
| = stress perpenof the uniaxial orientation.
I.
STRESS-STRAIN
TESTS
287
DUCTILE CRYSTALLINE POLYMER
(psi)
STRESS
29
100
200
300
STRAIN
Fig.
400
(%)
16
The tensile stress-strain behavior of ductile polymers:
Unoriented,
measured parallel to the direction of uniaxial
orientation,
and measured perpendicular to the direction
of
the
orientation.
crystalline,
polymers.
direction
has
break
be
may
the
unusually
molecules
the
or
high
previously
directions
deorient
as
elongation
by
the
then
started.
in
the
the
draw
tested
but
in
its
polymer
The
is
tested
reason
that
reorient
on
in
break
Figure
for
the
this
parallel
and
the
of
the
shows
with
the
direction
before
(114).
in
to
direction,
the
17
parallel
stretching
chloride
ratio
the
elongation
perpendicular
materials
polyvinyl
cold-drawing
measured
in
and
gets
for
oriented
direction.
Brittle
changes
polymer
strength,
of
material
process
or
that
transverse
force.
stress
yield
transverse
first
reorientation
orientation
than
oriented
applied
yield
higher
less
perpendicular
Oriented
the
how
the
degree
perpendicular
The
drawing
of
288
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
(psi)
STRESS
YIELD
DRAW
lasiger,
RATIO
Al'7)
The yield stress as a function of Orient
ation
for rigid polyvinyl chloride.
Tensile stress
parallel or perpendicular to the direct
ion of
[Modified from Rider
7, 829 (1969).]
was
In
done
other
above
a
achieved
the
at
71°C
for
(21026) ie
Considerably
at
the
to
the
the
are
not
the
high
the
properties
data
more
were
(at
tests
moduli
the
least
done
was
draw
so
90°C
in
of
for
17.
orientation
applied
bonds
was
ratio,
parallel
at
A2,
Figure
drawing
less
and
Sci.,
in
a given
covalent
poor
shown
the
for
because
strong
Polymer
molecular
for
curves
strengths
are
J.
shown,
orientation
orientation
by
the
temperature
between
have
largely
The
lower
to
Polymers
Chains.
T,)
which
perpendicular
Carried
(near
Hargreaves,
results,
differences
parallel
and
(draw ratio)
was either
the orientation.
the
than
at
71°C.
direction
loads
the
and
are
polymer
brittle
polymers)
I.
STRESS-STRAIN
in
the
direction
loads
are
Also,
if
These
loads
The
effects
Jackson
applied
and
made
the
oriented
on
effects
would
other
the
some
be
even
Properties
Birefringence
Tensile
of
Waals'
in
Since
the
their
was
pronounced
if
of
specimens
perfectly
For
this
the
2
Oriented
Strength
Polystyrene
Elongation
to
Break
al
data
not
orientation.
INioy 36 YO”
||
the
in
direction.
2 by
orientation
more
bonds.
concentrators
stress
Table
biaxial
the
orientation
orientation
polystyrene.
Table
Mechanical
the
strong
the
shown
der
because
imperfections
to
are
to
molding,
contained
Van
parallel
are
also
orientation
weak
or
cracks
orientation
(109)
the
the
perpendicular
injection
but
by
oriented
Ballman
by
uniaxial
reason,
of
to
cracks
small
become
they
for
primarily
are
there
direction.
289
perpendicular
carried
polymer,
were
TESTS
[|
Izod
Impact
Strength
i
Migr
te
ibe dk
3940
3440
2.4
a8
oh
5 BP
4.3
5340
4240
Sigil
Bod
oS
o2all
2)oat
6320
4110
2y5)
210
Sa
5410)
16.3
7550
4140
4.2
o®)
oS
GI
25.4
7640
3710
350
ibs {3}
A Sie
eal:
BOG 8)
7590
2630
6.8
133
=
=
41.4
8660
3440
Die
ae Al
Waeyte
6 048}
S\lbgts
10170
4550
4.4
Ped
LESS
a dlfs)
D0 1
8440
1290
Tea
Or
Tensile
strengths
Elongation
to
in
break
psi
in
%
=
=
290
5.
Specimens
the
were
more
orientation
molded
(126,
and
122,
Gon may
also
128).
somewhat.
strength
of
an
the
on
the
Uniaxial
tensile
decreases
Opposite
of
strength.
chains
tend
buckle
eliminates
Chapter
any
of
can
addition,
the
oriented
in
2.)
This
direction.
the
the
dkS2))5
the
undesirable
and
keeps
a
Biaxial
filaments.
and
etn
the
yield
but
the
unoriented
may
same
and
orientation
of
the
material.
is
important
be
put
on
also
the
improves
orientation
extent
the
loads.
orientation,
properties
the
cmearcmreie:
where
loads,
have
Thiepeeul
the
However,
orientation
large
brittle,
tensile
tensile
load
are
orientation
characteristic
a
shear
long
polymers
of
tends
is
(G@EZOF ee30)
plane
where
to
of
materials
Biaxial
(Gs
to
orientation.
high
of
Gop
strength
compressive
the
but
The
many
yield
than
polymers
constant,
polymer
direction
under
of
molecules
into
the
carry
those
(108,133-137).
up
of
while
the
the
greater
than
operations
many
If
unoriented
applications
materials
Properties
of
nearly
if
it
the
is
direction
better
practical
from
STRENGTH
injection
notation.)
increases
easily
biaxially
any
in
for
chains
2,
cold-forming
found
Polymer
are
oriented
is
rod.
direction
strength
properties
material
the
2 for
increases
yield
in
In
properties
remain
break
orientation
properties
in many
will
the
to
Figure
the
strength
Perfectly
(See
of
rod
in
what
compressive
in
thickness
shear
decreases
yield
as
uniform
orientation
Chapter
orientation
strength
compressive
AND
oriented.
the
moduli
rod
axis
the
with
(See
oriented
along
torsion
shear
somewhat
decrease
the
not
through
affects
The
increase
aligned
varies
is
BEHAVIOR
127).
Orientation
(107,
uniaxially
(birefringence)
specimens
specimen
perfectly
STRESS-STRAIN
uniaxially
the
desirable
increases
the
I.
STRESS-STRAIN
TESTS
modulus
and
biaxial
orientation,
the
elongation
(especially
for
brittle
increase
degrees
A
of
the
291
orientation
comparison
biaxial
Figure
tensile
of
the
orientation
strength.
the
Up
to
to
moderate
break
polymers),
elongation
to
behavior
for
polymer
a brittle
also
but
break
stress-strain
at
may
of
is
degrees
tends
of
to
very
high
decrease.
uniaxial
and
illustrated
in
reduces
crazing
18.
Biaxial
orientation
prevents
or
UNIAXIAL
)
greatly
the
PARALLEL
£ SoS
(psi
STRESS
5,000
UNORIENTED
0
2
4
6
8
10
l2
STRAIN (%)
Fig.
18
Schematic comparison of the stress-strain behavior of a
biaxially oriented, and ;
brittle polymer: Unoriented,
uniaxially oriented and tested parallel to the direction
of orientation.
292
5.
OL
bur etleppoliymers
stress
by
and
the
biaxial
basic
starts
required
orientation,
for
it
polystyrene
The
can
factor
of
a
liquid
environment
such
Polyblends,
Block,
Two-phase
polymers
are
least
two
added
to
to
Part
of
important
the
strength
and
deformation
usual
changes
amounts
of
in
the
polymers,
between
the
amounts
yield
point
phenomenon
the
rigid
rubber
The
phase
is
of
a
graft
shows
largely
an
continuous
is
the
or
to
flow
in
19
increase
polymer
temperature
the
Crazing
with
the
as
interval
components.
which
The
or
has
Larger
still
up
amounts
uniform
of
a
yielding
breaking
result
the
polyblends,
two
material
may
its
permanent
such
the
with
as
increasing
found
point
is
illustrates
adding
of
at
elongation
(often
undergo
cold-drawing.
generally
phase.
or
crazing
in
and
are
a rigid
yield
by
block
toughness
Figure
on
and
phase
to
of
times
rubbery
rubber
a
(140,145-147).
indistinct
A
temperatures
result
phase
1.
to
in
6
behavior
phase
trends
produce
the
polyblends
rigid
polymers
necking
now
as
a brittle
general
rubber
elongation
being
to
crazing
orientation
5 or
2.A
curves
more
Polymers
increase
(141-144).
the
which
as
stress-strain
tendency
phase
much
increased
is
biaxial
the
(136).
such
added
transition
continuous
produce
high
and
and
is
load
same
glass
Small
to
stress-strain
The
by
at
STRENGTH
both
are
strain
strain
as
Graft
their
its
rubber
polystyrene.
block
a
by
oil
polymer.
polymer)
under
corn
and
polymer
decrease
the
applications:
brittle
a block
or
systems
of
that
AND
Although
crazing
increased
air
as
for
areas
brittle
of
in
polymeric
major
a
break
3 times
induce
critical
be
a
L.
to
appears
(136,140).
2 or
BEHAVIOR
s(ls
5.13 sh3
ornls crasiohie
strain
variable
STRESS-STRAIN
the
of
of
elongation.
rubbery
occur,
but
I.
STRESS-STRAIN
8000
TESTS
293
0
zg
”
"ay
10
a
=
4000
20
50
100
0
0
2
4
6
8
0
12
14
16
18
ELONGATION (%)
Bagi
9
Typical stress-strain behavior of polyblends of a rubber
in a brittle polymer.
Numbers refer to the approximate
percent of rubber in the polyblends.
more
likely
there
production
polymer
of
two
are
more
and
mixtures
as
also
rubbers
are
below
voids
a
cavitation
resulting
from
phenomenon
dewetting
at
with
the
the
rubber-rigid
interface.
There
of
occurs
or
room
rubbers
other
(141,148-150),
less
of
miscible
rubbers
temperature
or
crystallinity.
types
as
to
and
(148).
crystalline
of
polyblends
mixtures
in
form
phase
one
crystalline
Such
such
which
systems
polymers
polyblends
polymers
the
with
a
as
mixtures
components
(151-154),
whose
generally
reduced
Tg is
behave
degree
of
294
5.
Most
commercial
polymers,
rubbery
rubber
are
of
good
to
are
Cooper,
a number
properties
have
been
and
of
of
polymer
for
be
if
so
this
is
the
so
II.
in
rubber
polymers
to
rubber
in
chains
flow
readily
of
phase
a
both
ends
not
to
of
to
crosslinked
occurs
in
the
fThere
polymers
(170).
a
excess
The
stress-strain
than
of
of
In
block
a
rubber
the
rigid
by
the
the
rubbery
rigid
will
filler.
abiek \ereale
di-block
at
reason
polymers
chain
phase
A
The
rigid
crosslinked
each
di-block
A polymer
containing
be
The
phase.
rigid
types
phase.
attached
Graft
continuous
both
appears
by
stress-strain
strengths
20.
rubber
dispersed
are
are
and
impact
(166).
different
in
the
Figure
is
(A-AAAB-BBB-BAAA-A).
is
forms
cases,
because
a rigid
therefore,
that
rubber
both
have
tensile
B polymer
illustrated
the
attached
and,
the
the
Tregear
polymers
higher
characteristics
However,
block
have
rubbery
that
aggregated
have
the
the
and
the
reviewed
by Aggarwal
discuss
(A-AAABBB-B)
tri-block
been
a
chains
high
(143,144,167-169).
Battaerd
on
adhesion
with
have
and
which
polymers
by
polymers
polymers
papers
polymers
than
(165)
chains
Good
polymer
polymers
with
grafted
phases.
tough
block
other
block
Di-block
tri-block
of
the
a
Tobolsky
reviewed
properties
these
for
properties
Estes,
and
STRENGTH
ABS
polymer
the
requirements
The
a rigid
grafted
matrix,
AND
including
The
between
(161-164).
of
BEHAVIOR
(155-160).
adhesion
strength
polymers,
polyblend
polymer
similar
the
high-impact
a complex
graft
promote
one
are
STRESS-STRAIN
are
elastomer
only
aggregates
of
one
end,
A polymer
phase.
Brittle Fractu
re
and r
r
Stress
e
tress Concen
Concentrator
trators
s
A.
Stress
Concentrators
ee
OES}
Cracks
and
other
stress
concentrators
play
a vital
role
in
II.
BRITTLE
FRACTURE
AND
STRESS
CONCENTRATORS
295
TRI- BLOCK ELASTOMERS
BiG.
Schematic of AB di-block and
Typical stress-strain
curves
the
strength
crack
to
or
the
a
of
brittle
notch
in
The
applied
the
crack
contain
of
the
20
ABA
are
tri-block polymers.
shown as inserts.
materials
sheet,
the
(171).
At
stress
is
the
tip
of
concentrated
a
according
equation
ga
length
a
ABA
of
0. b + 2(a/z) |
tensile
tip,
the
which
crack
naturally
order
of
stress
has
or
a
to
o.,
fo)
c
is
radius
of
curvature
depth
occurring
107°
is
(13)
of
the
flaws
107 ‘cm,
or
and
the
notch
maximum
(172).
inherent
with
r,
widths
stress
and
a
at
is
the
Polymers
cracks
with
approaching
may
a
length
296
5.
molecular
occur
diameters,
at
the
tips
a
stress
of
and
holes,
as
For
instance,
=
tangential
stress
the
angle
from
the
the
poles
of
the
edge
of
the
the
at
hole
is
equator
the
sphere
is
concentrated
by
inclusion
much
at
the
is
tensile
the
a
is
of
inclusion,
the
stress
B.
(8 =
0)
so
Fracture
the
the
can
stress
in
hole
applied
a
sheet
is
produces
tangential
the
has
a
stress.
stress
direction
and
Ope
tensile
At
is
perpendicular
value
factor
a material
act
The
greatest
stress
sphere
is
(90°
cavity;
of
about
than
the
if
In
of
of
305
at
to
the
the
called
sphere
the
is
is
then
modulus
of
the
of
very
the
to
matrix,
become
adhesion
a
stress)
stress
good
at
tends
applied
continuous
actually
case
concentrated
stress
concentration
the
the
there
this
to
If
May
as
tensile
two.
that
and
sphere
that
poles
compressive
between
rigid
of
separate
the
from
the
dewetting.
Theory
(176)
materials
determining
hole
in
matrix.
a process
Griffith
brittle
of
the
In
reduced
the
the
by
0),
empty
greater
and
matrix
are
stress
(14)
of
the
factor
stress
equator
of
an
sphere
sphere
of
STRENGTH
(173):
tensile
inclusions
occurs
the
cracks,
AND
hole.
(174,175).
the
as
edge
negative.
concentrators
when
the
(6 =
stress
Spherical
at
well
by
direction
i.e.,
stress,
concentrations
a circular
given
BEHAVIOR
gO, (1-2c0s26).
The
compressive,
high
cracks.
concentration
Oy
the
very
the
Inclusions
concentrators.
so
STRESS-STRAIN
developed
in
in
which
the
it
a
theory
was
strength
for
assumed
of
such
the
that
strength
cracks
materials.
of
were
To
the
II.
BRITTLE
FRACTURE
increase
least
by
length
equal
the
the
in
rate
of
the
crack.
decrease
surrounding
the
of
crack
surface
energy
is
tensile
strength
elastic
at
created
by
a
must
the
two
is
to
energy
least
the
sheet
be
available
new
surfaces
load
applied
An
must
op of
of
a crack
If
297
energy
energy
a material.
of
CONCENTRATORS
a crack,
surface
of
growth
energy
the
the
AND STRESS
the
volume
equal
the
rate
growth
of
the
plate
is
then
or
surface
Young's
For
modulus
polymers,
greater
of
energy
the
than
order
and
of
The
reason
and
cold-drawing
the
10°
the
energy
take
at
work
that
equation
185)
when
has
or
the
as
proposed
that
for
y
a
is
during
y,
E is
length
of
the
strength
is
much
is
that
the
found
polymers
pure
that
the
is
instead
surface
there
crazing
and
Therefore,
in
reformulating
plastic
flow,
(182).
form
as
Chen
the
multiple
contains
a modified
used
strength
by
of
design
engineers
objects.
The
small
has
Griffith's
cracks.
Griffith's
a
(177-181).
flow
of
amount
y becomes
(183)
of
growth
a
the
very
y is
plastic
is
the
crack.
energy
is
of
the
the
shown
equation
(184,
Williams
equation
co, = k (Ey/a) ¥?
be
The
energy
energy
same
is
It
value
fracture
a
predicts.
surface
which
crack.
surface
the
for
account
specimen
and
expected
polymer
the
crack
ergs/cm*
involved.
of
of
of
material
(15)
materials,
15
10°
the
into
plastic
holds
to
high
of
area
other
equation
polymers;
to
an
material,
ergs/cm*
for
total
theory
the
many
what
hundred
in
unit
of
few
cracks
per
length,
of
Op = (2yE/ta) Y2 ,
The
elastic
its
in
at
produced
produces
increase
to
as
such
(16)
in
solving
geometric
problems
practical
constant
k
is
of
generally
the
298
5.
approximately
of
any
shape
However,
y of
many
to
practical
of
behavior
various
such
as
a
crack
can
be
of
cracks
to
of
ability
equations.
defined
in
terms
of
factor
factors
In
K, or
are
made
EG.
Ke
EGa(
objects
fracture
of
computers.
energy
16
can
be
two
by
which
the
flaws,
other
at
tests
which
surface
geometry
the
energy
by
fairly
toughness
energy
thin
stress.
relate
a critical
following
the
containing
fracture
factors:
(For
or
load
specified
to
ava,
a
of
contain
fracture
strain
the
type
tensile,
the
of
resist
attempt
specimens
technique,
of
to
is
GTLe Cy
toughness
an
From
mechanics
fracture
specified
is
on
of
a critical
Ke =
a
The
length.
specimen
related
for
the
material
by
propogate,
either
STRENGTH
aid
equation
the
that
loads.
this
AND
the
fracture
materials,
are
a
as
mechanics
applied
for
before
fracture
crack
brittle
rapidly
of
toughness,
known
determined
with
known
the
of
complex
These
technique
test,
BEHAVIOR
work.
The
of
be
values
required
design
real,
calculated
intensity
the
(186-188).
cleavage
starts
be
fracture
kinds
artificial
for
a pre-existing
of
can
mechanics
fracture
measures
technique
the
will
equivalent
extension
This
tables
measuring
material
constant
classical
experimental
of
its
from
polymers
for
The
a way
This
reliable
adopted
or
1.0.
STRESS-STRAIN
is
stress
release
rate
Gu:
equations:
sheets)
(17)
or
where
E is
fracture
to
the
Young's
surface
critical
1
modulus,
energy
strain
v*)
and
y of
the
energy
Gee
aZvee
(For
v
is
thick
Poisson's
Griffith's
release
sheets)
rate
(18)
ratio.
equation
The
is
related
Gy by
(19)
III.
THEORIES
The
is
not
OF
YIELDING
AND
COLD-DRAWING
relationship
of
fracture
clear.
In
some
fracture
toughness
strength
seems
to
A simple
Young's
cases
modulus
and
the
in
the
fracture
holds
tensile
to
strength
but
as
relationship
toughness
impact
increases,
decrease
299)
other
for
many
strength
impact
strength
increases
cases
the
the
impact
toughness
increases.
materials
or
as
between
yield
strength
(189-
ESA) 3
Hake
Op
AG
(20)
and
oO
BSY:
il
These
approximations
conditions,
of
III.
of
Yielding
very
these
or
a
polymers
curve.
region
of
the
point
than
the
that
of
force
remains
after
the
process,
otherwise,
those
very
with
implies
means
the
kinds
pressure,
of
degree
(191).
important
high
a yield
can
be
the
impact
either
approaching
cross
portion
during
the
stress-
a distinct
maximum
slope
itself
becomes
stretching.
must
material
would
break
as
at
specimen
there
show
the
starts
that
essentially
strengths
in
zero
section
of
since
point
Necking
constant
point
are
stretching.
and
all
Cold-Drawing
point
remaining
nearly
yield
and
manifests
specimen,
under
crystallinity
Cold-drawing
during
the
of
polymers
temperature,
curvature
curve.
polymer
in
yield
strong
stress-strain
in
and
Yielding
The
of
many
cold-drawing
phenomena.
strain
degree
Yielding
and
tough
for
changes
and
Theories
all
hold
including
orientation,
1
be
a
in
a
necking
localized
much
while
the
less
the
Cold-drawing
a
strain
without
hardening
drawing
at
300
5.
the
reduced
cross
section
hardening
generally
increases
the
strain
strain-induced
increases
in
stops
a
the
failure
become
a
natural
increases
If
the
natural
the
orientation
about
In
by
the
a
fibrillar
(77)
polymers
consists
chain
are
with
of
the
three
2.
or
and
folded
is
cold-drawing
1.
stacks
Discontinuous
of
of
the
and
chains
length
material
before
of
with
before
that
(14,120,
cold-drawing,
the
sum
orientation
brought
constant.
spherulites
the
chains
stretching
ductile
Plastic
crystalline
crystal
transformation
in
direction.
deformation
lamellae,
of
crystallite
in
in which
the
a
the
of
temperature;
testing
structure
of
of
the
disrupts
in
ratio
increases
approximately
oriented
of
the
morphology
draw
temperature,
decrease
appears
chain
stages:
same
speed
and
section
stretching.
oriented
It
the
polymer
ratio
the
partially
chain
rotation
slippage.
of
weight
highly
believes
the
cold-drawing
extended
crystallites
is,
from
section
stretching
the
process
a
of
cold-drawing,
of
all
natural
further
direction
down
given
rapidly
cold-drawing
of
the
a
generally
decreases.
polymers,
Peterlin
and
ratio
of
function
increase
molecular
that
a
On
length
was
as
is
that
either
before
from
Spherulites
the
cold-drawing
crystalline
morphology
to
draw
the
to
material
the
the
ratio,
may
with
stress
in
draw
region
known
ratio
During
oriented
stretched,
193).
the
until
the
partly
necked
continues
variables.
occurs.
cold-drawn
it
draw
other
polymer,
highly
it was
The
and
soon
The
elongation
come
strain
which
However,
The
Cold-drawing
STRENGTH
The
orientation
might
(192).
AND
place.
strength.
polymers
stretching
BEHAVIOR
took
molecular
tensile
cold-drawn.
material.
cold-drawn
and
as
critical
Orientation,
from
crystalline
length
becomes
of
of
necking
recrystallization
specimen
at
results
modulus,
hardening
where
STRESS-STRAIN
of
of
the
twinning,
the
Iii.
THEORIES
OF
spherulitic
3.
Plastic
Many
of
the
a
deformation
of
the
but
the
of
the
subject
(or
(192,194-196).
the
by
theory
is
possibly
spot
at
prominent
makes
it
large
enough
Other
when
a
increase
in
the
be
and
some
of
cracks
contain
by
theories
about
consist
50
of
row
material
near
to
have
transition
glass
heat
polymers
of
to
energy
possibly
produce
the
put
based
upon
a dilation
of
If
this
increase
in
volume
lowered
to
the
Ty is
cold-drawing
cracks
oriented
of
of
voids
to
is
polymer
is
due
an
stretching
becomes
microvoids
yielding
similar
the
(6,15,198-201).
formation
that
process
This
Tg-
except
which
capacity
of
be
to
temperature.
craze
percent
a
heat
elastomer
very
assumed
polymers
polymer
crystalline
transition
the
and
appear
for
low
for
was
the
glass
the
point
One
developed
unacceptable
be
to
into
glass
suggest
voids
rubbery
a
secondary
then
an
to
spots
melting
temperature
the
of
accompanied
formation
cracks
that
spots
in
are
debated.
hot
amounts
secondary
actively
localized
small
volume,
stretching
may
craze
so
been
cold-drawing
of
applied.
free
temperature,
to
for
its
is
have
put
the
to
very
The
theories
stress
cold-drawing
was
believed
increases
above
chain
these
temperature
low
possible
material
with
energy
temperatures
(197).
temperatures
by micro-necking.
structure
being
as
of
stretching
cryogenic
very
is
Thus,
generally
now
still
temperature
polymers)
spot
and
process,
temperature
transition
structure
fibrous
wasthat
stretching
the
fibrous
yielding
proposals
raised
which
301
fracture.
chain
first
during
COLD-DRAWING
into
theories
proposed,
AND
structure
and
slippage
YIELDING
similar
The
or
dilation
craze
largely
to
cracks,
the
(15,40,202-204).
Although
true
actually
polymer
about
25
cracks,
they
(205-207).
Craze
to
size
200
A in
302
5. STRESS-STRAIN
separated
small
by oriented
angle
especially
impact
plastics
the
This
makes
force
(213)
emphasize
necking
broken
chain
of
for
motion
Finally,
chains
of
to
detected
polyblends
and
to
We is
the
in
(218-221).
direction
theories
formed
at
the
In
of
a collision
the
activation
(not
the
stress
break
chains
points
stress
of
possibility
one
chain
by
a chain
region
is
which
is
may
leads
the
to
is
from
the
of
the
theories
the
probability
of
the
is
This
free
the
new
chain
This
either
yielding
stress
and
k
is
may
favor
radicals
so
of
that
or
may
of
on
a
of
Other
a void
polymer
Boltzmann's
so
the
as
by
that
the
the
at
the
the
Another
breaking
around
at
stress
a
taut
among
develops
the
chain
constant.
stress
chains
nucleate
failure.
activation,
cold-drawing.
formed
contract
void
energy
redistributed
relaxation
ends
small
the
the
then
fracture
mechanism
is
(22)
stressed-biased
concentration
catalyze
(221).
is
stress
(220).
that
the
o,
AH
specimen),
equation
reaction
where
removed
the
first;
remaining
parameter,
volume,
on
probability
Chains
the
which
start
these
stress-biased
stress
unsymmetrical.
the
similar
applied
Ph is
A is
This
be
similar
Pi = Wo exp{- (AH-Agg) /kT}
where
by
high
concept
motions
chains
The
a
which
radicals
polymer
relax.
use
occur
are
free
process
quickly
rupture
be
appears
in
segmental
there
importance
fracture
viscosity
for
over-stressed
or
of
can
Crazing
cold-drawing
wells
easier
the
of
yielding
of
theory
potential
it
voids
(208-211).
the
theories
(214-217).
breaking
in
These
AND STRENGTH
(1,140,146,147,164,212).
other
Eyring's
makes
scattering
important
Still
to
x-ray
polymer.
BEHAVIOR
craze
of
it
the
on
them
crack
III.
THEORIES
OF
Possibly
YIELDING
all
AND
the
COLD-DRAWING
above
and
cold-drawing
may
and
the
importance
relative
from
one
polymer
like
the
following
are
not
and
strong
the
weak
chain
to
may
proximity
and
do
a cluster
a
As
regions
but
place
loops
several
entanglements
several
is
chains
regions,
a
acts
taut
chain
is
in
When
to
to
of
by
or
are
a
break
as
to
a polymer,
apart
to
form
or
small
20
voids
formed
as
x-ray
several
influence
of
the
coalesce
to
form
formed,as
they
hundred
applied
larger
illustrated
in
stress,
voids
the
single
they
develop
may
(220Raaie)r.
first
are
and
cracks
These
21,
be
can
enlarge,
reach
units
the
of
direction
Figure
of
Angstrom
in
strong
regions
when
scattering
A
axial
submicroscopic
section
close
by chains
above
weak
middle
angle
to
many
of
regions
as
a void
indicated
the
21,
Although
act
its
and
the
in
the
in
in
regions
stress.
structure.
it,
around
are
a cluster
surrounded
the
Figure
aggregates
Strong
stress
stress
applied
pull
about
the
grow
cracks
chain
voids,
detected
Under
the
illustrated
as
initial
size
of
or
break
voids
the
is
by
load
all
load
a
broken
in
the
weak
oriented
where
the
chain
point
carries
region
the
out
are
of
and
stress.
to
to
of
Polymers
are
part
another,
regions
parallel
a weak
easily
the
top
chains
segments
parallel
stretched
as
one
of
and
oriented
single
slack
it
direction
oriented
with
since
the
with
something
there
consist
several
vary
polymer:
but
the
can
in
chain
include
segments
in
may
scale,
a glassy
Yielding
mechanisms,
mechanisms
scale,
illustrated
to
chain
in
merit.
possible
a molecular
place
perpendicular
chain
On
entangle
some
different
imperfections
not
have
several
molecular
where
of
by
of
take
on
regions.
regions
theories
another.
homogeneous
ends,
which
take
303
voids
a
(208-210).
continue
until
visible
craze
bottom
section
of
304
5.
STRESS-STRAIN
WEAK IMPERFECTIONS
STRONG
sin th
I
BEHAVIOR
AND
STRENGTH
STRUCTURES
SUBMICRON CRACKS
gate,
Ail
Top: Regions of weakness and strength on a molecular scale
in a polymer which appear to be important in the developme
nt
of craze cracks.
Bottom:
Sequential steps in the development
of voids, oriented polymer,
and craze cracks as the result
of
a
tensile
Figure
21.
oriented
between
of
the
the
that
these
crazes,
they
in
which
In
will
the
the
regions
would
some
break
voids,
of
in
slippage
direction.
craze
material
These
tend
a
forming
will
a
originally
crack
result
chains
if
vertical
above.
a craze
process
the
cold-drawn
discussed
voids
voids
in
to
molecularly
structures
the
applied
addition
because
failure.
in
In
and
fractured
strong
stress
find
to
true
the
so
cannot
crack
consists
which
is
contained
oriented
prevent
crack
highly
much
occur.
and
not
some
easily
of
the
regions
coalescence
catastrophic
oriented
stress
of
on
These
polymer
them
broken
III.
THEORIES
chains
spin
OF
form
YIELDING
free
resonance
cracks
in
to
be
so
At
least
cracks
the
(ESR)
straight
rather
than
factors
encourage
craze
to
so
the
crack
one
other
then
interact
void
the
tend
and
‘and
chain
the
more
fibrillar
effects
secondary
glass
of
motion
so
polyblended
similar
materials
that
with
along
favor
while
the
in
aid
more
the
chain
stresses
of
the
around
growth
craze
which
are
cracks
not
pass
their
tips
Thus,
on
chain
of
the
of
fracture,
orientation
molecular
dominate
and
in
oriented
polymers.
ductile
more
with
cold-drawing
and
segments
are
position
cracks
slippage
of
Secondly,
longer
slippage
chain
in
ends
further
formation
void
and
short
direction.
combination
complex
pointed
(1,183).
yielding
the
transitions
freedom
fields
growth
further
dominate
some
Somewhat
stress
pointed
concentrators
single
tips
Crazing
stress
a
the
giving
of
into
until
by
regions
fields
length?
be
The
appear
submicroscopic
a colinear
grow
process
the
in
craze
the
will
same
two
polymers
brittle
the
stress
crazing
slippage.
in
the
stress
hand,
a
of
strong
craze
their
First,
stress.
themselves
concepts,
and
formation,
are
do
polystyrene
along
other
hinder
consists
as
by electron
Why
regions
the
coalesce
to
above
such
weak
to
the
overlap;
to
the
polymers
find
cracks
On
will
of
the
growth
another,
two
each
basis
further
(222-225).
involved:
cracks
cracks
(226).
colinear
in
detected
zigzagged
be
perpendicular
which
respect
must
formed
submicroscopic
be
measurements
polymers
two
305
may
glassy
direction
that
which
brittle
initially
two
COLD-DRAWING
radicals
these
if
AND
and
or
Some
orientation
groups
more
relaxed
easily
in
concentration.
phenomena
in which
are
involved
a rubbery
in
polymer
the
is
high-impact
dispersed
306
5.
in
a brittle
phase
are
capable
material
Many
to
which
Strella
and
temperature.
behaves
this
as
a rubber
In
temperature,
the
produces
lowering
of
are!
a
AV
is
the
tensile
elongation
e,
V,
is
emphasized
ductile
as
the
stop
of
role
of
first
start
to
the
run
into
since
the
radius
of
stressed
according
is
the
glass
tensile
load
coefficient
volume
change
associated
initial
cracks
the
212).
the
(174,230,231).
rubber
tip,
so
the
is
with
have
of
particles
greater
intensity
craze
cracks
crack
than
of
act
approximately
craze
The
tough
particles
number
The
the
unloaded
polyblends
particle.
particle
of
the
Rubber
tremendous
of
of
workers
in making
a
another
volume
Other
equator
to
which
volume
that
the
test
transition
the
so
crack
the
the
(23))
164,
of
of
a
146,
stress
they
curvature
particles
145,
near
matrix.
rubber
ratio.
craze
(1,
the
the
is
the
Poisson's
concentrators
perpendicular
until
is
materials
stress
cracks
v
on
particles
(1 -2v)e.
expansion,
and
rubber
around
(229):
ui is
(147).
to
is.
=
rise
two-phase
Bragaw
stress
break.
matrix
T, by
=~
the
to
giving
such
by
a
the
of
=
into
Ty of
lowering
thermal
polymer,
that
a polyblend
AV/V,,
of
STRENGTH
rubber
mechanisms
triaxial
the
AND
elongation
reviewed
theories
a dilation
polymer
behavior
been
matrix
when
the
free-volume
aAT
The
the
on
BEHAVIOR
a dispersed
high
suggest
lowers
Thus,
theory.
have
a dilational
stress
and
impact
(227,228)
put
triaxial
point
high
of
a brittle
proposed
theories
Newman
polyblends
This
been
and
These
amounts
converting
a yield
have
toughness
systems.
Small
of
has
theories
the
in
polymer.
STRESS-STRAIN
the
May
the
grow
then
radius
stress
III.
THEORIES
OF
YIELDING
concentration
rubber
to
thus
rather
of
other
dissipated
polyblends.
regions
shown
the
rubber
the
apparent
just
a
few
failure
if
generation
rubber
21.
rather
Craze
particle
to
straight
and
DiBenedetto
coworkers
and
of
initiated
in
could
by
of
crack
new
thus
act
the
in
energy
surfaces
as
rather
weak
occurring
tend
to
than
craze
are
in
artificial
polyblends
with
stress
of
naturally
particle
quickly
the
quantities
observed
upon
free
that
as
long
as
volume
is
generated
assume
Ty or
elastic
Mie
Both
components
near
Ty:
The
volume
¢,,
of
M
which
The
oe)
approach
elongation
at
In
this
a
is
equation,
ones
zigzag
going
cracks
oy is
the
volume
coefficient
amorphous
glass,
4,
were
the
is
really
a
at
in
in
single-
zero
curve
of
researchers
last
linear,
is
parts~=—a
a viscous
or
plastic
by
temperature
the
this
no
lowering
either
two
as
glassy
ey of
of
is
raised
is:
theory
strength,
thermal
Va and
eae)
;
92)
E
is
Young's
expansion
of
thermal
ie are
the
of
‘
part.
Ree
coefficient
crystal,
in
and
similar
up
a.)(52
yield
(201),
yield
These
made
ey is
and
Beck
somewhat
effective
is
ES
1S ‘a (a, a
the
glass
have
concepts.
yield
oy
fy >
all
and
stress-strain
the
Ce, =
part
Rusch
elongation
the
voids.
generating
in
(6,15)
for
based
polymers
free
(199,200),
coworkers
theories
quantitative
the
which
number
Large
cracks
line
are
hindered
than
rubber
large
polymers.
Litt
g
cracks
particles
polymer
the
cracks
not
in
the
of
craze
(1,183).
Figure
from
of
cracks
The
in
in
phase
than
307
Because
millions
catastrophic
fields
COLD-DRAWING
decreased.
particles,
polyblends
grow
is
AND
modulus,
the
expansion
specific
if
to
308
5.
volumes
v
is
of
the
amorphous
Poisson's
and
T is
the
importance
ratio,
test
of
glass
Ty is
and
the
temperature.
ae in
STRESS-STRAIN
the
glass
This
determining
BEHAVIOR
crystal,
the
yield
STRENGTH
respectively,
transition
equation
AND
temperature,
shows
the
behavior
of
glassy
polymers.
IV.
Impact
A.
Strength
Nature
Impact
the
tests
energy
tests
to
specimen
the
weight
impact
plate
the
The
and
the
in
a
tend
size
to
give
disagreement
sheet
or
from
of
the
ball
it was
type
the
area
impact
series
of
of
The
strength
to
(235,
242,
243).
kinds
than
of
is
does
tests
different
not
of
Thin
the
give
the
depends
normalize
thick
poor,
in
geometry
made
different
test
curve
(239-241).
polymers
is
strengths
the
test
tests
impact
impact
Still
under
stress-strain
constant.
attempt
size
a
weight
(236-238).
the
various
rank
the
dropped
measures
even
between
of
a
test
impact
energy
break
since
higher
kinetic
break
to
a given
specimen
in
to
determined
important,
constant
required
required
often
an
specimen
energy
a material
if
a
impact
dart
the
is
strikes
energy
loss
Charpy
falling
among
is
and
measure
or
agreement
which
the
falling
tensile
a value
Izod
which
ball
which
addition,
the
tests
weight
the
speed
In
to
the
of
is
and
from
In
impact
In
a high
order.
sample
bar),
amount
tests
fracture
hammer-like
determined
from
of
speed
specimen.
a
material
different
specimen
a
with
the
type
obtained
high
(232-235).
height
another
Tests
unnotched
is
tests
of
Impact
break
or
the
Tearing
are
a pendulum
(a notched
and
of
and
upon
values
specimens
ones.
indicates
The
that
Iv.
IMPACT
impact
STRENGTH
tests
properties.
1.
The
to
propogate
In
Two
factors
needed
a
used
tensile
tests,
stress-strain
kJ/m*.
is
factors
For
in
are:
Table
notches
that
is
most
tip
the
of
of
the
extremely
a
similar
as
are:
required
of
a
length
for
notch
takes
that
range
of
specimen
of
the
with
notch.
strength
Conversion
=
5.25
kd/m’.
notched
Izod
impact
is
The
with
notches
less
impact
main
tends
in
place
in
Ina
than
(1,245).
At
to
there
and
why
In
others.
take
notched
notch
deformation
stress
radii
small
place
specimen,
neighborhood
the
the
reason
The
strength
polymers
some
than
However,
13.)
Equation
specimen.
of
impact
specimen
reduces
in
units
1 ft-lb/in®
concentrators.
sharp
(See
area
(1,244).
stress
material
rate
unnotched
break,
f£t-lb/in*
deformation
the
of
apparent
to
(172,233,235,245).
the
deformation
2.5
a notched
are
on
confusing.
kilojoules/(meter)*.
=
tips.
why
energy
plastics
greatest
unnotched
or
be
terms
of
one
specimen
high
in
length
notches
so
defined
per
common
notch,
is
or
detrimental
more
the
throughout
physical
energy
can
tests,
typical
their
of
strength
energy
strength
reasons
unnotched
an
basic
behavior
The
similar
notch
the
unnotched
are
2.
tests,
impact
other
crack.
Charpy
The
curvature
are
of
some
concentration
of
impact
and
1 ft-lb/in
is
more
Izod
enectyOrsNOtehes)
this
for
terms
for
an
or
and
curve
Be
of
a
two
into
impact
strength
notched
3 lists
strengths
that
impact
foot-pounds/(inch)?
defined
enter
express
under
2.10
least
initiate
to
the
as
at
which
to
Specimens
such
by
crack.
speed
the
309
controlled
units
high
TEARING
are
energy
The
AND
of
the
experiences
an
in
compared
to
that
rates
of
deforma-
high
=
310
5.
STRESS-STRAIN
Table
Notched
Izod
Impact
Strength
BEHAVIOR
of
Rigid
Plastics
at
Impact
(ft
Polystyrene
ABS
STRENGTH
3
Plastic
High
AND
24°C
Strength
lbs/in
notch)
O24
impact
polystyrenes
OFS
polymers
8200
OleO)
a
Oe
Polyvinyl
chloride
(rigid)
0.4
=
Polyvinyl
chloride
(polyblends)
S50
Polymethyl
methacrylate
0
=
3.0
AD
Og 4a —
50)
ORS
Cellulose
acetate
Le
>
Byes
Cellulose
nitrate
Ho
=
Hol)
Ethyl
cellulose
S555)
=
oid)
Nylon
66
Ibo
=
shold)
Nylon
6
Ao)
=
Sin)
2
om
OSs;
=
2{8)5(0)
6S
=
2
db,
=
ALS
1
=
20
Polyoxymethylene
Polyethylene
(low
Polyethylene
(high
density)
>
density)
Polypropylene
Polycarbonate
Polyvinyl
(Bis
Phenol-A)
formal
Phenol-formaldehyde
(gen.
purpose)
Phenol-formaldehyde
(cloth-filled)
Phenol-formaldehyde
(glass
1
55
aS
10
=
Si)
Polytetrafluorethylene
Ao
=
40)
Nylon
6-12
SO
ae
lrr
Nylon
11
4s
=e
LSS)
=
(5
2
=
20
42
=
Bo)
10
>
Sil)
Polyphenylene
oxide
Polyphenylene
oxide
(25%
fiber-filled)
OR 5
16
glass
Polysulfone
Polyester
(glass
Epoxy
resins
Epoxy
resin
Polyimide
fiber-filled)
(glass
fiber-filled)
fibers)
0.9
IV.
IMPACT
STRENGTH
tion
a material
with
lower
notched
than
the
is
may
change
an
brittle
a
of
which
primarily
energy
initiate
to
and
this
the
crack
notch
in
(235).
are
very
high
specimen
of
22
is
polypropylene
in
increase
0°C
for
the
to
the
the
energy
to
propogate
1/4),
as
a
is
on
specimen,
emphasized
to
the
of
the
strength
of
several
this
material.
in
Figure
function
specimen
until
result
the
increase
the
above
The
of
polymer
a
strength
great
above
With
the
polymer
with
a
sharp
rate
of
notch
aS is
above
a
due
is
shift
in
the
chloride
specimens
this
of
illustrated
notching
Ty of
the
strength
tip
acrylic
increase
the
notch.
impact
the
part
20°C;
the
to
for
Ty with
in
in
due
propogate
temperature
the
raising
the
impact
The
specimens,
polyvinyl
of
the
crack
crack.
to
is
temperature.
is
about
of
for
apparent
not
a
of
an
effect
23
of
on
strength
is
The
crack
is
unnotched
and
to
a
apparent
polymers
compared
of
required
nylon
fracture
absorbed
sharpness
figure,
sensitive
an
in
energy
effect
increase
apparent
deformation
(IS
upon
a
upturn
(IS2)
notch
blunt
notched
affecting
initiation
energy
unnotched
The
(-10°C).
the
a
ductile
from
of
again
impact
comes
amount
In
as
both
factor
the
ABS
shown
notches
material
between
for
so
notch
impact
greater
a
The
impact
be
Another
to
a brittle
In
added
the
Figure
a
is
to
difference
can
(246).
a crack
(235).
on
(Pvc)
and
energy
the
specimen
involves
initiated,
dependent
a ductile
Thus,
a material
propogation.
already
from
materials
process
its
311
strength.
unnotched
sensitivity
being
and
TEARING
impact
and
for
AND
hardly
noticeable.
From
cuts,
and
scratches
discussion,
may
have
a
it
is
obvious
tremendous
that
effect
on
notches,
the
toughness
Sal2
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
(kJ/m2)
STRENGTH
IMPACT
1
2
4
8
NOTCH TIP RADIUS (mm)
Iysieja
16
32
WP)
Impact strength as a function of the radius
of the CUD NOr
the notch for different polymers.
[Reprinted from Vincent,
Impact Tests and Service Performance of Thermop
lastics,
The
Plastics
and
impact
Inst.,
strength
appraisal
of
practical
object,
specimens,
Menein
the
of
1971.
a material.
behavior
of
impact
tests
preferably
(17/2, PSS) «
London,
at
a
several
To
polymer
should
radii
get
in
be
of
any
the
made
realistic
form
on
of
a
notched
curvature
of
the
IV.
IMPACT
STRENGTH
AND
TEARING
40
8
rer
(kJ/m2)
STRENGTH
IMPACT
—~
-40
-20
0
+20
+40
+60
+80
TEST TEMPERATURE (°C)
Bag.)
of
Effect
with
a
with
from
[Reprinted
of
with
2 mm
a
a notch
Vincent,
Thermoplastics,
The
IS(2)
specimens.
a
radius
Impact
Plastics
curvature.
of
radius
with
strength
impact
the
unnotched
=
UNIS
notch
specimens
on
temperature
propylene.
23
Tests
Inst.,
of
poly-
of
=
curvature
and
Service
London,
specimens
IS(1/4)
of
=
1/4
mn.
Performance
1971.]
——<$<—<—$<$—$—$—$——————
Cc.
Effect
Impact
of
Temperature
strength
(51,172,235,247-252).
increases
For
as
the
amorphous
temperature
polymers
the
increases
impact
314
5. STRESS-STRAIN
to
dissipated
yielding
into
with
effects
of
high
by
ee
some
These
the
are
damping
peaks
transitions
or
second
polyblends
are
glass
groups
segments
or
more
effective
some
cases
can
to
in
than
256-260).
under
a
the
due
height
damping
and
of
the
peak
Orientation
The
effects
of
molecular
generally
parallel
poorer
increases
to
if
the
the
the
orientation,
force
(109,235,261-263).
high
impact
secondary
polymer
groups
between
impact
the
glass
peak
motion
(255).
low
the
Some
chains
of
are
MThus,
in
temperature
strength
holds,
even
glass
with
the
(249).
low
associated
orientation
stress-strain
impact
all
24
(247-249,
impact
increases
253,
strength
or
as
the
increases.
of
from
in
The
strengths
strength.
damping
Effects
predicted
and
impact
side
correlation
D.
be
of
to
correlation
the
Not
backbone
properties
When
the
the
(235)
prominent
as
be
possible.
secondary
phase
are
and
impact
have
either
which
damping,
23
high
increasing
motions
is
mechanical
as
in
can
becomes
Figures
very
rubbery
transitions
there
increases
area
in
materials
due
effective
secondary
254,
break
(1,161,162,249,253-256).
transitions
dynamic
a
to
have
impact
temperature
mechanical
shown
polymers
high
to
high
elongations
temperature
However,
below
heat
energy
much
concentrations,
stress
relieve
to
enough
great
are
motions
molecular
above,
Ty or
around
temperatures
At
it.
below
Ty than
above
strength
impact
greater
have
also
polymers
crystalline
Most
higher.
Ty or
of
neighborhood
the
STRENGTH
raised
is
temperature
the
as
dramatically
increases
strength
BEHAVIOR AND
strength
and
is
applied
In
practical
the
if
on
impact
behavior.
the
impact
perpendicular
situations,
strength
Orientation
impacting
force
properties
to
the
is
are
orientation
in which
the
impact
IV.
IMPACT
STRENGTH
AND
TEARING
315
300
100
230
€
x©
PS
-(do) 10
ae
lJ
a
cS
ioe)
3
—
oO
<—
a
a
POLYSTYRENE
r
a
00
Me
-50
1
0
Nl
50
TEMPERATURE
Fig.
tt
100
150
(°C)
24
for
(HIPS).
.]
(1968)
The impact strength as a function of temperature
/ polystyrene and high impact strength polystyrene
J. Polymer Sci., Cl6, 3845
[Modified from Jones,
may
loads
always
come
in
breaks
the
strengths
parallel
advantage
in
molded
test
give
The
effects
on
impact
to
practical
specimens,
very
may
weakest
of
the
which
strength
are
always
contain
strengths
molding
illustrated
Figure
an
object
impact
be
used
to
Thus,
injection
some
orientation,
(109,
conditions
in
high
seldom
conditions.
impact
injection
can
orientation
biaxial,
be
The
direction.
service
misleading
may
or
direction
any
from
on
25
235,
261-263).
orientation
(235).
The
and
316
5.
STRESS-STRAIN
BEHAVIOR
AND
STRENGTH
STRENGTH
IMPACT
(kJ/m2)
-30
-20
-10
0
+10
+20
TEST TEMPERATURE (°C)
ivaiep.,
+30
+40
75)
Impact strength of an ABS polymer as a function of
temperature for oriented specimens.
Specimens were molded
at 170°C
(high orientation)
and at 230°C
(lower orientation).
Along = stress applied parallel to the uniaxial orientati
on.
Across = stress applied perpendicular to the orientati
on.
[Reprinted
from Vincent,
Impact
of Thermoplastics,
The Plastics
higher
temperature
molding
lower
machine
strength
direction)
flow
as
and
a function
(170°C).
cylinder
There
to
the
is
to
of
a very
orientation
orientation
for
the
more
at
Similar
and
stress-strain
birefringence
(or
highly
are
the
at
the
in
flow
(across
the
oriented
shown
properties
Orientation)
than
difference
(along
especially
effects
injection
more
great
the
170°C.
the
relax
to
strength
of
the
orientation
perpendicular
molded
impact
in
the
parallel
direction),
Specimens
where
allows
temperature
impact
(230°C)
Tests
and Service Performance
Inst.)
/London,
19712]
for
are
in
Table
compared
injection
2
IV.
IMPACT
molded
STRENGTH
AND
specimens
biaxial
(109).
stresses,
experience
TEARING
than
Falling
tend
Izod
BL7
to
or
ball
correlate
Charpy
impact
better
tests
do
tests,
with
on
which
apply
practical
oriented
specimens
(261y2263.,264)m
E.
Other Factors Affecting Impact Strength
The
impact
strength
tends
molecular
weight
up
asymptotic
strength
53).
becomes
The
with
to
nearly
effect
of
crystalline
polymers,
melting
no
has
meaning
for
elastomers,
as
measured
be
can
crystallinities
transition
glass
tough
extremely
impact
to
strength
a brittle
imposed
on
crystallite
more
in
of
degree
the
determining
but
it
impact
the
impact
room
still
is
the
test
materials
occurs
of
with
are
temperature
crystallinity,
be
effect
An
compared
high
super-
Again,
become
of
the
strength
polymers
may
decreases.
strength
a
as
the
range
of
265).
spherulites
strength
such
percent,
238,
crystallinity
As
the
(53,
the
degrees
higher
polymer
morphology.
prominent,
factor
decreases,
amorphous
the
At
65
below
well
temperatures
materials.
to
40
roughly
from
of
below
Ty below
Ty:
As
crystallinity
of
In
polypropylene.
their
strength
Impact
of
behavior
degree
above
annealing
a
51,
pronounced
increases
by
have
which
high
fairly
a
and
polyethylene
in
the
if
most
(39,
temperature.
decreases.
impact
the
be
test
or
impact
weight
impact
materials
strength
impact
the
the
melt
the
the
However,
molecular
to
with
the
polypropylene,
such
point,
temperature.
as
where
seems
above
of
from
cooling
slow
of
result
of
decreases
Ty well
a
structure
spherulitic
the
such
somewhat
value
weight
generally
have
which
increase
independent
molecular
Crystallinity
polymers
an
to
of
the
larger
and
important
crystalline
318
5. STRESS-STRAIN
polymers
to
is
their
abiliby
the
impact
and
conversion
result
of
have
F.
is
sacrifice
but
the
the
high
elongations
have
high
is
rubbery
3.
Good
similar
well
least
particles.
must
There
or
break
more
with
room
20
to
40°C
in
an
can
a
of
ones
is
glass
in Chapter
of
be
a
and
of
and
the
than
4.
the
as
the
also
to
rigid
are
strength
of
the
the
(1,
elasto-
2.
in
between
grafting
phase,
the
the
polymer,
onto
by
for
The
dispersed
improved
To
rubber
compensate
adhesion
by
for
temperature.
to
phase
be
strength,
ability
test.
achieved
There
breaking
impact
lower
good
rubber.
conditions
test
impact
converted
compensates
high
second
be
may
can
temperature,
be
same
Adhesion
brittle
temperature
below
should
the
amounts
secondary
Three
at
form
adhesion
to
to
energy
deformation
material
polymer.
phases.
which
of
elasticity
transition
strength
chloride,
(104,266,267).
into
addition
stiffness.
be
brittle
polystyrene
a polyblend
should
small
discussed
the
of
and
glass
a Ty at
rate
elastomeric
rigid
The
impact
have
as
of
test
Polyblends
elongation
amounts
the
increase
polyvinyl
of
prominent
as
by
modulus
in
component
should
of
such
as
materials
plasticizer
produce
1.
good
ductile
greatly
near
polymers
polymers
of
can
addition
these
strength
to
161-164):
meric
of
large
essential
such
materials
increase
reduced
Ty is
Strength
impact
dissipate
if
with
polymers
high
polymer
these
the
Impact
into
they
suppression
by
Brittle
a
a
so
makes
of
the
transitions
two
and
Yes and
polysulfone,
plasticizers
The
of
However,
polycarbonate,
some
lower
strength
temperature.
the
yield
STRENGTH
break.
Plasticizers
a
to
BEHAVIOR AND
the
increasing
IV.
IMPACT
the
STRENGTH
similarity
using
a
in
copolymer
similarity
be
AND
in
to
Grafting
particles
is
impact
may
be
The
dewetting
Large
The
the
two
extent
of
to
The
particles
the
percent
before
small
same
as
adds
for
with
the
voids
is
the
addition,
adjacent
cold-drawing
than
impact
(160).
strength.
giving
rise
to
this
capable
of
craze
the
crazing
of
the
polymer
a great
absorbing
stress
in
appears
particles
particles
the
if
rubber
many
compressive
rubber
and
during
cold-drawing
the
the
The
producing
produced
strength
yielding
chapter.
in
triaxial
to
there
matrix
impact
area
along
of
adhesion,
high
in
surface
better
mixing
the
the
the
much
the
concentrators
large
rubber
have
from
to
one
increasing
good
not
particles.
those
earlier
the
must
in
by mechanical
with
by
The
soluble
of
particles
and
components
polymers
materials
Even
rubber
two
onto
way
made
process
In
acting
were
deal
the
to
only
concentrators.
impact
up
to
strength
some
phase
often
rigid
of
effective
Such
the
become
polymer
energy
stress
very
rubber
particles
proper
responsible
the
between
more
stress
the
the
of
they
polyblends
dewet
immediately
matrix
the
that
phases.
of
as
dewetting
of energy.
of
of
discussed
act
filaments
of
behavior
mechanisms
particles
as
polymers.
absorbs
cold-drawing
lead
the
or
(251,258,268,269).
essentially
and
of
than
particles
cracks.
both
one
the
dewetting
The
for
especially
strength
polymers
are
an
between
two
behavior
the
another.
319
solubility
solubility
increased
adhesion
TEARING
are
phase
the
limiting
affects
spherical
(259,272).
rubbery
with
increases
phase,
value
impact
in
the
size
the
of
rubber
(147,270,271).
The
morphology
(260).
The
rubber
strength
shape
Ata
the
with
spherical
concentration
dispersed
of
particles
inclusions
about
20
tend
to
320
5.
agglomerate
At
this
rapid
strength
to
phases
will
to
point
a more
tend
or
as
be
are
be
form
an
inversion
decrease
the
of
present
roughly
in
There
is
and
in
often
the
the
more
a
the
size
of
the
good
(257,259,260).
family
similar
of
specimen
peak
The
the
size
of
the
damping
modulus,
is
the
concentration
amount
that
of
of
some
rubber
rubbery
determines
size
of
tear
a
energy
to
analogous
to
impact
tests
are
generally
a cut
or
a
strip
of
rubber
are
pulled
the
notch
similar
in
apart.
the
that
plus
razor
shape
to
The
force
rigid
on
tensile
cut
on
to
of
inversion
impact
increases
within
a
may
factor
affect
determining
drop
phase.
It
but
rigid
the
in
the
is
not
total
particles)
peak.
The
a pair
two
phase
factors
occluded
an
the
morphology,
important,
made
phases
polyblends
best
phase
material
of
tests
is
rubbery
damping
strength
of
corresponding
is
Both
generally
biggest
the
rubbery
(273-275).
a
of
the
tensile
with
and
the
rubber
other
The
(rubber
the
The
be
peak,
phase
Tearing
may
extent.
present
G.
and
impact
7.)
strength
rubber
by
in
(Phase
properties
the
particles.
where
between
correlation
adhesion,
to
range
amount.
to
STRENGTH
accompanied
increase
Chapter
due
since
correlation
amount
in
AND
increases.
same
Impact
the
the
the
mechanical
materials
preparation,
large
correlation
damping
increases
a
starts,
concentration
(249,251,257,259,260,272).
as
than
rubber
detail
dynamic
spherical
and
of
in
rather
phases
in modulus
continuous
BEHAVIOR
the
concentration
discussed
strength
elongated
STRESS-STRAIN
is
polymers.
sheets
test
edge,
trousers
propogate
somewhat
the
Tearing
which
specimen
or
the
is
may
be
a
specimen
in which
cut
contain
the
legs
measured
IV.
IMPACT
as
in
STRENGTH
a stress-strain
With
very
broken.
scale
The
since
minimize
be
Similar
is
are
other
to
a
In
the
of
tear
of
in
energy
by
U,,
tear
to
the
generated,
is
given
this
length
test
equation,
of
the
piece;
extent
extension
(jaw
process.
or
A
HH ied
D
the
below
a
critical
strain
defines
to
the
relation
is
also
rubber
a
increases.
of
testing
or
and
W
to
The
be
for
the
that
a
must
is
be
a molecular
resistance
The
to
first
as
chains
the
tearing
energy
balance
break.
by
an
brittle
amount
unit
materials
of
work
amount
of
(276-279).
required
new
to
surface
(25)
thickness
the
of
total
& indicates
is
held
will
amount
of
limit
tearing
not
strain
that
grow
energy
Uy
mechanical
The
tearing
energy
rate
energy
increases.
a
the
in
the
of
the
tearing
critical
This
strain
critical
(280,281).
In
and
life,
fatigue
of
properties
increases
increases
is
degree
during
energy.
rubber
C
energy
the
below
dynamic
tearing
sheet,
constant
stored
for
the
the
tearing
on
broken.
analyzed
is
is
rubber
fatigue
(279,282).
E"
is
between
related
rough
rubber
(#2).
separation)
in
chains
least
and
the
by
subscript
cut
of
are
taut
which
tear
configuration;
Griffith
ee ee
tear,
the
taut
can
are
path
that
become
SS peat
In
a
process
used
a
to
process,
cracks
chains
chains
that
tearing
follows
those
tearing
tearing
extend
tear
number
broken
The
The
surfaces
the
proceeds,
rubbers,
the energy
high.
the
321
test.
crosslinked
generally
to
AND TEARING
as
slowly
the
as
addition
Ve
the
damping
the
speed
Wis
Summary
Stress-strain
does
not
it
depend
depends
cracks
of
behavior,
in
polymers
are
and
in which
there
of
than
they
studies
1.
Small
is
in
of
2.
the
study
of
the
breaking
including
the
of
for
determinations
chains.
of
the
the
yield
decrease
the
elongation
or
tests,
stress,
relatively
degree
crystallinity,
large
by
Microscopy
and
:
craze
formed
for
during
techniques
electron
microscopy
surfaces
as
crystalline
increasing
impact
yielding
areas
under
the
strength
or
the
and
speed
the
well
as
and
of
large
stress-strain
strength
yield
testing,
toughness
increase
the
are
For
strength
can
increasing
the
be
temperature.
generally
elongation
curve.
the
generally
ductility.
the
decreasing
by
which
tensile
polymers,
and
accompanied
factors
the
break
tough
by
ized
3.
the
and
to
increased
High
are
radicals
in
important
measurements
free
fracture
fracture
are
void
of
morphology
orientation.
process
scanning
chain
cold-drawing
brittle
(ESR)
fracture
polymers.
stress-strain
of
and
the
and
much
and
crazing,
which
measure
resonance
and
in
Tools
to
in
molecular
fracture
kind
cracks,
modulus,
ductile
radicals,
important
all
which
as
voids,
free
the
electron,
crazes,
spots,
formation,
fracture.
in
structure
involved
and
tearing
phenomenon,
void
more
and
polymer
viewing
of
spin
number
for
In
factors
scattering
Electron
optical,
two-phase
are
factors
x-ray
weak
slippage
ductile
the
angle
formation.
chain
factors
are
in
generation
and
complex
molecular
imperfections,
submicroscopic
the
these
and
Some
strength,
a very
is
chemical
material.
fracture
Some
upon
upon
the
impact
Fracture
fracture.
involve
as
STRENGTH
AND
BEHAVIOR
STRESS-STRAIN
5.
322
to
However,
character-
break
a
and
polymer
VI.
PROBLEMS
which
323
has
a yield
in
a brittle
are
ductile
brittle
manner
under
if
the
to
Unfortunately,
However,
orientation
can
Brittle
materials
it
is
Vi.
1.
by
well
the
its
to
a
direction
converted
addition
of
a
second
partially
conditions
high
of
impact
molecular
the
direction
weaker.
is,
of
orienting
an
the
orientation.
uniaxial
the
into
tough
high
phase
which
is
be
of
by
uniaxial
developed,
must
on
behavior
characteristics
be
with
the
that
be
crack.
effect
in
the
which
to
is much
strength,
can
what
polymer
by biaxially
only
to
but
conditions,
the
a
great
strong,
the
appear
or
Parallel
very
undesirable
is
notch
fracture
polymers
may
a very
lowest
overcome
theory
known
be
many
may
material.
impact
a rubber.
empirically
fulfilled
in
order
to
strength.
Problems
An
elastomer
the
with
an
M,
of
3000
elasticity
up
to
an
extension
curve
if
the
stress-strain
Prove
that
the
work
done
A polystyrene
gave
the
data.
to
Calculate
specimen
had
a
and
gage
a
under
area
the
tional
3.
be
have
service
by
the
a material
rubber
2.
most
polymers
the
produce
can
testing
conditions
contains
can
of
Also,
behavior.
perpendicular
of
speeds.
orientation,
determined
many
Although
the
speed
testing
impact
in
slow
specimen
polymer
perpendicular
properties
high
normal
and
the
is
a
orientation
stress-strain
alignment,
at
at
test
Molecular
object
point
in
obeys
length
kinetic
ratio
L/L,
density
of
stress-strain
deforming
following
plot
the
the
of
the
tensile
the
of
is
of
Plot
2.
is
polymer
curve
0.9.
propor-
material.
load-deformation
stress-strain
2 inches,
theory
curve
a wrath
ot
if
the
Oso)
Ine,
324
5.
and
a
thickness
of
1/8
in.
STRESS-STRAIN
What
is
BEHAVIOR
Young's
AND
STRENGTH
modulus,
om
and
in
the
Ep?
Load
Change
(lbs)
4.
A
tensile
modulus
total
Strain
5.
iat)
B52
0.030
385
0.036
(fracture)
given
by
Plot
yield
energy
to
e€
(inches)
0.010
0.020
table.
Eo!
Length
25
250
stress-strain
following
in
curve
the
stress
fracture
is
curve
and
points
calculate
7
elongation
the
material.
(psi)
Stress
the
at
Young's
yield,
and
Straanes
Stress
-005
250
-07
1660
-010
500
-08
1500
-020
950
.09
1400
.03
250
-10
1385
04
1470
all?
1380
205
1565
gals
1380
- 06
1690
In
problem
small
4 assume
section
cold-draw.
and
If
ratio
of
3.0,
based
on
the
cross
section
the
what
true
that
broke
the
polymer
before
necked-down
would
be
the
than
the
upon
entire
section
true
cross-sectional
rather
necked
the
had
down
specimen
a
natural
stress-strain
area
of
original
in
the
the
(psi)
(fracture)
one
could
draw
curve
smallest
cross-sectional
VI.
PROBLEMS
325
area?
Assume
point
where
value
of
In
some
up
to
the
cases
==
and
determined
Show
the
Ae
-
B
are
the
Q
ey:
E
is
curve
as
A polymer
has
loads
polymer
the
Poisson's
A
ratio
commercial
stretched
than
in
is
the
Derive
Maxwell
the
the
a
nearly
can
power
be
constant
approximated
series:
c/2ey )
and
E,
slope
is
of
Young's
the
modulus
stress-strain
curve.
hold:
at
E =
Poisson's
badly.
change
is
more
on
the
the
ratio
How
after
biaxially
in
point
stress-strain
do/de.
crazes
to
any
of
would
crazing
direction.
you
At
expect
but
the
film
(longitudinal)
How
high
starts?
oriented,
"machine"
0.35.
would
you
has
direction
tell
which
direction?
equation
for
the
stress-strain
behavior
element:
o =
the
c/oy)"*
transverse
machine
simple
relations
initial
film
been
reached
at
[2
by
an
developed
curve
Bye (2 ish
modulus
defined
a
initial
B,(1 -
the
curve
constants,
the
ORY,
E=
where
by
Be a
Ee
fully
stress-strain
following
|=
was
stress.
point
from
that
neck
stress-strain
yield
o
A
the
engineering
the
where
that
Kn[l
-
exp(-Ee/Kn)]
where
K =
de/dt.
of
a
5.
326
10.
A
tensile
of
0.50
specimen
inches,
curve
of
The
fracture.
pounds
and
the
in length.
the
Hake
4000
psi
If
showed
modulus
a modulus
of
10°
STRENGTH
a width
inches.
up
the
The
to
the
load
0.032
percent,
was
inches
in psi
and
the
point
500
increase
and
for
the
load
The
original
1 in.,
of
the
Plot
the
in
a
kinetic
has
a molecular
are
was
theory
in N/m’,
tensile
stress
linking.
The
curve
11,
tensile
to
is
sketch
a gage
the
a
break
the
in
0.10
final
in.
of
stress
of
50
up
to
l
curve.
approximate
length
length
point
of
linear
stress-strain
change
of
a yield
of
of
the
5 in.,
Assuming
dimensions
a
of
curve
specimen.
a width
Poisson's
the
specimen
uniform?
of
stress-strain
rubber
weight
weight
of
between
density
is
elasticity
300,000
predicted
for
polymer
before
crosslinks
1.0,
curve
of
a
crosslinking
5000
after
and
the
elongation
Problem
13,
plot
by
which
and
a
cross-
to
break
percent.
same
rubber
strain
curve
by
kinetic
the
had
psi,
elongation
versus
what
molecular
the
Problem
temperature
the
500
an
thickness
stretching
room
3000
approximate
specimen
and
of
and
(force)
0.50,
the
stress
dynes/cm’?,
stress-strain
sketch
polymer
For
when
AND
2 inches,
linear
in
the
the
ratio
14.
essentially
broke
of
0.125
break
failure,
For
is
of
is
a yield
at
percent,
er
thickness
is Young's
to
has
percent.
if
a
BEHAVIOR
psi?
A polymer
of
length
specimen
What
5 percent,
Ie
a gage
extensometer
elongation
in
has
and
stress-strain
STRESS-STRAIN
and
as
the
theory
in
biaxial
of
stress-strain
rubber
elasticity.
the
shear
curve
as
stresspredicted
VI.
MWS¥o
PROBLEMS
The
327
creep
of
2 polymers
obeys
the
Nutting
equation:
e = Kot"
where
K and
polymers
for
to
n are
while
which
constants.
n =
0.15
polymer
change
most
do
If
for
you
rapidly
K is
the
same
for
and
n =
expect
the
stress-strain
properties
changed?
the
speed
of
stress-strain
curve
given
for
testing
the
2
one
as
0.30
the
is
other,
Why?
Iey
A polymer
has
G.
UD
to
the
to
break
to
have
yield
for
this
is
During
a
in
shape
the
be
done
to
a
stress
a drop
with
a
of
However,
other
the
material
at
flexural
modulus
one
specimen
can
What
speed
on
an
direction
the
same
Young's
of
a
of
the
skin
the
two
of
which
is
specimen.
specimens
with
polymer
to
compare
impact
test?
modulus
in
is
specimens
A
molecular
type
a
under
test.
tensile
oriented
of
area
the
to
ball
the
the
Why?
middle.
the
falling
has
material
barrel-shaped,
meaningless
center
of
becomes
test
such
one
energy
equation,
polymer,
high
the
have
this
above
related
to
or
the
is
cases
parallel
dart
expect
the
effect?
measured
is
is
0.05.
in
is
Why
you
In
cylinder
curve
tension.
the
many
What
a ductile
bulges
curve
specimens
while
on
this
in
breaks.
Would
ey =
test
specimen
test
Two
and
short
stress-strain
orientation.
19.
of
it
strength?
in psi,
minimize
stress-strain
the
impact
strength
Impact
the
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the
in
a
constant
specimen
test
rate.
temperature
In
catagories:
three
creep
or
test
and
its
except
A
typical
for
is
length
that
not
is
the
sheeting
341
or
a polymer.
the
HDT
is
temperatures
of
a
information
is
thrown
Only
(1-6).
used
in
is
fall
tests
load
the
same
(D1637)(7).
heat
into
applied
is
as
manner
at
increased
tensile
in
the
is
tests,
tensile
ASTM
HDT
kind
temperature
measured
be
transition
some
generally
a
may
material
the
retained.
temperature
the
test
plastic
in
used
also
softening
useful
first
be
the
polymers,
or
softening
the
of
glass
thermomechanical
called
distortion
the
point
is
(DTUL)
can
Thus,
property
HDTs
single
load
which
time.
near
a
under
at
crystalline
deflection-temperature
entire
is
Most
entire
are
they
where
Russia,
one
if
HDT
softening
temperature
limit
important
point.
deflection-temperature
away,
and
the
a polymer
distortion
highly
defined
which
appreciable
the
for
at
temperature
practical
(HDT),
temperature
heat
any
polymers
temperature,
to
deflection
load
very
temperature
temperature
the
amorphous
closer
the
material.
considered
can
or
Properties
Temperature
maximum
rigid
Mechanical
distortion
temperature,
6
a
distortion
In this
test
a
342
6.
load
of
50
increased
case
is
at
it
obtained
a rate
as
starts
with
at
to
very
to
a
strip,
of
2°C/minute.
the
temperature
If
to
a HDT
figures,
proportional
except
applied
2 percent.
before
such
is
defined
becomes
In
psi
the
the
sheet
elongate
test
of
slope
the
linear
high
loads.
at
is
a
this
of
which
first
coefficient
break
temperature
the
of
in
may
in
of
this
curves
Figure
the
thermal
the
in
shrink
Typical
shown
part
is
elongation
it
rate.
are
PROPERTIES
temperature
oriented,
sort
MECHANICAL
the
HDT
rapid
the
The
and
The
at
OTHER
1
curves
(8).
is
expansion
curve
occurs
near
PERCENT
ELONGATION
75
100
TEMPERATURE (°C)
ivalep
Heat
distortion
temperatures
as
(25
150
al
determined
temperature curves.
The rate of temperature
A. Rigid polyvinyl chloride
(Load = 50 psi);
from
elongation-
rise was PENG Aa aL
B. Low density
polyethylene
(Load = 50 psi);
Cc. Styrene-acrylonitrile
copolymer
(Load = 25 psi);
D. Plasticized cellulose acetate
(Load = 25 psi).
HDT defined as temperature at which
elongation becomes
23.
I.
HEAT
DISTORTION
Ty for
from
amorphous
viscous
modulus
and
viscoelastic
the
flow
steep
which
part
of
the
accompanies
curve
the
results
drop
in
(9-15).
shown
in
polystyrene
Figure
temperature
is
HDT
a
amount.
in
free
of
relaxing
with
343
polymers,
or
Annealing
as
TEMPERATURE
given
volume,
of
to
2
This
part
frozen-in
crystalline
other
(15-17).
Ty the
but
and
polymers
The
less
the
the
closer
time
effect
of
polymers
is
due
effect
stresses.
in
the
mostly
also
may
to
HDT,
to
increase
the
be
effects
annealing
the
annealing
required
Similar
which
raises
reduction
the
result
are
increases
found
the
AA
oe
40°F
Y 66°C
O°F
MINUTES
TIMEANNEALING
TEMPERATURES NOTED ON CURVES
REPRESENT ANNEALING
TEMPERATURES
HEAT
DISTORTION
TEMPERATURE
(°C)
aie s A
The HDT as a function
injection molded bars
Cleereman,
J:9 52) Fon
Karam,
and
of
of
annealing time and temperature
[Reprinted from
polystyrene.
Williams,
ASTM
Bull.
No.
180,
37
the
for
(Feb.
degree
344
6.
of
crystallinity,
built-in
resins,
in
stresses
degree
temperature
An
of
for
a
load
and
expansion.
test,
temperatures
of
HDT.
HDT
to
An
the
of
Figure
at
applied
of
fupT
is
3,
depends
and
>
are
stresses
of
0,
stress
If
but
term
strain
Em is
modulus
and
involving
E°
E°
strain
the
is
at
proportional
In
results
the
from
how
the
modulus-temperature
heat
o,,
same
disitortion
respectively.
for
all
implicitly
The
stresses
relates
ae - ze)
arbitrarily
is
occurs
at
the
os is
the
of
with
higher
illustrates
and
(14,16
the
modulus.
the
the
at
HDT
is
also
the
HDT
modulus
the
the
upon
which
the
oe
to
equation
Young's
last
increases
in
deformation
deformation
De
in
deformation
approximate
E
stress
This
is
applied
a decrease
definition,
specimen
2 percent),
the
thermoset
distortion
decrease
the
1 or
is
relieves
in
about
heat
3 schematically
(‘uve cs en) oaks
where
By
the
stress
In
the
proportional
Figure
deformation
the
the
greater
load.
part
function
(14).
total
brings
causes
is
consequent
inversely
thermal
curve
stress
deformation.
HDT
a
and
or
Likewise,
often
Tyr
PROPERTIES
morphology,
phase.
time
effect
given
constant
as
curing
this
the
tensile
HDT
amorphous
applied
of
temperature
the
the
in
cause
with
to
the
crystallite
MECHANICAL
(18).
temperature
a
the
crosslinking,
increase
major
about
in
increasing
the
The
changes
OTHER
the
taken
at
modulus
generally
HDT
is
defined
in
terms
if
the
elongation
is
2 percent,
of
at
resulting
polymer
the
ee)
the
at
very
=
from
HDT
room
HDT
(generally
thermal
expansion,
corresponding
temperature.
small
1 percent
K
the
for
0.015.
The
The
glassy
elongation,
HDT
to
K
is
polymers.
=
0.005,
I.
HEAT
DISTORTION
TEMPERATURE
345
tol!
A€ = CONSTANT
MODULUS
LOG
108
TEMPERATURE
mshi
3)
Schematic modulus-temperature
curve illustrating how the
heat distortion temperature decreases as the applied load
increases.
T, is the HDT corresponding to a stress 0).
(Reprinted
from
estimated
modulus
load
from
of
A test
deflection
bent
in
polymer
to
temperature
flexure
1 by
is
plastics
similar
long,
Trans.
equation
several
for
5 inches
the
Nielsen,
1/2
by
inch
the
E.
Soc.
Rheol.,
Figure
243
(TIGS)
at
temperature
the
noting
9,
4 shows
HDT
the
which
function
a
as
i]
(14).
above
under
thick,
supporting
tensile
load
and
the
test
HDT
(7).
is
the
ASTM
In
this
test
1/8
to
1/2
inch
in
beam
at
its
ends
and
D648
a bar
width
is
applying
of
346
6.
OTHER
MECHANICAL
PROPERTIES
[
a
80
60}
V-LUSTRAN
O-H!I20,
I
IMPACT
POLYSTYRENE
O-SAN(LUSTRAN
O-HDPE
__
(DENSITY
SLOPE
88-1)
= 0.96)
(MPE> 40/6)
10
€)
(°C
ATI%
TEMPERATURE
DISTORTION
HEAT
(HT
A)
fea
eer Siren ks
100
i
ne
reel |
1000
LOAD
(PS1)
Page
4
10900
Heat distortion temperature as a function of tensile load for
several plastics.
Lustran I is an ABS polymer.
SAN is a
styrene-acrylonitrile
copolymer.
HDPE and LDPE are high
density and low density polyethylenes,
respectively.
Heating
Eater =
oF ZAS
—22'C//mamn.
96S) 4)
a
in
load
The
of
HDT
the
either
rigid
the
is
center.
defined
center
66
or
for
which
264
A
versus
the
from
Nielsen,
heating
rate
temperature
0.010
as
The
inches
load
transition
type
temperature
of
HDT
curve
at
264
such
defined
as
which
an
from
already
Soc.
the
the
as
below
per
minute.
deflection
load
generally
load
the
Rheol.,
degrees
applied
is
such
temperatures
is
two
psi
while
materials,
Trans.
is
under
of
polystyrene
crystalline
glass
second
as
psi.
such
softer
have
The
reaches
polymers
used
[Reprinted
of
66
of
used
psi
for
is
polyethylenes,
room
shear
illustrated
temperature.
modulus
in
previous
I.
HEAT
DISTORTION
Chapters.
test,
The
but
torsion
Many
TEMPERATURE
shear
more
is
shear
used
(21-27).
the
of
torque
is
defined
flex
applied.
in
terms
temperature
at
flex
The
curve.
The
(27).
temperature
66
which
which
at
occurs
psi
at
as
The
about
a Gehman
D1043
or
D1053
curves
10
have
is
seconds
after
the
modulus
closely
the
temperature
HDT
or
is
the
to
as
the
is
D648
ASTM
the
and
HDT
the
at
modulus
shear
the
where
the
which
temperature
psi,
10°
The
temperature
with
correlated
be
been
defined
is
G versus
log
corresponds
shear
at
from
the
curve.
this
psi;
10*
tests
been
have
temperature
is
(20)
calculated
temperature
T,
in
can
psi
the
or
temperatures
the
modulus
264
5 or
a dynamic
(19)
modulus-temperature
psi.
temperature
from
modulus
softening
defined
the
the
specimen
temperature
HDT
at
temperature
shear
45,000
inflection
the
near
HDT
is
modulus
the
Th is
temperature
shear
the
by ASTM
tests
Various
of
determined
described
these
in
be
a Clash-Berg
versus
In
twist
can
either
as
modulus
published
angle
modulus
generally
tester
such
347
ie) 3) se NO)” geysalc
The
third
penetration
‘Vicat
test
cross
a
test
softening
(7).
In
of
temperature
depth
of
decrease
at
1 mm.
in
Tg.
test
a
The
The
which
The
Typical
as
ended
into
Vicat
the
a
is
needle
for
low
the
must
be
is
type
by
the
of
ASTM
1 mm?
sheet
of
the
at
a
rate
temperature
penetrated
associated
molecular
penetration
very
this
test
of
heated
has
temperature
needle
thick
softening
penetration
or
of
described
polymer
materials,
A material
softening
flat
pressed
modulus,
uncrosslinked
above
is
hour.
27a).
temperature
1000g.
per
of
(27,
this
section
load
120°C
type
soft
test
is
is
the
circular
with
either
50
or
the
polymer
primarily
weight
a
D1525
polymer
of
the
is
to
with
a
the
amorphous
is
due
to
viscous
for
the
Vicat
needle
flow
to
(7)
348
6.
penetrate
Vicat
HDT
a polymer
softening
temperature
of
is
1mm.
higher
For
than
this
most
PROPERTIES
reason,
of
the
the
other
Fatigue
Up
to
associated
however,
life
is
point,
with
stress-strain
material
due
fatigue
life
bring
many
or
stress,
the
In
(31-33)
Prot
rate
rather
test
is
place
in
testers
a
testers.
stress
testing
two
number
a
decreases
in
some
for
some
deformation
than
low
on
modulus
a high
static
is
can
be
of
curves
cycles
saved
by
to
testers
Fold
in
tests
constant
of
the
Prot
failure
take
deformation
the
so
or
instruments
a
having
that
failure
material;
at
constant
stress
These
deformation.
advantage
develops
smaller
or
increased
compared
puts
materials.
of
a
Since
fatigue
Some
Constant
complete
modulus
before
deformation
stress
The
before
a
N
(28-30).
instruments.
a
crack
types
Fatigue
strain.
number
constant
cycles.
large
time
at
constant.
of
the
testers
stress
time
or
stress,
versus
Fatigue,
mechanical
stresses.
stress
maximum
beam
disadvantages
if
constant
the
much
of
been
stress.
on
held
First,
continue
Material
being
of
has
rupture.
oscillation
cycles
tests
the
creep
of
fatigue
rotating
material
or
the
of
test,
with
a
deformations
that
flexural
shorter
have
at
or
of
degradation
stress
oscillations
than
that
the
failure
applied
of
kinds
and
superimpose
the
as
failure
tensile
constant
a given
function
given
are
or
number
at
or
tests
failure
the
a
about
There
include
as
is
fracture
oscillatory
fractures
generally
to
to
defined
specimen
are
this
is
properties
to
a depth
MECHANICAL
tests.
if.
a
to
OTHER
on
stress
material,
the
test
occurs.
a
low
this
gives
(34)
are
the
can
Second,
modulus
an
advantage
another
type
II.
FATIGUE
of
fatigue
used
as
hinge
349
test
hinges
must
As
be
sustain
a
Fatigue
plastics
and
composite
Figure
stress
is
5 shows
high,
life,
occurs,
increases
some
endurance
can
be
times
at
that
frequency
low
in
test
per
the
frequency
temperature
of
as
be
the
the
the
or
may
life
if
specimen
temperature
more
a
a material
Thus,
the
can
the
lifetime
deformations.
so-called
in
engineerinc
load-bearing
be
off,
limit.
there
to
at
increases.
material
the
many
is
life
increase
The
(35).
fatigue
of
important
a
given
number
as
the
is
small
with
in
cycles
millions
fixed
effect
damping
of
for
decreases
fatigue
its
and
a
The
an
or
only
and
is
fatigue
It
holds
failure
decreases.
number
deformed
The
before
cycle
the
the
cycles.
cycles
generally
in
When
few
large
increases.
due
a
per
very
curve
decrease
great
become
curve.
levels
temperature
but
can
curve
a
oscillations
used
of
endurance
Fatigue
are
called
life
given
the
stress
stress,
the
many
of
for
after
fatigue
second.
of
maximum
material
in
strength.
life
number
infinite
below
at
frequencies,
decreases
an
The
each
breaks
fatigue
as
loads.
fatigue
the
maximum
to
stresses
as
the
the
failure.
fatigue
cycles
as
which
sections
used
that
repeated
important
typical
tests
load
or
thin
materials
indication
vibrations
specimen
of
limit,
remember
of
value
little
varying
expressed
subjected
‘without
to
other
tensile
materials
a
the
fatigue
Below
give
for
times.
fatigue
its
especially
subjected
structures
of
to
Many
oscillatory
fraction
are
and
or
A material
flexed
metals
tests
sheets
objects.
being
maximum
subjected
tests
for
applications,
the
only
object
of
replace
conventional
an
important
molded
capable
since
is
is
many
structural
important
of
in
plastics
critical
more
which
an
to
type
of
at
increase
the
Fatigue
life
often
life
350
6.
50005
FATIGUE
LIFE
OTHER
MECHANICAL
PROPERTIES
CURVE
5000
ee
= aod}
wn
wn
uJ
& 3000+
wn
>= 2000;
x<
—
= 1000
: lo!
102
103
104
NUMBER
OF
inalsiq
Fatigue
failure
105
CYCLES
106
10?
TO FAILURE
SS)
life, as defined by the number of cycles before
occurs,
versus maximum stress applied during a
cycle.
is
given
by
(28):
Log
where
N
is
constants,
of
the
fatigue
and
T
is
fatigue
life
for
a
the
specimen
the
in
raised
was
fabric
temperature
second
was
25
be
because
the
frequency,
(2)
number
absolute
from
-30°F
for
phenolic
of
the
the
is
of
58
to
the
same
material.
higher
proportional
of
the
(36).
B are
fatigue
life
the
The
decrease
temperature
increase
than
to
and
when
The
The
A
The
percent
80°F
damping.
square
cycles,
temperature.
decreased
considerably
specimen
and
in
percent
laminated
may
+ B/T
life
polymethylmethacrylate
temperature
the
N=A
temperature
the
energy
the
maximum
of
ambient
dissipated
loss
modulus
deformation
per
BY
or
in
II.
FATIGUE
stress.
351
The
percent
of
fatigue
the
static
reinforced
plastic
correlated
with
Fatigue
of
cracks
develop
value.
the
load
grows
point
it
growth
tearing
more
resistant
A
materials
second
polymers
heat
is
easier,
up.
a
with
Below
Ty!
E"
occurs.
so
If
much
an
by
E"/E'
that
rate
of
equilibrium
radiation
and
as
increase
can
increases
the
and
make
at
an
are
life
the
it
because
of
dissipation
polymers
becomes’
temperature
fail
its
worse
low
is
reached
conduction
as
fast
as
growth,
stiffness.
from
in which
it
is
so
until
crack
resulting
temperature
builds
Thus,
rate
by
of
resulting
of
growth
faster
tear
cracks.
strength
doesn't
energy
and
situation
even
the
these
fatigue
material
fails
and
temperature.
the
this
crack
to
in
during
at
This
propogate
the
some
the
materials
crack
with
of
size;
others;
The
which
related
damping
(41-46).
growth
polymers
be
to
(32).
amount
more
in
test
above
small
determining
decreases
is
or
Some
than
temperature,
life
to
mechanical
increase
temperature
a critical
lost
and
temperature
the
their
a
rigid
appear
in
flaws
stress
40
a Prot
strength
failure.
difficult
factor
by
to
progressive
one
both
tearing
more
of
grow
(37,38).
material
fatigue
damping,
is
decreases
softens
Below
the
the
failure
it
to
so
small
that
in
to
is
important
related
build-up
génerally
it
the
cause
in
material
type
microscopic
and
occurs
one
contain
cracks
longer
20
the
Eventually
no
resistant
to
if
only
tensile
the
always
cracks
is
measured
Materials
properties
the
as
due
process
of
of
In
generally
rapidly
fatigue
energy
inherently
percent
is
propagate
The
limit
cycle.
it
polymers
strength.
microscopic
each
tearing
rubbers.
is
The
until
may
or
40
37-42).
of
most
fatigue
submicroscopic
critical
cracks
the
failure
into
for
tensile
about
(29,
peak
limit
the
heat
produced
352
so
6.
that
above
fatiguing
the
critical
temperature
Very
factors
little
of
flaws
Factors
increases
Fatigue
orientation
Orientation
is
a
in
the
appears
which
can
to
specimen
can
cause
may
The
result
of
generation
polyvinyl
Studies
methacrylate
theory
of
fatigue,
factors
a
of
great
in
reduction
materials.
actual
In
to
the
in
also
the
tend
weight
(47-48).
crazing
of
of
common
fatigue
scratches
on
especially
crosslinked
polymer
(49).
polypropylene
life,
of
such
stress
Since
or
fatigue
to
weight
molding
and
5.
applied
notches
and
Chapter
failing.
in
molecular
imperfections
decrease
fibers
fracture
to
molecular
before
cracks,
and
formation
molecular
parallel
flexures
chemical
which
affecting
However,
a polymer
limiting
important
on
the
fatigue
include
(41,50),
Much
has
fatigue
nylons
(45),
of
life
of
rubbers,
chains
and
the
is
not
the
been
(29),
experimental
(41),
work,
by Andrews
polymers
(32,33),
polymethy1l-
(29,40,41,46),
polycarbonate
reviewed
plastics
polystyrene
polyethylene
(29,33,38,41),
(35,42).
by
growth
polytetrafluoroethylene
epoxies
a
4.
related
increasing
the
structural
factors
briefly
of
to
and
crack
as
specimen,
radicals.
free
chloride
be
from
literature
extensive.
up
of
the
However,
occurs.
the
the
ease
discussed
Thus,
in
Chapter
how
strength
many
the
notch-sensitive
fatigue
was
of
PROPERTIES
apparent.
chemical
cracks
molecules
take
due
the
of
the
to
the
about
affect
increased
largely
for
known
MECHANICAL
failure
discussed
life
of
until
Some
is
not
production
life.
life.
fatigue
is
rise
is
fatigue
increase
life
heat
formation
fatigue
or
about
a material
which
increase
to
a polymer
in
of
were
The
occur
known
nothing
propogation.
hinges
is
damping
practically
as
rate
affecting
structure
not
continues
mechanical
and
does
OTHER
rubbers
and
crosslinked
along
(39)
(a 74spee
with
and
the
Hearle
(49)
III.
FRICTION
MARIE,
355
| laheslrolesikorat
The
frictional
practical
situations
polymers.
a
road
or
It
is
surface
plastic
role
in
the
must
be
moved
first
u
surface
is
a
is
of
the
the
force
of
a
the
by
F
is
the
a normal
depend
load,
between
load
have
many
nature
of
and
rolling.
apparatus.
by
and
Conant
frictional
Glaeser
Tabor
Liska
Friction
and
can
by
be
The
(52),
of
molten.
motion
coefficient
of
polymer
measured
they
are
of
of
friction
motion
pressed
into
different
or
of
has
bearings
has
of
of
area
the
and
been
4)
(S375
been
friction
of
sliding,
the
of
of
type
reviewed
has
been
by
reviewed
ene
reviewed
by
(56).
by
a great
variety
of
-
friction
velocity
rubbers
Schallamach
classes
classes
rough),
at
together
three
coefficients
lubricants,
friction
by
produce
divided
polymers
of
to
temperature,
(smooth
and
Pinchbeck
be
The
as
absence
(51).
behavior
(55)
such
behavior
frictional
when
These
surfaces
or
measuring
can
values.
factors
the
required
surfaces
Friction
presence
and
two
W.
surfaces,
Bowden
force
different
upon
The
polymers
become
the
a
(3)
tangential
dynamic,
generally
plays
by
interface
static,
against
bearings
also
DOA)
where
of
including
granulated
resisting
The
tire
plastic
polymers
many
scratching
Friction
where
in
surfaces,
in
snow.
surface.
and
many
wanted
where
of
wear,
against
is
important
friction
extruders
section
another
is
high
against
a measure
against
defined
sole
skiis
the
have
friction
section
into
polymers
abrasion,
to
shoe
Low
coated
Friction
one
of
tile.
plastic
of
involving
desirable
or
floor
for
behavior
instruments
354
6.
from
a
simple
inclined
force
to
drag
a
force
required
rounded
to
Unfortunately,
the
data
data
from
reason,
of
friction.
which
The
include:
1.
are
adhesive
forces
in
and
at
3.
Mechanical
is
a major
factor
automobile
tires.
a
rolling
over
depresses
ball
If
a
the
deforming
the
ball
snaps
for
object.
Thus,
rolling
variables
of
not
the
the
(57-65).
phenomena,
agree
with
the
As
back
of
and
pushes
damping,
dissipated
on
friction
change
the
as
as
have
part
of
the
should
the
with
by
no
when
ae
behind
the
energy
leaving
of
the
damping
with
LOLS
from
correlate
damping
mechanical
polymer
ball
side
surfaces.
displaces
friction
the
two
scratch.
wheel
heat,
the
elastic
no
or
the
experienced
the
back
should
the
The
such
but
a
factors
from
on
material
produce
in
several
results
perfectly
it,
factor
where
asperities
a ball
relative
of
points
friction.
should
The
up
force
to
or
front
made
For
coefficients
another
harder
friction
friction.
lower
is
is
of
the
in
metals.
This
contact
wheel
have
junction
internal
pushing
which
force
were
is
friction
do
contact
which
mechanical
polymer
to
polymers
in
available
the
in
or
a surface
factor
against
of
surface.
energy
and
tend
in
rolling
If
has
important
interaction
or
polymer
polymer
an
contact.
points
in
often
measuring
surface
across
of
PROPERTIES
instrument.
polymers
the
smooth
immediately
the
apparatus
shearing
damping
rigid
wheel
frictional
process
material
damping,
of
intimate
A ploughing
softer
complexity
materials
The
smooth
the
polymers
total
surfaces
2.
two
a
of
is
polar
the
across
MECHANICAL
apparatus
or
adhesion
than
complex
a ball
another
nonpolar
friction
hardness
type
with
Molecular
of
roll
one
to
stylus
because
obtained
this
plane
OTHER
less
rear.
in
elastic
rolling
damping,
affect
the
the
III.
FRICTION
355
coefficient
The
of
equation
damping
been
rolling
friction
relating
was
derived
proposed
by
the
by
Gent
in
the
same
coefficient
Flom
and
(58,68).
Henry
See 5
manner
of
rolling
A
corrected
(58,60,65-74).
friction
Uy, to
equation
has
(73):
Ys
W
ae Fr ( -)
where
W
is
dynamic
the
with
similar
equation
mechanical
the
of
rolling
of
has
the
friction
data
E"
modulus
E"/E'
of
(60)
Grosch
and
on
a
on
friction
glassy
glass
coefficient
part),
some
a
cases,
it
different
W-L-F
the
the
In
may
(72).
transitions
as
Other
but
are
of
with
to
been
(at
and
and
with
changes
that
velocities
The
Tg:
may
in
a
Schallamach
(ald)
the
loss
with
with
correlates
in
maximum
secondary
peaks
super-
through
goes
maximum
the
least
velocity
(60,71,75).
correlates
the
Low
coefficient
temperature
transitions
not
A
dynamic
found
velocity.
varies
(65).
friction
friction
general,
friction
due
has
the
0.48.
time-temperature
maximum
but
the
temperature
equation
expected,
correlate
of
about
temperatures
reduced
surface,
surface.
the
follow
smooth
correlates,
maxima
state
the
that
rough
friction
wheels
between
are
which
rolling
report
a
constant
E"/E'
for
relationship
at
a
and
derived
against
plotted
when
K is
E'
of
coefficient
the
for
and
R,
a value
should
by
radius
has
and
obtained
curve
of
but
close
In
superimposed
maximum
been
friction
principle.
master
ratio
coefficient
position
be
ball
properties,
properties
variation
the
Poisson's
Because
can
on
mechanical
slightly
for
load
(4)
correlate
molecular
in
the
with
adhesion
(60).
356
6.
With
crystalline
affected
by
Friction
increases
polymers,
spherulite
the
friction
is
its
boundary.
Figures
size
with
greater
6 and
of
of
temperature,
generally
the
mechanism
decreases
of
ploughing,
CH
friction
coefficient
of
if
by
spherulite
at
the
as
a
friction
the
the
of
of
The
of
PROPERTIES
friction
morphology
polypropylene,
a
spherulite
changes
the
in
from
friction
is
with
load
typical
and
friction
However,
the
sliding
rolling
at
velocity
of
if
(74,76).
the
variables
coefficient
is
than
(51,59,63,77-79).
increase
say
in
typical
load
may
of
size
load.
changes,
type
crystallite
center
with
MECHANICAL
coefficient
function
and
slowly
friction
or
and
7 illustrate
coefficient
sliding,
the
OTHER
to
friction
(58,65,
TSNtKO)))
If
surface
one
is
of
a
the
surfaces
stylus,
the
is
a
smooth
coefficient
of
sheet
and
friction
the
may
other
depend
COEFFCIENT
OF
FRICTION
VELOCITY OF SLIDING
Bigne6
Coefficient
of
friction
as
a function
(logarithmic scale).
A. Rubber,
C. Rigid or glassy polymer.
B.
of
Glass
velocity
of
sliding
transition
region,
III.
FRICTION
357
FRICTION
OF
COEFFICIENT
NORMAL
LOAD
—zo
=
OO
wo
Www
ae
set
(See oe a eee
TEMPERATURE
Lablefe
Coefficient
a
function
upon
which
of
of
to
Other
material
plough
coefficient
increases
as
is
into
the
factors
of
in
(79,82).
The
effect
concentration
may
of
1 lists
The
normal
list
affect
be
due
to
load
is
and
as
give
a higher
For
as
the
increases
in
friction.
instance,
compliance
with
This
(64).
chloride
increase
stylus
compliance
as
increases.
coefficient
compiled
hard
friction.
also
the
to
A
increase
polyvinyl
plasticizer
the
and
the
tends
in
(81).
sheet
coefficient
plasticizer
polymers.
of
stylus
softer
friction
concentration
Table
function
the
also
plasticizer
the
a
temperature.
material
tends
the
friction
97
of
from
friction
various
for
sources
some
common
using
358
6.
Table
Coefficients
of
MECHANICAL
PROPERTIES
1
Friction
Polymer
OTHER
of
Polymers
Metal Against
Polymer
Polymer
Against
Polytetrafluoroethylene
Polyethylene
(low
Polyethylene
(high
Metal
0.04
density)
sdb >
2
density)
Polypropylene
Polystyrene
Polystyrene
Polymethyl
polyblend
methacrylate
Polyethylene
Nylon
66
Nylon
6
-4
terephthalate
low
Polyvinyl
chloride
Polyvinylidene
Polyvinyl
eS
chloride
a
fluoride
=
sd, =
Boll)
5S
Polycarbonate
Phenol-formaldehyde
Rubber
Rubber
(near
Cellulose
Tg)
acetate
Polyacrylonitrile
different
comparable.
make
these
techniques,
The
low
materials
so
the
values
suitable
values
for
are
often
not
directly
polytetrafluoroethylene
for
bearings.
and
nylon
IV.
ABRASION,
IV.
WEAR,
Substance
action
(83)
from
from
Abrasion,
closely
force
the
softer
material.
quite
elastomer
moves
over
wear
materials
surface,
occur
as
where
upon
where
has
these
process,
these
developed
temperatures
asperities
At
hot
points,
chemical
ouch
to
of
occur
which
a pueeeas
purely
the
work
automobile
instruments
(83,
speed
mechanical
on
have
and
been
Common
When
tire
the
force
an
does,
of
the
hard
deformations
pieces
are
theory
of
may
produced
rubber
of
one
localized
be
surface
rate
of
considered
contact
stresses
reactions,
the
be
such
and
as
abrasion
as
or
corrosion
wear
wear.
abrasion
tires,
86-88).
up
can
a
in
frictional
tearing.
the
concepts.
high
the
the
small
of
since
scratches
localized
and
frictional
processes,
asperities
tears
(53,84)
of
to
of
important
make
of
are
process
the
automobile
the
If
elastomer
based
an
large
contrast
test
scale
a
in
is
or
a microscopic
and
component
and
component
produce
(83,65).
flooring,
grooves
and
can
similar
materials
elastomer.
these
are
all
loss
a mechanical
another.
scratching
material
oxidation,
Most
plough
the
areas
and
by
against
abrasion
abrasion
to
about
ploughing
in
two
progressive
brought
ploughing
abrasion
localized
The
the
Shallamach
the
other
the
unwanted
resistance
of
can
enough,
or
strains.
of
The
on
off.
In
In
the
surface
important
tends
contact
abrasion
Wear
friction.
similar
great
broken
in
359
a body
one
to
deformations
surface
of
scratch
hardness
material
as
of
and
surface.
harder
the
surface
especially
a
wear
rubbing
related
relative
are
the
wear,
is
large
defines
the
scratching
in
RESISTANCE
Abrasion, Wear, and Scratch Resistance
Gavan
is
AND SCRATCH
and
wear
other
rubber
developed
abrasion
has
for
been
goods.
rubbers
machines
done
on
Many
and
include:
kinds
other
360
6.
Taber
abraser
Wear-Ometer
(ASTM
(ASTM
D1044)
D1242)
DuPont-Grasselli
abrader
tester.
the
Most
against
a
of
sandpaper
instruments,
surface
is
the
polymer
loss
in
rank
is
in
contact
another
21
same
in
or
in
Table
was
study,
kinds
may
particles.
of
wear
thickness
evaluated
the
by
abrasion
Comparison
of
Three
Gardner
the
In
In
or
gradually
is
of
sandpaper
other
become
measured
by
An
of
a
The
by
in
very
extreme
series
methods
data
from
often
example
of
(83).
were
filled
the
change
instruments
materials
(91).
specimen
continuously,
or
order.
wear
some
clean
used
flooring
Table
the
a
different
machines
(7),
is
performance
different
D1630)
rotate
specimen
kinds
three
(ASTM
and
abrasion
different
Olsen
polymer.
away
the
various
2 where
seven
or
of
entirely
the
PROPERTIES
(89),
surface.
surface
Wear
The
(7),
abrader,
with
abrasive
surface
appearance.
coverings
on
the
abrader
abrasive
Armstrong
MECHANICAL
abrader
instruments
other
always
materials
shown
D394)
the
weight
optical
(ASTM
as
abrasive
with
NBS
abrasion
or
Armstrong
(7,90),
such
instruments
so
(7),
OTHER
floor
In
tested
the
2
Abrasion
Loss
Machines
(cm?)
Material
Olsen
Wear-Ometer
Armstrong
Abrader
Linoleum
Rubber
Vinyl
tile
asbestos
tile
CorkeeLle
Taber
Abrader
OST
0.68
Oyad bal
IV.
ABRASION,
different
WEAR,
AND
machines
correlation
with
required
using
actual
in
the
hardness,
factors
The
in
discussed
High
by
rate
amount
of
wear
is
polymer,
W
and
tear
its
polymer
to
in
and
t is
the
and
Zapp
(96)
or abrasion
the
the
Young's
predict
away
small
=
an
its
are
of
(92)
tearing
(95)
been
by Brunt
energies
Lewis
life,
a polymer.
have
and
of
important
of
rubbers
pieces
fatigue
should
predicts
(93).
reduce
that
KWvt
the
(5)
depends
load
per
surface,
of
of
by
which
the
upon
unit
v
of
the
area
is
rubbing
equation
the
properties
that
velocity
time.
Juve
the
following
of
presses
the
Long
amount
of
the
K
fatigue
abrasion
is
of
and
the
the
sliding,
Veith
form
for
(94)
wear
to
a
life
since
the
energy
tangential
of
should
(6)
or
and
W
surface,
t
is
inversely
polymer
the
area
friction
friction,
abrasive
constant,
the
5
2
tearing
the
W
= xt
ce
coefficient
is
'
= SE
the
F
polymer
modulus,
test.
U, is
'
:
loss
curve,
uw is
pressing
to
is
loss:
equation,
wear,
the
caution
testers
polymer,
Thomas
high
loss
duration
stress-strain
the
and
Thus,
probably
tearing
given
abrasive
give
the
(86,94,95).
normal
:
this
poor.
characteristics
and
and
is
Abrasion
In
another,
tearing
of
wear
Lindley,
constant
the
was
strength
the
abrasion
is
one
abrasion
the
strength
Gent,
a
from
tensile
abrasion
K
with
tests
involves
Abrasion
where
361
behavior.
strengths
of
agree
data
involved
tensile
the
the
determining
factors
RESISTANCE
not
actual
abrasion
material,
its
did
performance
Since
SCRATCH
the
force
is
the
E'
is
high
the
causing
normal
the
duration
correlate
undergoes
under
with
load
dynamic
of
the
the
localized
362
6.
deformations
rough
during
surfaces
Table
in
type
desirable
especially
to
on
and
resistance
does
in
by
as
is
is
high
a
the
plastics,
very
poor.
imply
loss.
to
poor
scratched,
but
it
melamine
formaldehyde
resins
have
very
good
scratch
used
in
Table
Relative
Nylon
Wear
such
purpose
phenolic
6
66
scratch
scratch
wear
because
of
its
low
abrasion
resins
and
some
resistance;
as
Plastics
Loss
0.057
-64
Nylon
trans-
very
Polystyrene
polyethylene
the
or
oakley)
density
the
abrasion
Polytetrafluoroethylene
High
ruin
3
of
It
possible,
poor
-015
polyblend
of
polymers.
as
applications
Abrasion
General
(98).
these
However,
has
hard
often
of
glass,
Polyethylene,
very
Plastic
of
a number
rank
scratches
Compared
is
weight
as
The
are
would
abrasion
surfaces
for
resistance
tests.
laminates
smooth
scratching
some
their
The
data
abrader
scratch
necessarily
easily
of
PROPERTIES
order.
polymers
of
that
abrasion
of
appearance.
not
terms
type
MECHANICAL
(86,92,97).
from
(99)
abrasion
have
most
hardness,
loss
of
optical
of
low
another
transparent
resistance
behavior
different
a different
Another
testing
Marcucci's
Possibly
materials
parency
be
3 lists
plastics.
is
can
abrasion
OTHER
-0016
(grams)
phenol-
therefore,
table
and
V.
HARDNESS
counter
poor
AND
tops.
to
of
resistance
reviewed
by
is
by
polymers
and
Although
and
(87),
most
people
or
disulfide
(88)
Table
Cellulose
nitrate
Polyvinyl
chloride
they
Nylon
4
Scratch
Hardness
Hardness
LORS
IIE gil
ibe 3)
acetate
Cellulose
Unsaturated
polyester
methacrylate
Phenolic
(mineral
Melamine
resin
filled)
as
scratch
The
it
intuitive
TOR
66
Polymethyl
an
have
Note
Polystyrene
its
solid
measure
8.7
chloride
a
Bernhardt
and
Scratch
Vinylidene
such
In
have
been
(101).
Tests
believe
Bierbaum
with
to
high,
is
graphite.
instruments
a
method.
plastics
of
some
scratch
a polymer
of
of
indicate
another
plastic
the
Wiinikainen
the
by
wear
The
(101).
the
values
(101)
have
hardness
5 lists
friction
filling
polyethylene
High
Table
of
Indentation
as
scratch
(100).
Bernhardt
poor
by
such
Bierbaum
4
molybdenum
as
Gouza
Hardness
The
scratching.
decreased
such
lubricant
polymers
coefficient
the
be
can
363
Table
measured
as
if
in
resistance
scratch
Vv.
softer
shown
resistance
general,
TESTS
resistance.
are
resistance
nylon
The
scratch
plastics
high
INDENTATION
Se
oS
Pills P
32.4
feeling
364
6.
Table
Scratch
OTHER
MECHANICAL
5
Resistance
of
Pol
Scratch
Resistance
Polyethylene
-0014
Polyvinyl
SOMES
chloride
Celluloid
SOUS
Cellulose
nitrate
-015
Nylon
-016
Polymethyl
Phenolic
for
methacrylate
the
Gouza
-046
laminate
hardness
hardness
1.
which
(87)
of
materials,
measure
there
a number
classifies
Hardness
of
hardness
are
tests
indentation
by
indenter.
Examples
Vickers
Knoop
indenters,
Barcol
and
durometers
load
(102).
applied,
load
is
resistance
a
sharp
and
of
test
type
test
are
standard
including
some
the
2.
and
the
Hardness
to
Moh
ASTM
Rockwell
test
the
or
by
Bierbaum
3.
Rockwell
Many
are
and
Shore
with
indentation
measure
another
the
material
or
Hardness
tests
Examples
hardness
a combination
of
or
by
scratch
of
tests
the
after
hardness
the
to
hardness,
indentation
hardness
of
a material
Brinell
that
resilience.
D785.
tests,
the
residual
hardness.
various
include
tests
of
categories:
of
hardness,
scratching
are
efficiency
the
the
three
resistance
measure
measure
Examples
rebound
the
tests
a material
Measure
of
Some
removed.
point.
resistance
by
an
the
kinds
properties.
into
that
measure
different
complex
tests
the
PROPERTIES
which
this
as
described
tests,
classes
i andes
V. HARDNESS
AND
Tests
loaded
case
INDENTATION
which
are
elastic
of
This
has
flat
theory
depth
of
surface
the
very
the
a
loaded
been
of
the
2s
E,.
and
sphere
of
radius
making
greater
specimen,
up
the
v,,
worked
by
a
other
1a
ratio
is
of
the
respectively.
Ris
than
that
then
specimen
F.
the
If
of
The
the
the
E,
a
in
the
(103)
the
material.
and
indenter
of
others
into
and
is:
sphere
the
other
of
the
the
force
of
or
of
and
total
modulus
(a7a)
that
modulus
(104).
the
2/3 - 1/3
AS
-
polymer
Young's
by
theory
elastic
material
oe
sphere
modulus
the
softer
E,
the
out
spherical
1 - ve
=|
+
a material
Timoshenko
the
or
of
a Young's
into
h of
Poisson's
Vv,
flat
Hertz
reviewed
of
is
much
measuring
plastic
modulus
penetration
sphere
hi
Young's
specimen
really
3 Ae
We
E (-.---
he
The
the
penetration
surface
365
materials.
penetration
The
measure
indenter
of
TESTS
the
flat
flat
or
load
sphere
on
is
material
in
material
is:
3(1 - v? |
E,
When
a
circle
sphere
of
is
contact
= ACY
pressed
into
a
aa
:
(8)
flat
surface,
the
radius
of
r
is
ees
ye
Secu
bt
1/3
(9)
(10)
the
366
6.
This
pressure,
area,
is
1.5
contact.
times
The
direction,
of
which
a maximum
the
average
maximum
occurs
contact.
is
in
This
stress
flat
stress
the
pressure
tensile
the
at
OTHER
MECHANICAL
center
over
of
the
Oper which
specimen
at
the
PROPERTIES
the
contact
entire
is
in
edge
area
the
of
of
radial
the
circle
is:
(1 - 2v,)F
oc, = ——————
The
is
Hertz
much
greater
penetration
when
of
the
of
the
the
the
than
is
less
thickness
of
thin
the
contact
thickness
of
the
sheets
or
following
sheet
on
empirical
thickness
of
of
the
spherical
indentor.
and
is
(105).
(106)
layers
the
sheets
plastic
Aklonis
that
diameter
for
of
and
assume
the
circle
Chapoy
soft
equations
(11)
at
only
least
Other
rubber
flat
and
Taylor
and
surfaces,
equation
to
five
studies
or
hard
becomes
hold
the
the
effect
Kragh
radius
include
(107).
and
the
The
constant
surface
for
sheet
times
on
Taylor
the
g = 0:36 Fy (2 : h Jap
those
For
Kragh
shear
of
found
modulus
G:
Hey
R
In
this
g is
the
equation
is
acceleration
Spherical
based
D
indentor.
upon
the
the
of
The
empirical
Bv=" 0,000L7B
where
R is
on
F
in
R and
is
cm,
the
h in
h is
this
gravity,
ASTM
of
and
D1415
equation
the
F
sheet
is
the
hardness
of
Scott
or
load
test
coating,
on
for
the
rubbers
in
force
in
hundredths
empirical
is
(108):
Res"? Hees
indenting
and
thickness
(13)
kilograms,
of
equation
Es)
ine kq/emae
millimeters.
The
exponents
are
the
same
not
quite
as
V. HARDNESS
those
AND
INDENTATION
predicted
by
Equations
moduli
from
such
spheres
as
occur
ASTM
The
penetration
M,
and
E
the
in
with
these
Rockwell
minimum
of
and
tests
curve
as
a
Ty
are
E
the
As
function
test
a microscope
left
by
of
is
determined
6 lists
by
used
not
rank
do
rigid
thermoset
hardest
polyethylene
correlation
by
have
of
all
resins
all
to
the
the
hardness
of
or
can
slippage
types
the
load
give
a
a
data
curve
In
Rockwell
R,
caused
been
with
the
the
by
L,
a
removed.
a
(or
(7).
is
important
the
pronounced
curves
inverse
Vickers
diagonals
Thus,
by
damping)
microhardness
of
the
pits
(104,113).
on
several
tests
(phenolics
with
of
temperature,
resilience
measure
methods
of
metals)
depth
hardness-temperature
to
of
the
the
has
of
deformation
function
polymers
lowest
measures
D1415
(Durometer
hardness
recoverable
a
hardness),
penetration
the
indentor
hardness
several
tests
than
whether
D2240
However,
temperature.
a diamond-shaped
Table
test
of
The
similar
(Rockwell
(Vickers
depth
scales
(111,112).
very
E92
most
or
R,
these
the
after
tests.
near
elastic
or
upon
that
hardness),
applied.
the
hardness
M,
so
of
other
cones
depends
D785
hardness
load
rebound
L,
shapes
and
(109)
lubricated
rubber
and
measure
indentor
amount
are
calculation
with
penetration
for
scale
the
indentors
include
standard
scales
spherical
tests
alpha
the
(105,109).
elastomers),
Rockwell
for
cylinders
indentor
hardness
of
of
of
depth
interface
(International
hardness
equation.
developed
flat-ended
and
the
at
Hertz
been
The
sheet
the
not
367
penetration
(110).
wedges
the
have
the
TESTS
in
and
shown.
hardness.
elastic
polymers
(100,113-115).
the
soft
Thus,
modulus.
The
different
The
order.
same
melamines)
The
as
generally
is
are
such
plastics
there
very
a
rough
as
368
6.
Hardness
of
Plastics
Polymer
as
Measured
by
OTHER
MECHANICAL
Different
Rockwell
R
Polystyrene
66
High impact
polystyrene
20-80
Polymethyl
methacrylate
72
WANS
Polyvinyl
60
WAS}
chloride
124
50-100
Polycarbonate
120
Low density
polyethylene
AKO}
High
20m
density
polyethylene
Polytetrafluoroethylene
Polyacetal
Nylon
66
Polyethylene
terephthalate
Phenolic
resin
Phenolic
filled)
(mineral-
Phenolic
(wood
flour-
filled)
Polyester
resin
Cellulose
nitrate
Cellulose
acetate
Vinylidene
Melamine
chloride
resin
Polypropylene
PROPERTIES
Methods
Bierbaum
Scratch
VI.
SUMMARY
369
Some
can
be
ductile
polymers,
fabricated
techniques.
like
These
metals
tests
sheet
of
less
rigid
plastics
have
been
in
that
as
by
fabrication
hardness
VI.
such
a very
polycarbonate
polymers,
and
cold-forming
techniques
are
analagous
indentor
Punching
discussed
ABS
punching
rigid
plastic.
and
by
and
several
is
to
pressed
into
cold-forming
authors
a
of
(116-120).
Summary
Many
constants
of
the
tests
which
are
described
for
standard
tests,
ment
and
upon
conditions
complex
combination
value
of
field
use
such
tests
in
certain
correlations
under
certain
try
to
the
same
a variety
is
to
is
generally
determine
the
determine
Most
useful,
of
and
variables.
characterize
the
they
For
the
the
of
a
of
are
not
instance,
have
in
problem
important
may
a plastic
single
distortion
instru-
The
practical
end
use
a
or
with
These
proper
tests
closely
and
as
in
find
which
ones
in
a given
important
not
be
the
often
possible
the
to
the
instrument
test.
of
the
factors
same
which,
factors
bearing.
limited
a wide
testing
These
use
results,
measure
the
as
yield
tests
with
conditions.
sole
cover
The
using
material
too
a
by
to
not
The
a material.
instance,
shoe
wear
heat
of
as
the
For
tests
do
so
of
phenomena.
found
the
type
correlations
difficult
really
application.
wear
test.
operating
usage
a
practical
which
be
affecting
are
the
of
do
a material.
the
applications
often
variables
find
of
chapter
upon
of
of
field
factors
it
depend
specified
simulate
However,
many
can
this
characteristic
even
the
in
in
scope
enough
of
be
spectrum
temperature
behavior
to
does
generally
of
not
a polymer.
Not
370
6. OTHER
only
is
at
single
a
the
several
or
complete
load,
loads.
designer
ability
under
of
all
can
VII.
1.
2.
but
kinds
the
curves
With
such
a
make
much
more
a polymer
temperature
similar
deformation
of
does
to
situation
temperature
should
be
curves
its
to
determined
of
dimensionable
this
type
many
other
single
of
needed
using
an
estimates
A
PROPERTIES
curve
available,
reasonable
conditions.
provide
applies
versus
of
maintain
service
not
set
MECHANICAL
engineer
the
stability
heat
distortion
information.
A
tests.
Problems
Why
does
the
heat
distortion
as
polyethylene
polymers
such
upon
applied
the
A polymer
as
shown
has
in
distortion
HDT
with
a
than
a Young's
the
load
of
psi?
at
which
(°C)
the
as
table.
with
a
to
the
modulus
following
500
tend
does
temperature
temperature
Temperature
load
temperature
be
HDT
a
The
of
HDT
elongation
Young's
crystalline
more
of
is
80
370) x to"
85
2
Oc Lone
90
Pei
se Nid ©
95
ILetl se alot
100
Both se ilaye
105
8.0.x
.10°
110
Lea
10
115
ioe)
se AL}?
polymers?
temperature
tensile
psi?
defined
becomes
modulus
of
the
100
is
dependent
glassy
function
What
load
of
What
as
2%.
(dynes/cm?)
heat
is
that
the
VIII.
3.
REFERENCES
From
the
and
the
Why
do
Bal
data
T,
during
gradual
modulus
fatigue
the
two
rigid
coefficient
smooth
have
were
A
rough.
steel
of
a higher
ball
natural
butyl
Rubber
Use
is
generally
tests
sheet
sphere
by
does
a
the
than
smooth
a
smooth,
of
does
when
has
might
the
to
a
take
place
give
a higher
just
than
two
two
materials?
as
a
soft
a
spherical
indentor,
the
a
thick
a
of
surfaces
sheet
sheet
of
of
sliding
material.
hard
amount
the
the
coefficient
coefficient
as
surface
if
onto
higher
a
cases?
onto
dropped
the
However,
rigid
the
rubber
double
be
flat,
the
involving
not
specimen
this
friction
when
rubber
rate
0.5.
increase
surfaces.
dropped
for
is
damping
may
higher
it
test
change
surfaces
considered
tests
expect
in
Why
reversed
hardness
flat
the
VIII.
be
hardness
In
Which
the
differences
than
friction?
friction
some
rubber
and
rough
coefficient
the
fatigue
a
ratio
Th
Why?
against
bounces
rubber.
rolling
a
Why
of
of
breaks?
block
temperature
Poisson's
you
most
friction
flex
life?
Would
would
the
that
decrease
materials,
of
rubber
fatigue
test.
specimen
are
surface
may
or
what
Assume
the
its
change,
before
may
on
reduce
a
2,
temperature?
dynamic
For
problem
scratches
generally
The
in
Why
do
material?
indentation
of
doubling
indentation.
the
into
load
on
Why?
References
A. P. Rudakov and
from Russian),
L,
Polymer
N. A. Semenov,
#3, 22)
(1965).
Mech.
(Engl.
transl.
6.
G. S. Semenov,
N. G. Ryzhov,
and A.
Polymer Sci. USSR,
9, 258
(1967).
B.
Ya.
Teitel'Baum,
Polymer
M. M. Shteding,
V.
Polymer Sci. USSR,
V.
G.
Korshak,
Danilov,
P.
. G.
wad
<<a
ASTM
Pay
L.
Regeta,
G.
M. Gorchahova,
10, 61 (1968).
N.
Yarmilko,
Pyankov,
Polymer
Amer.
Nielsen,
M.
Mech.
Soc.
M. T. Watson,
G. M. Armstrong,
PUAS tarps 4 pL OOM(NOViemL
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J.
W.
Liska,
Ind.
Eng.
S.
Newman
G.
R.
36)
L.
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543)
W.
W.
S.
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J.
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Materials,
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Co.
Kennedy,
Modern
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D.
L.
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Brashkin,
L.
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S.
Monsanto
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1129
Worf,
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Modern
46,
Witnauer,
29
J.
Plast.,
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Sci.,
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Nielsen,
J.
A.
Melchore
K.
J.
Cleereman,
NOP
P.
A.
36,
J. A. Sauer,
F. A. Schwertz,
227, 053) (Mare 1945)ne
PROPERTIES
P. Danilova,
and
11, 2996
(1969)
and
Chem.,
10,
S.
(Engl.
data,
MECHANICAL
Kravtsov,
and
Testing
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I.
USSR,
V. A. Sergeyev, M.
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Standards,
Lo0R
E.
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H.
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Karam,
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R. H. Boundy and R. F. Boyer, Styrene and its Polymers,
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H. P. Wohnsiedler,
I. H. Updegraff,
Ind. Eng. Chem.,
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dr.
and
S. D. Gehman,
D.
ind. Eng. Chema,
D.
- A.
J.
24.
Katz
V.
and
A.
RR.
M.
Tobolsky,
D.
Katz,
M.
Sci.,
A2,
2749
R. F. Clash, Jr.
(July, 1949) .
and
R.
M.
C.
Reed
and
Bexg,
J.
M.
Harding,
J.
and
Ind.
E. Woodford,
and
39), 1108)
(947)r.
V.
Tobolsky,
Polymer
1953).
Bull.
C.
Eng.
S.
Polymer
Takahashi,
(1964).
Berg,
Ind.
R.
Modern
H.
Hunt,
Chem,
UJr.,
34,
Wilkinson,
Sci.,
and
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R.
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ENG sm Cees
1224.
Jr.,
1595
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Schaffhauser,
21,
417,meOrb
119
(9.4.9).
VIII.
REFERENCES
Zeke
689
26.
A.
373
elawbence:
(1949).
and
Ee
Bb.
McIntyre,
Fitzhugh
and
R.
N.
Crozier,
J.
Palm,
Appl.
F.
22 See O52)ie
27.
27a.
L. P. Witnauer
shy)ik (ARIES)
C.
E.
and
Stephenson
and
Publ.,
No.
247,
O59
p69).
28.
29%)
W.
E.
A.
Amer.
H.
Willbourn,
Soc.
Testing
Polymer
Sci,
Polymer
ASTM,
8,
os
Sci.,
Spec.
Mater.,
41,
Bae
2,
is
Techn.
Philadelphia,
Pa.
Aw
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J
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ate
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2
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hen
=
o—
i
:
:
Peasy!
seal
eS
10h)
9 _ ae
7
:
2
Cain!
=p
: -)
a
iu
_
vitvey
Chapter
7
Particulate-Filled
I.
Introduction
phase
matrix
continuous
discrete
or
interpenetrating
cell
and
foams
“they
are
often
ABS
and
blends
formulations
Many
of
reasons
simpler
of
mats
in
used
such
rubbers,
fillers,
for
and
using
homogeneous
meshes
or
as
polyvinyl
materials
composite
Some
polymers.
1.
Increased
stiffness,
2.
Increased
toughness
3.
Increased
heat
of
strength,
or
impact
distortion
SHAS)
and
and
wire
a
There
plastics.
rather
these
poly-
containing
resins
fiber-filled
although
chloride
tile
floor
than
reasons
temperature.
great
are
the
are:
dimensional
strength.
open-
material.
some
include
filled
as
con-
two
composites,
are
Examples
thermosetting
glass
with
filled
Skeletal
filled
include
class
such.
applications
of
consisting
up
made
3.
composites.
materials
foams,
materials,
last
this
polymeric
considered
not
filled
coatings,
variety
sintered
commercial
Many
composites
network
Examples
phases.
tinuous
Fiber-filled
2.
particles.
of
a
of
phase
filler
discontinuous
a
and
general
three
into
consisting
materials
Particulate-filled
1.
classes:
a microscopic
on
least
divided
be
may
materials
Composite
scale.
at
phases.
more
or
two
of
consisting
of
up
made
materials
as
defined
be
heterogeneous
be
must
materials
Such
Systems
may
and
components
more
or
Composite
materials
Composite
two
to
Polymers
stability.
380
7.
Not
4.
Increased
5.
Reduced
permeability
6.
Modified
electrical
7.
Reduced
all
of
must
be
desirable
The
against
complex
techniques
as
damping.
to
gases
and
liquids.
properties.
features
advantages
balanced
include
POLYMERS
cost.
these
composite.
mechanical
PARTICULATE-FILLED
that
well
as
a
found
composite
their
rheological
are
reduction
and
in
any
single
materials
undesirable
behavior
in
have
properties,
difficult
some
to
offer
which
fabrication
physical
and
mechanical
properties.
The
properties
properties
the
the
obtained
II.
of
with
can
by
the
and
system,
Thus,
composites
adhesive
bond
of
The
behavior
flow
reasons
for
important
this
the
2.
of
have
origin
equation
for
Most
the
of
shape
by
the
the
determined
the
nature
variety
of
alteration
important
filler
of
the
the
property
of
is
by
the
phase,
interface
properties
of
behavior
can
be
morphological
the
the
interface
strength
of
phases.
suspensions
filled
importance:
involve
theory
the
mechanical
of
in
polymers.
The
are
Suspensions
composites
their
by
An
between
Rheology
is
just
affect
materials
a great
properties.
greatly
liquids
composite
components,
phases.
interface
which
the
the
morphology
between
or
of
of
in
of
the
the
systems.
1.
flow
of
Many
theory
viscosity
of
rigid
particles
There
are
fabrication
suspensions
theories
composite
of
of
of
the
systems
a
the
of
at
in
least
two
techniques
for
liquids
or
molten
moduli
of
composites
viscosity
of
suspensions.
starts
suspension
with
of
Einstein's
rigid
spherical
by
II.
RHEOLOGY
OF
particles
SUSPENSIONS
381
(1):
n=n,(1
The
of
viscosity
the
the
suspending
volume
fraction
scripts
1 and
filler
or
holds
the
to
of
(1)
phase,
have
Einstein
$,.
In
matrix
in
up
equations,
related
very
to
two
koe
phase
Einstein's
the
or
the
most
the
subthe
equation
viscosity
high
and
and
concentrations.
for
of
viscosity
materials,
continuous
dilute
moderate
only
the
composite
or
proposed
to
coefficient
respectively.
been
spheres
n is
the
the
particles
equations
these
Wine
filler
2 refer
rigid
suspensions
all
liquid
of
o,)-
suspension
dispersed
fot
hundred
Of
of
+k,
only
Over
of
concentrations
useful
a
ones
(2).
will
be
discussed.
An
equation
describes
entire
the
over
suspensions
equation
that
the
viscosity
concentration
of
many
is
range
kinds
the
of
Mooney
(3):
k
&n(n/n.)
The
The
fraction
difficulties
is
known
obtained
packing
of
fraction
volume
volume
and
viscosity)
intrinsic
that
from
of
the
om =
the
>, while
have
can
in
some
particles
but
measurements
under
o
dispersed
for
is
because
it
or
vibratory
is
from
the
spheres.
the
maximum
of
packing
The
contacts.
cases,
(or
coefficient
2.50
value
is
filler
sedimentation
dry
the
filler
(2)
Einstein
the
has
:
particle-particle
theoretically
from
as
known
kp is
constant
= oe
mn
quantity
generally
the
maximum
motion.
True volume of the filler
Apparent volume occupied by the PAST
(3)
382
7.
Theoretically,
hexagonal
(random
Table
close
close
is
packing,
values
rods.
particle
shape
state
method
Agglomerates
and
For
dm 18
more
(cubic
the
as
value
of
like
of
Except
a
in
few
theory,
is
particles
generally
dispersed
spheres,
(4).
spheres
with
volume
in
0.637
mn varies
o. from
sedimentation
spheres
packing)
packings
fraction
POLYMERS
so
have
an
smaller
ke can
other
than
often
be
estimated
with
fair
the
Einstein
accuracy.
If
1
Packing
Fractions
Type
Packing
of
Hexagonal
close
om
packing
0.7405
Face
centered
cubic
0.7405
2
Body
centered
cubic
0.60
a
Simple
cubic
4
Random
close
packing
0.637
Random
loose
packing
0.601
M
cases,
used.
y
Fibers
and
(5).
Maximum
Spheres
for
0.524
different
Table
Particles
or
0.74
agglomeration.
nonspherical
particles
coefficient
of
dn is
practice
packing
predict
such
in
bin for
and
to
of
spheres)
maximum
experimental
spheres
of
of
value
but
The
difficult
¢,, than
maximum
packing
1 gives
aligned
it
the
PARTICULATE-FILLED
O26
Parallel
hexagonal
Parallel
cubic
Parallel
random
Random
packing
packing
packing
orientation
0.907
Os
IS
0.82
OF 5.2:(@2))
the
II.
RHEOLOGY
OF
particles
clusters
SUSPENSIONS
are
rigid
which
are
coefficient
is
given
of
Vo
agglomerate,
entrapped
For
large
packing,
which
value
ellipsoids
of
would
shear
Einstein
the
of
an
of
the
spheres
volume
of
the
matrix
of
the
agglomerate.
surface
increases
the
Einstein
ellipsoids
a
rods
for
the
the
are
coefficient
kp as
occur
or
at
case
very
rods
of
low
and
the
of
decrease
made
up
typical
that
is
Thus,
viscosity.
cubic
(5).
Particles
shape
also
ratio
oriented
shear
the
a
1 gives
axial
randomly
rates
in
Figure
of
in
4.77
rod-like
(6).
function
and
particles
approaches
in
is
fluid
coefficient
spherical
coefficient
of
that
volume
the
with
agglomerate
the
of
the
particles
(6).
High
effective
value
rates
of
the
coefficient.
Figure
2 shows
aggregates
spheres,
aggregates
A
the
strong
(4)4
on
orient
Einstein
rapidly
and
Einstein
or
shape,
give
%
actual
Vz, is
elongated
expected
as
the
Einstein
the
in
to
(5):
fraction
agglomerates
increase
such
is
within
the
are
volume
while
agglomeration
by
agglomerate
spherical
a
the
spheres,
which
ee)
ars
o, is
spheres
roughly
Re
where
383
second
of
many
concentration
equation
all
of
the
kinds
equation
for
dispersed
three
spheres,
and
large
Viscosity
spheres.
and
which
of
Mooney
of
consisting
containing
with
viscosity
plots
also
fits
with
many
suspensions
the
increases
state
experimental
is
of
aggregation.
data
(Aye
—=— 26 5
iQ e.
ny
hese 2
On
very
(5)
on
384
7.
=o
PARTICULATE-FILLED
POLYMERS
RANDOMLY ORIENTED RODS
w 80
as
=
z
wl
Ts
we
3©
6.0
=
=
m
50
=
Lv
40
6
8
10
ialep5
The Einstein coefficient as a
diameter ratio for rod-shaped
This
equation
upon
9, for
implies
particles
that
of
the
any
concentrations
of
generally
experimental
become
the
non-Newtonian
rate
values
the
of
and
The
if
fits
filler,
shear
may
be
Cross
al.
function of
particles.
size
or
neither
either
Such
viscosity
the
holds
decreases
for
as
length
very
only
high
equation
because
may
to
depends
the
viscosity
suspensions
or
At
2 nor
accurately
thixotropic
often
shape.
and
the
viscosity
equation
behavior,
changes.
equation
apparent
increases
in
16
L/D
relative
data
14
12
ASPECT RATIO
5
suspensions
changes
have
yield
dilatant.
non-Newtonian
the
rate
of
suspensions
shear
Y
(8,9):
nen
+
——
as
(6)
II.
RHEOLOGY
OF
SUSPENSIONS
385
Vy
RATIO
VISCOSITY
Oo
J
i
VOLUME
x)
4
5
FRACTION OF FILLER
Lyaleiys
74
The relative viscosity of suspensions of spheres as
“ predicted by the Mooney equation for: 1, dispersed spheres;
3, aggregates of 3 spheres, ~, very large aggregates with
cubic packing of the spheres.
The
constants
are
1/2
n,
1s
or
the
Newtonian
some
shear
lower
rate
8
2/3.
and
m
The
viscosity
behavior
limit
depend
viscosity
at
the
is
dependence
upon
very
at
high
viscosity
reached.
is
due
It
to
the
system;
zero
rates
rate
of
decreases
is
some
typical
of
shear
shear.
structural
is
of
ve while
For
non-
shear
rate
until
assumed
that
the
with
generally
values
change
in
the
m
shearing
forces.
proposed
by
Other
Krieger
Concentrated
is
there
of
loys
Og:
stress
yield
stress
Relation
The
should
be
rate
the
shear
systems
of
shear
the
deformation
below
a critical
the
cases,
Casson
in
which
value
often
equation
same
shear
in
in
which
the
ratio
of
this
one
(7)
and
k,
is
an
Viscosity
and
form
the
the
for
relationship
a
modulus
the
between
viscosity
and
shear
instrument
equation
is
constant.
Modulus
equation.
phase
and
Shear
given
viscosity
matrix
0.5,
for
empirical
an
filler
is
relative
geometry
just
Thus,
is
by
filled
having
rigid,
viscosities
(14-17).
replaced
for
elastomer
phase
modulus
a
there
and
is
relative
moduli:
equation
G,
is
has
same
Equation
the
points
equations
the
ieee
while
Rei
strain
in
simple
is
Between
of
Poisson's
if
yield
+ k,7¥
theoretical
The
In
(Gila)
Gillespie
by
(Ay, 3s} 8
III.
a
and
been
show
such
In
have
theories
(10)
often
any, shear
o@ =k
The
Dougherty
suspensions
little,if
shear
the
shear-dependent
and
byene
agglomerates,
of
up
breaking
the
as
such
suspension,
POLYMERS
PARTICULATE-FILLED
7.
386
the
a
G
the
shear
can
however,
continuous
(8)
is
theory
theory
8,
Ge
phase
shear
modulus
for
be
the
used
modulus
of
the
viscosity
to
of
unfilled
of
estimate
is
accurate
only
is
0.5,
the
and
the
a
the
when
filled
matrix.
filled
shear
of
Thus,
system,
then
modulus.
Poisson's
rigidity
material
the
ratio
filler
of
is
IV.
MODULI
very
OF
much
modulus
FILLED
greater
ratio
A more
POLYMERS
is
that
theoretical
ratio
of
the
Le
this
assumed
the
ES
that
filler
Otherwise,
the
than
viscosity
ratio.
below
the
which
0.5,
compensates
is
for
(18):
2550(@7= 100.)
oes Re Se
go Cae
LS( ie ya)
i
1] 2
Ye
vv, is
matrix.
equation,
1
equation
the
less
matrix
(2
In
of
considerably
accurate
Poisson's
than
387
Poisson's
ratio
particles
of
are
the
matrix,
approximately
and
it
is
spherical
in
shape.
IV.
Moduli
A.
of
Regular
The
modulus
of
However,
far
too
high
the
ratio
of
which
reduce
not
when
equation
predicts
the
if
there
can
be
(21)
is
more
rigid
be
used
simplified
than
the
in
some
polymer
the
(19).
moduli
which
are
are
of
the
matrix,
For
the
of
stresses
thermal
the
filler
the
For
matrix.
of
of
The
of
the
Poisson's
are:
modulus
phases.
cases.
Some
modulus
the
equation
calculate
between
shape
particles
equivalent
to
any
predicted
modulus
spherical
shear
there
and
for
material.
than
0.5,
the
the
of
shear
rigid
lower
than
the
adhesion
fillers
modulus,
nearly
or
a
than
less
greater
can
is
being
effective
(20)
some
greatly
matrix
is
matrix
equation
approximately
rigid
modulus
the
holds
containing
containing
Shtrikman
much
equation
Mooney
infinitely
polymers
Kerner
Mooney
the
for
Polymers
Systems
rubbers
the
seasons
is
Filled
any
modulus,
Hashin
of
a
Kerner
fillers
equation
the
and
composite
equation
which
are
becomes,
388
up
7.
to
moderate
foams
and
15(1l
8 -
=v.)
$3
10v,
¢,
rubber-filled
polystyrenes),
the
Kerner
ie Sy
rigid
ie
RS
for
C of
the
ratio
D of
or
Figure
reduced
of
0.35
Figure
shear
3 is
the
a rubber-filled
Halpin
and
many
other
general
the
and
form.
equation
be
takes
into
and
any
the
value
defined
is
such
ratio
relative
1.0
for
of
the
Kerner
a polymer
in
with
which
shear
for
of
equation
a Poisson's
Gye.
modulus
shown
moduli
and
that
can
Nielsen
still
be
the
=o,
of
a
put
(25)
in
then
further
Kerner
Curve
foam
shear,
factors
the
moduli
showed
very
how
to:
e
a?)
Young's,
as
The
the
or
geometry
matrix.
of
equation
a more
1 + ABO,
1 = Bid,
modulus—
account
Poisson's
account
its
is
1
reduced
generalized
M,
M
to:
ae
spheres
have
for
(19)
a
where
rigid
(22-24)
Lewis
impact
polymer.
equations
can
G/G,
predicted
Tsai
high
Si
prediction
modulus
rigid
as
GEN) eC 2
the
with
(such
reduces
eee
3 gives
filled
(10)
polymers
equation
Gls Gir |)
Curve
POLYMERS
concentrations,:
s- = 1+
For
PARTICULATE-FILLED
M,/M,
Na
/
Mao
The
of
filler
the
constant
filler
large
bulk.
and
ratios.
B
takes
matrix
The
constant
phase
into
phases;
quantity
as
° = M/M,
+A
ee)
B is
A
IV.
MODULI
OF
FILLED
POLYMERS
389
4.50
4.00
3.50
3.00
2.50
2.00
G/G,
MODULUS,
RELATIVE
1.50
1,00
0.50
Oo
>
0
0.1
0.2
VOLUME
OrS)
FRACTION
0.4
OF
FILLER,
0.5
0.6
po
ipsopn, oS!
Theoretical prediction of the relative modulus of various
types of composites:
A. Mooney equation for spheres ina
matrix with Poisson's ratio of 0.5 and a maximum packing
fraction
$,
of
0.71;
B.
The
modified
Kerner
or
Halpin-Tsai
equations with $, = 0.64; C. The original Kerner equation
for spheres; D. The original Kerner equation for foams;
E. The modified Kerner equation with ¢, = 0.64 for foams.
= 0.35, and one of
In cases B through E, Poisson's ratio
the phases is infinitely rigid compared to the other.
390
The
7.
factor
» depends
filler.
Two
boundary
conditions
upon
empirical
the
maximum
functions
PARTICULATE-FILLED
packing
which
fraction
fulfill
the
POLYMERS
bmn of
the
necessary
are:
Loe
Y= 1 ‘ieee
(14)
Om
and
=
vo,
The
quantity
For
on =1,
equation
=]-
vo,
p=
14,
concentration
is
exp
can
1.
be
The
shown
¢, for
in
the
o,
ee
ee
visualized
reduced
(15)
as
a
reduced
concentration
Figure
case
.
4 as
where
a
the
volume
vo,,
function
maximum
of
as
fraction.
given
the
packing
fraction
o- #57050).
$2
Y
igeikepa
Reduced concentration
DyYSequatilonel4s ormnd
Yo2 aS
ls OMS
2
a function of
Omand dm = 1.0.
$,
as
by
predicted
IV.
MODULI
OF
The
FILLED
POLYMERS
constant
coefficient
A
is
391
related
(1)
Spheres
of
in
pointed
a matrix
deformation
modulus
ratio
with
of
is
out
with
matrix
Burgers
(6)
ellipsoidal
or
of
particles,
for
than
of
kp
fillers,
to
theoretical
with
a
(and,
value
as
their
values
Poisson's
therefore,
of
when
case
of
A
for
the
filled
a
kp for
function
kp are
of
shear
0.5.
rigid
the
the
any
type
shear
Poisson's
to
of
the
ratio
of
such
given
in
For
long
is
oriented
Figure
rods,
much
l
the
greater
particles.
of
particles
according
randomly
For
modulus)
spherical
with
modulus,
of
diameter.
of
ratio
composites
given
the
0.5
of
(GE)
particles
For
is
of
for
values
containing
equation
ratio
the
tabulated
particles
shear
a suspension
=a
composites
the
for
general,
for
shape,
2.5
is
has
the
kp =
In
rod-like
the
matrices
value
Einstein
(16)
a Poisson's
shear.
spherical
the
length
generalized
aly
that
AS
the
the
kp by
IN es Pee
Einstein
to
the
nearly
modified
spherical
Kerner
by:
a =
1
+
5
ABO
31
(18)
oS
where
IN =
If
the
particles
5v
are
Cfo,
and
erat
not
B
=
-
#
We
rie
dispersed
but
are
strong
(19)
aggregates,
the
392
7.
factor
A
already
(and
thus
discussed
The
value
of
the
viscosity
reduction
the
for
as
as
in
as
experiments
viscosity
of
There
several
at
the
be
2
dm
generally
suspensions)
as
possible
increases.
interface,
that
independent
experiment:
as
1.
If
by
of
of
less
is
is
as
agglomerates.
than
0.5.
17
larger,
The
that
for
extent
expected
of
to
be
(18).
aggregates
Einstein
.
'
Poisson's
vy
elastic
the
show
size
an
will
particle
reasons
for
As
the
size
moduli
of
size
this
decreases,
polymer
adsorption,
the
increase
the
is
be
the
of
a
less
than,
in
decreases
surface
in
at
vy
(or
(19,26).
between
area
of
some
manner
properties
should
Different
a
kp
particles.
modulus
2
Coefficient
for
Ratios
composite
filler
discrepancy
changed
then
a
Ratio
be
and
for
the
Table
Relative
will
16
Table
case,
indicate
However,
particles
in
suspensions
ratio
9,
becomes
POLYMERS
spheres.
should
and
equations
viscosity
material
theory
Poisson's
tabulated
the
of
coefficient
unless
by
coefficient)
viscosity
Einstein
theories
are
Einstein
the
defined
dispersed
The
for
case
approximately
Also,
the
PARTICULATE-FILLED
Poisson's
ee
the
IV.
MODULI
change
2.
OF
with
As
This
a
effect,
a
ness
is
later
already
being
that
measured
error
decreases
The
modulus
Mixtures
of
a
as
om!
concentration.
diameter
thread
so
by
a
their
that
very
The
efficient
Kerner
and
adhesion
between
adhesion
is
most
of
filled
many
a
the
so
not
squeezing
if
because
filler-polymer
a
7
there
is
cooling
force
on
can
1,
thick-
error
which
makes
too
small.
has
as
the
the
more
of
between
The
assume
the
filler
not
be
any
extreme
a
sizes
given
differ
particles
larger
that
in
can
particles
in
the
by
external
the
the
thermal
of
poor
In
coefficients
matrix.
motion
good
between
stresses.
theoretical
relative
is
good
forces
fabrication
the
case
there
Actually,
frictional
applied
from
than
particle
for
the
(27-31).
densely
the
phases.
the
down
on
(28).
all
a mismatch
effect
particles
small
occur
an
suspensions
the
matrix
long
The
skin
polymer
ina
pack
if
poor,
interface.
in
shown
modulus
is
may
volume.
Most
rich
tests
of
adhesion
there
to
be
also
lower
passages
by
tends
3.
This
distribution
to
and
as
area.
packing
is
will
an
can
equations
filler
the
sizes
sizes
packing
exceeded
that
cases,even
valid
the
important
It
mixtures,
similar
systems
expansion
imposes
are
not
are
phases
the
through
which
surface.
viscosity
about
powders
moduli.
torsional
therefore,
of
of
surface
decreases.
Thus,
bimodal
factor
way
size
particle
and
For
and
in
maximum
introduces
the
particles.
a
size.
particle
and
in
"skin"
against
particle
change
increases
surface
flexural
different
larger
decrease
"skin"
of
the
agglomeration
particle
this
composites
monodispersed
gives
to
distribution
of
a
molded
from
of
discussed,
have
proportional
section
moduli
decreases,
specimens
of
because
corresponding
as
result
393
size
size
with
composite
POLYMERS
particle
particle
increase
as
FILLED
temperature
Thus,
in
equations
across
adhesion
the
gives
394
7.
results
are
which
free
to
have
derived
poor
adhesion
are
move
around
an
equation
surface
filler
particles.
for
between
dramatic.
show
The
the
the
the
B.
foams,
studies
the
lower
bounds
the
of
practical
equation
called
equations
some
of
and
cases
12
to
for
the
the
becomes
G
G
in
Figure
and
no
away
from
concentra-
The
adhesion
the
difference
can
applied
defined
is
the
by
the
ratio
the
factor
modulus
of
the
of
B.
continuous
in
some
composites.
block
moduli
the
filler.
systems
matrix
so
that
phase.
Practical
polymers.
the
Such
examples
In
some
theoretical
are
not
exact
but
are
Although
the
upper
and
lower
dispersed
do.
Deer oie 2
1-5, v 4,
The
Inversion
the
theoretical
very
stress
of
equations
systems,
For
the
need
not
respectively,
inverted
upper
correspond
case,
(33):
1
be
adhesion.
upon
greater
the
spherical
3.
under
(32)
relatively
filler
occur
generally
pulls
of
of
poor
as
case
function
depends
moduli.
regular
they
of
Furukawa
the
break
Phase
and
and
POLYMERS
particles
of
may
the
Sato
concentrations
and
inverted
polyblends,
bounds
inverted
becomes
a
which
high
filler
poles
adhesion
the
Systems
inversion
phase
include
as
Me
ratio,
at
the
illustrated
phases,
Inverted
are
is
the
matrix
at
modulus
if
intermediate
elastomer
composite
especially
rigid
the
perfect
a
modulus
systems
or
of
foam
cavity.
characteristics
two
Phase
for
agglomerates
modulus
composite,
more
of
a
cavities
The
cases
of
of
greater
give
to
their
an
cases
Weak
many
moduli
to
several
the
in
in which
filler
tion
equivalent
PARTICULATE-FILLED
(20)
in
to
Iv. MODULI
where
OF FILLED
for
spherical
8 A.
a
=
14
particles
G,/G,
eee
B;
15
replaced
also
still
by
is
hold
the
dispersed
phase
in
subscript
1 still
rigid
system
is
In
than
the
some
inversion
half.
be
The
curve
the
of
equations
give
that
two
BI,
this
two
the
by
An
at
at
the
phases
very
fraction
a
phase
will
$,, of
the
regular
values
for
the
experimental
will
be
value
to
close
of
values
G
in
the
of
occurs
can
mixing
by
or
is
dispersed
in
a
of
and
where
This
range
of
average
to
a)
system.
this
of
two
the
of
by log
M, +
$, log
equation
My and
My are
the
M,
upper
-
partly
logarithms
equation
(22)
(inverted)
the
It
SES
M =
of
The
range.
the
the
range
(1 -
region
according
an
inversion
between
the
inverted
polymers)
continuous
modulus
an
now
3.
composition.
occur
is
the
one
there
partly
modulus
about
Generally
with
of
fraction
of
rapidly
which
block
intensity
are
phases
and
low
equations
phase,
volume
which
these
Figure
mn is
the
illustration
in
Equations
that
of
In
polyblends
(34-36).
theoretical
log
In
as
shapes.
except
continuous
shown
occurs
both
and
systems
phase.
foam
(such
particle
system.
the
composition
phases
continuous
(S55
a
continuous
system
the
(2a)
packing
to
phases
changes
inverted
of
¢
other
inverted
filler
for
where
overlapping
appears
the
solvents
modulus
for
maximum
considerably
compositions
the
the
exact
changed
presence
1
inverted
refers
systems
of
valid
for
oi
more
-
GU Geeane
i
factor
and
395
10v |
=—
oN)
The
POLYMERS
and
lower
396
7.
(regular)
bounds
centration.
region
%
in
The
between
the
to
the
modulus,
quantities
(1 -
overlap
on)
region,
between
Ye aiael
(iL
bm) *
Overlap
region
that
is
illustrates
the
_
ieee
U
on = (1
In
these
dn:
between
for
component
packing
fraction
of
mn
the
to
of
conoverlap
concentration
(Gl =
fraction
(33,38).
chosen
the
[on =
of
overall
5
composition
-
the
the
the
maximum
inverted
more
packing
system,
rigid
and
component
(23)
o)
fraction
a
in
is
the
of
the
the
softer
1
|
—=VOL. FRACT. OF RIGID PHASE
0
Bigs,
the
more
rigid
component,
!
1
5
Modulus and composition variables import
ant in
of phase inversion.
¢, 18 an arbitrary volume
low
maximum
M
LOG
MODULUS,
of
bm]
the
Figure
pe eeeaiaee
Ta aa
Malst
on is
in
or, is
some
'
modulus
arbitrary
co and
tna i
eric
o)
equations
some
fraction
POLYMERS
a given
limited
that
Likewise,
at
$;, are
At
by is
definitions
_
respectively,
by and
and
PARTICULATE-FILLED
the region
fraction
one.
bc:
IV.
MODULI
by +
OF
$y, =
FILLED
1.
For
volume
fraction
of
low
the
the
of
the
modulus
A number
in
POLYMERS
Figure
of
6.
SIE
special
case
where
rigid
phase,
and
material
cases,
Another
for
including
calculated
that
at
high
Spheres.
volume
curve
styrene
Phase
by
However,
morphology
content
from
using
such
the
inversion
fractions
matched
fits
15
occurs
80
cannot
of
the
is
a high
volume
is
is
shown
data
the
very
is
range
7
(39).
assuming
as
polystyrene
data
of
and
parallel
also
into
the
on
Figure
dispersed
of
take
illustrated
well,
The
outside
fraction
results
in
percent.
series
the
a:
polybutadiene
systems
oy, is
experimental
realistically
two-phase
the
1,
systems,
polymer
over
a combination
models
of
experimental
the
to
value
using
block
Pa =
oy is
inverted
illustration
a styrene-butadiene-styrene
The
any
dn =
can
be
models
(40,41).
account
region
of
the
phase
inversion.
There
ordinary
The
dispersed
factor
curve
as
A;
expressed
express,
A=
=
about
modulus
the
1/A
.
=
©
A
is
equation
the
to
same
maximum
Gr
system
It
the
in
holds
at
it
the
Oo, trG5e
possible
can
"rule
of
for
if
the
often
a
gives
same
ratio
convenient
Exheeeue
shown
infinity.
that
the
any
IN oie
IMG
For
the
generalized
mixtures":
(24)
and
is
the
result
to
to
of
8.
and
is
then
rotation
95
modulus
systems.
material;
for
for
the
modulus
180°
0.5
equations
inverted
more
modulus
$, =
zero
be
the
systems
for
Figure
between
0),
is
lower
symmetry
vary
becomes
dispersed
relation
of
=
A
Gee
This
relative
between
equations
inverted
cases.
can
(or
the
for
illustrated
factor
A
and
the
center
is
symmetry
both
This
its
of
equation
for
cases
symmetry
of
systems
G/G | in
both
The
case
in
as
i=) =
curve
The
A
degree
be
7.
398
PARTICULATE-FILLED
POLYMERS
NY RIGID
PHASE
YZ RUBBER
PHASE
MODULUS
RATIO,
M/M
aupaer
9)
02
G04 | 06108)
O10
VOL.FRACT. OF RIGID PHASE
inalejig
Relative modulus
polymer in which
that
of
the
GS
of composites
containing rubber
the rigid polymer has a modulus
and a rigid
1000 times
rubber:
Rigid
Rigid
Rubber
polymer
polymer
and
and
dispersed
rubber
rubber
as
in
in
parallel.
series.
spheres
in
rigid
matrix
Rigid
2 on
'
polymer dispersed as spheres in rubbe ic
matrix,
om = 1.
Rubber dispersed as spheres in rigid matrix, om
0.64.
Rigid polymer dispersed as spheres in rubber
Meveta ics Om = 0.64.
Phase inversion in which both phases are continuous
Occurs
5 and
in the
6,
range
of
volume
fractions
between
IV.
MODULI
OF
FILLED
POLYMERS
Sh)
—+——+
© EXPERIMENTAL
aes
=
ra
Ww
|
=*
3
2)
.
S
=
(an)
oO
|
&
Se
=
wo
”
©
S
mu
=z
=)
=
aI
=
J
10 2
S
|
wf
4
~o
02
9
ye
04
VOLUME
06
FRACTION
PSiey5
08
10
OF POLYSTYRENE
7
Modulus of styrene-butadiene-styrene block polymers as a
function of composition.
Phase inversion takes place over
the range of volume fractions of polystyrene between 0.15
and 0.80.
The central solid curve is the fit of the
experimental
data using A = 3.0, ¢, = 0.80, Aj = 0.86
(polystyrene
spheres),
and $m = 0.85 along with the logarithmic rule of mixtures.
expected
connected
with
the
when
in
the
two
parallel.
force
applied
materials
An
making
example
parallel
to
is
the
up
an
the
composite
aligned
fibers.
fibrous
When
A =
are
composite
0,
the
400
7.
Fig.
PARTICULATE-FILLED
POLYMERS
8
Relative moduli of composites for various values of A and A
at
as a function of composition.
G,/G,
= 100, and $m = 1.0.
The same curves are obtained if A is substituted by 100/A;
or
if
about
A
is
the
substituted
central
point.
for
100/A
followed
by
a
180°
rotation
IV.
MODULI
lowest
OF
FILLED
possible
reduces
POLYMERS
modulus
is
are
obtained,
equation
gives
connected
C.
in
Errors
Many
composite
the
equation
in
of
Composite
the
materials
are
of
most
composites
torsion
or
flexural
expense
of
(19).
thicker
using
error
specimens
particles
extrapolation
" produce
and
of
to
errors
cross
for
of
as
so
can
many
because
the
be
an
when
surface
particle
of
are
measured
to
smaller
size.
two
materials
by
molds,
polymer.
stress
at
the
emphasized
at
the
of
the
moduli
thicker
due
to
the
and
skin
effect
percent
skin
can
in
be
specimens
are
and
carrying
error
in
is
size
twenty
the
Thus,
thickness,
to
For
of
using
This
on
effect."
infinite
ten
(42).
literature
"skin
values
as
cases
the
walls
maximum
corrected
and
a
the
excess
the
in
of
by
extrapolating
large
The
in
the
smaller
zero
specimens.
corrected
expected
reported
imposed
where
interior,
This
low
has
tests
properties
the
data
too
surface
the
be
Moduli
moduli
restrictions
surface,
to
series.
the
or
by
out
an
can
some
cases
of
approximately
of
rectangular
section,
=|=
a
where
generalized
(25)
results
of
thin
the
o,
eeus
Because
low
and
to
i
= tee
This
401
M
modulus
is
the
in
torsion
Sof oesShores EMD S| 3 he
(M =M,)(D
= @)* + M, D*
true
actually
calculated.
diameter
of
the
Young's
tests;
The
particles
modulus
M, a
is
the
thickness
is
d.
in
flexural
corresponding
of
the
(26)
tests
or
the
apparent
specimen
is
shear
modulus
D while
the
are
greater
the
above
the
skin
is
about
equal
to
of
radius
the
air
the
if
error
the
for
correct
to
used
be
can
still
equation
However,
flexure.
or
torsion
in
moduli
true
the
than
which
moduli
apparent
gives
skin
the
materials
foamed
For
POLYMERS
PARTICULATE-FILLED
7.
402
bubbles
the
in
foam.
of
a
There
is
rigid
composite
temperature
relative
at
most
the
(or
to
in
in
high
the
induced
is
nearly
slightly
modulus
as
This
(i.e.,
slope
found
in
stresses
of
the
o*
of
its
the
the
the
great
is
polymer
stress-strain
of
to
stresses
is
the
of
K
polymer
is
a
in
the
expansion
thermal
stresses
illustrated
in
stresses,
the
particles
is
near
unstressed
the
polymer,
set
in
Figure
modulus
less
the
put
the
(43).
polymer
where
its
less
The
than
thermally
are
constant
of
tensile
filler.
o* = KE, (0, - a,) (T, - T)
where
lowered.
and
is
or
noticeably
to
curve
curve)
the
temperature
mismatch
enough
modulus
expect
temperature
stress-strain
absence
of
due
of
portion
would
effect
expansion
be
one
quite
thermal
the
transition
decreases
of
may
glass
the
from
stresses
make
independent
often
lowered.
to
a polymer
resulting
nonlinear
value
be
of
tends
the
polymer
thermal
modulus
the
relative
Below
point)
to
which
the
coefficients
The
low.
decrease
temperature
stresses
too
G/G,
only
the
phenomenon
melting
modulus
Actually,
as
another
than
unity,
a,
is
and
is
the
9 where,
the
the
is
state,
Ty
(generally
of
E lo
at
because
polymer
modulus
of
(27)
the
the
modulus
coefficient
temperature
Ty) of
of
The
the
the
of
at
which
concept
thermally
surrounding
unstressed
the
is
induced
filler
polymer.
As
the
IV.
MODULI
OF
FILLED
POLYMERS
STRESS,
o*=
403
E,( a, -a,
) (To-T)
STRAIN,
Fig.
K
€
9
showing how the
curve of a matrix polymer,
Stress-strain
The modulus
decreases with stress.
(slope)
Young's modulus
of the polymer surrounding a rigid embedded particle is
less than the usual modulus because of the stress o* due
to thermal shrinkage stresses.
is
temperature
so
the
ture
may
is
modulus
In
lowered.
be
only
example
in
relative
lowered,
of
Figure
about
the
10.
quantitatively
the
of
half
value
the
theory
explains
the
of
the
observed
Nielsen
observed
of
and
as
decreases
from
expected
dependence
temperature
The
composite
cases
extreme
stresses
induced
thermally
the
theory.
slopes
of
tempera-
the
modulus
relative
relative
Lewis
increase,
A
modulus
(43)
these
typical
is
nearly
curves.
shown
404
7.
PARTICULATE-FILLED
POLYMERS
RELATIVE
MODULUS,
G./Gio
[ To a
IDalfsjg
The
relative
modulus
wollastonite
filler
between the melting
Ty
=
125°C.
Volume
of
ee)
ALLO)
polyethylene
as a function of
point T, and the
fraction
of
filled
with
the difference
test temperature
filler
are
On, M305 MN, Ooi),
[Reprinted from Nielsen
Ure OlyMe eo Gurew, iM
The MAO
(UG 31
:
+,
and
0520);
Lewis,
T.
V.
STRENGTH
AND
D.
STRESS-STRAIN
Experimental
Many
moduli
of
listed
papers
in
V.
Strength
and
Rigid
increase
the
the
Generally
are
arises
the
curve,
at
least
the
of
the
there
is
fact
standing
between
the
that
is
papers
a
upon
the
much
the
and
particle
to
fracture
surface,
the
slope
of
adhesion.
good
in
of
the
elongation
tensile
break
actual
to
strength
of
especially
a
with
stress-strain
than
the
is
such
results
if
the
filler
often
results.
if
rather
the
present,
in
Figure
all
the
there
giving
equation
path
is
tends
simple
under-
adhesion
to
a perfectly
is
expected
However,
good
expected
go
from
smooth
to
12.
sche
the
and
semi-quantitative
If
by
elongation
Bigiden
is
mechanism.
fracture
than
following
a
experienced
matrix,
part
at
fillers
illustrated
and
fracture
and
rigid
measured
filler
incomplete
exact
Ep with
elongation
phenomenon
very
experimental
particle
fillers
initial
Typical
to
polymer
the
qualitative
phases,
the
greater
part
is
and
particulate
decrease
rubber.
This
from
complex
of
these
(68).
(69).
comes
give
of
exceptions,
elongation
specimen
depend
results
in
the
case
decrease
numerous
11
in
in
dramatic
often
black
Figure
the
a
are
matrix
elongation
models
also
specimen
Although
theory
cause
the
polymer
rigid
from
decrease
from
discussion,
measured
carbon
in
The
few
experimental
Behavior
as
but
shown
A
the
3.
preceding
Fillers
as
on
polymers.
Stress-Strain
fillers
material,
published
modulus
stress-strain
fillers
been
Fillers
From
break.
have
Table
405
Examples
particulate-filled
are
A.
BEHAVIOR
be
7.
406
Table
Moduli
of
PARTICULATE-FILLED
POLYMERS
3
Particulate-Filled
Polymers
Filler
Reference
Number
44
Polystyrene
Mica,
asbestos,
45
Styrene-acrylonitrile
copolymer
Acetanilide,
anthracene
46
Styrene-acrylonitrile
Glass
beads
etc.
copolymer
42
Polystyrene
Glass
beads,
47
Polyethylene
Clay,
siltca,
48
Polyethylene
Carbon
49
Polyethylene
Aluminum
50
Polypropylene
Asbestos
yi
Elastomers
By
Plasticized
polyvinyl
chloride
Glass
polyvinyl
chloride
Calcium
black,
Vermiculite,
53,
Plasticized
Epoxy
55
Epoxy
56
Epoxy
Glass
beads
yf
Epoxy
Sand,
air
a9
Epoxy
Glass
beads
58
Epoxy
59
Epoxy
Glass
phenolic
Glass
Polyurethane
Salt
Polyurethane
Salt
62
Urethane
Aluminum
63
Polyisobutylene
rubber
Ethylene-propylene
rubber
Glass
rubber
Carbon
Glass
66
Rubber
Carbon
67
Polyethylenes
Kaolin,
and
powder
trihydrate
beads
61
Natural
clay
flakes
60
65
etc.
Flakes
polyester
64
silica
carbonate,
Aluminum
and
etc.
beads
54
and
salt
powder
beads
black
beads
black
wollastonite
V.
STRENGTH
AND
STRESS-STRAIN
BEHAVIOR
407
30
15
30
20
ce
SS
45
wo
Oo
”)
10
i?)
WJ
a
=
(¢p)
re)
4
fe)
50
100
150
ELONGATION
wateje,
Stress-strain
curves
of
salt.
Numbers
volume
Bree,
fraction
U.
approximately
S.
of
Dept.
correct
a polyurethane
salt.
on
the
Rept.
rubber
curves
[Modified
Commerce
(52,
(°%%o)
dal
powdered
rock
200
from
AD
the
plotted
equation
is
dramatic
decrease
small
elongation
amounts
of
in
in
and
69):
to
(28)
break
12.
Figure
elongation
filler.
with
the
(1967).]
1/3
eB is
to
Nederveen
655634
en eee (2 - 6,
where
filled
refer
If
of
This
that
there
the
is
can
unfilled
curve
be
poor
shows
This
polymer.
the
very
brought
about
adhesion,
or
if
by
only
the
408
7.
ELONGATION
PARTICULATE-FILLED
TO BREAK OF FILLED
MM MB
POLYMERS
POLYMERS
ounstretcHeo
0.8
0.6
0.4
0.2
RELATIVE
ELONGATION
TO
BREAK
O
0.2
VOLUME
0.4
0.6
0.8
FRACTION OF FILLER
asi
AA
Theoretical curves
filled polymers as
there
is
fracture
more
good
surface
gradually
instances
at
for the relative elongation
to break of
a function of filler concentration when
adhesion of the polymer to the filler.
is
than
where
same
time
filled
with
rigid
to
or
of
rubbers
really
due
act
as
fillers
have
often
induce
to
ductile
a
crazing
28
would
stoppers
than
and
elongation
introduce
greater
Fillers
the
equation
fillers
the
equal
smooth,
that
elongations
yield
The
or
to
in
Only
growth,
to
the
yielding
a
may
crazing,
unfilled
points
polymers.
effect
crack
the
break
indicate.
additional
to
of
to
in
rare
and
do
break
decrease
perhaps
polymers
which
polymer
are
(70).
stress-strain
phenomenon
dewetting
effect
curves
is
in
which
V.
STRENGTH
the
AND
STRESS-STRAIN
adhesion
so
that
At
the
between
there
same
dilation
is
time,
(52,
of
the
voids
of
the
or
filler
go? .
The
in
following
critical
size
of
strong
enough
flaw
this
and
equation
unfilled
The
4 for
_Table
becomes
more
but
undoubtedly,
tions
at
high
changed
change
face
the
effect
dewetting
at
1l.
The
Hookean
high
behavior
13
(71).
The
upon
the
surface
be
(70)
a
function
predicts
occurs
results
undergoes
in
area
of
the
before
premature
a
fracture:
(29)
yield
stress
of
the
composite
behavior
adhesion
and
Some
is
illustrated
filled
chloride
the
or
of
filler
with
of
powdered
aggregates,
increases,
filler
lower
at
occurs
breaking
in
concentra-
(74,78).
the
the
Narkis
dewetting
also
promoters
and
from
material.
point
Figure
should
concentration
the
adhesion
polymer
the
of
by
79-82).
in
depend
which
polyvinyl
elongations
(59,
yield
Figure
thus
Dewetting,
as
stress-strain
The
a
the
respectively.
(77).
evident
of
micro-cavitation
oro are
a plasticized
carbonate
specimen
destroyed
of
= (¢./%m\" |.
polymer,
calcium
the
in
and
develops
oy and
detrimental
and
should
Nicholais
if
modulus
deviations
and
is
the
shown
shown
polymer,
“V7 yo
In
is
behavior
of
relation
clearly
curve
the
theory
is
phases
in
development
the
dewetting
matrix
created
The
stress-strain
and
decrease
are
filler
409
filler
dramatic
accompanying
yielding
of
the
71-76).
concentration
dilation
a
BEHAVIOR
and
nature
the
of
of
the
hydroxyl
of
of
the
agents
filler-polymer
appear
the
can
polymers
coupling
silane
silanes
groups
filled
many
to
filler
react
which
inter-
with
surface,
be
both
and
410
7.
PARTICULATE-FILLED
POLYMERS
0.20
O15
NOMINAL
STRESS,
psi
o,
0.05
O
0.25
0.50
NORMALIZED
VOLUME
CHANGE,
AV/Vo
075
STRAIN € (IN./IN.)
Maley
Als}
Simultaneous
stress-strain
curves
(solid lines)
and
dilation
(or increase
in volume)
curves
(broken lines)
of
a filled rubber.
Volume
fraction of filler = 0.73.
[Reprinted
trom Parris).
wi. INOS
BoOlwiGie Set. , 8, 25
(1962)oj
thus,
they
increase
composites
composite
have
with
has
better
Composites
strength
adhesion.
increased
been
soaked
strengths
with
when
than
untreated
dry,
but
The
tensile
in
treated
strength.
water,
after
the
may
often
Especially
composites
composites
fillers
fillers
with
with
untreated
have
fairly
material
is
after
treated
the
filler
fillers.
high
soaked
give
in
tensile
water,
the
V.
STRENGTH
AND
STRESS-STRAIN
BEHAVIOR
411
Table
Density
and
Stress-Strain
Chloride
4
Behavior
Filled
with
of
Plasticized
Calcium
Polyvinyl
Carbonate
_
Parts Filler per
100 Parts Plastic
*Dewetting
was
[Nielsen,
J.
Technomic
tensile
evident
from
Composite
Mater.,
1,
Inc.]
a
strength
from
showing
of
size
has
reason
in
a
effect
for
in
effect
strength
interfacial
must
on
data
this
on
rock
phenomenon
per
area
be
The
an
(1967) , published
as
a result
of
interface.
Some
silanes
are
illustrated
in
has
little,
the
Table
effect
on
5
particle
strength
(47/ p Bn OS 9 7S.
as
particle
size
salt
urethane
in
not
entirely
volume
important
fields
of
factor.
near
rubbers
clear,
filler
A
as
second
a particle
but
decreases.
The
(74).
the
particle
factor
are
(83).
the
tensile
increases
is
any,
adhesion
typical
agglomeration,
of
absence
the
if
by
poor
the
unit
stress
100
at
size
composite
large
important.
of
Elongation
Young's
| to break
(%) | Modulus
appearance.
probably
adsorption
particle
6 shows
decreases
be
water
Tensile
84-88).
Table
a
decreases—
the
Although
modulus
(psi)
clearly
Publishing,
resulting
data
Tensile
Strength
increase
size
may
also
independent
412
7.
Table
Effect
of
Silanes
on
PARTICULATE-FILLED
POLYMERS
35
Stress-Strain
Rubber*
Behavior
of
Clay-Filled
Silane
Tensile
2330
Strength
Elongation
to
break
clay
in
700
Modulus
*80
parts
[L.
P.
IGS,
polychloroprene
Ziemianski,
Fb,
SS)
C.
A.
Pagano,
of
Particle
Size
of
Rock
Stress-Strain
Particle
Size
and
M.
W.
Ranney,
Rubber
World,
(UGW/ON61
Table
Effect
rubber.
Volume
Fract.
6
Salt
in
Urethane
Rubbers
on
Properties
Filler
(3)
(ai)
Tensile
Strength
Ultimate
Elong.
33-40u
50-60
104
90-105
73
210-300
42
300-480
(a)
10°N/m?
36
(L0°N/m?
= 14.5
psi)
[F.R.Schwarzl,
H.W.Bree,
and Cc. J. Nederveen,
Proc.
INO ny
Wig lo MOS, Jails part 3, Interscience,
New
4th Int.
Congr.
York,
US
jee
V.
STRENGTH
of
the
AND
size
STRESS-STRAIN
of
the
that
experiences
with
particle
within
an
this
area
of
reduced
are
given
size,
so
volume
to
detrimental
occurs,
the
larger
Particle
increase
the
initial
material
and
break
A broken
agglomerate
particles,
the
though
dispersed
These
rubbers
the
but
at
nearly
filler
modulus.
produce
well
behaves
as
strong
be
a
a
larger
in
the
black
has
mixing
a
or
millrolling,
the
same
time
increase
its
tensile
strength.
is
very
difficult
melts
and
to
get
good
especially
inside
of
decreases
the
entrapped
great
from
air,
as
effect
contain
the
determined
on
the
powders
dispersions.
particle
density
fine
more
or
expected
the
stress-strain
and
value.
viscous
reason,
entrapped
of
air,
entrapped
Small
behavior.
break
compound
highly
this
density
filler
to
which
this
less
them.
in
rubber
into
For
agglomerates,
from
the
to
the
paragraph.
tendency
of
in
containing
black
modulus
a
to
primary
carbon
the
mix
of
concentrator.
the
decrease
to
void.
composites
strong
dewetting
applied
previous
compounding
voids
points
stress
than
in
weak
than
be
enough
is
strong
within
after
strength
are
stress
materials
increased
composites
a
may
explained
known
actual
have
as
are
weaker
all
of
the
flaw
large
the
reduce
increases
will
so
larger
polymer
exists
Also,
strength,
the
when
of
large
strength
Agglomerates
easily
Carbon
Thus,
to
a
flaw
(90).
particle
tends
large
to
agglomerate
then
a
finding
agglomerates,
It
polymer
ones
the
(66,91,92).
agglomerate.
'up
than
volume
concentration
tensile
theory
small
the
of
If
the
agglomerates
are
stress
Griffith's
particles,
effects
of
increases.
fairly
since
they
However,
probability
agglomeration
even
addition,
the
the
material
In
(89).
value
also
413
concentration,
according
more
particle
a
stress
BEHAVIOR
air
quantities
the
composite,
The
modulus
414
7.
and
the
tensile
increases.
strain
strength
Thus,
a
properties
and
upon
the
for
at
and
change
amount
of
of
two
the
air
given
reasons:
tension.
In
However,
the
the
by
of
the
Compressive
data
produce
if
the
boride,
and
very
achieve
expected
all
the
flake
on
top
over
of
2.
compensate
other
In
for
many
the
The
mixing
up
mixing
particles
agglomerates
may
change
in
compression
decrease
generally
40
the
the
as
have
beads
in
in
strength.
increases
results
glass
well
breaking
produce
Typical
percent
as
in
been
Nylon
36500
psi
11500
psi
14200
psi
large
but
materials
these
The
It
are
66,
same
few
as
cases
have
misaligned
stress
the
mismatch
for
or
polymer
coefficients
are
than
align
overlap
flakes
and
was
of
could
difficult
perfectly
optimum
flakes
a plane
aluminum
lower
concentrators
matrix
in
the
to
in
composites
strengths
difficult
time
modulus,
mica,
flake
high
reasons
is
in
predominantly
Theoretically,
1.
act
increases
oriented
flake
the
A
filler
psi
are
are:
another.
each
often
unusually
at
break
of
4200
strengths,
and
may
time
Filled
flakes.
strengths
the
stress-—
Unfilled
experimentally.
flakes
strength.
To
high
and
of
air
obtained:
Typical
glass
entrapped
range
given
2.
made
For
flakes
(44,54,55,97,98).
to
were
a
intensity
(93-96).
(95).
of
POLYMERS
composite.
be
polymer
have
mixing
fillers
Strength
Flakes
have
can
Strength
especially
the
fillers
Strauch
following
Tensile
in
compression,
strength
the
The
amount
can
dispersion.
tests
tension,
in
reported
of
the
treatment
1.
entrapped
Stress-strain
upon
surface
degree
as
composite
depending
kind
least
decrease
PARTICULATE-FILLED
of
stacked
reduce
too
one
the
brittle.
thermal
V.
STRENGTH
AND
expansion
flakes,
STRESS-STRAIN
and
a
to
BEHAVIOR
properly
ductile
415
transmit
matrix
which
has
most
of
the
stress
good
adhesion
to
the
to
the
filler
of
polyblends
is
required.
B.
Polyblends,
Block Polymers, and Foams
The
containing
rubber
discussed
rigid
in
are
For
may
often
a brittle
in
rubber
by
the
the
matrix
The
stress
yield
since
increase
unfilled
to
This
loosens
the
about
rigid
tensile
has
to
to
strength
been
added
increases
decrease
decreases
is
a
elongation
temperature
(102).
to
a
further
also
increasing
bring
the
stress
were
phase
adding
rubber
strength
temperature
matrix
and
point,
yield
of
polyblends
the
size
The
phase,
and
to
yielding
(101).
at
be
structure
a
expected
so
even
that
for
a
an
the
or
The
phase
rubbery
both
can
can
properties
of
can
be
structure
a
is
the
given
system
(38,
dispersed
or
103,
the
the
occluded
droplets
the
polymers
continuous
the
phase
define
partly
contain
in
two
zmportant
only
either
be
phase
phases
network
also
com-
define
similar
other
and
particles
the
to
enough
not
system
the
of
shape
rubber
interlocking
inversion.
of
morphology
matrix,
rigid
is
properties
the
The
an
the
rubber
required
modulus
a yield
with
of
and
enough
rubber
continuous
form
Once
of
morphology.
of
the
tensile
of
effect
strength
concentration
systems;
104).
opposite
rigid
polymer.
The
pletely
in
is
a rubbery
while
decreases
concentration
stress
of
cause
The
constant
an
addition
produce
concentration
(99,100).
a
rubber.
to
behavior
in
impact
greatly
gradually
smaller
the
fracture
dispersed
The
has
increase
to
5.
instance,
decreased
and
particles
Chapter
polymer
filler.
break
stress-strain
if
region
often
of
can
phase
be
changed
416
7.
greatly
rolls
by
the
(101).
phase
separation
The
nature
the
rigid
phases
of
the
such
rigid
than
similar
have
total
the
properties
similar
In
but
strengths
to
made
tests,
with
yield
apparent
result
of
the
yielding
of
of
have
foams
modified
as
well
mostly
the
The
been
gas,
any
theory
phase
in
of
part
of
the
particles.
plus
alone.
common
mixtures
impact
the
important
factor
Most
constituents
differences.
or
nature
the
tend
behave
Thus,
these
have
polyblends,
materials
to
brittle
similar
to
several
seem
low
the
to
all.
is
to
with
foams,
have
compressive
polymers
generally
Kerner
that
and
relatively
theories
density
rigid
ductile
rather
agree
suggest
in
and
point
structure
(112-115),
experiment
be
However,
yield
cell
For
rubber-filled
elongations,
Although
(116).
of
tension.
apparent
equations
and
having
which
an
the
high
phase
rubber
high
proposed
other
rubber
as
rubber
the
subtle
may
of
polymer.
the
is
polymers
points,
Halpin-Tsai
as
from
collapse
in
of
increases
such
inside
chains
between
rubber
ductile
foams
strengths.
adhesion
the
of
(111).
measured
stress-strain
grafting
the
polymers,
the
when
of
of
can
degree
generally
morphology
systems
with
properties
foams
ultimate
inside
volume
block
contrast
polymers,
volume
mill-
(34,35,105-108).
polyblends,
dispersed
two-phase
polymers,
the
on
also
the
important;
phase
complex
is
solvents
phases
is
rubber
a
material
polymer-polymer
the
POLYMERS
example,
changing
by
improving
have
for
different
Commercial
phase
just
from
also
the
by
the
occluded
rather
low
onto
often
cases,
mixing,
properties
interface
continuous
of
inverting
(99,109,110).
rigid
graft
by
properties
polystyrene,
type
films
the
or
polymer
desirable
and
Casting
dramatically
change
In
extent
PARTICULATE-FILLED
than
of
the
a
the
equation
high
true
modulus;
or
experiment
which
Young's
the
about:
are
modulus
E
V.
is
STRENGTH
AND
given
STRESS-STRAIN
BEHAVIOR
417
by
)
Has wat
eee
where
K
is
a
constant
proportional
typical
(30)
to
the
between
density
compressive
2
of
and
the
(expressed
generally
somewhat
in
pounds
Direction
the
Figure
curves
per
anisotropic
Thus,
foam.
stress-strain
densities
6.
of
cubic
because
a
foot
the
modulus
14
foam
shows
for
(117).
effect
is
of
various
Foams
gravity
T
Direction L
60
Direc tion
Fa
T
Direction L
n”
3.5 pcf
°
Oo
40
20
ta
Direction
O
O
2.0
40
6.0
Strain
Fig.
L
8.0
14
Stress-strain curves of rigid polyurethane
compression.
L = longitudinal direction, T
direction.
Density of foams are expressed
cubic foot
(pcf).
[Reprinted from Benning,
Vol.
2,
Interscience,
New
10.0
(%)
York,
from a report by B. Hughes and R.
College of Technology,
England.]
1969,
L.
p.
Wajda,
foam in
= thickness
in pounds per
Plastic Foams,
200.
Taken
Battersea
are
and
restraints
cells
in
collapse
during
the
foaming
the
thickness
the
cell
(T)
L direction.
are
Figure
shown
tions,
in
and
collapse
contact
has
If
foam
tensile
the
one
is
the
than
size.
increasing
The
on
For
a
a
other
given
load
and
Rigid
fillers
is
very
the
from
polymer
foam
difficult
than
much
walls
the
curves
higher
after
to
in
stress-strain
to
elonga-
complete
are
less
than
forced
into
are
an
rubber
upon
many
practical
seats,
the
or
the
same
as
curve
of
some
and
increasing
compressive
similar
much
a
for
decreasing
high
lower
Some
rubber,
curve
polyurethane
have
a
a
stress
property.
stress
for
a
uniformity
In
rubber
have
the
of
The
as
compressive
foams
(118).
mechanical
natural
break
acts
car
important
to
unfoamed
cell
initiate.
and
the
elongation
dependent
average
than
an
load.
foams,
hysteresis
stress
(11
for
load.
Relaxation
tend
to
as
long
Often
is
for
the
resilient
such
strength
starting
The
nearly
are
creep
the
furniture
made
Stress
particles.
filled
in
deformation,
of
cell
the
direction
increases
rubber,
will
stress-strain
Creep
components
the
is
hand,
decreasing
VI.
a
load
more
the
lower
than
hysteresis.
compressive
the
as
those
little
of
tearing
behavior
very
a
larger
stress-strain
have
is
extend
the
properties
such
as
of
curves
much
is
that
A
where
such
elongate
thickness
rapidly
have
polymer
applications,
foams,
It
part
because
stress-strain
concentrator
The
stress
foams
less
cell
the
to
another.
tension,
polymer.
of
the
occurred
with
In
the
then
in
Only
14.
is
direction.
structure
longitudinal
process
POLYMERS
PARTICULATE-FILLED
7.
418
the
decrease
as
there
decrease
closely
both
in
is
the
not
elastic
serious
relative
approximated
by
the
creep
and
viscous
dewetting
of
compliance
reciprocal
of
of
the
VI.
CREEP
AND
relative
strain
STRESS
RELAXATION
elastic
or
modulus
dynamic
@
in
if
this
making
and
(Ga.
polymer
not
change
Figure
15
ethylene
as
E,/E
that
itself
in
just
the
the
filler
a
with
great
creep
of
case
That
deal
the
of
does
the
by
stress-
is,
time
moduli
change
of
of
equation
31
does
Equation
31
can
saved
the
filled
This
filler
the
of
does
polymer.
hold-—
be
poly-
visualized
factor
the
by
curves
compliance
be
properties
the
times
can
polymer.
the
instance,
retardation
(67).
of
unfilled
not
For
where
creep
of
a
manner.
kaolin
shift
(120).
high
at
long
dewetting
of
the
filler
creep
rate
31
equation
Figure
in
in
the
curves
dewetting
can
be
delayed
particles
and
by
treating
upturn
behavior
a
test
or
the
at
the
load
another
same
the
undesirable
decreases
time
material
it
the
decreases
can
bear
effect
due
effects
smaller
to
sized
as
to
increase
effect
on
creep
so
elongation
creep
the
without
the
by
illustrated
is
using
by
surface
the filler
often
Dewetting
too.
creep
strength
has
Dewetting
adhesion.
minimized
and
The
and
increase,
catastrophic
The
(122).
16
When
occurs.
dramatically
formation
vacuole
by
accompanied
dewetting
filler
high
at
surfaces
(121-123).
valid
is
longer
no
and
creep
occurs,
dewetting
and
times,
elongations,
concentrations,
in
measured
(67,120).
measuring
and
some
illustrates
filled
At
of
as
(ae)
distribution
a vertical
system
tests
valid,
by
polymers
the
same
TH
is
tests
implies
the
E
6
equation
unfilled
the
ATE eer ree
creep
equation
of
mechanical
Te
Thus,
419
to
break
rupture
fracturing
(122,
Wee)
The
stress
dependence
of
creep
generally
is
proportional
to
420
7.
"Hf
X «= PREDICTED
T
PARTICULATE-FILLED
T
T
100
1000
POLYMERS
VALUES
UNFILLED
(%)
ELONGATION
CREEP
f
\
10
TIME
(MIN)
jaaliefn,
Creep
of
kaolin,
polyethylene
¢,
=
calculated
sinh
For
0.20,
from
the
(0/o,)
where
o
various
types
of
Nielsen
(67,125)
concentration
Materials.
filler
(p =
T
=
the
had
However,
that
the
in
=
modulus
applied
same
400
stress
(120)
found
polypropylene
G/G,
in
for
filled
X
and
nearly
value
and
psi.
ratio
fillers
0, was
Cessna
concentration
load
particulate
found
and
INS)
0.950)-unfilled
60°C,
dynamic
is
10
=
=
with
creep
3.15.
ope is
a
constant.
polyethylenes,
independent
unfilled
that
when
Og
the
and
of
filled
increased
filler
filler
was
with
glass
fibers.
As
a rigid
rigid
occur,
expected
polymer
polymer.
equation
from
previous
increase
the
As
long
31
should
as
discussion,
compliance
crazing
predict
or
the
elastomeric
over
stress
that
of
whitening
behavior
fillers
the
in
unfilled
does
approximately.
not
VI.
CREEP
AND
STRESS
*
tensile
RELAXATION
421
rupture
¥ unloading
for recovery
experiment
strain € ,°/
|
15
td
=
Tensile creep of a polyurethane rubber filled with the
amounts of sodium chloride
shown on left.
Load = 3.0
Ko/ciie a
LeleC ee Par-tuclemsizen—s2
Ol toms OOM
min
mex
point of rupture.
[Reprinted from Struik,
Bree, and
Schwarzl,
Proc.
& Sons,
London,
copyright
London. ]
After
more
occurs,
stress
anticipated
relaxation
after
fillers
Rusch
the
by
creep
equation
of
rate
the
is
Rubber
creep
behavior
of
such
ones
of
is
E,(t)
up
to
The
increased
the
rate
dewetting
point
of
for
to
increase
much
31.
filled
the
Industry,
expected
of
modulus
onset
Institution
behavior
pronounced.
the
Rubber Conf.,
Brighton,
Maclaren
205.
Reprinted
by permission
of
relaxation
from
elastomeric
becomes
the
predicted
The
by
owner,
crazing
than
Internat.
1967,
p.
where
both
materials.
fillers
rigid
by
stress
polymers
dewetting
relaxation
rigid
and
or
can
The
and
be
stress
decreased
crazing
greatly
increases
elastomeric
(126,127).
(128)
studied
the
stress
relaxation
of
polyblends
which
422
7.
appear
to
general
region
be
distinctly
was
more
relaxation
by
Shen
for
essentially
of
and
diffuse
but
Lim,
VII.
and
held
transition
of
each
at
illustrated
modulus
above
75 than
this
the
larger
modulus
ratio
therefore
above
the
the
Ty°
Less
larger
thermal
Poisson's
Fillers
in
also
temperatures
Slope
of
The
in
the
18.
the
the
(44,60).
modulus
of
The
on
by
the
the
that
the
the
two
EV/S,
a
it.
The
the
to
Halpin-Tsai
In
W-L-F
glass
These
of
the
the
Also,
at
halgh@eiehber
fillers
on
modulus
pronounced
the
the
rigid
to
of
et
effect
in
reason
for
when
glassy
larger
this
effect
of
have
the
state;
is
presence
are
induced
been
materials.
curves
to
higher
concentrations,
transition
damping
effect
main
the
composite
in
larger
already
in
decreases
Schwarzl,
equations
factors
moduli
mechanical
components
contributing
Ty and
of
have
of
compared
dynamic
data
break
curves
most
the
polymers.
on
below
above
Ty:
rigid
found
temperatures.
between
block
was
of
for
found
Fillers
factors
ratio
section
shift
effects
Figure
B of
below
the
18.
state
important
stresses
discussed
and
rubbery
factor
(131)
fillers
the
the
hold
intermediate
rigid
17
in
not
region
raising
is
did
stress
studied
glass
Figures
polymer
been
behavior
in
is
has
The
of
similar
of
clearly
transition
homopolymer.
polymers
more
Properties
effects
are
the
type
the
for
than
(130)
Tschoegl
in
pure
glass
POLYMERS
W-L-F
equation
Mechanical
general
(60)
a
rather
The
block
factors
temperatures
properties
al.
shift
only
Dynamic
The
the
W-L-F
Cohen,
factors
transition
for
(129).
the
temperature-time
shift
than
around
systems
systems.
styrene-butadiene
temperatures
contrast,
phase
two-phase
Kaelble
components,
one
PARTICULATE-FILLED
G"/G'
fillers
region.
are
is
the
shown
the
VII.
DYNAMIC
MECHANICAL
PROPERTIES
423
G N/m2
free
vibration
vol %e NaCl
=On
Qe
°
|
SRS
>
peak
aN
9
1Hz
‘SY
10
®
ie)
a
15.4
a
§60
v
36.2
o
6.46.6
125-150 pum
©
59.8)
x
69.9)
(210-300
um,
33-
40mm)
10!
108
150)
.-100
-50.
10
50
Big
100.
150
de/)
a polyof sodium
for
temperature
Shear modulus G at 1 Hz versus
urethane rubber filled with increasing amounts
broadening
used
for
in
the
of
This
fillers.
great
Dr.
(1966),
270
from
[Reprinted
chloride.
5,
flake
making
transition
broadening
fillers
some
materials
(132-134).
expressed
by
G"/G';
Steinkopff
of
such
vibration
Fillers
in which
by
region
as
graphite
damping
often
case
and
and
sound
decrease
the
mica;
damping
is
]
of
concentrations
region
transition
the
Darmstadt.
Verlag,
high
Acta,
Rheol.
al.,
et
Schwarzl,
Dietrich
especially
this
effect
deadening
the
can
damping
as
generally
be
is
424
7.
Free
= 510)
tan
polyurethane
sodium
6 =
G"/G',
rubber
chloride.
Rheol. Acta,
Darmstadt.]
approximated
(1966),
damping
the
polymer,
of
0.2
Hz
versus
temperature
increasing
amounts
from
Dr.
Schwarzl,
Dietrich
et
for
a
of
al.,
Steinkopff
Verlag,
(37,67):
GU /Gua— a (Ge/Ge)e
The
50
Ls
with
[Reprinted
5 270
~
by
at
filled
POLYMERS
vibration 02Hz vol*/. NaCl
QO
3600/227
0
O
3600/211
30
4
3600/212
40
VY 3600/ 97
60
0
Page
Damping,
PARTICULATE-FILLED
most
so
rigid
(GE/GS)S
However,
there
damping,
probably
are
OpecraGS/GL)
fillers
is
numerous
by
the
nearly
cases
is
>,
very
zero
where
introduction
of
-
(32)
low
and
compared
can
fillers
new
be
to
that
neglected.
increase
damping
the
mechanisms
of
VII.
DYNAMIC
which
MECHANICAL
are
not
mechanisms
touch
3.
present
include:
one
another
friction
where
Excess
induced
tion
At
low
tion
19
what
appear
Figure
18
same
not
this
case.
the
damping
The
shift
size
this
to
As
a
shows
shift
the
Ty should
effect
is
a good
density
and
surface.
of
in
packing
orientation
of
rigid
in
where
Figure
if
easily
is
in
the
20
(49).
agglomera-
weak
broken
lowered,
may
agglomera-
any,
by
and
curves
which
the
particle-
of
the
since
the
restricts
fillers
that
the
may
the
filler
polymer
filler
surface
in
shifts
onto
in
either
as
and
be
due
filler.
the
molecular
the
of
area
should
effect
chains,
segments
occur
(44,121,136-142).
adsorbed
polymer
all
concentration
with
chain
to
indication
to
becomes
of
surface
damping
drop-off
temperatures
a surface
onto
Although
cases
increase
which
a
temperature
decreases
filler
increased
damping
proportional
should
polymer
polymer
the
This
be
or
damping.
the
particles
of
are
in
transition
conformation
concentrations,
modulus
high
higher
Adsorption
of
to
Ty to
the
conformation
the
peak
the
the
which
are
in
changes
formed
interface.
of
little,
high
the
because
the
shown
is
At
at
example
and
is
there
there
the
of
damping
However,
in
An
maxima
glass
and
The
particles
Particle-polymer
polymer
of
damping
where
interface
treatment
case.
rise
the
in
expected
result,
gives
changes
to
be
the
friction.
filler
temperature.
so
filler,
be
2.
adhesion
(135).
excess
of
in
friction
does
how
damping
of
would
near
changes
shows
the
cause
forces.
particle
or
no
new
friction
agglomerates.
polymer
stresses
particles
applied
the
the
concentrations
of
the
essentially
the
agglomerates
at
is
in
These
Particle-particle
particle-polymer
from
polymer.
there
increase
be
modulus
pure
weak
Figure
from
may
1.
the
in
thermal
greatly
result
in
425
as
damping
morphology.
can
PROPERTIES
motion,
the
and
modifies
the
neighborhood
increase
or
7.
426
:
)
A
B
G
PARTICULATE-FILLED
POLYMERS
UNFILLED
UNTREATED MICA
TREATED MICA
0.4
0.2
0.1
2) °
DAMPING
(LOG.
DEC.
N
0.0 4
0.02
-20
fe)
20
40
TEMPERATURE
60
80
100
°C
Bigs
Damping of a mica-filled phenoxy resin.
mica treated with dichlorodimethylsilane
Curve C is for
on the surface.
120
-
DYNAMIC
MECHANICAL
PROPERTIES
427
(DYNES/CM®)
MODULUS
SHEAR
CEOGSDEG?)
0.2
DAMPING:
0.1
0
0.2
0.1
VOLUME
Dynamic
mechanical
aluminum powder.
perfect adhesion
Boehme, J. Appl.
0.4
0.3
OF
FRACTION
Fig.
20
properties
of
Dotted
with no
Polymer
0.5
0.6
ALUMINUM
polyethylene
filled
with
curves for
lines are theoretical
[Modified from
agglomeration.
(1968) .]
Sci., 12, 1097
428
7.
decrease
always
the
damping
increase
because
the
decrease
in
G"/G'
the
the
materials
effects
result
between
in
and
of
material
sharp
3.
graft
each
drops,
and
146-154).
The
relative
determined
by
morphology
of
polystyrenes
of
rigid
by
amount
the
particles
Casting
morphology,
will
peaks
bring
phase.
the
stress
damping
are
nearly
the
following:
is
broken.
of
glass
2.
such
transitions
show
two
of
the
two
components
the
system.
of
the
commercial
rubbery
The
of
not
of
determined
rubber
plus
by
the
phase
the
the
amount
inclusions
curves
of
high
inside
is
and
by
inclusions
the
rubber
the
the
impact
for
pure
show
(34-36, 106%
peaks
peak
polybleng
characteristic
containing
damping
broken.,
as
peaks
concentration
dispersed
craze
become
the
is
stress
modulus-temperature
curves
of
adhesive
many
particles
damping
size
The
in
phases
independe
These
The
result
than
modulus
1.
two
a
any
strain
the
Many
is
for
increases.
polymeric
The
or
of
polystyrene.
phase
the
two
This
composites
heights
have
rubber
have
in
amplitudes,
Agglomerates
polymers
in
low
particles
two
nearly
compensates
prominent
polymer
of
G".
damping
of
filler
consisting
block,
two
the
modulus
properties
the
more
and
polymer.
Composites
the
or
fillers
POLYMERS
(G"/G')G'.
higher
and
such
than
=
At
mechanical
filler
around
the
G"
more
at
the
more
(143-145).
one
G"/G',
of
G'
much
decreases
the
concentrations
cracks
are
However,
from
part
equation
dynamic
amplitude.
by
modulus
polymers
filled
bond
in
effects
unfilled
the
imaginary
in
amplitudes,
of
the
measured
increase
Amplitude
with
as
PARTICULATE-FILLED
but
rubber
(155-157).
from
different
including
about
(34-36,106).
phase
changes
This
in
solvents
can
inversion.
the
relative
phenomenon
is
bring
about
These
changes
sizes
of
illustrated
changes
the
in
in
two
in
morphology’
damping
Figure
39
VII.
of
DYNAMIC
MECHANICAL
Chapter
its
4
damping
PROPERTIES
(34).
peak
The
for
tend
to
tend
make
a polymer
to
change
the
that
they
peak
(35).
In
from
a
appear
the
to
be
the
to
the
the
the
how
on
modified
the
fit
A;
the
¢, =
about
points
made
up
styrene,
both
continuous
phases.
the
rubber
appears
the
polystyrene.
Above
to
be
a volume
spheres
up
to
fractions
of
0.15
networks
volume
a dispersion
of
and
is
are
of
3.0
A =
of
rods
fraction
fraction
spherical
for
0.5
short
0.80
and
3.0,
A =
into
elongated
curves)
lower
value
This
polystyrene.
section
The
and
upper
the
points
the
(38).
ratio
a polystyrene
styrene-
in
Poisson's
interlocking
rubber.
experimental
and
is
where
the
of
values:
polystyrene
form
in
series
the
concentra-
following
agglomerated
phases
higher
the
for
As
region
inversion
as
rubber
rubbery
with
0.35
volume
and
discussed
method
(shown
and
of
The
damping
polymers
little
dispersed
a
one
phase.
rigid
still
for
phase
0.85,
Between
0.15.
the
by
in =
the
At
(39).
0.80,
that
indicate
polymers
a
composition
changes
equations
experimental
the
possible
morphological
adding
the
a
polyblends
block
of
is
solvents
only
a dispersed
becomes
undergoing
systems
On
place.
modulus
predicted
polybutadiene
is
the
series
for
even
some
and
both
is
is
drying
polyblends
a
higher
poor
It
with
becomes
this
while
materials
other,
rigid.phase
Halpin-Tsai
0.86,
=
would
or
of
moduli
the
takes
block
accurately
be
of
increases,
phases
rubber,
7 shows
rubber
butadiene-styrene
can
freeze
phase
rubber
continuous;
become
Figure
by
the
solvents
phase.
(38,39,41,152,158-161).
phases
of
much
is,
Good
phase,
dispersed
single
of
tions
continuous
so
concentration
of
a phase
composition.
composition
polymer,
inversion
continuous
a more
component
occur
rigid
it
morphology
pure
changes
to
make
changing
one
more
a given
polymer
to
429
of
poly-
both
of
particles
0.8,
in
430
7.
Viti
Other
A.
Mechanically
Impact
which
largely
not
of
in
Propeneues
by
Figure
concentration
in
a
rigid
a polymer
clearly
determined
illustrated
stress
fillers
strength
are
POLYMERS
Strength
Rigid
impact
PARTICULATE-FILLED
polymer
(93).
understood,
generally
There
but
the
the
dewetting
and
21A
a
stress
that
tensile
results
in
are
a
few
impact
crazing
decrease
exceptions
strength
is
phenomena.
produces
dewetting
the
and
a
type
G2<G,
0,
2il:
(Left).
Dewetting of a rigid filler
of lower modulus.
(Right).
Crazing
a filler particle
(or void) when the
modulus
than the filler particle.
of
cavitation
Oo
Bigne.
As
particle
in a matrix
of a polymer around
matrix has a higher
at
VIII.
the
OTHER
MECHANICAL
poles
takes
to
of
a
place,
tend
to
the
as
the
are
adhesion
materials
was
rather
in
to
temperature.
The
was
in
discussed
temperature
Fillers
can
often
crystalline
it
for
glassy
temperature
modulus
the
versus
addition
behavior
filled
load
of
20
of
arbitrarily
1%.
Table
levels.
BSC
of
Chapter
6.
large
as
the
7 lists
The
filler
the
strengths
strength
The
mostly
on
as
if
of
good
such
much
increase
is
a
0.95)
kaolin
distortion
at
which
distortion
the
10°
more
of
heat
transition
or
temperature
20°C
than
or
the
shape
of
their
modulus
same
In
on
temperature
polymer
this
may
deformation
distortion
increase
deformation
temperature
the
of
they
in
the
(168).
more.
distortion
the
with
creep
distortion
increase
compares
(density
of
the
heat
heat
the
temperature
temperature
result
and
22
in
to
distortion
as
distortion
temperature
due
glass
in
much
polymers
percent
heat
increase
curve
heat
is
distortion
the
heat
heat
heat
in
Figure
raised
the
increase
temperature
the
as
5.
high
The
filler.
the
of
so
elastomeric
impact
of
materials
the
with
impact
increase
often
temperature
test,
filled
The
modulus
crosslinked
volume
dewetting
changes
equator
reduction
large
polyethylene
with
type
of
the
high
phases.
the
any
such
at
very
increase
polymers.
for
After
concentration
polymers
This
and
increase
and
163).
21B.
Chapter
effect
be
162,
Temperature
(164-168).
due
crazing
the
in
(89,
stress
having
generally
modulus
than
of
Distortion
a material
increase
or
rigid
between
Fillers
of
hand,
discussed
Heat
the
Figure
in
capable
exists
of
cracks
shown
431
particle
nature
other
particles
Bre
spherical
produce
particles
On
PROPERTIES
at
tensile
be
defined
equals
two
temperature
stress
24
to
432
7.
PARTICULATE-FILLED
POLYMERS
FILLED
UNFILLED
FILLED
UNFILLED
2.
fp [e]
a
°
a
ELONGATION
PERCENT
40
60
80
TEMPERATURE
100
120
(°C)
Hague
Heat distortion temperature as measured by a tensile
elongation test in which the temperature
is increased at
a rate of 2°C/minute.
Polymer is polyethylene
(p = 0.95),
either
Ofer
unfilled
or
filled
with
kaolin
Table
Heat
Distortion
Filled
Unfilled
Filled
a
volume
fraction
7
Temperature
of
AARP
Load
Unfilled
to
OZ.
(psi)
Heat
Polyethylene
STR
AA
Distortion
90
114
72
Temperature
(°C)
VIII.
OTHER MECHANICAL
C.
Hardness
Rigid
by
most
the
hardness
to
Abrasion
wear
by
in
in
same
increased
the
the
coefficient
rate
of
that
of
wear
10%
above
example,
However,
in
tires
and
filled
the
fillers
polymers
filler
when
the
abrasive
filler
Wear
actual
use
floor
did
not
if
the
and
abrasion
tests.
In
covering
machines
and
particles
particles
good.
in
(171).
agree
many
the
large
the
results
another,
and
on
21
from
the
of
spherical
particles
polymer.
rate
tile,
it
of
It
the
wear.
has
of wear.
to
the
to
kinds
size
of
of
is
least
size
of
the
matrix
correlate
seven
is
with
different
abrasion
different
correlation
wear
Wear
and
of
been
The
relative
program
the
rate
doubled
filler
tests
test
the
of
abrasive.
between
tested
of
the
particles.
the
compared
cooperative
the
upon
difficult
particles
with
the
rate
hardness
of
particles
floor
the
of
adhesion
Most
one
size
are
were
with
of
to
as
and
shape
unfilled
increased
kinds
(53,171),
the
shapes
spherical
dependent
materials
of
to
and
found
the
shaped
decrease
are
one
of
applications
increased
that
Possibly
addition
shaped
Both
that
fillers
strongly
particles
over
increase
composites.
materials
in
measured
fillers
such
friction
(174).
over
greatly
is
times
as
polymer.
of
in
irregular
compared
the
that
wear
factors
irregular
friction
the
covering
of
instance,
In
found
of
and
Other
polymer
such
important
floor
several
plastics
that
polytetrafluoroethylene
particles
noted
than
that
abrasion
coefficient
For
of
also
over
especially
are
factor
was
a
the
harder
surprising
(172,173).
wear
oxide
not
composite
is
particles.
aluminum
is
much
(169,170),
tires
affect
are
are
bearings
filler
wear
the
433
Wear
it
hardness
automobile
which
so
of
and
plastic
and
fillers
tests,
related
PROPERTIES
with
machines
practical
adhesive
bond
decrease
the
come
in
contact
irregularly
can
shaped
instance,
of
particles
excessive
cause
For
with.
wear
to
very
the
hard
fillers
of
injection
parts
with
filled
polymers
they
material
whatever
of
wear
the
increase
greatly
may
and
paper
sand-
of
characteristics
the
of
many
on
take
may
polymers
filled
these
hand,
other
the
On
a polymer.
of
wear
of
rate
will
fillers
polymer,
the
and
filler
the
between
strong
a
is
there
if
Usually,
poor.
generally
was
tests
wear
POLYMERS
PARTICULATE-FILLED
7.
434
as
such
silica
molding
machines.
Fillers
effects
depend
are
so
fillers,
the
can
difficult
strongly
and
conflicting
instance,
the
or
talc
the
in
fatigue
(176).
including
of
an
can
the
rubbers
brittle,
with
or
if
the
of
Polymers
most
rigid
expansion
of
the
is
final
of
for
give
life
of
On
poor,
the
tear
strength
of
may
For
polyvinyl
the
to
improve
fillers
of
properties.
adhesion
silanes,
type
Similar
resistance
the
the
the
fillers
other
(175).
good
if
and
abrasion.
fatigue
the
on
above,
many
The
properties
machine,
noted
rate
properties.
other
hand,
compressive
to
the
the
make
polymer,
tear
the
strength
polymer
resistance
too
decreases
concentration.
of
have
fillers.
some
adhesion
filler
As
lowers
by
the
interface
blends
However,
Coefficients
the
impact
which
treated
(165,177).
increase
D.
resin
many
testing
found
rubber
Fillers,
those
the
be
improves
epoxy
of
of
degrade
because
phases.
decrease
chloride-acrylonitrile
fillers
type
nature
evidence
or
predict
the
between
increase
enhance
to
on
upon
adhesion
either
either
Thermal
much
This
components
Expansion
larger
coefficients
mismatch
in
the
making
up
a
of
expansion
coefficients
composite
of
produces
than
thermal
several
VIII.
OTHER MECHANICAL
important
curing
effects:
This
frictional
surface
good
less
increase
filler
polymer
A number
coefficient
often
of
of
equation
However,
which
of
of
a
the
is
reduce
and
than
because
the
data
of
agree
equations
what
would
for
Some
mechanical
the
with
G/G,
may
of
can
be
down
be
will
of
squeezing
the
a
of
curves
of
polymer
in
the
composite.
from
lowered
values
to
materials.
for
The
calculating
from
equations
coefficient
data
coefficients
from
the
the
material
different
a different
calculated
mismatch
stresses
strength
the
tensile
composite
experimental
predict
be
strong
The
a composite
values
composite.
other
all
of
the
tensile
proposed
(20,178-180).
different
given
been
most
near
3.
composite
if
polymer
of
structural
other
expansion
components
a
a pure
of
have
the
even
in
modulus
high
prevents
same
the
(43).
the
the
to
of
relative
such
of
The
on
forces
stress-strain
modulus
raised
expansion
nearly
a result
the
polymer
large
subjected
the
and
and
equations
is
or
pressure
the
for
2.
as
If
produce
metals
while
less
mixtures"
filler
of
against
adhesion.
be
fabrication
squeezing
modulus
may
the
except
direction
crack
quite
nearly
are
poor
may
thermal
the
predict
expansion
one
of
a
the
expected,
of
exerts
filider
characteristic
values
from
expansion.
may
it
down
interface
Thus,
particles
characteristic
constants
the
the
temperature
the
that
high
of
particle
coefficient
The
fit
non-Hookean,
is
what
as
polymer
and
of
is
polymer
than
cooling
tangential
coefficients
435
the
at
filler
the
in
rigid
the
a
In
poor.
is
both
of
forces
4.
motion
for
cases
the
tight
adhesion
the
1.
temperature,
filter.
the
PROPERTIES
of
agree
with
equation
of
expansion
simple
matrix
restraints
of
the
dispersed
in
a matrix,
(77).
"rule
by
the
particles.
For
nearly
spherical
particles
Kerner
(20)
436
7. PARTICULATE-FILLED
derived
the
expansion
following
of
a
equation
for
the
coefficient
of
POLYMERS
volume
composite:
eee
B,
The
volume
polymer,
moduli
coefficients
and
of
deviate
filler
the
from
impose
mechanical
fibers
do.
the
randomly
Thomas
the
oriented
a better
for
=O
the
a,
the
case
=
10
Ga eel 07
of
coefficient
the
pure
curves
the
of
theories
expansion
filler
where
the
are
and
B,
of
and
are
B,.
the
the
Equation
since
matrix
rod-like
directions,
or
it
logarithmic
the
Kerner
nlOg
Oj
phase.
filler
the
33
to
the
shape,
is
believed
of
Log
not
and
that
are
that
a.
the
gives
(34)
for
where
pertinent
material
coefficients
Ch, =
aoe:
u10F!
is
do
mixtures,
equations
be
not
extent
in
rule
bulk
does
spheres
different
must
The
equation.
o>
the
composite,
respectively.
mixtures"
on
of
=—%
Kee
All
ao,
three
than
compares
expansion
a na
particles
equation,
estimate
23
a,
"rule
in
LOGROR
Figure
expansion
restrictions
filler
(179)
thermal
components
much
If
are
of
B,
incorrect
a smooth
there
Gomes
Selo
particles
are
all
in
the
of
be
extent
that
composition
a break
contact
are:
=-5
9221044
to
must
constants
K, e267
function
Actually,
le
of
in
with
the
up
to
the
one
another
IX.
SUMMARY
437
COEFFICIENT OF EXPANSION
OF MIXTURES
10
210747°C
=10°9/°C
10°
EXPANSION
OF
COEFFICIENT
x
ie
4
VOLUME
6
FRACTION OF FILLER
Imatei,
the
maximum
packing
particle-particle
Xe
fraction
contact
may
be
$2
228}
Coefficient of thermal expansion.
B = Equation 33, € = Equation 34.
at
10
bac
A =
In
"rule
of
practice,
mixtures,"
this
error
due
small.
Summary
The
main
effect
of
rigid
fillers
is
to
increase
the
elastic
to
438
7. PARTICULATE-FILLED
modulus
The
of
a
composite
important
tion
of
the
relative
adhesion
the
factors
filler,
of
pack.
The
the
tend
The
creep
polymer
if
dewetting
an
creep
Such
tions
as
and
distortion
increase
A
has
state,
sound
second
not
occurred.
class
of
than
composites
and
high
impact
which
are
less
than
those
of
to
break,
and
often
than
that
of
X.
Problems
1.
The
at
the
relative
low
rates
polymers.
unfilled
viscosity
of
material
with
relative
modulus
the
to
are
to
largely
also.
relative
the
unfilled
has
especially
undesired
the
the
result
of
increase
inverted
in
systems
composites
unfilled
polymer.
have
strength,
liquid
epoxy
and
heat
the
Tyg:
such
as
moduli
However,
impact
in
vibra-
increase
large
occurred,,
dissipation
Inverted
their
the
dewetting
Fillers
the
composites.
break
from
dampen
any
of
in
are
their
greater
polymer.
n/n,
shear.
The
a Poisson's
G/G,
to
is
due
important
energy
of
determining
fillers,
high
used
effect
foams
elongation
Some
materials.
This
in
of
the
degree
behavior
After
concentra-
which
the
very
behavior
unusually
be
and
in
elongation
rapidly.
may
rather
are
creep
the
coefficient),
manner
predicted
the
cause
temperature.
be
and
deadening
in modulus
can
are
factors
stress-strain
very
composites
the
important
the
suspension.
(Einstein
interface
factors
often
fluid
modulus
and
drastically
increases
agglomerated
very
and
a
particle
the
these
composite
rate
damping.
but
behavior
the
of
not
reduce
of
the
of
the
components,
are
modulus
the
of
strength
to
viscosity
determining
nature
modulus,
determining
Fillers
in
the
generally
elastic
the
shape
modulus
particles
or
POLYMERS
if
of
a
suspension
ratio
G,/G,
of
is
0.4.
very
is
suspension
cured
What
large?
is
to
give
the
is
a
3.0
rigid
expected
X.
2.
PROBLEMS
A
439
rubber
filler
containing
has
a
10,000
down
a
A
where
becomes
stresses,
3.
times
what
suspension
relative
nature
that
is
of
that
G/G,
2.426
the
of
of
a
rubber.
its
the
rigid
The
filler.
of
What
is
0.35,
the
a
cooled
and
no
its
thermal
cooled
composite?
a
filler
has
you
say
of
can
nas
transition
Assuming
percent
1.26.
Waller
rubber
becomes
modulus
spherical
the
glass
ratio
5 volume
n/n,
OL
below
relative
containing
the
of
Poisson's
the
viscosity
of
100°C
its
0.10
percent
modulus
temperature
temperature
modulus
volume
relative
modulus
to
30
a
about
the
filler?
4.
Prove
that
E/E,
5.
Prove
that
the
=
G/G,.
1 + ABO
equation
M/M,
=
po
becomes
the
law
of
that
A approaches
Zz
mixtures
zero,
when
the
A
approaches
equation
infinity
and
FAa
a
o, ¢
becomes
1
6.
give
would
concentration
7.
A
rectangular
spheres
0.001
flexure
to
8.
For
a
of
the
action
is
1072
of
the
than
packings
volume
same
the
for
composite
a
in
rather
two
the
of
which
hexagonal
a perfect
lattice
cubic
simple
a
the
the
expected
error
in
polymer
above
its
greater
rigid
dynes/cm’.
E/E,
modulus
relative
than
Ley
Calculate
of
the
The
is
as
the
that
any
value
to
the
filler
due
of
modulus
modulus
is
measurement?
assume
Ty:
in
measured
What
2.5.
modulus
dynes/cm*
crystallites.
was
modulus
Young's
contains
thick
inches
0.025
specimen
diameter.
inch
crystalline
modulus
in
filler?
composite
give
of
magnitude
of
2
packing,
modulus
higher
the
a
in
random
usual
more
the
in
or
lattice
packed
close
2
packed
be
could
particles
spherical
If
as
a
the
crystals
function
of
the
440
7. PARTICULATE-FILLED
degree
of
crystallinity
dispersed
Are
phase.
either
of
(b).
these
assuming:
The
crystals
assumptions
POLYMERS
(a)
The
crystals
are
the
continuous
realistic
for
are
the
phase.
a crystalline
polymer?
9.
A
polymer
filled
with
a water-soluble
relative
modulus
G/G,
of
in
for
water
voids
salt
10.
where
were
long
the
of
the
polymer
has
a
modulus
1000
A
polymer
rigid
filled
a good
break
A series
with
of
following
styrene,
aspect
has
entire
of
bond
with
the
of
a
dispersed
of
in
4 to
the
in
spheres,
is
$¢, =
volume
0.35.
the
0.7.
fractions
1000
times
Plot
composition
is
the
range
of
dm =
0.3
voids?
2%.
At
relative
zero
you
a
The
polymer
would
expect?
the
of
poly-
have
an
fraction
of
forms
to
have
of
concentra-
appears
fraction
to
be
rubber
in
occurs
over
the
0.7.
The
polystyrene
rubber
and
a
modulus
to
has
elongation
small
rubber
the
The
which
filler
packing
to
1003
of
relative
polystyrene
inversion
leaving
particles
salt
of
what
0.7.
the
of
soaked
polystyrene
maximum
Phase
from
in
then
concentrations
packing
that
break
this
is
thus
a
polymer.
The
low
from
the
polymer.
Is
has
the
the
rigid
polystyrene,
and
of
rubber
The
is
a
At
rubber
of
0.3)
the
and
to
particles
1.
If
0.5,
that
percent
polyblends
a modulus
ratio
volume
were.
what
=
salt,
spherical
elongation
1%.
rubber
polystyrene
of
an
the
with
of
as
is
ratio
dispersed
range
10
great
all
shape,
ratio
composite
the
of
as
in
(¢,
composite
once
polymer
characteristics:
polystyrene
tions
particles
Poisson's
has
The
extract
spherical
times
the
to
extracted
adhesive
of
time
salt
nearly
modulus
is
ll.
a
2.42.
salt
G/G
Poisson's
rubber
Over
polystyrene.
the
X. PROBLEMS
12.
An
unfilled
with
the
stress
values
are
20
volume
that
of
the
creep
The
=
and
time
is
in
some
and
as
n =
With
seconds.
filled
polymers
The
The
of
of
¢”
of
polymer
2000
the
subscripts
Ko
a modulus
a graph
obeys
=
units
same
has
load
plot
to 10*
the
a
e(t)
0.25.
filler
polymer,
$, where
equation,
seconds.
kaolin
filled
7
Nutting
polymer.
1 second
of
the
5 x 107
percent
the
damping
aoa
K =
unfilled
of
from
obeys
of
psi,
with
specimen
13.
polymer
twice
psi
its
ona
expected
equation
F and
U refer
to
filled
U
the
14.
A
equation
composite
filler.
Give
instead
V6~ue
creep
tests
the
rods.
(b).
How
does
the
lot
G/Gra
with
a
at
The
creep
versus.
1,
(a)
load
differ
for
a
of
0.5
=
of
a particulate
the
unfilled
1.8
=
G/G,
why
parallel
applied
cases?
two
0.64,
in
¢, =
flakes
polystyrene
0.35.
if
om =
What
1 and
gives
is
the
Gi/G,
a relative
Einstein
=) 00)
to
rods.
the
to
perpendicular
for:
rods.
oriented
short
of
is
load
The
of
suspension
33-9,
=",
form
the
the
in
that
of
expected.
applied
is
0.40
reasons
be
in
of
times
2 possible
made:
oF
1.8
normally
ratio
G,/S,
of
a filler
are
fraction
l.
spheres
Me
mn =e
G,/G,
=
a matrix
in
10,
4.
10);
=a
G,/G,
0.64,
o, =
Gere.
G./
Mica
might
Poisson's
I
Soa3
volume
least
at
what
Two
a
a modulus
contains
A polymer
NS)
17.
of
Gy ¢, hold?
contains
It has
polymer.
15.
Ge =
not
does
Why
made.
be
must
assumptions
what
stating
clearly
equation,
this
Derive
respectively.
materials,
unfilled
and
modulus
G/G,
coefficient
of
of
8.0
the
mica
7.
442
NABhe5
What
is
the
shear
undergoing
phase
dynes/cm’,
b_ =
volume
phases
Assume
A
suspension
of
a mixture
0-75.
At
is
of
10’
which
Cor
composition
ratio
inversion
system
dynes/cm’,
overall
spheres
is
0.5
starts,
relative
Cope.
upper
limit
a
the
is
107%
is
for
composite
spheres
of
modulus
=
particles.
surrounding
of
in
concentration
the
the
cubical
the
a
Assume
Estimate
=
POLYMERS
50-50
both
dispersed
spheres.
uniform
mixture?
G,
The
phase
of
much
following
Poisson's
suspension
how
the
0.64.
A
dm =
20.
01 =
Before
are
of
inversion?
percent.
components.
ILS)-
modulus
PARTICULATE-FILLED
of
35
has
a
different
volume
decreased
sizes
percent
by
0.63.
has
a
spheres,
using
the
100.
expected
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the
Einstein
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(Assume
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cubes
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to
make
the
cubes
behave
of
spheres
matrix
9, =
enough
as
of
spherical
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23
A
composite
shear
made
modulus
modulus
below
is
of
of 10’
10''
Ty so
is
the
concentration
maximum
eons
dynes/cm*
dynes/cm*.
that
10*°dynes/cm?,
What
up
the
and
of
packing
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The
the
ratio
modulus
a
G/G,
spheres
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30
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have
is
unfilled
changes
above
volume
which
spheres
temperature
of
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.
The
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in
polymer
percent?
T.
to
becomes
0.50
below
a
a shear
lowered
from
and
has
g
Assume
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0.35.
at
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ei, Sily
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124.
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lana
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606
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unpublished
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Washington
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I.
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USTs
A.
Yim
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M.
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St.
T.
E.
Polymer
Pierre,
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Ji.
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Sci.
ll,
TAS)
Polymer
Ya.
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P.
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B7,
Vasilieko,
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237
(1969) =
and
4, 920
7. PARTICULATE-FILLED
450
139%
Niue
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Oe
LidpauOv,
Kraus
and
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J.
T.
Uli
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chica
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412
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L.
E.
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J.
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20,
SLO SiG) ie
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AAC
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Sci.,
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J.
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dia
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LS) 6
J.
P.
Thomas,
U.
S.
180.
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A.
Shapery,
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380
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287826.
(1968).
Chem.
Chapter
Fiber-Filled
I.
posites
glass
and
of
the
have
materials
used
fibers
in
fibers
and
Other
in
epoxy
from
or
carbide
in
importance
the
fact
that
and
specific
strength
best
of
Composites
polymers,
unfilled
spectacular.
Many
tremendous
advantage
in
of
certain
weight
the
surpass
superior
1.
When
of
The
the
specific
values
for
even
by
fiber-filled
composites
direction;
proper
this
compared
are
composites
composites
are
can
design.
the
are
composites
the
453
high
material.
offered
by
largely
arises
improvements
applications
some
and
of
values
polymer
one
alumina
of
offer
they
fibers
the
fibers
the
in
as
unusually
have
strength/density)
The
strength
polystyrene
such
composites
can
given
can
as
glass
graphite
crystal
and
laminates,
(1-3).
materials
(tensile
Table
resins
include
chopped
and
whiskers,
a
and
boron
com-
composites
are
single
small
for
fabric
such
fiber-filled
such
glass
materials
applications
of
These
resins
temperature
as
phase.
fiber-filled
phenolic
called
are
considered
epoxies,
Other
high
strong
metals.
in
illustrated
with
in
(modulus/density)
the
and
in
stiffness
strength
filler
developments
aerospace
The
modulus
the
thermoplastic
Super
silicon
promise
fibers
Recent
resins
as
vessels.
numerous
nylons.
traditionally
polyesters
asbestos
polyimides.
to
fibers
filament-wound
include
or
and
Introduction
Most
in
Composites
8
be
are
anisotropic
used
to
454
8.
FIBER-FILLED
Table
Specific
Modulus
and
COMPOSITES
AND
OTHER
COMPOSITES
1
Strength
Material
of
Some
Materials
Specific
Modulus
Specific
(inches)
|Strength
Aluminum
jaa
Stainless
steel
Wi
8.8 x 10°
Polystyrene
15:95.
Epoxy
DA
3
Grice nhOe
resin
Uniaxial
glass
- epoxy
2
Uniaxial boron
composite >, =
- epoxy
.7
3 Oh
composite
>, =
.7
x
102
NO”
LO”
Uniaxial graphite - epoxy
composite.
High modulus
fiber, >, = .6
Aad,
3
Uniaxial graphite - epoxy
composite.
Low modulus
Bot)
se TO’
fiber,
Oy
Us =
Property
are
woven
continuous
fibers
4.
Injection
II.
Moduli
Most
1.
of
(g/cm?) .
a variety
Impregnated
fabrics.
around
3.
an
of
mats
fabrication
of
Filament
axis
polymers
Fiber-Filled
fiber-filled
inches.
fibers.
in
of
i
ELV
in lbs/in 88
x Density
of
molding
aD
AS set
Density
0.036
used
include:
and
SADE
fraction
Fibers
sheets
=
(lbs/in*)=
volume
These
IY
o6
.
Specific
Density
=
(inches)
of
fibers.
winding
rotation
containing
to
techniques
2.
Laminates
of
resin-coated
form
short
are
anisotropic,
of
a vessel.
fibers.
Composites
composites
(3-6).
and
as
II.
MODULI
OF
discussed
FIBER-FILLED
in
independent
different
Chapter
in
such
illustrated
moduli,
These
one
four
are
are
the
transverse
to
shear
Gp
in
a
modulus
to
the
Gop
to
in
give
Figure
1.
modulus
which
which
the
Chapter
important
the
to
in which
The
fibers
Of
the
in
most
is
equations
(7-19).
will
systems.
In
stretch
very
be
the
the
long
tension
is
have
Only
equations
The
moduli
and
the
and
for
a
been
few
of
discussed
6
situations.
2.
Ey,
The
applied
longitudinal-transverse
fibers.
stress
4.
The
stress
fiber
and
fibers,
is
given
the
for
in
the
polymer
transverse
applied
shear
perpendicular
these
matrix
or
most
uniaxially
same
the
of
oriented
force
amount.
Young's
¢,.
the
case
The
top
Therefore,
modulus
where
transverse
equations
E,/E,
fibers
=
The
25
(glass
modulus
most
the
of
1 is
Eo,
and
E
are
fractions
of Figure
Young's
(7-17).
in
(1)
volume
curve
tends
by:
and
matrix
these
accurate
a tensile
the
longitudinal
accurately
estimating
simplest
direction,
the
the
proposed
for
longitudinal
corresponding
The
many
5 or
modulus
¢
$,
are
material
fibers.
load
6
are
Young's
the
the
shearing
shearing
5 or
oriented
2.
longitudinal
3.
the
a uniaxially
The
the
along
all
most
ie
least
properties
Often
parallel
E,,
at
the
fibers.
in
their
1 of
applied
the
that
have
fibers.
moduli
‘for
is
direction
Many
to
in
Young's
perpendicular
acts
so
following:
modulus
materials
considered
load
455
directions.
direction
the
in which
such
moduli
different
aligned
as
2,
elastic
in
COMPOSITES
two
a plot
fibers
Ep has
convenient
in
been
of
respectively,
phases
are
of equation
1
epoxy
resin).
estimated
by
an
these
equations
456
is
8.
the
Halpin-Tsai
FIBER-FILLED
(13-15)
COMPOSITES
equations
as
AND
OTHER
modified
COMPOSITES
by Nielsen
(20,
Zaleas
E
LEE
VABO
Ey
ie
BYO,
Lee
(2)
where
A=Pipa
0.5
Sages
casa+A
ae
- E/E
2
oe
1
and
1-
y=
Ll +],
Oe
——
o,
-
(4)
om
The
of
factor
the
fibers
fibers,
in
y takes
on =
general
close
as
0.785,
packing
glass
case
the
fibers
small;
in
that
modulus
in
The
is,
account
discussed
om will
illustrates
into
in
while
lie
the
Chapter
for
?,
=
these
variation
an
resin.
fibers
are
a direction
not
very
estimated
from
(13-15,
G
1
+
to
to
shear
the
E
E,,
in
their
A
=
1.0,
and
equations
3 and
by
the
G,/G,,
curve
of
4,
B
Figure
Figure
of
very
increasing
the
length.
modulus
Grp
can
be
20):
ABO,
(5)
and
w are
except
modulus
of
is
G ~ By,
T=
where
of
random
curve
el
om
0.907;
concentration
effective
perpendicular
longitudinal-transverse
near
Ep with
packing
bu =
lowest
Compared
fraction
cubic
packing,
The
of
packing
For
limits
0.82.
expected
epoxy
7.
hexagonal
between
where
maximum
that
ratio
1 shows
given
that
by
the
Eos os of
of
the
G
=
1
is
two
same
equation
phases.
much
smaller
expressions
3 is
The
replaced
middle
E
than
as
aa but
1
l
II.
MODULI
OF
FIBER-FILLED
COMPOSITES
457
30
20
=i
>
=
eit
—
=}
Bey
So
=
a8
—_
=
—
iim 3
2
L5
1.09
Ol
O2
03
VOLUME
04
FRACTION
05
OF
06
O7
FIBERS
IDaieiG al
Relative moduli as a function of volume fraction of fibers
for uniaxially oriented fiber-filled composites for the case
of glass fibers in epoxy resins in which the modulus of the
Maximum
fibers is 25 times the modulus of the matrix.
packing fraction of the fibers is assumed to be 0.85 in
calculating Gpepe Cope and En:
somewhat
The
greater
than
shear
transverse
Gop
eet
Gps
where
A =
0.5,
and
E,/E,modulus
Gop
can
be
estimated
ABO,
lL =sBteLe
B
and
from
y are
(6)
defined
by
equations
3 and
4 with
458
8.
E,/E,
replaced
by
2
6,
that
and
As
by
shows
pointed
the
use
of
FIBER-FILLED
G,/G,E,/E,
out
the
Figure
in
and
1,
or
Grp/G 1
Chapter
modified
COMPOSITES
7,
a
can
(20,21)
COMPOSITES
of
essentially
moduli
Halpin-Tsai
OTHER
comparison
are
all
AND
equations
the
be
same.
calculated
equations
il ap a
M,
%I-
s/s
For
fiber-filled
given
in
Table
related
to
The
longitudinal
oriented
Figure
of
diameter
times
result
for
to
Young's
a
of
very
the
realize
Experimental
fibers
of
were
that
maximum
strength
aspect
Equations
mendous
90
for
change
degrees
so
predicting
and
1 and
in
that
the
the
of
modulus
2 or
Ey becomes
Young's
in
ratios
of
1.5
of
very
fiber
oriented,
over
100
are
of
kp —
fibers;
matrix.
length
than
curves
to
100
ina
in
to
a modulus
has
spheres
composites,
is
relative
shaped
fibers
A =
long
fiber
for
A
the
for
the
greater
the
are
7 that
a polymer
sigmoidal
from
are
are
required
composite.
which
confirm
the
the
required
to
1 show
when
the
that
test
transformed
modulus
E, at
there
direction
into
any
is
E Tr
pre—
obtain
angle
a
tre-
is
The
a
infinity
(22,23).
Figure
modulus
of
behavior
uniaxially
ratios
moduli
The
potentiality
diction
case
the
full
well
the
holds
where
Aspect
fairly
only
A
equation,
case
the
short
the
(ratio
changing
on
Chapter
ratio
fibers.
results
from
factor
aspect
matrix.
A
1)
in
L
the
kp by
smaller
for
the
E,.
the
of
recalled
expected
of
fiber)
the
values
coefficient
the
factor
long
be
give
function
that
the
modulus
fibers
the
(7)
mixtures (Equation
2 illustrates
as
will
Einstein
short
modulus
100
It
of
rule
-
composites,
2.
the
BY,
rotated
equation
9 from
the
a:
II.
MODULI
OF
FIBER-FILLED
COMPOSITES
459
Table
Values
Type
of
of
A
for
2
Fiber-Filled
and
Ribbon
Composites
Composite
Uniaxial
Orientation
(Long)
is]
Uniaxial
Orientation
(Transverse) |
ie]
Uniaxial
Orientation
Q
Uniaxial
Orientation
Gor
ORD
Uniaxial
Orientation
(Bulk)
i|
B
0
Random
Orientation;
3-D
G
2.08
Random
Orientation;
3-D
G
2.84
Random
Orientation;
3-D
G
3.80
Random
Orientation;
3-D
G
4.93
Random
Orientation;
3-D
G
6.20
Random
Orientation;
3-D
G
8.38
Random
Orientation;
3-D
G
©
Ribbon-Filled
(Longitudinal)
E
Ribbon-Filled
(Transverse)
E
2 w/t
©
Ribbon-Filled
(Transverse)
E
0
Ribbon-Filled
G
(w/t)”?
Ribbon-Filled
G
0
Ribbon-Filled
G
0
io//0)
i}
of
ratio
aspect
width/thickness
w/t
fiber
1
Ho)
where
direction
_
cos
EU
v
LT
4
fe +
is
is
the
ribbons.
(24):
Gad
=
of
(2)
length/diameter.
=
fibers
=
T
2v
8
+
e-
Poisson's
LT
-
ratio
=
ie
of
)sintecos?@
the
composite
(8)
for
a
tensile
8.
460
u
3
FIBER-FILLED
10
COMPOSITES
30
AND
OTHER
100
COMPOSITES
300
000
ASPECT RATIO, L/D
Big.
2
Relative
longitudinal Young's modulus
aspect ratio for discontinuous
fibers
which
load
applied
equation
taining
that
E/E,
about
direction
the
65
slight
of
100.
parallel
8 for
only
=
as a function of
for the case in
to
case
the
of
volume
fibers.
a boron
percent
misalignment
applied
load
Figure
fiber-epoxy
fibers
of
the
results
3A
in
(25).
fibers
a
is
composite
The
with
drastic
a plot
figure
respect
decrease
of
conindicates
to
in
the
the
modulus.
The
shear
1
modulus
1 +
Go
Yur
also
1 +
changes
with
angle:
Vert,
Caeegee,
|lap ema
Ema eee
oe
LT
L
ie
sin*@cos*6
LT
(9)
II.
MODULI
OF
FIBER-FILLED
COMPOSITES
461
40
)
= 30
A
wn
Qa
oO
i
E5/E,2120
2 20
s
uJ
10
0%
30
60
90
ORIENTATION ANGLE,@
lg “A
en
:
z
ae
oe
ee
CA
Wa
ZZ
:
|
%
30
ORIENTATION
60
ANGLE,6
igite;.,
Young's
A.
function of
3}
of aligned
modulus E,
the angle between the
=
E2/E1
stress.
120,
fiber
fiber
approximate
the
90
composites as a
axis and the tensile
value
for
boron
fiber-
epoxy composites containing 65 volume percent fibers.
the orientation
shear modulus versus
The longitudinal
B.
angle for the case of G2,/Gi = 120 and $2 = 0) -OS5
where
to
Vern is
the
related
the
direction
by
the
ratio
Poisson's
of
the
fibers.
load
for
a
The
two
applied
Poisson's
perpendicular
ratios
are
equation:
5
(10)
462
8.
Figure
for
3B
a
shows
typical
goes
matrix
a
moduli
practical
a
large
good
can
be
moduli
low.
In
is
materials.
A
Their
but
of
of
fibers
which
are
2D
uniaxially
from
least
or
or
fous
plane.
Young's
L
the
modulus
with
Tsai
aoe
(25,31)
in
of
as
orthotropic
(26)
oriented
a
load
developed
a
a composite.
experimental
are
lower
developed
a
composites
studies
than
the
simpler
containing
His
equation
T°
is:
(11)
either
Young's
be
modulus
experimental
fiber
composites,
equations
1 and
2.
with
form
a plane
direction
a plane.
oriented
composites
oriented:
to
randomly
such
results
oriented
longitudinal
Ep Can
for
some
modulus
in
to
fibers
angles
biaxial
any
that
uniaxially
fibers
most
so
directions,
of
Chen
fibers.
Therefore,
different
for
the
a part
isotropic
and
modulus
agree
Young's
at
long
theoretical
5
layers
2 for
Nielsen
are
design
three
nearly
containing
to
direction.
several
Young's
to
or
Chapter
(28-30).
Sige
two
are
2 of
the
one
cross-plied
randomly
modulus
fiber
at
results
cases
equation
transverse
oriented
in
calculating
E
estimated
only
a high
ones
method
from
in
Figure
this
other
this
applied
calculating
experimental
In
difficult
composites
theoretical
in
is
composite
in
the
it
oriented,
in
method
direction,
force
in
other
one
of
shear
very
illustrated
applied
the
have
Such
is
where
modulus
composites
laminates.
has
shear
6,
fiber
stacked
a plane
The
angle
oriented
properties
in
degrees
at
uniaxially
applications
be
45
COMPOSITES
amount
in
can
modulus
composite.
at
OTHER
greatest
randomly
fibers
shear
AND
the
stress
get
maximum
transfers
COMPOSITES
longitudinal
fiber-epoxy
large
Although
high
the
boron
through
the
Gor
FIBER-FILLED
or
E,
and
values
they
can
the
obtained
be
Figure
4 compares
uniaxially
composites
containing
very
long
(27)!
II.
MODULI
OF
FIBER-FILLED
COMPOSITES
463
~~
M/M,
RATIO,
MODULUS
=
O
Ol
0.2
0.3
VOLUME
Fig.
Relative
E »/E,
=
moduli
composites
two
or
A
25.
in
three
as
a
O4
FRACTION
function
0.5
of FIBERS
4
of
fiber
concentration
for
comparison of uniaxial composites with
which the fibers are randomly oriented in
directions.
464
8.
fibers
randomly
fibers
have
EG / Bae =
an
epoxy
is
high
than
This
considerable
The
ot
Young's
oriented
of
a
modulus
in
a
plane
is
shown
may
be
is
a very
Nielsen
(32)
too
large
this
when
the
order
4
+e
the
modulus
in
the
same
in
truly
randomly
of
a
E,:
fibers
are
(14,31)
An
is
in
three
this
is
dimensions
to
generally
approximate
equation
(30):
En -
that
concentration
is
4 also.
although
(13)
equation
sacrifice
to
there
possible
randomly
case
believes
for
Figure
oriented
this
achieve
great
in
experimentally.
in
lower
(a)
materials,
achieve
modulus
to
in
a plane,
approximately
much
1
4 illustrates
order
is
in
composite
is
Thus,
i.e.,
fibers
random
which
the
matrix,
tz eta
wae
In
composite
where
modulus
in
COMPOSITES
glass
the
composite.
maximum
case
of
the
the
oe
Figure
matrix,
in
also
to
the
of
sacrifice
isotropic
difficult
modulus
OTHER
polymer
case
directions
Gpp/G,
truly
the
AND
the
the
all
road
ee =
Fibers
for
of
of
in
oriented
Goa
AVolotr
that
the
for
modulus
shear
randomly
that
approximately
to
COMPOSITES
plane
times
a uniaxially
a high
one
Although
compared
achieve
in
25
is
matrix.
EL of
give
oriented
a modulus
25
FIBER-FILLED
for
the
properties
maximum
13
oriented
is
in
all
achievable
equation
fibers
case
predicts
three
below
where
Ba / es =
directions,
there
modulus.
values
which
dimensional
about
2516
40
are
composites
v/o.
He
proposes:
log
It
has
been
in which
The
the
Esp
nearly
fibers
fabrication
=
o,
log
impossible
are
E)
+
to
randomly
techniques
nearly
%,
log
prepare
oriented
always
E,
ZA
(14)
experimentally
in
three
partially
composites
directions.
align
the
III.
STRENGTH
fibers
14
in
have
OF
a plane.
not
A
been
number
composites
are
Lee
and
of
The
as
clearly
fracture
complex,
because
of
of
of
of
case
the
tested
a
simple
mixtures
on
the
the
above
studies
equations
13
and
moduli
theoretical
include
(22),
of
and
the
Noga
fiber-filled
equations
work
and
by
Woodhams
(27),
Fibers
of
practical
the
of
adhesion,
at
long
fibers
aligned
relationship.
fibers
to
the
In
this
the
ends
in
of
fibers,
one
the
is
special
not
terribly
case,
but
great
perfection
components.
the
of
is
strength
materials.
are
and
adjacent
nature
the
heterogeneity
the
ductile
parallel
such
dewetting,
of
ends
the
and
fracture
concentration
of
of
composites
anisotropy
modes
composites
moduli
fiber-filled
of
importance,
fiber-filled
as
possible
stress
Composites
great
of
infinitely
tension
in
its
because
or
of
(33).
understood
overlap
brittle
relative
of
These
interfacial
alignment,
degree
the
only
studies
most
behavior
several
importance
fiber
of
merits
experimentally.
Lavengood
phenomena
not
tested
Oriented
spite
465
relative
Fiber-Filled
Uniaxially
stress-strain
nearly
and
Bernardo
In
and
that
accurate.
Strength
A.
the
experimental
Anderson
(29),
III.
Thus,
indicate
(23),
COMPOSITES
adequately
of
reasonably
Lees
by
FIBER-FILLED
of
fibers,
the
and
Only
direction
strength
the
rule
in
and
given
of
holds:
(5)
In
this
matrix
tensile
equation
and
Tn)
o,,
of
the
the
are
respectively
fibers,
strength
and
while
composite.
tensile
on,
is
strength
the
of
the
longitudinal
466
8.
For
uniaxially
oriented
three
important
modes
These
strengths
are
transverse
The
factors,
0°
parallel
and
to
important
the
factor
is
the
fiber-filled
tensile
The
shear
strength
generally
often
the
less
roughly
these
1
eee
BO
and
the
o
tends
the
of
to
the
strength
load
decreases
Equations
similar
have
proposed
function
BL
at
an
is
o
B6*
some
of
by Jackson
which
of
takes
the
and
the
the
of
failure.
than
are
16
to
different
Cratchley
the
matrix
shear
Cnn
well
fiber
that
is
material—
account
°BT
angle
the
strength
in*
eo
Peer
shows
For
broken.
angle
the
the
fiber
angles
into
orientation
Equation
For
the
reasonably
@ between
as
the
is
of
greater
tensile
load.
important
comparable
agrees
angle
mode
fibers
:
)cos*osin*s
dramatically
to
since
strength
of
the
higher
much
is
strength
failure
the
transverse
often
Bey
BS
on,
equation
which
(aa1
is
BL
tensile
An
a
o
of
At
BS*
composite
The
mode
applied
failure.
45°
other
approximately
tensile
and
determine
matrix
the
as
strength
been
strength
and
data
5°
shear
Op /2-
applied
about
is
the
Spc.
among
the
least
Sone
strength
and
of
at
strengths.
strength
load
mode
are
depends,
fibers
the
COMPOSITES
important
shear
longitudinal
and
than
BL
tensile
the
matrix.
a cos *6
The
tensile
a
strength
of
factors
experimental
where
the
strength
of
the
composites,
strength
the
OTHER
there
tensile
between
6 between
strength
three
strengths
determining
angles
transverse
of
in
determining
composite
most
fibers,
factor
Orientation
5°
and
these
AND
composites
and
Opp,
of
angle
about
COMPOSITES
longitudinal
strength
the
fiber
failure
importance
upon
Between
of
the
tensile
relative
FIBER-FILLED
with
0 is
az
all
(25):
(16)
direction
the
tensile
® increases.
terms
(34)
in
and
equation
by
16
III.
STRENGTH
OF
Ashkenazi
(35).
shear
strength
since
few,
Not
of
FIBER-FILLED
are
if
all
In
equation
16.
general,
467
transverse
determined
by
fibers
are
broken.
experimental
studies
any,
the
COMPOSITES
Another
the
proposed
tensile
strength
agree
equation
strength
of
the
matrix
with
the
predictions
is
(36):
opr
(flexural)
tensile
voids.
of
tion
made
by
Points
of
contact
between
shorter
fully
in
not
for
this
as
continuous
decrease
in
strength
of
each
end
the
matrix
the
to
concentrators.
fibers
the
3.
are
fibers.
Fibers
all
if
l.
Appreciable
The
which
fiber
composites.
are:
do
fiber
not
in
require
are
fibers
fiber
ineffective
2.
the
discontinuous
direction,
one
strong
as
Even
fibers.
act
The
overlap
reasons
lengths
as
one
care-
composites
transmitting
ends
can
However,
winding.
molding
injection
as
such
fibers
continuous
filament
as
methods
techniques
discontinuous
or
long
very
fabrication
oriented
are
(3,38).
containing
such
damaging
especially
be
are
fibers
different
can
which
concentration
elimina-
the
by
cases
some
in
filament
of
strength
longitudinal
the
doubled
fabrication
other
that
and
Paul
voids.
as
such
of
alignment
and
packing
of
perfection
the
affected
greatly
be
can
composites
(Gio)
17
equation
obey
orienta-
fiber
the
of
function
which
of
strengths
transverse
Composites
be
a
be
stress
of
points
as
the
5 illustrates
Figure
could
composites
wound
to
found
(37)
Thomson
strength
imperfections
by
and
fibers
the
as
factors
such
9 > 10°.
strength
tensile
The
by
as
composites
two
for
angle
tion
long
as
composites
of
kinds
different
of
a number
for
hold
to
found
was
equation
simple
This
(17)
Sind
~
R9
and
near
load
stress
another
from
468
8.
FIBER-FILLED
+)
140
COMPOSITES
BRITTLE
COMPOSITE
-©- DUCTILE
COMPOSITE
AND
OTHER
-—}- UNFILLED
BRITTLE
MATRIX
-©-UNFILLED
DUCTILE
MATRIX
COMPOSITES
120
100
80
60
(K.S.1.)
STRESS
FLEXURAL
ULTIMATE
40
20
O
10
20
30
FIBER
40
50
ORIENTATION
insley,
ANGLE
60
70
80
(DEGREES)
&
The flexural strength of an aligned glass fiber-epoxy
composite as a function of the angle between the fibers
and the applied stress.
[Reprinted from Ishai, Anderson,
and
Lavengood,
J.
Mater.,
5,
184
.]
(1970)
III.
STRENGTH
OF
appreciably
4.
In
with
cannot
general,
short
Many
made
FIBER-FILLED
on
contribute
is
impossible
fibers
as
with
studies,
both
the
Kelly
(42),
Rosen
Riley
(47),
Piggott
Dow
(50).
of
Sutton,
and
the
only
and
the
ends
from
the
ends.
ends
and
gradually
of
the
than
load
less
on
fiber
the
plateau
or
must
in
have
the
factors
of
the
length
fiber.
as
the
middle
the
The
at
interfacial
have
been
Outwater
(41),
Cottrell
and
Rosen
(46),
and
are
Lavengood
those
(22),
to
bond,
tensile
stresses
for
the
the
load.
In
Lo
of
shear
to
length
the
matrix
are
a maximum
two
of
length
the
reach
to
load
its
Criticalon
of
words,
other
the
phases,
of
the
a
maximum
upon
depends
strength
carry
ends
the
near
of
portion
central
the
the
at
zero
are
away
zero
to
portion
achieve
(3,
matrix
tensile
end
fiber
moduli
sum
The
the
Lo since
least
fibers
the
called
often
the
in
are
the
fibers
the
polymer
in
decrease
a plateau
section.
the
the
the
in
in
of
part
is
composites
stresses
gradually
loads
critical
relative
fiber
shearing
and
carrying
of
and
Longitudinal
required
length
a
(40),
investigations
stresses
increase
fiber
in
orientation
Theoretical
(45),
(49)
Anderson
phase.
value
ineffective
Allen
tensile
end
each
(44),
discontinuous
maximum
ineffective
are
the
Chen
fibers
Thus,
fibers.
Sutton
shearing
The
composites.
(39),
(1),
perfect
theoretical,
Dow
through
the
of
near
as
composite.
(51).
or
These
fiber
experimental
Flom
fibers
the
and
Tarnopol'skii
Ishai
fiber
39-50).
17,
the
continuous
to
applied
(48),
Rosen, and
short
of
the
fibers.
experimental
work
of
achieve
continuous
(17,43),
few
Lavengood
In
is
A
strengthening
to
discontinuous
include
469
to
it
oriented
studies
COMPOSITES
the
the
fibers
fiber
stress
such
strength
matrix,
and
470
8.
the
tensile
perfect
adhesion,
before
yield
strength
the
of
in
FIBER-FILLED
the
which
interfacial
COMPOSITES
fiber.
In
either
bond,
if
the
the
the
AND
OTHER
special
matrix
matrix
or
18,
D,
fiber,
strength
of
the
Matrix.
In
this
the
is
the
and
as
total
the
critical
length
interface
require
10,
The
shear
case,
if
L
Lor
by
>
is
the
tensile
strength
the
a modified
This
one
Tp, >,
fiber
the
ratios
of
of
tensile
the
strength
rule
of
mixtures,
o,,
>,
<
of
a
fiber
carry
or
of
(41).
Lo
increases
friction
correspond
even
can
never
continuous
fibers.
composites
containing
The
tensile
that
more
fibers
ends.
adhesion
mechanical
which
100
reasons
fiber
Poor
(19)
1000
aspect
much
to
the
Although
to
are
at
some
ratios
greater
achieve
L/D
and
maximum
strength.
must
fiber
L.
values
the
continuous
is
+
placeof adhesion
of
longitudinal
te
iL
1-
since
Lo lengths
portion
fiber
to
the
length
tensile
another
tinuous
is
experimental
aspect
longitudinal
=
the
take
predict
as
of
fiber
must
theories
is
op,
be:
The
low
diameter,
TR,
given
on,
due
plastic
(18)
fiber
special
composite,
should
as
break
behavior,
equation
of
of
fibers
a
Lig SD Nes 2 tee.
In
case
the
shows
COMPOSITES
be
why
as
theory
is
load
composites
than
the
composites
strong
of
discontinuous
strengths
adjacent
because
of
end
of
of
the
fiber
composites
(47)
fibers
greater
rest
the
containing
as
Riley
to
than
the
disconcontaining
predicts
can
6/7
never
of
that
have
those
detrimental
of
effects
(44).
TII.
STRENGTH
The
is
an
OF
strength
important
especially
strength
only
FIBER-FILLED
in
affected
case
o
is
BT
However,
gives
a somewhat
bonding
restrain
the
adhesion
theory
of
some
may
Cooper
have
and
the
where
O;
The
=
on,
is
clear.
filler
breaks
of
surfaces
may
no
of
the
as
a
result
expansion
of
work
and
because
the
the
temperature.
of
course,
is
no
the
the
reduced
with
The
(20)
bond.
interfacial
the
If
bond
matrix
there
separate
phases
even
though
to
a
coefficients
of
perfect
the
gradations
of
no
the
the
two
case
the
out
of
a block
exerted
on
the
of
composite
adhesion
the
in
fiber
force
squeezing
not
even
However,
pull
is
or
is
to
contact.
many
fibers
composite
required
filler
down
Between
be
of
required
cooling
and
strength.
interfacial
is
in
the
é
bond.
the
does
ifp
interfacial
mismatch
can
conditions,
bonding
predicts
the
in
matrix
than
adhesion,
stresses
adhesion,
be
bond
adhesive
biaxial
205 es
work
of
good
composite,
tensile
the
strength
perfect
and
is
of
6,
of
the
to
appear
matrix
(52)
a
phases
transverse
of
good
transverse
strength
there
matrix
the
higher
+
the
before
adhesion,
of
there,
If
to
ip
strength
of
cases
these
2|—
T
essentially
surfaces
tion
the
-
concept
always
adhesion,
1
The
strength
tensile
rise
Kelly
b,
fo}
Br
other
of
interfacial
composites,
transverse
under
the
the
two
longitudinal
fibers.
than
of
giving
break;
short
less
In
of
the
strength
The
strength
kinds
higher
matrix,
to
the
between
the
strength.
relatively
(52,53).
elongations
poor
in
bond
determining
generally
Oni
poor
in
by
of
471
interfacial
transverse
the
strength
the
factor
the
is
of
COMPOSITES
and
the
thermal
from
no
partial
fiber
the
fabrica-
adhesion
adhesion.
472
8.
Uniaxial
tudinal
FIBER-FILLED
fiber-filled
tensile
composites
strengths,
but
strength
is
generally
54-56).
The
smaller
the
and
lower
the
buckling
and
poor
the
adhesion
strength.
In
predicted
that
less
are
the
the
diameter
is
cases
of
of
the
have
buckling
the
fibers
high
longi-
of
the
the
fibers
greater
strength.
detrimental
to
fibers
strength
COMPOSITES
compressive
a
the
OTHER
very
compressive
where
compressive
can
AND
longitudinal
because
especially
certain
COMPOSITES
is
Voids
compressive
buckle,
should
be
it
has
given
by
been
(52):
G,
CBr
Transverse
of
the
matrix
strength
shown
an
in
tensile
large
and
is
greater
resin.
strength
diameter
so
$6,
3 for
72
The
of
than
in
Direction
of
which
has
Uniaxial
Tensile
Transverse
by
the
longitudinal
tensile
aligned
case
psi.
strength
compressive
compressive
strength
strength
glass
probably
Boron,
a Young's
modulus
as
fibers
has
which
is
in
a
forms
six
times
3
Glass
(psi)
Longitudinal
limited
this
10,000
Table
Strength
the
percent
resin
and
is
transverse
volume
less
(21)
transverse
the
pure
fibers
than
the
than
e
strength
less
However,
Table
epoxy
IT-
compressive
(3).
considerably
=
Fiber
Strength
Composites
Compressive
Strength
275,000
200,000
8,000
20,000
(psi)
(3,
III.
STRENGTH
that
glass,
of
Strengths!
up)
The
of
strength
inside
the
with
the
with
an
be
of
on
the
or
shear
increase
in
void
much
as
100
percent
or
more
with
an
different
epoxy
the
to
produce
content
space
kinds
are
of
of
is
is
compressive
a
shear
the
(57).
large
by
as
measure
a
shearing
a
increases
matrix,
and
it
nearly
all
the
strength
composites
force
longitudinal
strength
If
shear
another
measured
failure
of
normal
can
decreases
voids
be
containing
increased
0.5
(58).
strengths
summarized
Table
Strength
there
strength
over
void
matrix
so
generally
interlaminar
percent
of
is
strength
Interlaminar
tensile
eliminated,
The
tends
beam.
shear
It
beams,
which
high
unusually
with
interlaminar
short
473
(3).
psi,
composites.
beam
of
COMPOSITES
composites
tov3507.000)
test
splitting
can
makes
so-called
flexural
as
OF FIBER-FILLED
of
in
unidirectional
Table
4
(59).
composites
The
4
Unidirectional
Longitudinal
Tensile | Compression
Fibrous
Composites
Shear
Strength
Transverse
| Tensile | Compression
Boron
leZeeele
E-Glass
6.0
Carbon
4.0
(Thornel
25)
Carbon
(Modmor)
Strengths
11.0
are
in
thousands
of
psi.
oa
eS
et
—
474
8.
longitudinal
strength
fibers.
shear
with
The
fiber
B.
of
desirable
laminates
are
posites
fibers
can
be
are
properties
fiber
in
a plane
fibers
in
to
two
the
or
with
to
of
decrease
a plane;
in
have
the
axis.
fiber
all
be
of
greatest
sacrifice
a somewhat
smaller
commercial
processes
a
is
dif-
such
in
to
must
properties
achieve
be
generally
in
good
a sacrifice
uniaxially
decrease
com-
a plane.
desirable
there
direction
is,
directions
However,
directions,
have
constructed
that
directions,
By
multi-layered
layers
can
& Laminates
generally
by making
various
dimensions.
longitudinal
modulus
in
allthree
three
The
COMPOSITES
Composites
of
composites
properties
three
or
the
isotropic
in
Fiber
direction
in
directions,
in
composite.
tensile
fibers
aligned
achieved
compared
the
desirable
OTHER
concentration
tend
composites
in
essentially
have
fiber
only
the
orientation
which
If
in which
with
strengths
Oriented
oriented
orienting
AND
(59).
Randomly
properties
COMPOSITES
increase
transverse
concentration
Uniaxially
ferent
properties
and
Strength
randomly
FIBER-FILLED
oriented
in
the
tensile
strength.
Objects
with
and
to
30,
33,
(33)
in
5 and
Table
polystyrene
increased
not
as
the
oriented.
Bernardo
are
have
approach
29,
by
fibers
partially
made
27,
short
made
in
random
In
short
the
data
Table
great
as
or
glass
of
by
would
the
be
arranged
laboratory,
attempts
have
of
(29)
Young's
filled
randomly
dimensional
the
fibers
Lee
polymers
partially
three
Typical
6.
dramatically
the
two
60-63).
for
fibers
from
results
in
expected
are
short
glass
and
tensile
modulus
fibers.
composites
polyethylene
for
However,
for
been
the
similar
those
as
(23,
of
given
fibers
in
strength
increases
composites
are
III.
STRENGTH
OF
FIBER-FILLED
COMPOSITES
475
Table
Mechanical
Properties
Fiber-Filled
Property
Tensile
of
High
Randomly
Density
Weight
Strength
5
Oriented
Glass
Polyethylene
Percent
3700
6060
8840
10130
3000
6410
9750
12290
(psi)
Flexural
Strength
(psi)
Flexural
Modulus
125,000
352,000
584,000
795,000
(psi)
Heat
Distortion Temp.
aeoo psi, cE
160
240
264
266
90
60
48
41
Tensile
Impact
(ft-lb/sq in)
Drop
1S;
Ball Impact
(an=1p)
Izod
Impact,
(ft-lb/in
*Fibers:
Notched
of
1/4
inch
Second,
many
polymer
6.
and
for
of
them
during
be
the
are
although
the
The
noted
fibers
partly
the
broken
molding
are
during
not
the
were
the
Izod
impact
truly
or
randomly
biaxially
initially
processing
specimens.
data
the
considering
when
uniaxially
fibers
of
for
greater
are
improvements
except
polystyrene
First,
were
processing
fibers.
should
undoubtedly
but
oriented.
long,
and
5
Tables
oriented
points
Two
before
long
than
polyethylene
strength.
in
strands
infinitely
containing
for
233
notch)
The
1/4
of
inch
the
first
476
8.
FIBER-FILLED
Table
Mechanical
Properties
Glass
of
COMPOSITES
OTHER
COMPOSITES
6
Polystyrene
Fibers
AND
Randomly
Filled
with
Short
Oriented
Property
Flexur al Strength
(10
psi)
Flexural
(10-*°psi)
Modulus
10.9
Ixod Impact Strengt
(ft lb/in of notch)
*Fibers:
1/4
inch
LeStetemnperacune
factor
tends
reduces
the
It
of
to
laminates
difficult
by
is
to
such
Much
better
possible
the
layers
in
shown
that
the
same
which
in
have
are
while
the
stress
all
7
tensile
the
by
processes
of
second
use
Figure
factor
of
the
layers
in
any
by
the
60°
properties
laminates
testing
laminates
with
similar
parallel
direction
Typical
or
of
specimen
degree
injection
laminates
angle
is
and
laminates.
curves
the
as
Cross-ply
Cross-ply
6 if
kind
(cross-ply)
the
stress-strain
in half
of
90°
upon
the
properties
directions.
(65).
in
over
quasi-isotropic
dependent
Table
schematically
the
processing.
control
control
through
With
Matrices
strength
fabrication
are
illustrated
the
achieve
(quasi-isotropic).
properties
before
strength.
alternate
nearly
strands
—23cGe
increase
(64).
a plane
chopped
==
orientation
molding
in
is
PA AL
is
to
as
brittle
the
one
oriented
to
have
the
such
fibers
III.
STRENGTH
OF
FIBER-FILLED
COMPOSITES
Table
Moduli
70%
477
7
of
Cross-Ply
Laminates
Boron
Filaments
in
Fiber
Tension
Compression
Orientation
& Direction
of Stress
Modulus
Modulus
Polymer
Poisson's
Ratios
1 ply
——
2
——
plies
—_—_
2 plies
_
Moduli
in
in
these
where
layers
stress.
PSI
layers.
the
The
elongation
stress-strain
becomes
great
curves
enough
in which
the
fibers
are
oriented
Beyond
the
break,
essentially
often
to
show
form
cracks
perpendicular
all
the
a break
load
in
to
is
the
the
carried
by
478
8.
CROSS —PLY
FIBER-FILLED
COMPOSITES
AND
OTHER
COMPOSITES
LAMINATES
ine)
“S902 LAYERS CRACK
04psi
STRESS
Xx
ELONGATION (%)
Big.
Stress-strain
of
the
fibers
curve
are
of
16
a cross-ply
parallel
to
the
laminate
tensile
in which
stress.
half
IV.
OTHER
the
PROPERTIES
layers
In
rather
such
than
sheets
the
unwoven
are
found
used.
in
Other
fibers
laminates,
those
reviewed
IV.
in which
many
as
479
including
are
in
melamine
the
and
to
cord
used.
mechanical
books
parallel
tire
fibers
The
several
are
In
properties
fabrics
other
table
(6,
stress.
fabrics,
still
resin
articles
the
laminates,
tops,
of
paper
laminates
are
66-68).
Properties
A. Creep
Creep
is
Matrix
(69-71).
posite
compared
by
about
the
materials.
is
the
to
That
creep
moduli
measured,
can
be
an
as
unfilled
the
ratio
the
creep
polymer
of
the
of
fibers
of
the
creep
composite
of
the
at
the
unfilled
to
of
each
can
the
the
be
moduli
validity
Slight
measuring
modulus
the
reduced
of
the
€, (t)
if
if
has
22
composite
must
moduli
kind
and
between
used
for
ratio
been
fiber-filled
the
is
the
the
fiber-filled
Young's
those
and
polymer
of
upon
and
Thus,
equation
variations
and
t,
known
the
of
The
depend
orientation.
is
system
justified.
strongly
of
time
matrix.
filled
creep
particular
be
any
unfilled
for
for
a
a com-
should
two
to
(2)
polymer
composites
for
the
unfilled
filled
used
addition
approximation
the
its
fiber
of
However,
use
of
the
of
before
of
that
estimate
made.
established
first
by
(ft) B/E.
behavior
the
greatly
is,
mle
the
a
factor
corresponding
creep
of
As
same
E(t)
e(t)
reduced
be
composites
of
fiber-
exact
the
the
fully
degree
specimens
creep
480
experiments
can
instance.
was
less
than
that
predicted
equation
proposed
after
of
long
glass
test
Experiments
Be.
and
Matrix,
equation
22
(72).
equations
greater
22
also
cut
cases
the
that
transverse
creep
for
uniaxially
from
creep
equation
much
be
than
valid
cracks
develop)
should
22.
Silane
especially
improved
oriented
creep
not
if
rate,
of
is
or
the
creep
because
in
should
occurs
such
Other
reduction
expected
can
for
polymers
probably
creep
The
fatigue
behavior
not
clearly
understood.
is
or
associated
with
bonding,
life
Ductile
matrices
matrices.
Up
the
factor
80).
The
interface,
adhesion
greater
fiber
to
in
stiffness
to
the
and
(70).
than
composites.
generates
and
increases
decrease;
as
of
fibers
of
heat
which
high
loads.
still
more,
the
a
fatigue
catastrophic
200,
Heat
life
at
As
the
be
the
the
in
stress
life
com-
(76-78)
is
than
fatigue
the
polymer-
effects
high
increased.
brittle
life
can
be
increases
another
frequencies
especially
.
near
(79,
the
dissipated
easily
at
temperature
rises,
the
polymer
failure
cracks
of
is
damage
build-up
composite,
cannot
and
two
applied
about
(76).
fatigue
damping
the
longer
ratios
of
destruction
of
composites
fatigue
generation
the
give
decreasing
mechanical
the
combination
aspect
of
fiber-filled
However,
decreases
tend
frequencies
damping
a
greatly
length
major
by
of
with
dewetting
or
Fatigue
high
fibers
percent,
fiber-filled
in
rate
COMPOSITES
Fatigue
generally
with
the
of
OTHER
of
(dewetting)
creep;
AND
creep
times,
show
longitudinal
fiber
during
over
the
by
COMPOSITES
hundreds
Equation
fracture
increase
of
predict
(73-75).
composite
treatment
plex
22
which
interfacial
greatly
errors
experiments
does
the
in
some
been
in
FIBER-FILLED
In
have
after
result
8.
can
strength
follow
and
quickly.
IV.
OTHER
PROPERTIES
The
481
fatigue
of
cross-ply
single
ply
stress
fields
around
in
layers
in
which
perpendicular
to
the
appliec
where
two
adjacent
the
uniaxial
especially
Thus,
fatigue.
that
improbable
is
effect
heat
point
near
the
when
the
in
filled
glass
importance
curve
heat
of
in
Table
temperature
amorphous
distortion
fibers
transition
the
modulus
determining
in
increase
great
with
composites
of
take
ences
STeuaclOn
in
time
to
failed:
the
heat
5
heat
and
(33)
is
polymers
(70).
temperature
may
the
or
shape
distortion
temperature.
in
For
of
more
the
for
crystalline
the
approach
polymers
somewhat
(27).
7
Figure
increased
amorphous
while
in
fibers
distortion
generally
temperature
and
to
due
effects
striking
most
for
failure.
properties
it)
before
use
removed
be
detected
be
in
gradual
are
Temperature
illustrated
than
from
composite
distortion
crystalline
polymers
would
the
is
composites
The
failure
the
of
One
This
impending
Distortion
Heat
C.
In
damaged
the
remove
a
such
occurs.
useful
a
as
types
mechanical
failure
before
just
(81).
increases
can
several
elastic
the
catastrophic
of
dynamic
in
changes
the
of
object
for
found
has
touch.
changes
an
first
concentrated
are
considered
the
danger
is
there
(72)
Nielsen
most
properties,
to
If
the
develop
develop,
be
might
of
approximately
damping
mechanical
the
mechanical
appear
that
changes
to
Stresses
cracks
as
that
tend
oriented
fibers
monitoring
before
are
stress.
for
However,
place
fibers
tests
service
that
the
from
Lamination
Cracks
mechanical
dynamic
from
fibers.
dynamic
technique
the
the
and
decreases,
modulus
differs
composites.
observed
been
has
It
fiber
laminates
melting
soften
higher.
The
modulus-temperature
temperature
was
discussed
482
8.
FIBER-FILLED
COMPOSITES
AND
OTHER
COMPOSITES
Styrene- MAA
Copolymer (95/5)
Polystyrene
Vicat
softening
temperature
(°C)
0.0
Ol
Volume
0.2
0.3
fraction
asbestos
ber,
0.4
7
Vicat softening temperature of composites containing
randomly oriented asbestos fibers in either polystyrene
or a copolymer of styrene
(95%)
and methacrylic
acid
(5%).
[Reprinted
from
Noga
(1917/0) rea]
in
Chapter
distortion
real
rate
increase
Woodhams,
SPE
J.,
26,
#9,
23
5
6.
For
amorphous
temperature
increase
creep
and
since
due
in
the
temperature.
of
the
is
important,
to
system,
is
the
the
higher
the
rather
so
high
more
of
increase
softening
Above
materials
an
molecular
from
rather
temperature
the
increase
apparent
results
modulus
glass
than
the
or
transition
modulus,
weight
a
than
be
good
than
decrease
from
a
a
in
true
transition
temperature
and
heat
increase
glass
may
in
the
the
viscosity
factor
interfacial
that
IV.
OTHER
PROPERTIES
adhesion
tend
amorphous
to
crystalline
to
the
that
fibers
of
of
test.
impact
impact
material
the
of
dissipate
energy
dewetting
a
throughout
by
drastically
the
area
occur
at
rise
to
1.
to
temperature
mostly
is
regions
the
part
played
polymer.
the
to
due
tough
and
some
is
the
Correlations
and
of
another
to
have
throughout
a
by
mechanism
energy
in
complex
establish,
results
be
fails
least
two
the
a
high
for
as
large
a
concentrated
brittle
in
pull
out
manner,
At
8,
the
the
to
tends
mechanisms:
to
elongation
same
and
dewetting
stop
the
impact
1.
Fibers
generally
areas
of
thus
poor
of
propogation
the
Stress
=n
concentration
reduce
2.
the
in
energy
stress
and
and
stresses
of
of
break
dis-
time
to
curve.
ends,
the
matrix
dissipates
region
tend
for
Controlled
2.
the
also
of
localization
Figure
and
fiber
mechanisms
friction.
stress-strain
around
two
may
spreads
Fibers
the
very
If
(52,82).
(83).
under
more
the
absorbed
prevents
region,
reduce
even
difficult
be
be
is
the
to
Fibers
larger
least
to
must
at
illustrated
at
of
there
by mechanical
process,
crack
fibers
of
low.
fiber
the
strength
is
the
as
of
contradict
material
along
fibers,
the
the
fibers
the
be
possible.
the
area
of
as
of
one
temperature
distortion
composites
addition
may
energy
energy:
out
pulling
heat
because
material
stored
give
of
may
general
strength
Fibers
sipation
a
volume,
impact
in
reality
in
volume
small
in
addition
polymers
test
For
the
a
the
strength
to
spreading
in
on
interface
strength,
of
increase
softening
modulus.
unfilled
the
kind
apparent
Strength
correspond
type
The
impact
of
and
which
in
Impact
The
the
polymers
increase
Ds
one
raise
polymers.
of
than
483
may
reduce
concentrations
adhesion,
and
8.
484
A.
HIGH
FIBER-FILLED
STRENGTH,
COMPOSITES
AND
OTHER
COMPOSITES
LOW IMPACT
FIBER
FRACTURE
B.
STRENGTH,
LOW
HIGH IMPACT
DEBONDING
-Q-—>
7
PULL- OUT
—q-—
Schematic diagram of the behavior of fiber-filled
composites near the tip of a growing crack.
The fibers
can: A. Fracture;
B. Debond or pull out of the matrix.
regions
where
the
nature
can
cause
of
the
fibers
the
contact
composite
apparent
one
and
impact
another.
the
Thus,
type
strength
of
to
depending
impact
either
test,
upon
fibers
increase
or
decrease.
If
the
impact
impact
strengths
and
the
if
fiber
mechanical
of
the
are
fibers
length)
so
is
applied
obtained
are
that
friction
fibers
load
short
the
(about
maximum
during
(84-86).
if
can
pull-out
long
to
adhesion
equal
energy
the
Very
parallel
fibers
the
is
fibers,
relatively
to
the
be
dissipated
process
with
highest
poor
ineffective
and
good
by
by
debonding
adhesion
IV.
OTHER
PROPERTIES
decrease
the
485
impact
the
strength
because
of
reduced
plastic
applied
perpendicular
even
the
transverse
fibers
are
is
that
and
the
if
the
adhesion
is
required
transverse
impact
strength
pure
matrix
material
the
of
for
possible
mechanisms
is
the
than
lower
generally
load
composites
uniaxial
For
toughening
the
break
largely
However,
good
(88).
The
strength.
to
matrices
inoperative.
theoretically
y=
yo
(86).
For
Chawelin
2
20%
o
2 6
“oR
Se
by
or
debonding
estimated
be
can
pull-out
fiber
new
of
amount
a unit
forming
by
dissipated
either
by
surface
strength
than
tough
(87).
fibers,
strength
lower
for
elongation
matrix
the
direction
energy
The
to
impact
this
in
the
impact
generally
is
least
reduced
of
impact
longitudinal
since
flow
moderate
for
also
greatly
at
pull-out:
by)
(23)
CL < Lg).
(24)
(b>
Cc
(25)
In
these
energy
is
the
dissipated
tensile
in
the
Lo
is
defined
by
equation
If
the
forming
strength
fibers,
fibers.
is
y
equations,
of
critical
pull-out
18
is
and
the
a
the
unit
L
fibers,
"ineffective"
Ly is
major
the
of
amount
new
the
is
length
debonded
mechanism
that
is,
surface,
Op,
energy,
surface
fracture
of
of
length
of
length
energy
the
fibers
the
of
the
as
the
dissipation,
486
8.
the
impact
fibers
strength
is
equal
a composite
Thus,
the
the
breaking
impact
oriented
glass
in
5
Table
are
notched
Izod
tensile
impact
to
drop
are
of
a
and
ball
drop
on
the
strength
is
sensitive
fibers
different
must
be
all
are
careful
of
the
to
tests
to
use
practical
the
tests
and
have
fibers.
However,
it
of
polymers
such
tough
often
the
impact
improvement
brittle
is
as
to
about
2.9
percent
glass
fibers
its
foot
of
ease
of
out
of
in
on
lbs.
per
On
of
instance,
Izod
inch
the
other
propogation
5,
random
notch
hand,
is
at
an
the
bonding,
35
of
more
greatest
with
fibers
strength
the
strength
fibers;
The
One
with
impact
fibers
impact
of
impact
addition
the
decrease.
For
Izod
changing
adding
use
elongation
properties.
the
may
the
tensile
interfacial
by
by
The
the
Chapter
By
the
the
content,
correlates
improve
actually
poly-
only
crack
interest.
to
Bernardo
notched
polyethylene
notched
(91).
the
improvement
strength
the
randomly
decreased
which
strength
(29,87,90).
increase
the
different
test
difficult
increase
reduce
of
fiber
pointed
measure
shown
strength
impact
matrices
polystyrene
0.25
in
the
to
decreased.
while
as
impact
which
tables
with
decreased
application
fibers
might
an
(89).
fiber-filled
both
fibers
really
cracks
data
these
reflect
Thus,
adhesion
tend
the
In
impact
the
the
poor
containing
glass
increased
of
present.
impact
particular
length
addition
and
which
by
(29).
ball
of
of
composite.
for
strengths
break
when
6
strength
impact
ones
COMPOSITES
length
debonding,
polyethylene
data
Table
result
and
OTHER
the
notches
illustrated
Similar
impact
same
of
is
in
to
AND
when
a
fiber-filled
fibers
shown
as
pull-out
the
strength
(33).
styrene
as
COMPOSITES
a maximum
sensitive
such
strength
be
Debonding
less
strength
The
and
L c°
factors,
impact
should
to
makes
FIBER-FILLED
from
weight
unfilled
very
in
about
IV.
OTHER
PROPERTIES
polycarbonate
approaching
glass
is
16
fibers
ductile
ductile
ft
and
lbs/in
an
Izod
of
20
percent.
brittle
wires
or
a very
strength
The
can
high
impact
Polycarbonate
impact
ones,
metal
has
notch.
has
concentration
especially
487
be
screens
of
impact
instead
filled
about
greatly
of
with
3 at
strength
improved
strength
of
by
brittle
a
fiber
polymers,
using
glass
fibers
(92,
9:3)7s
E.
Coefficients
Uniaxially
unusual
cases
which
In
of
have
the
much
the
and
can
reason
small
at
be
for
expansion
matrix
is
of
than
the
that
value
the
forced
is
matrix
to
thermal
of
of
of
expand
to
by
the
more
the
of
is
the
small
fibers,
matrix.
On is
coefficient
polymer.
The
fibers
prevent
rigid
longitudinal
than
in
In
expansion
the
unfilled
the
(or
Oy
a polymer
fibers,
the
two
expansion
coefficient
because
in
have
expansion.
imposed
compared
concentrations
high
of
restraints
direction,
greater
composites
coefficient
coefficient
low
the
fiber
the
mechanical
transverse
larger,
even
a
Expansion
coefficients
direction,
the
Thermal
oriented
three)
longitudinal
because
of
normal
direction,
so
in
the
transverse
and
has
derived
expressions
for
the
‘direction.
Schapery
relatively
(94)
has
reviewed
simple,
yet
quite
of
coefficients
thermal
expansion
ya
L
This
equation
literature
accurate,
The
expansion.
the
longitudinal
coefficient
of
is:
a,E,>,
iam
E,?,
assumes
+ a,E,¢
. 22.
+
(26)
AE
that
Poisson's
ratios
of
the
components
488
8.
are
not
too
far
apart.
FIBER-FILLED
The
COMPOSITES
transverse
AND
OTHER
coefficient
COMPOSITES
of
expansion
Shs
Ce
where
7
closely
gO
is
Orre yan oemOe,
the
by
longitudinal
equation
composite
as
26,
closely
volume
equation
fractions
27
is
of
coefficients
of
fibers
as
in
Figure
9 for
v is
+
of
=
(1
+
predicted
by
which
is
given
ratio
of
5
than
Vi)a,¢,
+
a
SB
about
function
equations
0.2
the
or
ia :
26,
27
0.3,
(29)
of
and
volume
fraction
29
plotted
are
case:
Matrix
Fiber
a, = 6x10 °/°C
a, = 0.5 x 10 /°C
Beeb
Ey =
010 bec
Vy,
0.20
Vv,
=
ex Oe:
values
Figure
the
psi
0.35
These
9
it
elastic
fiber
are
is
thermally
lamallae
moduli,
induced
in
typical
obvious
composites.
very
(28)
by
following
(27)
by
closely
as
5)
Poisson's
greater
expansion
the
the
Vedi
fibers
approximated
On
The
vio,
erates
coefficient,
approximated
yp =
At
and
Pere
Ne
that
are
As
for
a
or
the
very
fibers
in
coefficients
anisotropic
result
stresses
cross-ply
glass
=
of
this
in
pat
|
|
polymers.
of
From
expansion,
nature
anisotropy,
may
occur
in
the
other
types
of
laminates.
matrix
for
like
aligned
large
between
IV.
OTHER
PROPERTIES
489
EXPANSION
OF
COEFFICIENT
ol:
Oe
O
Ot
0
Oe
0
O
O.
U
VOLUME FRACTION OF FIBERS
iter,
©
Thermal coefficients of expansion for a uniaxial
composite.
Curve A corresponds
to equation 26.
corresponds
equation
fibers
to
29.
equation
27.
Coefficient
Curve
of
is 0.5 x 107°/°C while
107*/°c.
The corresponding
and 5 x 10° psi.
The
which
should
the
coefficient
fibers
are
of
randomly
expansion
of
that of the matrix
moduli
expansion
oriented
in
for
are
a
three
10
B
is 6 x
x
10°
in
composite
dimensions
be
Om
uae
20
SoD in
The
corresponds
volume
Young's
thermal
C
fiber
Curve
to
the
values
of
a.
L
and
3
a,,
HE
T
can
(30)
be
estimated
from
equations
26
and
27.
490
8.
V.
Ribbon-Filled
The
same
to
make
to
fabricate
can
width
much
composites
cross
strength
and
in
more
decreased
or
Ribbon
to
a
get
of
ribbon
moduli
around
have
the
the
of
Matrices
composites.
stringent
These
the
and
did
not
requirements
nearly
fulfill
all
be
all
the
discussed
for
in
a
the
are
fiber-filled
resistant
is
their
to
through
greatly
polymers
a
ribbon
tortuous
(95).
great
potential
been
verified
only
composites
the
past
requirements
requirements
than
very
However,
ribbon
for
with
to
are
long
have
times.
of
a
the
predictions
composites
will
shown
because
property
ribbon
have
many
get
ribbons
is
high
compared
follow
a
composites
advantage
to
ribbon
ribbon
have
be
liquids
must
of
than
to
order
impermeable
strengths
values
Matrix
for
molecule
can
sheet
used
has
fibers
such
tend
and
A
perpendicular
third
In
these
a
also
gases
materials
experimental
which
to
of
A
calculations
such
theoretical
plane
be
elliptical,
containing
Thus,
used
section
advantages
composites
sheet.
the
be
are
can
which
cross
can
direction
composites.
composites,
the
the
the
The
it
composites
objects.
diffusing
Theoretical
COMPOSITES
that
ribbons.
section
possible
composites
mies
kinds
composite,
path
of
in
but
Ribbon
in
permeability
other
OTHER
winding
aligned
a cross
shape,
over
plane
by
AND
composites
thickness.
several
isotropic
puncture
its
section.
the
filament
fiber-filled
with
in
rigidity
composites.
to
than
are
as
containing
fiber
composites
circular
much
a
There
tape)
ribbons
as
rectangular
instance.
such
oriented
greater
generally
(or
techniques
defined
COMPOSITES
Composites
uniaxially
be
FIBER-FILLED
are
fiber
later
much
of
for
recently
approached
work
used
for
such
|
more
composites.
paragraphs.
|
V.
RIBBON-FILLED
A
schematic
Figure
is
COMPOSITES
10.
given
The
drawing
volume
this
D
is
ribbons,
W
the
and
t are
thickness
and
Bo is
the
two
total
with
below.
In
the
symmetrical
is
the
amount
B
Ribbon
in
Figure
ratio
ribbon
fraction
ribbon
where
a
of
composite
ribbons
is
in
shown
such
a
in
composite
1
(le Dt) (useB
equation
ribbons,
of
of
by:
03
In
491
W/t),
ribbons
of
composites
11
of
the
in
of
either
overlap
six
and
shown
of
of
the
between
edges
of
the
next
layer
in
Figure
10,
a
layers
given
above
Br =
or
2B
ribbons.
elastic
of
layer
both
very
the
case
moduli
are
approximately
RIBBON
thickness
polymer
overlap
case
have
width
In
(96).
the
the
moduli
wide
as
illustrated
ribbons
given
by
(large
simple
COMPOSITES
LLLL/
_
a
ee
oS
ee
oT
IPikefe
JbO)
Schematic diagram of a ribbon-filled composite.
shows primarily the ends of the ribbons.
The
view
aspect
492
8.
FIBER-FILLED
RIBBON
COMPOSITES
AND
OTHER
COMPOSITES
COMPOSITES
——8
|
PLAN
|
NS
Sit
Gut’
iMalere
Schematic diagram
ribbon composite.
equations.
and
Ens
The
showing
longitudinal
the
and
Grr
IMAL
six
elastic
transverse
moduli
Young's
of
a
moduli,
EL,
are
ee
ee
eeOt
Eo
The
longitudinal-transverse
the
rule
of
G
S
shear
(82)
modulus
Gin
also
is
given
mixtures:
=
Gio,
te G,o,
<
(33)
by
V.
RIBBON-FILLED
The
other
COMPOSITES
three
493
moduli
i
are
ees m4
in
have
only
three
large
If
transverse
high
aspect
are
ite
mixtures.
In
predicted
to
Young's
Gy
rule
of
(35)
G,
unidirectional
fiber-filled
modulus,
ribbon-filled
ratio
the
materials
materials
can
by
modulus
less
this
the
of
En and
than
what
case,
ribbons
the
the
is
not
very
M,
of
by
aspect
case
aspect
approach
moduli
ratio
the
rule
of
can
be
ratio
equations
(36)
Geil
of
high
of
A =
about
achieve
been
transverse
(27)
2W/t,
and
for
10
100
is
The
greater
to
modulus.
ribbons
ribbon
has
E,,
maximum
the
to
be
It
ratio
the
of
moduli
M=
the
=e)
i
An
have
shear
BNA Mae.
the
which
large,
longitudinal
predicted
effect
Halpin-Tsai
is
ML cape
ee
For
mixtures:
moduli.
the
modulus
inverse
ee
contrast
one
the
a
ee
Coup
GF
Gpipt
Thus,
by
%,
oe ee
1
given
and
a
matrix
high
composites
assumed
tensile
the
that
and
the
greater
listed
ribbon
strength,
generally
The
modulus.
are
M= Gia,
in
A =
needed
values
of
Table
2.
computer
the
A
(14,97).
to
difference
must
composites
(w/t) ¥3
in
the
aspect
for
should
the
all
have
calculations
a
494
8.
verify
this
generally
is
given
weak,
tion
assumption
the
be
low
The
achieve
high
strength
between
the
ductile
with
the
fabrication
of
left
polymer
the
to
ribbons
This
critical
value.
a
the
or
yield
matrix
rather
than
C-273)
is
ore of
the
In
ribbons,
the
is
of
simple
aspect
sure
that
5.
The
to
For
should
composite
shear,
than
practical
the
test
to
any
be
to
of
the
the
arrangement
are
above
voids
the
greater
the
some
in
overlap
if
or
tensile
than
its
fracture
by
transverse
failure
of
the
shear
multiaxial
lap
than
strength,
should
a complex
but
of
few
highest
matrix
to
be
from
overlap
regular
from
enough
transmitted
a
be
minimize
be
required
areas
must
rather
is
adhesion
stresses
must
greater
maintain
all
there
the
ratio
to
must
to
adequate
stress
required
fulfilled
stresses
be
perfection
order
ribbons
polymer
the
in
subjected
a good
order
an
adhesion.
6.
possible
the
matrix
there
must
have
thermal
the
concentra-
experimental
order
to
fully
There
the
Also,
strength.
of
3.
A high
be
strength
breaking
The
to
value.
poor
shear
4.
due
have
bonding
excellent
The
in
addition,
transmit
requires
ribbons
Of
In
to
all
process
critical
areas
over
get
ribbons.
of
process.
ribbons.
to
fabrication
concentration
be
2.
elongation
the
be
must
COMPOSITES
tests
ribbon
not
must
There
OTHER
interfacial
with
does
ribbons.
ultimate
stress
elongation
matrix
1.
the
the
adhesion,
conditions
(98):
and
a high
effect
the
following
polymer
the
the
If
good
AND
experimental
rapidly
with
because
properties.
(97).
decreases
even
COMPOSITES
However,
strengths
However,
may
(96).
strength
(96).
values
low
FIBER-FILLED
shear
evaluate
state
test
the
of
(ASTM
shear
matrix.
stress
D-1002
or
strength
(99).
that
the
composites
ratio
B/t
must
exceed
fail
the
by
transverse
value
given
fracture
in
the
of
V.
RIBBON-FILLED
following
equation
10)
Jee
In
this
Ons
is
the
of
le
y
lay-up
repeat
the
minimum
thickness
minimum
the
rule
tensile
This
carry
of
and
x
stress
lay-up
in
10
in
isotropic
the
Vie
D)
x/y
mixturesas
strengths
over
process
strength
forty
the
tedy)
been
times
ribbons
contrasts
is
approaches
have
composites
with
equal
the
=
The
than
maximum
half
transverse
tensile
longitudinal
the
lay-
however,
enough,
which
strengths
ribbon
is
composites
ribbons.
The
is
composite
Ay
Be
Spi
Equation
1.0.
By
made
that
are
x/y
1/2.
less
to
entire
c
matrix
the
the
number
ratio
in
a ribbon
of
t
fx
2
of
of
plane
strength
tensile
The
that
so
strength
longitudinal
by
thickness
transverse
give
to
devised
be
minimum
the
great
is
W/t
ratio
aspect
the
is
be
maximum
the
half
one
for
10,x/y
Figure
is
required
Figure
must
In
ribbon
load
layers
ribbons,
lap
carrying
adjacent
the
a
pattern.
B of
ribbons.
of
measured
a
in
strength
fracture
as
section;
polymer,
high
repeated,
t aF Yop,D
of
matrix
given
the
can
Xo,
tensile
the
a
transverse
The
be
strength
layers
ribbons
vce
matrix
to
of
of
If
B
the
number
actually
nearly
Ba
of
fraction
the
maximum
tensile
the
patterns
be
the
strength
approach
the
of
of
strength.
can
is
overlap
tensile
is
thickness
of
width
on,
strength
that
the
up
(38)
pattern
ribbons
the
B2
shear
test,
495
(98):
relation,
the
shear
COMPOSITES
of
split
using
which
have
the
matrix,
becomes
39
the
transverse
and
longitudinally
unidirectional
proper
in
(98).
fiber-filled
496
8.
composites
in
which
considerably
polymers
VI.
than
that
may
have
higher
A.
Types
of
istics
of
aluminum
more
have
Materials
The
filled
or
the
tortuous
for
path
strong
resistance
filled
polymers
orientation
and
by
of
rule
theoretically
mixtures.
the
It
is
difficult
regions
that
of
is
a
other
achieve
required
insufficient
long
also
have
objects
The
to
been
the
(108,
high
overlap
to
to
of
predicted
preeduce
ratio
(length
109).
of
flake
Strength.
of
other
tensile
plane
made
Flakemost
values
aspect
go
(101).
compared
perfection
for
the
composites
of
factors
the
of
(95,100).
to
approach
function
extremely
take
parallel
have
materials
liquids
102-107).
may
flakes
must
moduli
(100,
and
the
have
because
sharp
high
modulus
as
and
to
by
Attempts
moduli
thickness)
overlap
Flake
include
materials.
and
molecules
direction
shear
by
and
flakes.
fillers
such
flakes
is
character-
flakes,
oriented
permeability
permeating
flake
so
gases
any
the
plane,
of
composites
divided
flakes
generally
and
the
techniques,
permeation
unusually
in
a
biaxially
puncturing
have
particulate-filled
fabrication
in
of
aluminum
the
the
to
Typical
of
impermeable
measured
of
low
that
the
and
is
cross-ply
many
orientation
the
this
around
tion
COMPOSITES
Ribbon-filled
than
have
flakes,
oriented
planar
to
flakes
glass
behavior
with
reason
the
strengths
with
By most
less
resistance
modulus
strength
matrix.
composites.
graphite,
diboride.
be
high
the
OTHER
Polymers
ribbon-filled
kaolin,
often
tensile
AND
Composites
Flake-Filled
Polymers
will
of
COMPOSITES
laminates.
Other
mica,
transverse
less
also
Similar
the
FIBER-FILLED
adjacent
orienta-
Misaligned
flakes
VI.
OTHER
create
the
TYPES
defects
matrix
ribbon
flake
COMPOSITES
greatly
reduce
must
fulfill
the
also
Entrapped
composites.
to
stress
An
create
adhesion
a
between
sheet
the
sensitivity
probably
fections
mechanical
materials
Part
this
of
mica
or
material
is
B.
two
other
tion
least
from
seal"
as
at
the
at
the
of
cracks
Most
flake
the
of
such
the
these
large
two
brittle
with
be
low
notch
number
the
strong
may
The
in
quite
of
imper-
materials.
and
plastics
For
this
contain
sliding
are
good
destroys
a very
materials
(106).
from
result
as
composites
cracks
into
or
often
have
reason,
flake
from
over
Thick
one
high
vibration
fillers
layer
another
(111-113).
of
layer
a
flake,
when
such
the
can
Interlayers
composites
there
moduli
coefficients
and
interface.
in
which
used
gradually
other
tend
for
at
in
to
may
the
from
An
the
of
the
strength
and
in
the
forma-
There
are
at
resulting
problems
of
"graded
A
1.
properties
those
proper-
introduces
result
the
the
expansion,
reduce
interface:
2.
of
mismatch
solving
the
change
of
dewetting.
which
component.
a mismatch
This
or
debonding
approaches
be
is
stresses
the
introduced
layer
the
with
because
stresses
approach
those
and
may
the
possible
two
between
acts
interface
properties
interfacial
to
most
components
stresses
squeezed
which
generally
Composites
such
be
serious
for
deformed.
In
ties,
problem
a
and
(110-113).
graphite,
be
flakes
elastomers
damping
may
strength,
as
effectively
results
damping
damping
bubble
high
requirements
which
built
Flake-filled
can
For
air
notches
already
same
air
However,
to
strength.
of
strength.
insensitive
as
air
concentrator.
impact
497
which
composites.
flakes
low
OF
of
one
interlayer
of
a
thick
component
a
softer,
498
8.
ductile
material
phases.
This
stresses
by
adhesive
bond
layers
are
filler
with
a
as
to
be
ductile
to
matrix
thicker
silanes,
attempts
form
an
properties
strength
of
aligned
an
which
are
then
tensile
increased
fifty
Spheres
20
in
an
percent
layer
over
adhesion
to
increase
fatigue
that
of
a
both
strength
may
be
during
the
1.
filler
2.
may
In
the
thermal
thermal
coefficients
without
it
can
breaking.
and
relieve
Thus,
the
an
ten
the
to
on
glass
the
about
inter-
have
good
interlayer
may
times
The
(117).
several
possible
the
surface
of
type
reduced
by
measured
of
the
concentrations
tends
the
fiber
strength
composites,
a better
If
over
impact
by
seal"
interlayer
be
strength
interlayer.
the
3.
could
a hundred
interlayer
increases
stress
An
fibers
the
interlayer
interlayer
protects
expansion.
(114) 2
without
in
tensile
glass
composite
matrix.
of
surfaces
doubled
to
tensile
properties
are
the
same
the
the
by
"graded
of
inter-
improvements
nearly
resin
the
without
also
thus
stresses
the
filler
applied
composite
factor
improve
and
or
transverse
elastomeric
that
interlayer
induced
ductile,
a
the
be
is
the
same
the
fabrication
fiber.
the
essential
The
of
increases
improved
the
These
Dramatic
epoxy
resin
by
matrix
treating
coat
may
resin
another
composite
Interlayers
mechanisms:
epoxy
An
life
by
The
composites
in
of
to
resulted.
is
similar
made
percent.
that
It
formed
of
itself
phases.
COMPOSITES
and
some
either
(114-117).
strength
epoxy
(115).
an
imbedded
longitudinal
by
been
have
of
OTHER
instance.
fiber
interlayer
AND
filler
relieve
filler
those
interlayer
of
when
and
have
number
can
the
breaking
than
for
COMPOSITES
between
without
the
much
placed
interlayer
deforming
Several
so
can
FIBER-FILLED
match
of
the
of
interlayer
by
deforming
to
prevent
the
is
very
|
VI.
OTHER
TYPES
OF
COMPOSITES
dewetting
and
4.
concentration
Stress
filler
crack
particle
factors
are
studies
related
and
formation
from
very
by Matonis
is
around
reduced
touching
high
to
499
at
the
by
of
interlayers
one.
been
one
Stress
contact
have
particles.
preventing
another
points
filler
or
concentration
(38).
made
fiber
Theoretical
by Alfrey
(118)
(119).
Cc. Interpenetrating
Network Composites
Few
good
network
composites
of
is
data
the
Examples
of
foams
one
mats
of
which
which
3.
are
have
Van
and
material
have
been
Many
meter.
networks
made
by
by
phases
are
the
or
for
the
lack
composites.
are:
1.
Open-celled
material.
2.
cross-over
points
other
matrix
concentration
filled
foam
has
been
Wire
and
material.
range
in
which
the
filled
points
of
the
wires.
kinetic
between
of
simultaneously
crosslinks
as
mechanically
the
rubber
with
mixture.
continuous.
was
This
is
the
determining
the
spacing
somewhat
in
elasticity
is
studied
(121)
parameter
mats
rubber
(122-128).
crosslinked
polymerizing
of
polymer-polymer
prepared
techniques
a
theory
by White
Williams
important
An
mats.
described
and
Moreen,
of
been
swelling
in
Parikh,
examples
such
subsequently
a
weight
have
a polymer
at
properties
the
molecular
with
such
another
together
interlocking
reason
composites
with
sintered
fiber
metal
to
analogous
the
of
cross-over
between
fabricating
network
blends
(120).
mechanical
in
One
or
occurs.
example
Vlack
interpenetrating
studied.
filled
impregnated
impregnated
the
been
interlocking
inversion
An
of
difficulty
Polymer-polymer
phase
or
examples
which
para-
important
interpenetrating
These
mixing
materials
two
of
a monomer
In
these
can
be
polymers
and
mixtures,
both
500
8.
Apparently
mechanical
no
that
the
with
mixtures
M
unusually
estimated
axially
isotropic,
the
accuracy
to
network
the
composites
structure
the
COMPOSITES
explain
moduli
by
be
either
Young's
All
+
1, log
are
and
is
random
probably
logarithmic
M,
6
modulus
of
so
can
be
rule
of
(40)
or
the
the
must
decreases.
shear
as
the
by
The
modulus.
simple
of
primarily
such
the
shear
and
strength
for
composites
fibers
can
also
be
longitudinal
the
the
can
estimated
tensile
properties
transverse
uni-
of
the
tensile
strength,
are
determined
strength
are
affected
impact
by
the
the
other
of
strength
Matrix.
lengthened
the
be
largely
Maleate
and
and
as
by
can
laminated
generally
as
more
equations
moduli
such
anisotropy
or
moduli
however,
properties,
by
one
strength,
fibers
On
in
oriented
of
be
stiffness
randomly
properties,
fibers
characterized
containing
strength
the
fibers
increase
composites.
properties
be
6 independent
accurately
interlaminar
menetie
and
5 or
determined
strength
between
the
Some
Other
length
of
The
crudely.
may
strength
composites
estimated.
the
composites
high
fibers.
bond
network
M
reasonably
Strength,
the
are
the
os log
can
oriented
of
only
by
made
OTHER
Summary
directions.
be
if
M =
Fiber-filled
and
been
AND
(32):
modulus
and
have
COMPOSITES
interpenetrating
reasonable
leg
Vales
of
However,
composites
estimated
The
attempts
properties
theoretically.
FIBER-FILLED
as
To
the
hand,
the
bond
of
the
achieve
strength
impact
adhesive
high
of
the
and
the
bond
strength,
strengths
decreases
by
adhesive
tend
as
the
to
fiber
VIII.
PROBLEMS
length
501
decreases
to
a
Ribbon-filled
advantage
over
isotropy
in
require
limiting
value.
and
flake-filled
composites
can
aligned
fiber-filled
composites
because
a plane.
matrices
However,
that
must
ribbon
have
order
to
achieve
the
optimum
these
composites
are
difficult
imperfections
properties
which
are
comparable
generally
can
be
fibers
oriented
fibers
in
to
near
in
addition,
without
introducing
strength.
and
great
composites
In
to
ribbon
of
properties
fabricate
of
a
flake
Many
composites
fibers
by
laminating
directions
or
by
layers
randomly
of
orienting
a plane.
Interpenetrating
field.
special
detrimental
with
several
flake
strengths.
to
those
obtained
in
very
high
very
and
have
These
network
materials
may
composites
have
some
represent
very
an
useful
unexplored
mechanical
properties.
VIII.
1.
Problems
Compare
a
polymer
Gop
of
G,/G,
the
2.
the
the
same
with
0.64
as
glass
polymer
bn =
=O
a
function
spheres
filled
for
of
with
with
for
the
shear
modulus
oriented
glass
fibers.
(2
on =
and
spheres,
the
composition
ieKe
fibers.
of
function
cases
the
Long
glass
composite
a
oriented
glass
fibers
aspect
ratio
of
the
of
=
0.3
andinoys=
fibers
are
randomly
of
in
function
$,
which
of
E,/E,
=
in
the
0.6.
in
Estimate
of
the
=
composite
matrix
Calculate
fibers.
E,/E,
a
epoxy
an
oriented
120.
concentration
of
modulus
Young's
longitudinal
the
Estimate
as
modulus
filled
consisting
3.
shear
25.
Assume
a plane
Young's
fibers.
as
a
for
on =,
ina
modulus
Al
502
8.
A
composite
consists
How
much
the
transverse
of
greater
0.62)
E/E.
Everything
What
is
is
the
aligned
of
Ofel2
7 000m
These
How
as
is
a
of
E/E,
A
a
psi.
volume
Assume
has
and
transverse
a
fibers
ihe
bn =
0.82.
of
winding?
fibers
matrix
of
strength
filament
than
fraction
tensile
The
matrix.
modulus
4 except
percent
COMPOSITES
rubber
dynes/cm?.
by
volume
a
Young's
problem
made
in
OTHER
an
The
with
a
tensile
tensile
strength
75
weight
is
=22.5
x
typical
the
of
and
the
cubic
packing
have
in
aligned
and
fibers
in
a
the
the
=
107
modulus
aligned
contains
Two
creep
to
to
the
rods.
If
the
rods
approximate
E,p/E,
packing
case?
Assume
the
a
filler
tests
rods.
How
have
ratio
(b)
does
an
are
in
the
made:
The
form
(a)
load
is
of
short
oriented
The
load
applied
the
creep
differ
in
aspect
ratio
L/d
10,
of
the
creep
in
the
of
two
the
is
applied
perpendicular
two
what
cases?
is
directions
the
at
time?
A weak,
psi.
fiber
hexagonal
other
fibers.
of
Bo
of
polystyrene.
Young's
for
moduli
density
dynes/cm?,
differ
fibers
of
the
transverse
composition
which
and
glass
relative
of
percent
1.0,
10'°
Young's
100.
=
parallel
10.
are
in
polymer
any
10’
in
matrix
E,
does
case
rods.
at
longitudinal
65
the
2.5.
function
one
as
containing
composites
in
same
longitudinal
values
much
E, =
10".
composite
the
density
Fibers
=
250,000
composite
The
modulus
AND
psiv.
Estimate
a
fibers
longitudinal
Young's
expected
COMPOSITES
aligned
the
contains
strength
of
is
the
fiber
composite
FIBER-FILLED
brittle
expansion
is
put
fiber
in
a
of
low
coefficient
thermoset
resin
of
which
thermal
is
cured
at
IX.
REFERENCES
503
200°C.
At
stresses
the
re
tend
fibers
Sketch
which
the
of
a
in
at
rubber
oriented
as
a
composite.
for
N/m?
4.
in
both
In
going
to
a
in
a plane,
the
IX.
load,
i.e.,
50
5 x
volume
or
will
10°
45°
of
Young's
rubber
psi.
to
long
and
this
the
fiber
the
with
Young's
when
oriented
is
composite
glass
direction?
Plot
as
and
for
fibers
a randomly
moduli
composition
10'°
aligned
structure.
Young's
2/73.
a matrix
are
a
the
the
the
function
Young's
second
of
the
components
N/m*
for
the
are
composites.
from
in
which
relative
the
relative
uniaxially
an
composite
H.
1203
Vo®
component
other
tensile
the
fibers
strength.
are
often
modulus
composite
fiber-filled
oriented
randomly
oriented
more
decreases
Why?
References
W.
in
section
=
composite
composite
moduli
x/y
in
uniaxially
network
cross
of
psi
What
of
first
of
10’
composite
the
percent
of
modulus
the
ribbon-filled
tensile
transverse
function
the
thermal
tension,
in
Another
for
The
under
point
interpenetrating
and
induced
any
of
matrix.
composition
modulus
of
angle
a
modulus
consists
longitudinal
of
at
of
shear
an
for
ribbons
the
the
fibers
pattern
transverse
composite
a
the
a Young's
and
will
buckle?
modulus
measured
One
to
consists
with
a Young's
WB
break
the
composite
modulus
to
lay-up
carry
fibers
temperature
tend
2/3
must
A
room
Sutton,
(1964).
B.
W.
Rosen,
and
D.
G.
Flom,
SPE
J.
ZO,
than
504
8.
Dye
ReeuiseMehany
1889
eye
L.
Wei
FIBER-FILLED
motto
sci
COMPOSITES
Glen
eae
AND
Herzog,
OTHER
AIAA
COMPOSITES
J.,
4,
(1966).
J.
Broutman
and
Addison-Wesley,
4.
P.
Morgan,
Dis
S.
S.
Plastics,
D.
J.
Duffin,
airs
S.
W.
Tsai,
Rept.
NASA
Sie
Z.
Hashin
Or
Z.
Hashin,
10.
J.
J.
and
J.
Mass.,
1967.
Composite
Plastics,
Iliffe,
Mohr,
Handbook
New
York,
1964.
Plastics,
Structural
Behavior
of
London,
1961.
Reinforced
Reinhold,
of
Materials,
New
Composite
York,
1966.
Materials,
(1964).
CR-71
B.
W.
AIAA
Rosen,
J.,
Hermans,
Modern
G.
Laminated
and
Krock,
Reinforced
Reinhold,
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Appendix
Chemical
Structure
of
I
Common
Polymers
; H
‘
Polyethylene
Aiea
H
H
ee
H
Polystyrene
ara t
"©
: H
Polyvinyl
chloride
ar
(e:
ial
Polymethyl
methacrylate
3
Aes
H C-O-CH,
il
O
io
Polypropylene
Sane
H
Polybutadiene
(1;4
CH,
addition)
ia
eee
H
H
Polyoxymethylene
\
Ae
H
Syl
r
512
APPENDIX
Polyvinyl
methyl
ether
i
none
H
|
O-CH,
i
Polydimethyl
siloxane
ae egos
CH,
Ove
ia
Polyvinylidene
=C3e=
fluoride
fae
HF
CH
abe
Polycarbonate
of
bisphenol-A
3
NA.
Polyethylene
terephthalate
O
yt
ll
-O-C-C-0-C —
Q
i
c=
HH
WS} 6
(Nylon
14.
“N- (CH)
6)
Polyhexamethylene
(Nylon
HRSe
i
Polycaprolactam
adipate
6-6)
Polyphenylene oxide
(Poly-2,6-dimethylphenylene
i
.-C-
H
HO
fe)
|
LI oat
Ul
-N- (CH, ) ¢-N-C-( ec
CH,
oxide)
(o)-o-
CH
I
Appendix
Conversion
To
Convert
Factors
for
Moduli,
II
Stress,
and
Viscosit
From
Multiply
by
Newtons/meter ? (N/m2)
dynes/cm?
dynes/cm2
newtons/meter?
psi
N/m2
Gols
x
N/m?
psi
1.450
x 10 *
dynes/cm2
kg/cm2
1.0201 4 Oe
dynes/cm?
kg/sq.
mm
1.020%
kg/sq.mm
dynes/cm?
9.806
x 10’
dynes/cm?
psi
1.450
x
10°
psi
dynes/cm?
6.895
x
10*
psi
kg/sq.mm
TOS
kg/sq.mm
psi
LOD
se ig
dynes/cm?
atmospheres
9.869
x
atmospheres
dynes/cm?*
WoOUS
s< LO’
atmospheres
N/m?
IoOus
se WO~
psi
atmospheres
68
dynes/cm?
bars
Je00ne
psi
bars
6.895 x 10°
g/denier
dynes/cm?
8.83
x 10°
p*
g/denier
psi
1-28
LOX
p%
bars
N/m 2
LOO
s< I@*
*o
=
density
513
10.00
(N/m?)
0.100
OY
1007
ex 1DOs
10”
oA Ce-
0G.
514
To
Convert
APPENDIX
From
Multiply
II
by
N/1n*
oO
se Aa)
poise
N+ S/m 2
1, O00
x 1G *
stokes
m*/S
1.000
x
dynes
newtons
1S (OOO
S106)
(N)
10°
tS
Appendix
Glass
Transition
Temperature
ILI
and
Melting
Points
of
Polymers
!
Polymer
|
Polyethylene
Tee)
=120
Polypropylene
(isotactic)
(=130)
=10
Polyisobutylene
7p
lA)
DTG
(US2))
EAR
(5) #
Polyisoprene
(cis)
=13}
28
(36)
Polyisoprene
(trans)
-60
74
(65)
Poly
1,4-cis-butadiene
=108
Poly
1,4-trans
=i}
Poly
1,2-butadiene
butadiene
(ils)
al
148
(92)
=u!
120
Poly-l-butene
-25
132
(26)
Poly —l—pentene
-40
PS
(Asko)
Poly—W-ocirene
=615)
Eis:
2S
250
Polyoxymethylene
35
Sal
Polyethylene
-66
66
ch}
144
2)
86
—Sy72
64
Poly-4-methyl
(isotactic)
(-95)
pentene-1l
oxide
Polyvinyl
methyl
Polyvinyl
ethyl
ether
ether
ether
Polyvinyl-n-butyl
=A)
dS
88
260
siloxane
SILAS,
-A0
(atactic)
100
Polyvinyl
isobutyl
Polyvinyl
tert.
Polydimethyl
Polystyrene
ether
butyl
ether
515
(105)
=
(CALSHE))
CGS))
516
APPENDIX
III
Polymer
Polystyrene
(isotactic)
100
240
Poly
a-methyl
styrene
9:2,
(180)
Poly
o-methyl
styrene
nS)
(1225)
>
Poly
m-methyl
styrene
(82)
215
Poly
p-methyl
styrene
Poly
p-phenyl
styrene
Poly
p-chloro
styrene
Poly
2,5-dichloro
Poly
o-vinyl
acrylate
Polyethyl
acrylate
Poly
styrene
(iS })
360
(6)
acid
(zine
106
acrylate)
>
Polymethyl
methacrylate
(syndiotactic)
Polymethyl
methacrylate
(isotactic)
Polyethyl
methacrylate
Poly
n-propyl
Poly
n-butyl
methacrylate
Poly
n-hexyl
methacrylate
Poly
n-octyl
methacrylate
360
(126)
naphthalene
Polymethyl
Polyacrylic
110
(250)
methacrylate
(97)
300
dS
45
(105)
(55)
|
|
65
35
Polyvinyl
fluoride
40
(-20)
200
Polyvinyl
chloride
87
(81)
BED
(PYS)
198
(190)
Polyvinylidene
fluoride
-40
(-46)
Polyvinylidene
chloride
Ale)
(=L7)
Poly-1,2-dichloroethylene
145
Polychloroprene
=50
Polytetrafluoroethylene
WAG
SOM
(G5)
S27,
(aS))
(3 30))
APPENDIX
III
Sly
Polymer
a
EE
ee
Polyacrylonitrile
eee
eee
(syndiotactic)
104
Polymethacrylonitrile
(130)
120
Polyvinyl
acetate
Polyvinyl
carbazole
208
Polyvinyl
formal
105
Polyvinyl
butyral
eM)
(C158),
Cellulose
triacetate
105
?
Ethyl
28
cellulose
Polyvinyl
Polyethylene
306
carbonate)
85
870
?
150
267
(220)
69
ZOE
S25)
40
22
terephthalate
Polytetramethylene
(150)
43
alcohol
Poly (bisphenol-A
Sily/,
terephthalate
Nylon
3
260
Nylon
5
223
Nylon
6
Nylon
10
42
Nylon
11
43
. Nylon
12
42
Nylon
66
Nylon
(Polycaprolactam)
(Polyhexamethylene
adipamide)}
6-10
(Polyhexamethylene
sebacamide)
Poly-2,6-dimethyl
Poly
50
phenylene
oxide
(40)
(46)
WIT
(CLSYA),
189
(194)
LYS)
50
(57)
265
(260)
40
(44)
POSTE
MB2SY)
Z0))
481
220A
p-xylene
Polyvinyl
22 See (2a)
37,5
pyrrolidone
86
Polyacenaphthylene
321
j
Note:
Parenthesis
indicate
alternate
values
reported
in
the
literature.
Appendix
Relations
Between
Tensor
The
in
biaxially
the
of
perpendicular
orientation
biaxial
plane
in
most
to
as
the
is
of
evident
the
relationships
expressed
are
in
terms
The
compliances
of
inverse
from
These
simpler
are
of
tensor
plane
1 of
of
for
is
and
elements
2.
For
parallel
to
However,
be
moduli
the
expressed
the
are
rather
than
law
terms
in
is
uniaxial
moduli.
engineering
36
independent
can
Hooke's
and
symmetry
Chapter
the
tensor
of
Sj j is:
eS
1
21
elements
compliances
generalized
has
5 independent
symmetry
engineering
the
to
orientation
5 tensor
if
notation
uniaxially
This
Figure
Moduli
Materials
elements
For
symmetry.
of
Tensor
tensor
36
there
plane
5 independent
in
cases.
direction
orientation.
of
of
and
Anisotropic
law
complex
a plane
Moduli
these
polymers
orientation
terms
moduli.
reduces
oriented
result
For
Hooke's
Symmetry
elements
a
Compliances
generalized
elements.
as
Engineering
IV
0
S31
S39
S33
S34
S35
S36
Sui
Si
Si3
Say
Sis
Si6
dats
D eas
eA
on
Ss
S
S
iS
Ss
S
S
59)
55
s
56
ih Pe d oe
q
2)
06
520
€.
Ei
APPENDIX
is
the
strain
in
j direction.
Si
from
in
a
stress
anisotropic
is
Oy
Se
ee
On
ony
=
Sy 3
Saye
SF
EAS
Sie
=
See
y,,
is
symmetry,
in
reduces
and
o5
is
the
the
i direction
For
uniaxially
c
ermec
he
Seer
age
wise
nO
0
0
0
Steno
0
0
0
0
s4y
0
0
0
0
0
0
oo
ah Oe
ae
+
Sao
Bnm
Oe
this
in
the
resulting
biaxially
to:
13
hand,
stress
and
Hz
long
POE
€,
this
Hoa
ey.
where
of
in
strain
j direction.
materials
e, =
out
i direction,
the
the
|
written
the
IV
0
0
0
0
|,
(2)
0
becomes:
So
aeriaee
ene
en
ric
Bio +
avg
O,.
(3)
Wie
Van
the
shearing
and
Y,,is
the
force
for
shearing
planes
force
normal
in
the
to
the
plane
plane
of
symmetry.
For
to
and
the
uniaxial
directions
3 refers
to
orientation,
the
perpendicular
the
direction
to
of
directions
the
1 and
direction
orientation.
of
The
2 refer
orientation,
compliance
APPENDIX
S,,
to
IV
521
refers
shear
to
in
longitudinal-transverse
planes
compliance
the
the
S,,
normal
refers
for
uniaxially
EE =
materials
The
that
are:
(8)
TO asoa5
Yor
=~
SS e/g
Yor
7
Bern
(9)
Bie acl
(10)
of
orientation.
width
is
the
that
direction
direction
to
forces
Poisson's
plane
plane,
in
the
due
of
is,
is
2 produced
(direction
1)
in
ratio
symmetry
Vor
contractions
of
characteristic
symmetry
Ver
within
same
ratio
is,
engineering
(7)
plane
transverse
oriented
coordinate.
symmetry,
Gan = 1786,
the
unit
shear
of
(6)
within
the
plane
or
The
1/S,,
Poisson's
within
the
in
symmetry.
(5)
the
contractions
of
E, = 1/S;,
is
per
shear
plane
(4)
Vert, =
of
the
coordinate
1/s,,
Grip =
LT
to
transverse-transverse
moduli
v
to
shear
which
due
the
by
to
direction
is
due
forces
transverse
a
divided
the
load
by the
in
to
applied
contraction
the
other
elongation
in
directional.
The
moduli
also
Ue
can
AES
be
expressed
by
other
relations
such
(leis)
as:
522
APPENDIX
=
=
iz 2(S,,
Se¢
IV
(12)
S,,)
or
E
G
Se
Eyso
Eyso
agSs.
is
Sa
iat
10a
et
33
Zig + V pp
25
(R=
aes
44
ims
See
LT i)
at
(14)
ey
LT
7
the
to
45°
il
il
te
ite
measured
modulus
Young's
the
(123)
Sra)
=
orientation
direction.
4-45-28
-4s
sb
me
C450
4y
-
+28
13
ou
+8
33
i
2
=4-+4+4—
-+5
TT
is
by
oe
'
1
LT
(15)
T
ae
oo eee
Gyo
is
the
axis
analogous
of
L
SE
oe
to
Gripe but
orientation.
If
G
In
general
Gyso
Gy5o/Grn
=~
of
is
twist
modulus
0.9.
Gggo
is
is
given
E,, >>
less
moduli
perpendicular
axis
can
to
the
(S
+
of
En
= E
slightly
Shear
the
torque
is
45°
then
x
than
be
to
(az)
Gp pi
a
typical
measured
direction
value
in which
of
the
orientation.
of
axis
This
by:
2S
=
8S
})
(18)
APPENDIX
IV
S48}
Similar
in
which
the
orientation
relationships
plane
as
relationships
The
moduli
For
of
shown
symmetry
in
Figure
for
is
biaxially
parallel
2 of
oriented
to
Chapter
the
2.
materials
plane
Some
of
of
these
are:
Eafe 2/S,, Sl/S55
(19)
Bead /o5
(20)
oS
AT Ey
(21)
Ge
l/s.
(22)
engineering
Cay
hold
rather
uniaxially
moduli
than
in
can
be
expressed
terms
of
the
anisotropic
Cee
tensor
in
terms
of
compliances
tensor
Si
materials,
a Seve)
(23)
Cel oaeu,7 (eae eo)
(24)
Cuares
(25)
Si
C=
Seih Ae
6G
'
= em se)
(26)
(27)
a
7
on : oi =
te
O59 hee
>
*
miro
dalaw
4b
erie
henley
>
APPENDIX
List
Numbers
A
refer
of
Cross
a
crack
sectional
of
of
to
the
i th
related
of
A
modulus
constant
of
Overlap
edges
A
the
of
in
to
of
symbol
shear
face
il
coefficient
in
equations
in
free
vibrations
coefficient
in
systems
Y
composite
time-temperature
shift
the
moduli
factor
ratio
(sum
of
the
of
3
the
7
in
adjacent
layers
in
ribbon-
8
to
the
of
ratio
of
composite
both
ribbon-filled
the
moduli
systems
edges)
of
composites
of
the
7
ribbons
in
adjacent
8
modulus
of
the
matrix
phase
of
composites
y
Bulk
modulus
of
the
filler
phase
of
composites
7
of
a
equations
Bulk
Width
appears.
vi
ribbons
inverted
overlap
layers
a
Einstein
composites
related
components
of
Einstein
inverted
composites
constant
Total
the
ik
components
filled
which
oscillation
to
related
of
area
composites
the
moduli
or
Williams-Landel-Ferry
Bulk
in
5
related
constant
the
chapter
area,
moduli
the
Amplitude
for
first
Symbols
3
constant
for
A
the
constant
Length
A
to
of
V
test
specimen
of
rectangular
525
cross
section
2
526
APPENDIX
(e
Length
of
a
(e
Number
of
moles
unit
C-.
tear
volume
Stress
of
im
direction.
An
between
d
Diameter
of
D
Thickness
D
Distance
between
D
Diameter
of
D
Thickness
of
Young's
E,(t)
part
E"
Loss
modulus
Ep
aligned
two
or
Young's
modulus
in
dimensional
fiber
aligned
E,
E,
Young's
modulus
Moduli
of
indentation
a
a
Appendix
cross
2)
3
IV.
4
composite
cross
7
section
1
1
section
2
layers
of
ribbons
function
of
time
of
damping
of
plane
of
composites
in
of
the
6
dynamic
term
of
a
3
1
Young's
equivalent
uniaxially
modulus
to
tan
oriented
a biaxially
oriented
composite
2
uniaxially
unfilled
4-element
spherical
6
1
al
polymers
2
oriented
polymer
model
indentor
4
3
in
polymer
polymers
2
unoriented
of
modulus
composites
modulus
springs
test
Young's
part
modulus
the
a
fiber-filled
of
modulus
as
dynamic
fiber-filled
or
E,,
the
8
modulus
factor;
Young's
Young's
in
(Figure
between
im
polyelectrolytes
circular
layer
imaginary
Transverse
Ey
per
al
complex
Longitudinal
or
Eo
of
Dissipation
Young's
a
strain
rectangular
surfaces
composites
relaxation
Real
and
in
a
matrix
particles
with
with
from
modulus
cation
shearing
modulus
E'
E,
and
filler
polymer
agent
al
Stress
E"/E'
the
specimen
specimen
of
resulting
of
anion
test
ribbon-filled
E
element
spherical
crosslinking
4
i direction
Distance
Decibel
tetrafunctional
polymer
d
DB
3)
of
the
V
a Hertz
APPENDIX
E,
V
527
Young's
Hertz
modulus
of
indentation
the
material
test
with
Young's
modulus
of
the
continuous
E,
Young's
modulus
of
the
dispersed
Eon Young's
modulus
in
the
plane
Ean
Young's
in which
modulus
oriented
in
fibers
of
three
directions
Frequency
in
£
Resonance
frequency
EF
horces
g
Acceleration
G
Shear
G*
Complex
G'
Real
part
G"
Loss
modulus
G"/G'
of
Critical
G
One
of
materials;
One
of
the
Gop
Coup
of
in
fibers
which
7
7
a biaxial
oriented
in
are
a plane
8
randomly
i
i
complex
the
of
part
1
modulus
shear
dynamic
see
dynamic
shear
Transverse-transverse
See
Figure
See
shear
1,
1
2
2
2.
1,
Figure
anisotropic
oriented
of
modulus
modulus
Chapter
anisotropic
oriented
2.
Chapter
shear;
in
5
biaxially
of
2,
54
rate
Chapter
2,
Figure
tan
biaxially
of
moduli
material.
to
release
moduli
Figure
shear
See
equivalent
tests
mechanical
dynamic
for
Longitudinal-transverse
material.
sheet
Hz
imaginary
energy
shear
anisotropic
a composite
randomly
modulus
factor
term
materials.
composite
i
stress
the
in
a
6
complex
the
or
modulus
G
the
in
1
shear
the
damping
ina
8
or
gravity
dynamic
of
surface
il
Dissipation
a
G
cycles/second
modulus
shear
are
phase
phase
of
composites
f
flat
6
E,
composite
a
2.
a
uniaxial
Chapter
a
of
2
2.
uniaxial
2
anisotropic
528
APPENDIX
Ge
Shear
modulus
composite
of
the
continuous
Shear
modulus
of
the
dispersed
Gop
Shear
modulus
in
the
plane
h
Depth
H
Heat
randomly
of
He
a dynamic
Distribution
5
to
of
the
in
in
a
8
indentation
6
per
cycle
per
test
1
break
a composite
sheet
a plane
mechanical
energy
phase
of
in
or
dissipated
Hysteresis
H(t)
oriented
penetration
energy
during
phase
7
G,
fibers
(matrix)
for
unit
7
composites
volume
of
with
material
5
relaxation
times
3
eee
at
Polar
moment
J
Compliance
J*
Complex
of
J'
Real
J"
Imaginary
part
J
Compliance
at
inertia
part
of
independent
Steady
k
Boltzmann's
k
Einstein
K
A
K
Rate
K
Critical
L
Length
L
Initial
Lo
Critical
of
the
the
creep
complex
IL
compliance
low
enough
for
applied
stress
3
compliance
constant
5
coefficient
7
ak
the
compliance
3
al
strain
stress
=
de/dt
or
of
factor
5
1
a test
ineffective
8
5
intensity
specimen
length
composites
of
compliance
stresses
constant
of
dl!
complex
state
of
2
iL
compliance
J
V
specimen
fiber
length
1
in
fiber-filled
to
be
APPENDIX
Ly
V
529
Debonded
length
composites
L(t)
fiber
of
retardation
m
Mass
m
A
specimen
M
Mass
M
An
M
Molecular
weight
Mo
Molecular
weight
of
Ma
Molecular
weight
between
constant
on
of
end
elastic
during
the
of
Cross
times
fiber-filled
3
a
equation
specimen
modulus
7
2
2
3
a monomeric
weight
between
i.
Molecular
weight
of
attached
unit
a
crosslinked
Molecular
the
points
entanglement
hydrogen
atoms;
average
molecular
weight
at
ne
Weight
average
molecular
weight
3
M,
Elastic
modulus
of
the
matrix
M,
Elastic
modulus
of
the
dispersed
n
A
constant
n
A
constant
n
Number
of
3
crosslinked
generally
Number
1
points
trifunctional
mM
26.
in
plus
4
composites
phase
atoms
7
composites
7
ak
in
the
average
crosslinks
Nutting
number
of
equation
atoms
in
8
polymer
backbone
between
il
nj
Mole
fraction
N
Number
of
segments
N
Number
of
cycles
N
Newtons
N
Avogadro's
P
Period
Py
Stress-biased
of
of
2
M,
their
fracture
8
Distribution
of
of
of
group
in
to
i
a polymer
cause
Appendix
II.
number
3
oscillation
i
in
probability
chain
failure
seconds
of
chain
in
8
a
fatigue
test
JL
rupture
5
6
530
APPENDIX
Maximum
a
pressure
flat
surface
6
ratio
3
Swelling
Electrical
fe)
FS)
KE}
charge
the
on
Radius
of
curvature
at
Radius
of
circle
contact
a
surface
of
Mean-Square
end-to-end
sphere
polyelectrolyte
into
4
the
tip
of
when
a crack
or
notch
5
sphere
is
pressed
into
a
between
network
distance
of
juncture
network
points
S
chains
in
free
stress
in
the
4
constant
ve
Resilience
ve
Radius
Shear
of
a
al
a
circular
specimen
displacement
Strain
in
the
direction.
sphere
2
iL
i direction
An
or
element
of
resulting
the
from
compliance
a
matrix.
Appendix
j
IV.
3
Time
Thickness
to
Time
of
ribbons
break
Temperature,
in
ribbon-filled
generally
°K
ak
temperature
Glass
transition
temperature
Glass
transition
temperature
chemical
Melting
composition
transition
Secondary
8
at
which
shear
modulus
is
6
psi
Glass
composites
5
temperature;
45,000
same
a
6
distance
Flex
of
of
‘ll
Mean-square
Gas
penetration
counterion
tan
flat
6
Hertz
Q-Factor,
space
ij
in
V
glass
point,
transition
generally
of
as
temperature
1
uncrosslinked
a crosslinked
of
polymer
temperature
°K
1
A
polymer
one
of
iL
1
4
|
APPENDIX
re
m
V
Sel
Melting
point
weight
of
pure
homopolymer
temperature,
Temperature
Energy
to
Tearing
at
which
break
generally
the
shear
energy
Specific
volume
Specific
volume
of
amorphous
Specific
volume
of
crystalline
Volume
1
Original
volume
volume
Volume
of
surface
volume
collision
Degree
of
Normal
Width
liquid
that
aggregate
ri
a
Minimum
actually
thickness
polymer
in
in
a
of
of
a
the
test
i
in
a
ribbons
in
lay-up
a
6
of
component
Mole
fraction
of
the
iy
an
and
on
aggregate
Y
ib
5
during
monomeric
tearing
5
test
8
composites
i
composite
ribbon-filled
thickness
A
a
6
equal
to
which
are
the
that
repeat
8
pattern
fraction
a polymer
within
theory
specimen
component
stress
up
unit
ribbon-filled
in
of
making
fracture
Mole
in
psi
5
entrapped
repeat
friction
ribbons
carry
10”
4
in
energy
number
is
5
phase
is
spheres
crystallinity
fraction
Weight
=20
2S
the
parameter
load
of
al
of
strain
modulus
glass
solvent
of
volume
3
i
of
an
°K
3
matrix
of
Actual
Total
molecular
5
2
A
high
5
Velocity
Molar
very
-
Reference
Molar
of
1
units
crosslinked
532
APPENDIX
x
Approximate
y
Number
of
for
Deflection
or
Z
Average
number
Z
Weight
Volume
Oo
Difference
atoms
number
the
4
ribbon-filled
be
to
a beam
of
backbone
composite
repeated
8
resulting
from
atoms
in
between
the
an
entanglements
backbone
of
a
polymers
a
3
polymer
thermal
glassy
states
or
Volume
coefficient
for
in
coefficient
(discontinuous)
constant
Shear
of
a
crystal
thermal
component
i
5
expansion
A
thermal
expansion
of
a
polymer
in
the
of
thermal
expansion
of
a polymer
in
the
expansion
in
the
longitudinal
the
transverse
of
the
continuous
of
the
filler
state
of
of
aligned
coefficient
phase
of
of
aligned
coefficient
direction
transition
aL
rubbery
for
crystalline
expansion
of
1
4
and
liquid
Volume
polymers;
coefficients
coefficient
(matrix)
expansion
liquid
Volume
Volume
of
thermal
volume
state
Volume
of
the
glassy
y(gamma)
a
in
coefficient
A
in
crystalline
Volume
8 (beta)
of
amorphous
coefficient
direction
a,
of
Ty of
oe
QO,
in
pattern
lay-up
coefficient
in
Cn
ribbons
atoms
3
Volume
a-transition
On
crosslinked
2
average
chain
a(alpha)
Op
of
displacement
force
oe
of
the
applied
in
fraction
layers
required
y
mole
V
of
strain
thermal
fiber
of
the
al
composites
thermal
fiber
thermal
composites
phase
of
ik
thermal
in
expansion
composites
in
8
expansion
7
expansion
composites
Nutting
8
equation
7
3
APPENDIX
Y
V
The
533
work
required
fracture
y
Rate
The
phase
§
Solubility
tan
6
A
Logarithmic
AH
Energy
parameter
of
of
e(epsilon)
difference
eB
Elongation
tests
dL
and
term
iL
decrement,
a
damping
term
1
per
or
heat
mole
of
during
strain
in
of
reaction
unit
1
4
crystalline
repeat
ul
break;
to
ultimate
break
of
elongation
the
matrix
il
phase
(unfilled)
of
a
applied
stress;
7}
Ep,
Strain
in
longitudinal
En
Strain
in
direction
transverse
strain
ey
Elongation
or
EG
Initial
at
friction
of
Viscosity
a
Real
yn"
Imaginary
the
point
i
n
Apparent
n,
Viscosity
of
molecular
weight
of
of
a blend
a
3}
polymer
viscosity
complex
viscosity
of
factor
or
melt,
suspension
aL
complex
part
Consistency
yield
liquid,
viscosity
of
to
3
Segmental
part
2
1
strain
Complex
direction
perpendicular
strain
n'
n
surface
4
activation
at
stress
damping
composite
ay
new
a
Strain
Strain
n(eta)
of
factor,
fusion
Ep
t(zeta)
area
between
mechanical
Dissipation
Heat
a unit
4
dynamic
AH,
form
5
of shear
S(delta)
to
viscosity
a polymer
made
1
up
of
melt
melt
4
fractions
3
polymer
Al
4
of
different
3
534
APPENDIX
ie
Viscosity
at
reference
temperature
No
Viscosity
at
zero
of
n,
Viscosity
of
the
Non,
Viscosity
iMes
Limiting
8
Angle
from
8
Angle
between
Ay
A
Ay is
the
blend
to
the
suspension
rates
aligned
1)
3
shear
7
1
stress
fibers
5
and
applied
7
5
i in
number
average
7
model
of
Chapter
L/Lo
the
number
a
applied
component
of
of
composites
ratio,
for
4
high
of
3
4-element
2,
of
fiber-filled
ratio
a
(Figure
direction
factor
in
very
direction
Extension
shift
liquid
at
angle,
the
in
shear
dashpots
viscosity
Shear
(lambda)
matrix
of
8(theta)
stress
rate
ve
V
polymer
average
molecular
mixtures.
Sometimes
molecular
weight
of
a
weight
component
i
of
3
A
Activation
u(mu)
Geometric
Table
U
u
1g
volume
shape
3.)
the
factor
of
friction
Coefficient
of
rolling
Poisson's
ratio
ve
Effective
number
vy
Poisson's
ratio
Vim
Virz
ratio
direction
of
Poisson's
ratio
direction
of
Density
Density
o(Sigma)
at
Stress
in
process
torsion
of
5
beams
(See
Chapter
6
friction
crosslinked
the
for
for
the
the
uniaxial
chains
continuous
a uniaxial
a
6
a
of
of
Poisson's
p(rho)
fracture
2
Coefficient
v(nu)
Qo
in
force
phase
applied
material
force
per
applied
anisotropic
1h
temperature
volume
composites
Ts.
Zi
the
longitudinal
in
the
transverse
material
5
5
in
2
3
reference
in
unit
2
2,
APPENDIX
V
om
Shear
stress
OF
Tensile
Ole
Critical
By
Stress
oD
Maximum
strength
a
single
of
cee
Maximum
Oy
Tangential
ce
Initial
stress
the
stress
at
at
or
strength
weight
Stress
break
longitudinal
Ins
Shear
Opp
Tensile
the
of
strength
bond
edge
circle
in
of
applied
a hole
to
aligned
with
fiber-filled
in
aligned
the
a
fiber
fibers
phase
Py)
Tensile
strength
of
the
fibers
in
Tn9
Tensile
strength
of
an
Volume
matrix
9 between
phase
aligned
the
applied
retardation
fraction
of
an
of
in
a
direction
composite
of
a
7
composite
composite
8
composite
and
time
3
measured
the
is
made
particles
I
that
8
fibers
up
of
V
monomeric
unit
fraction
of
filler
Maximum
packing
fract ion
of
the
inverted
the
8
stress
aggregate
packing
in
a
or
fraction
a
fiber
Maximum
phase
of
time,
spheres
in
8
matrix
solid
high)
composite
composites
the
Volume
(very
composite
of
6, (phi)
5
infinite
strength
Relaxation
composites
8
matrix
the
3
a
3
Tensile
t(tau)
in
5
Sn
angle
creep
contact
fiber-filled
Yield
an
of
stress
a polymer
of
of
of
So
at
stress
of
5
of a crack
direction
perpendicular
dependence
5
an
strength
stress
edge
tip
the
of
1
6
the
stress
to
at
test
molecular
Cnr
break
chain
interfacial
stress,
Tensile
to
polymer
penetration
Strength
stress
characterizing
tensile
oO;
FR
or
stress
on
Hertz
a
composite
A
al
dispersed
systems
7
(low
modulus)
8
536
¢,
0)
APPENDIX
Volume
fraction
posite
materials
Volume
fraction
composites
X(chi)
Y(psi)
w
Q
of
the
neighbor
Specific
filler
(discontinuous)
interaction
packing
of
Angular
in
the
of
phase)
in
com-
phase
in
moduli
of
which
of
the
takes
filler
composites
frequency
in
the
equation
Cross
which
in
determines
a liquid
al
factor
fraction
parameter
a polymer
capacity
concentration
maximum
A constant
(continuous
behavior
damping
calculations
w(omega)
matrix
7
solubility
A reduced
the
the
7
Nearest
the
of
V
radians
per
7
into
account
phase
in
7
second
AL
i
AUTHOR
Numbers
work is
numbers
INDEX
in parentheses
are reference numbers and indicate that an author's
referred to although his name is not cited in the text.
Underlined
give the page on which the complete reference is listed.
A
AtkKAnNSOnyneeia)
Abitz, W., 27(89) 36
Aclin, J. J., 496(104), 509
Adachi, T., 116(157), 136
AdanspaCe i pues Ass),
Sul C261)
Adams, iG, 197)(232)), 246
Adams?
Nie,
294(169),
335,
es
Pia
eleCome ON(iG5))unl oi7)
Ainbainder,
S.
B.,
270(35)
366, 376
Albert, W., 216(306),
334
448
pad
,ss29
Tivo,
Wop
S280)
250,
re
BAY,
L297,
as),
Backman,
REGies
20,
USAT) Pel 36r
118, 119(165),
137, 499(118),
509
INIA Ue Ne 486 (90), 51
508
nied
AuilentaGeymee2 (Soc)
Naeeom:
Ale
nteiHeGn
A469)
Alden)
VieseR et,
3907 13'3
OnE SHELWieec
H.,
> OOmmE
COE
411(87),
SUZ Ou
meseS
447
aa
Ambartsumyan, S. A., 198(241),
Amberg, L. O., 406(64), 446
Ambrose, E. J., 198(250),247
Anderson,
A.
A.,
285(112), 332
Anderson,
R.
M.,
458(22),
Andrews, R. D., 198(243),
225(378), 254
DCO,
Re
Angier
Dewi
251,
Ton
247
wk
373
328
ZONA
202,
Cae.
G.
M.,
247, |
ary
247,
J.
39,
388(23),
493(14),
Atack,
E.,
D.,
504
355(66),
444,
481(81),
508
R.,
406(56),
445
P.,
58(60),
428(154),
Bauman,
ey,
22e)
252
A.
Bauwens,
J.,
J-C.,
Baxter,
S.,
Beaman
Re
Beardmore,
65,
383(7),
C.,
443
302(217),
302(217),
416(116),
448
GermroulC ove
P.,
292,
464,
Jr.,
301,
Becker,
R. H.,
3017'(200))
G. W.,
194(203),
Beecher,
374
537
J.
iow
306(145),
294(159),
334
508
334,
33 6:, 415 (102), 447
pull laos.
OTe)
245,
337
337
Beaumont,
P. W. R., 486(89),
Beck). Hen Niccolo
Beck,
335
216(301), 250,
450
Bauwens-Crowet,
236,
198(242),
455,456,
ecoILy,
los)
W.,
372
62,
/ sim 21) (40)
J.
Bauer,
loo pels 71029)n,
40(2),
mmm Sic
F.
Arnold, R. G., 278(60), 330
Noadayadepeoa22)
pres, Lis), il4e(25)),
129, 84(38), 130, 167(121), 240
Ashkenazi, E. K., 467, 505
Ashton,
2eon
Bascom,
W. D., 473(58),
506
Battaerd,
He As Um, 2944170)
isos
343(9),
224
225
132
IR),
Barnet,
ZO2 e225 (239) pee ailey 220s,
229(268), 248
Armstrong,
K.,93(79),
USD,
Barlow,
Arends, C. B., 294(157), 334
Arisawa, K., 84(37), 130
Armentadesi;
195,
Bartenev, G. M., 355(72), 355,
356
(74), 3501078):
Bartoe, W. F., 363; 367(100),
376
450
629.4 (L5o5)
66,
QIG(ON)
7 250,
Bares,
J., 84(41),
130
Barish) La, eos) Messe
Barker,
Uz., R. Be, 28m 229337),
Barlow,
D+ Aa,
356(80))>.
375
IS LZ)
SOUS) ¢ BS, 2A
428(151),
D.
De,
Balwit
465,
467(36), 469, 505
Andrew, E. R., 201(271), 248
Andrews, E. H., 351, 352(39),
Andrews, J. M., 265, 300(14),
59(74),
(176), 243, 20d e202395 (239);
22,
ZOU COZ, 229 (268), 248
ZTOMS SSS)
poe.
ok.
Baer Mayo O17
3) OO ee LOM S10)
col,
AN
SUEKAGS)
7 SS, 319(271), 339,
415(104),
448, 728 (149), 450
Batley, diay 285, 290(108), S32 mr
Badly Geet c423) (Se)e a 40 eee Oia loli)
509
245
Ballman, R. L., FOO(99) FSS, e285 me Oo
TN)ay
vt,
SS,
Slo),
Ssy 29 OMGUZ
B55)
a.
Balloupn Weyl oo
Lo oy, 204(31), 236
293(153),
S25
M.,
(Al) - 263,
222825)
eel Smee ee mez Oloc
On
PROMI,
ASS, OHMS) , 232,
229(384), 255
nek
AGoldi ym Gey ia Cl33)i 24s
NICS,
wy Uo, ALESSI
282,
Alter,
tOOlmmncita nce 6!
B
Baccaredda,
416,428(106),
Akeni
INN
Do (Oey
354062) > 374m
Aggacwal),) Salie, 59/7) 66),
WAS ASE, Bale (ule) , Sse
mbes,
Bete
(2:90)
250294100), esse
S95)
428(36), 444
et
222233) eee Oly
Axilrod,
B. M., 290,
292 (135), BSS)
406(51),
F.,Seo),
66,
445
123,
538
AUTHOR
1,
335,
Bid (als) , Beak,
416, 428(106),
Beecher, N., 496(109),
Bekkedahl, N., 19(21),
BOCA), 7
448
509 —
33
BS
Glo 2a PE(GO),
Seipealeey,
(140), 241
aa
Bely, V. A., 356(76),
375
Benbow, J. Le BONDS
Sicks
Bender, B. We Se
uae 339
Benning Cais
4 Lilie) peas
Berezknitskiy,
Berg,
R.
Berge,
M.,
Wis
Bergen,
L.
T.,
139 (4),
ise,
Reigns
337
372
ACs,
4(sooie
465,
4747,
4381:(33)),
486, 505
Bernhardt,E. C., 363(101), 376
Bersy, Gin Ceo) (Sl)
Odin o7 oO)
105(92),
eisave
Wo
104(106),
133
a,
UO),
(178-180),
Bersch, Ge Ea,
MSS
ey
335
U2 (183)
E38
Bevilacqua, E. M., 319(268), 339
Bhatejay Sia hs 217101032)
On me
Bande ysis
Olli(9G) Se
6 aan
Birnboim, M. H.,
139(52), 237
Bischoff, J., 84 (28), 12.9 ata
Bishop, E. T., 59(69), 660, 217
(SUG)i e257 292) 29400143)
334, 397, 429(39), 444
Bisset,D. C., 409(73),
446
Bixler, H. J.,
Blanchette, J.
498(116),
509
A., 59(66), 66,
216 (302), 250, 428(148),
450
Blasenbrey, S., 223(364), rt a
Bobalek, E. G., 421(126), 449,
434(175), 457
ar
Bodner, S. R., 414(96), 447
Boehme,
RIG,
eR. Ce,
348),
351,
35229),
B73
Bohn, L., 195, 218, 225(228), 246
31137) 34 (247) 338) olel(2Go)me
339, 423(133), 449, 497(112), 509
Bondi, A., 111, 113(146), 136, 185,
186(168), 243
a
Bonnin,
M.
J., 120(181),
Boonstra,
B.
B.,
406,
138
41/1;yeesi(66)
446, 413(91), 447, 421(127), 449
Boor, Laa 363, 3671100) , 376
a
BOOEN IClmee 2913.80)
5 5mm
Borders, Brot Ma 292, 293(141), 334
Bostwick, R., 406, 411(47), 445.
Boundy7 Rew tS 49117)
Soe
Bowden, F. P., 353, 354, 356(51), 374
Boviet Rem Eee 91(29))aeee2i (Aull) ms.
22\(43)
FSO) (98)
Sees TP
BU, QU
PAUP),
BESS. 216 (309),
2519 222 (363), 254, 273 330, 314
G53), 338, SadeTene 320(260) «
339, 343(17),
Boyer-Kawenoki,
193(200),
Bradford,
Re
217 (313),
428(106),
Bragaw,
334
372
F.,58(52),
245
Deares
(TL)ys OG
65),
rae
251, 294(169),
743.
(C.)G.,m292,
302)
H. W., 393(31), 444, 406, 422(60)
445, 405, 409, 411(74), 446, 419
(122,124), 449
tae
S.
Ye.,294(167),
416(108), 448
Breuer, H., 135 Z2A (LO)
225(123), 240
Bra loin, dey eles
9)
335,
me
23541
lOO
eos
306),
Broutman, L. J., 349, 352(35), 373
406, 409(59), 445, 453, 454,_
467, 469, 472, 473(3), 504,
480(80), 507
>
Brower,
F.
M.,273(43),
pedestal os
335,
416
SLIIAT)
329
Brown, A. W., 406, 414(54), 445,
496(100), 508
Sa
BEOWMN pacGisn Mie melelON LOA ien OLH,
Brown, J. E., 198, 209, 210; 226
(248),
247
Brown) N apecobl (leciee
22) bm 2C10) (eee
33370299) (LID) ss
Bruenner, R.S., 431(163), 451
Brunty
N. Alsy,)
Ll 8iGh72)\
320(274) , 339,
Bryant,
Bryant,
Ki.
Wie
281(83),
Loki
361(93),
375
'C., 4091(73)),)
446
Mie Dawn e27) (SieA ey,
Buccaredda,
331
M.,
59(74),
66
Buchdahl, R., 26(69), 35,56(43),
64, 58(53), 65, 78%“39, 1023),
128, 95(82), “732., 97 (93, 94),
S305 18) (67) eelTi9, eo
USE KCGDY,
R. D. 406, 425(49), 445
Sop AUS, CE, SIG, Vac
Boettner
Bree,
Brodnyan, J. G., 393(27),
444
Brooks, R. E., 281(80,84),
331
235m
262) 5 aod
Bernardo,
Brandrup,
J., 206(281),
249
Brashkin, M. A., SANG)
mou:
Brauer, G. M., 9\(23)),
34
Bresler,
305(226),
3471923),
Ws,
ab
INDEX
Ask,
Mey,
alse
S))
238, iss, 19¢. 202(109), 240,
T89\(195)i5 244) 20 a(287) 2491.
us
COSOLMBY , OG, Pally Wa
(SSO), Bil, BOB) , 252,
222/)(856)"7, 253), 2237 22665),
SN
Die, WI, 317(39), 329,
284 (97), 285 (106), 382702 0ae
314,
318(161),
334, 7294.
(34,
318 (162), 335, 299(190), 336,
428(146), 450
aan
Buckley, D. J., 293(149),
334
Bucknall, C. Be 292), 302(140)),
296, 302, 306 (146), 334,
B1S250) Fe SSI 428 (155), 450
Buckser,
Bueche,
S.,
A.
275(54),
M.,
273,
330
275(48),
330
355167) sae
oa
Buecheyw Earn
O23525)
26136) Poa
2915) pe S51 23.0) aROSPEET. OF OITE
OD, TOMO, UAE, 97 (50, 91), 99
(96), 104(105), 108(91), ISS)
105(113), 134, 108(127), 138.
Gl eh) 5 SK
le
Ks 189 (143),
242, 185 (163), 243, 265(19),
328, 278 (62), 275.66) , 279
(6
ae
,68),
280(67,68),
Rey ROlaee
198,
330
199,200(260),
248
Bulgin, D.,
362(98),
Bullman,
W.,
G.
376
108(130),
135
Burgers,
J. M., 383(6),
391,.443
Burns, H., 308(234),
338
AUTHOR
539
INDEX
Cleereman,
Busse,
W. F., 100(100),
133
BUSSE
aU, SLO
peop eZee 359),
2525, Si4(254)
339
Butta, Ee), 591(7,4)), 560, 0195), 6224
(214), 245, 216(307), 250,
Dye 22825) 2) e che
2201320) ee lez 22858),
253, 229884) 255
J.
Campbell’,
Dis,
Berk
R.,
118(168,169),
tole 246,
137
284(102,103),
305/(222),,
337
445,
418(119),
Carswell,
Be
505,
462,
506,
ous
on.
S4i(2.8)i
Gimuacuhy
—
e2on,
Se
M.,
A.
508
245
J.,
mae
100(98),
A.
W.,
133
270(38),
329
Git, We Bia, Bar, B95 2HOW24) 5 S22)
Chusko, Al Ae, 4un(16 4); 450
Chung aCe Le
e222(855)i, 25S
Bignei, Cn, SUG) 7 G3, Pin);
25S
es20(272)en S39 18428
(156), 450
—
Cimlin)) Estey 195). 297 (228 )i e245
Cizek, A. W., 360(90), 375
re
Clamroth,
Clark, H.
Clark, R.
R.,
A.,
C.,
162(98),
409(79),
414(94),
GlashyeOse,5 Re hemo
Claver, G. C., 294,
Gdlayton
Day
eo2y
239
446
447
235
Cohen, V., 290, 292(133), 333
Colwellve Rs hr. LoOOts9)- 25cm
Combs, R. L., 104(108), 134
Conant pmb
oer meob s(52) sai)
Cooks -0).74651(33)) 8 50S)
nnn
Ni.
2)
Go
309\(120)
Aw,
Se
471,
506,
508
le
sim
472,
484(84),
O70) i mG Gimcda7,
(S04)
2a
(159),
451
ei
W.,
104(108),
Coover,
H.
2947
335i 429
134
Corten) He. Ty, 298188), 556),
455(19), 504
"eal
Cotten, G. R., 421(127), 449
Cottrell, A. H., 299(189), 336,
469 506
aoe
Cox5n We PD O42)
O4 O07) iy
160,-161(78), 238 27025).
IAG) 5 AA See (LD)
AGE:
Cramer,
We
S40
h7 (9),
Cratchley,
D.,
Crissman,
33
a
466(34),
505
Wiehe,
1947,
22210206) —
AEN PB
PRIS)
Pisa
CrossyeM. M., 384 (8.9), 243)
Crowety Can 26 51Gl6) SoZ Cae
Crozer,
Rom
Ney
S47 (20)eoTS
ErugnodaymeAry eels ene 4i(s4 9)
Cuddihy Ee bi 2291(390) 6255m
Cuevas,
J.,
Cute pice
Cummings,
Cwesit,
406(56),
445
47) (G3)i, O27 moor, 9 21(43)
J. D., 92(65), 131
Oo
Wop
Cuthrell,
R.
iLO
meer
28S(ULe) > Sas.
E.,
181(157),
242
J.
334
Ho,
202273),
248,
218)
229337)
eco
ih
Dally, J. W., 349, 352(35),
373,
480(80),
507
aa
Dammont, F. R., 110(138),
135, 215,
229628)
252
Dandlovprivie
Gepost) iy Se
Danilova, M.
Danusso, F.,
P., 341(5), 372
113, 114(149),
136
econ
Daren See RpecCi
M. W., 119,
Darlington,
138202) (269) ia 2ac
Date,
M., 139(59),
Datsyshin,
Davies, Ge
80) (59) ya SS)
120(179),
237
337
A. P., 305(226),
Rie, 202(278)0
249:
374
De Coste, J. B., 354, 357(64),
Deeley, C. W. 194, 215, 222(205),
DAS
4 (lon23) es ee
318(163), 335
S02(140)),
GRAS) -
308(242),
338
222)(185)5, se),
449
ae
Daane,
LOBF
Chorné, J., 469(39);, 505
Chow, T. S., 455(16), 504
Christiansen,
Cul,
D
139(37),
Ue p Osby a) tosh
209(201),
Chompff,
494(96),
B.
Non
a7 406 (57)).0 4451
SOT CLS3)r469, 470(44),
491,
Chernyshev,
ts
Cohen, L. A.,
Cohenye Re ER)
422(131),
Cooper;
elZole
84, 92(30), 129, 84(33), 130,
W6i(L55) Some
<a
Cayroliebs maZZoueeD)i 25o
Cessna, i. Coy) 419) 42010820) 448
480(79), 507
ras
Chaeym
loupe
(25,0)
724.0
Chadaidze, VIN.) 302 (218)
9mss7
Ghamic) | CaGer4 551012)e 504, maior,
474(59), 506
San
Chang, M. S., 279(65), 330
Ghapov, Lali
.6
cr Ol
Chappel, F. Pa, 198i(253), 247,
283(94), 332
rns
Charch, W. H., 198(257),
248
Charrier, J-M., 292, 294(144), 334,
415(103), 448
ig =
Chartoff, R. P., 104(109),
134
Cheatham, R. G., 119(177,178), 120
(AGG GED) , eke, GER, AOOULOW) -
332Be
oh
4 0120)
eeeESey ec Ocl>) mS ZS
Casson, N., 386, 443
Calsiee ere AolGU4ine
Chen
eae
CockspaGenGere
483(52),
487(93),
Case plene
er e7OG3704)9 oe)
Cassie, AS uD epson
SO2(49))
292(136),
are
Cooper,
448
290,
BGs 6s43)) 324 (16) 32
mls op Ota OA Gseiy pagent
Cook
Gannon GetGan 2331(94)) moon
Canter, eN).eH
O04 (100)i meso
Carey
mH o 2164) peti a remote.
352(50), 374, 406, 411(47),
J.,
Gee
Cohen yslewd
c
Caldwell,
K.
348
de Farran,E.
Den
Hartog,
SDL ym ObIe (S2)i7 ous!
Moncunill,
J.
P.,
472(56),
48(22),
63
Dekking, P., 139, 219, DDE (Wy
M.E., 139(21), 236
de Morton,
506
PES
540
de
AUTHOR
.,195,
Petris,
245,
224(214),
ZO,
Eldridge, J. E., 165(111), 240
mete VAG Wop Se
SWZ) 5 Sista) 375
E1Miotty A. , 198(250) 7247)
Eilyashy levi we 73852) eo S0
229
Pile 2D 229 (326),
(384), 255
Desper, C. R., 198(255), 248
Deutsch, K., 219(343), 252
inXss WarleySo ag SE) 5 BE, 302,
303(220), 305(224,225), 337
Dew Wise tyler mel 3 91(50) aezoray 161
(80), 238
Diamant,
Di
Y.,
23,
24(59),
Emmett,
RSE,
307(15),
265(17),
328,
Erhardt),
425
(141), 450, orl (Saie, SOGhm 481
(32) =50Sie
Drier, INo Cage, was), NAG,
We,
Is, COSC
1S) , PET),
See
285, 290(107), 332, 479 (66,67), _
507
rae
Dillon, J. H., 48(29), 63, 139(5),
2357, 1391 (63)
rose 348 (28), 373
Di Marzio, Bis Aes T9(30), Ste PeEIS
Dingman,
E.
(105),
G.,
414(98),
a7,
509"
Riek,
Dobizyi7)
Dale
ns9i,
245
Dodgé,
C.
496
92(44),
130
Done)ie 657, 193(200)),
Dixon,
W.
ELY,
23(54),
H.
U7 TCL)
Dougherty,
242
T.
J.,
386,
443
Dow, N. F., 469, 505, "469, 506
Doyle, Mic Eye 283190), ss
Drexler,
Li.
H.,
97:(87)),els2
Droste, D. H., 425(141),
450
Drumm Me Be 231(54)09 35) maT
(UST) e242
<a
Duckett,
(Re
Aan
290(122),
PASI
290(129), 333
Thadin,
LS9(24)) 236. 278
(62), 279, 280(68),
330
Dusen Demure 54477 916)ae504
Dukes, W. H., 261(3), 328
Dulangy) LeeNe, 9 7(233)nme246
Dudek
Dumbleton,
J.
H.,
84(29), 129,
169(124), 240, 198 (263), 248
Dunell 7, Bi. Aa, 78 (29), 63, 139(63),
HS ON75) peel S91 TON 238
Dunne
Ce
Dzyura,
Mw
BE.
Ral
A.,
241
20)(
en ieammlisis
52(34),
64, ~170 (128)
E
Eagling,
R.
F.,
59(67),
66,
214,
216 (290), 250, 284 (100), eps
Bosh 428 (36), 444
Eby, R. K., 229(389)pm255
Ecker, R., 58(54), 65, 216(293),
250
Eckert, R.E.,
ee
265(9),
138,
Eisenberg,
207,
255
Sib,
Seal
443
119% nee TRC
GAL7/EN)
409(78),
A.,
446
19(34,35),
208(285),
249,
=
34, 206,
229) (385)
A.,
Hin,
293(151) ,17334
QED),
ae
Pa,
244
(283\(87)meos.:
Estes, G. M.,
253 294
Evans, H. es.
Evans, R. M.,
59(70), 66, 217(314),
35, 429(159) , 451
793(148), 334
421(126), 449
Eveson,
G.
jase
ByYing,
ee, A) Shey ((alils}) He, 904647).
F.,
393(29),
(213), 337
444
376
130
302
1
498(114),
Dist
509
Raising
de
Haldichky
Panaday,
Gere
498(116),
509
(©. Ss Na, 202)(277)em249
Rarlde; Ee Dc) 109) 9135
=A
Farnham, A. G., 218, 224(341), 252
Marriisi. Re Jie 39330) 444004
(La Pd) 5 LEW
ro
Farrow),) Gai) 2251373), 9254
HaucGher
rgd
Ava
EGO),
2G
oS eel OlCeO)
sts,
CISD),
0 Cm
oo
MOS,
PAL (Paay
Beil,
PQA (ST).
254, 284, 318(104), 332
Fedors, R. F:, 279 (69), 330), 3720
(275), 339
Ferry,
J. ian! 4, DL
2K(3) SB 4s nese
(2a) 6 Sro 7, Tap UNG),
15 (QO)y U2, OV 5 MOM, LOGE) 7 VO9 TIA CUES),
1222 5128:; 97(95)), LOOM03))7 133%
107 C23) i et s4, 109 (134, 135), mEB
139, 156, 7 (2), alge 192(1);
235, 139(49, SAG 2p USO, WIAWGGS) ,
150 (67) , 157 (68), $2387 1650).
240, 171(130-132) , 172, TGS
Yap)
241, 195, 215(220), 246, 306(229),
Save 422 (130), 149
Fettes, E. M., 294(155), 334, 498
(116), 509
Fielding-Russell, Geese 139(40,58),
23ur 217332), 252, 416(107). 448
Fields, J. E., 206 (283), 249
ie
ine
laletpyet 5 ins
aly,
476(65),
507
Findley, W. N., 47(16,17 peal, BE
JOINS 52) coo Soe Se alae
neal, wale Te)
Fisch, | W., 23(GINe
Fischer,
Fitchmun,
328
Economy, J., 406(55), 445, 496
(107), 509
Edwards, R. H., 306(230), 338
Einstein,
A.,
Bigcheese Bye
=
R.
Ws
Engelter, C., 92(60), 131
Enjoji, H., 187, 188182),
Epps) tra 224 (372)9 e254
35
Benedetto, ING GG BNE SIS, AG (GIS)
O27 265204
SsOd SOONG 5t
301,
INDEX
EB
Fitzgerald,
Fitzgerald,
Wis
D.
E.
Fletcher,
R.
249
A. F.,
K.,
36
188 (192) , 244
W. E.,
206 (282),
Fitzhugh,
ay
Roy
13949) e237
19,
21(28), 34,
347(26),
294(156),
373
ee
SEL
415(100), 447
Flocke, H. A., 23(61), 35, 167,
U7, UG).
DEO. 322
(359, 360), 253, 392(26), 444
=
AUTHOR
Pilom,
INDEX
Die
541
Gaus
Sy
SO4),
SKS
Cash
Garner,
355(67), 355, 356 (68), 374,
ASS,
BOSp Oo, S00"
iy
Meigs: I5 Ginn We), GaSe sey,
23\(50)5,
35,
27:(90)),
Sores] (Soy
30:02 ,93)),
mloc el Omi(d2 4)
sd
Mg HAs); Asse wala) | asta
GGL),
Bail, WSEAS), Weer,
273\(45,,46) 0274, 329, 275156),
278(58), 330
cae
Foden,
E.,
352(48),
374
Ford, R. W., 281(82),
331
Moe ies 4 We, Sth, SSCs,
siyvdl
NOGEnCT EG were 20134)
Scone
Were,
INa 5 dak,
Hox
Tea Gu
(ORSS)
absiy
ay
OMI
S2)Ne 340,002s
so Sesils2nn o4e
97(88,89,92,95),
105(92),
EraZzenr
Wisi)
99(92,97),
133
ee ollO2)),)
(158),
334,
S30),
416(109),
448
Frenkin,
E.
445
Friedman, D. W., 499(122), 510
DheaicKeN, io Co, LOOUPN,
sOup
Prisch,) HH. lie, 188 (191,194) 244,
216 (308), 250, 429(160), 451,
499(125,128), 510
—
MAIOGgal, We Gap LS, ASAGGs) , “eal
Prosam’ p)Vie eD Oli? 4)
266,80195,,
(152), 450
Fujimoto,
IanO,
T.,
Ka,
100,
SU),
saa
101(104),
Gi,
133
s(iyp
Wey,
SAS2) nls O),. Ss
pmlc
4peetel6 (aaa) se
DS6y USO)
28617 216 (2916), 250
Budokai
08) eSi(238)i S55)
Fujisawa, T., 83(22), 129
BugriccayeHeee05) (> )ap oe
Fukada, E., 139(59), 237
Rule
CSl(22) oS LS) lL a2 5),
12016 8418'S)bas 0m LO7 (U2) 240)
Fulcher,
Diohhe,
Fuoss,
K. U.,
iio) tien
R.
M.,
217(332),
19(25),
254
Furno,F. J.;
369(120),
Furukawa,
394,
J.,
D.,
H.
F.,
122(186),
510
Gerngross,
O.,
27(89),
292(139),
le
A.
239,
Gabaraeval
AD
eeeol ets)
ooZ
Galperin,
I., 425(136),
449
Ganzpse
Nie 4.911233)
4a
Garbuglio,
Cr, Lavl(i33)i, 241
Gartielidimeticn 1p
Oo Gat)i, 34
4991223),
se:
162,
164(90),
163,
ce
9 0) 921056)
Csi
De,
386,
21.0)
443
eo
ioe
Gildham td cake aS O72
oS 0) maeOa) a,
236, 224(372), 254, 229(393), 255
Giusti, P., 224(367), 254
Glaesery Ws Any) 555\(55)ymsta 8433
(170),
451
Goettler,
L.
A.,
462,
464,
474
(30), 505, 476(64), 507
aCe
meo)21(65) haeloilpmmlelGry
137
2.
Goldstein, M., 19(31), 34, 90
(54), 131, 197(234),
246
Goodier, WJmmNics 2 (82) gLss.,
296(173,174), 306(174),
335, 386(14), 443, 413,
431(89), 447
Gohn
Goppel,
J.
M.,
ches
273,
(Sess
acwed/
M., 341(4), 372
194, 218(208),
Gorchahova,
V.
Gordon,
G. A.,
245
Gordon, J. E.,
483(83),
508
35
Gordon,
M., 25,26(66),
35
GCouza pp isndiy
SO
7S OS(87)7
186(170)
444
Grechanovskii,
U.
Greensmith,
Griffith,
H.
A.,
W.,
ReiKewise
395,
52(34),
64,
265(20),
328,
340
7,(Le)
A. A.,
413(90),
25 o!
,243,
241
321(278,279),
Gregory
364,
,
Anas
e2olSe
li
pcm Oeics)
imeOs
R. W.,
424(37),
170(128),
epee:
139),
36
428(144) , 450
Gillespie,
225(375),
G
334
92/75)
M.,
246
Gieniewski
Cratch
ST
375
rage
Gezalov, Ms) Any) SO 2;ms03(209)n, 337
Gezovich Dee Meym eco4)
saesos
Ghensane De 20 41(LOM) nooo
Ni,
tio Won IS(30) , By ws) 4
Gray,
444
Buschisalo meNipenelan(3))
George,
252
34,
508
George,
375
Granato,
LOCA) » Se
509
481(81),
S74, SID),
Sk
136,
eS,
Nia, AACE) Go, TIAA)
283(96), 332, 285(124), 333
Gent Aw Nievelle (63)
els SOAS),
2B
eee SULA
0) boobs O1C202)ie,
SENG, SAAR),
BO, TIS 7 SKSGHEN)
ol, S620) 5 Ss CaS Ge pikey)
418(118), 448
2240
(Qi) 24576201
202 (267) 5, 2418,
DIG (307)50, 21513255326)
eee
(3255826)
220) (S26)
ecole 22353)
253), 229(384) 255)
Bj
eo
(G2)
eo.
Fujiky, T., 187 (sil) pees
Fujimoto, K., 58(59), 65, 216(297),
250, 293(150), 334, 428, 429
498)(116)),
V.,
Gehman; S-Di, 13955), 235318947 54) +
Pole lO2 (85780) 7 coos ame) iy
Gessler,
335,
—_
I., 406(48),
F.,
J.
Gavan, F. M., 359(83), 360(83,89),
Geckler, R. D., 393(28), 444
Gee, G., 26(73)), 36
o Fe
Gesimnskiy
204
Hreeston a 0 Le Wiel Dic 2051(10)e meo201
301(197), 336
——
French, D. M., 279(65), 330
Frenkel, S. Ya. 294(167),
416(108), 448
F.
Gauchel,
yOS
296(176), 335,
447
Grimer, F. J., 486(90),
508
Groeninckx,
G., 84, 113, 114(40),
USO
esi (Si)iy LL6y, LlS6:
Grosch, K. A., 354, 355(60),
Gruenwald,
G.,
369(116),
376
374
542
AUTHOR
Gruver,
J. T., 58(57), 65, 104
COM) 7 OE (UlaLy) 5 Ne
Pile (OO)
250, 425(140),
450, 429(161),
451
Gruver,
R.
M.,
(103),
Guilcking-"
414(97),
447,
-
204(236),
496
509
HemDe,
22(44
E.,
48(27),
63, 386(16),
279(66),
Herzog,
330,
M.,
362(97),
388(23,24),
444
464, 493(14)
494(97),
376
Hamme Cen Haale
2 oat
o) iss
Hammock,
T. J., 225(378), 254.
Hammond,
R.
Handler,
Bs,
J.,
56(47),
320273),
64
Harpe
inne
E.,
285,
So) (50)
339
287(114),
imo,
332
Harris, B., 472(56), 506
Harris, M., 273(41,42),
329, 352(47),
374
Harris, W. D., 43(6), 62
Hart Weyl
bey Nicine26i(7/3))
6
Harwood)... Aw Ce 280)(7i So
Hashimoto, F., 195,225(230),
246
Hashin, 2., 386(17), 387, 443, 455
(8,9), 504
aa
Hata, T., 58(60), 65, 214, 216(289),
249, 395, 416,9428, 429(35), 444
Haward, R. N., 105(114), 134, 294
(156)),, 334, 301 (203) ,"3s6, 319
(269), 339, 415(99,100), 416(99),
447
Hayakawa, K., 362(97), 376
REYES; Re Nop BIS), Sar
Hearle; Jd. W. S., 35249). 374
Hearmon, R. F., 39(1)), 40(1)
62,
—
198(240), 247
Heffelfinger,
C. J.,
33570356
73)) 75 SD:
ui. ba Mem
con ony 36
iK., 27)(89)!, 36
J. J. , 455(107 16), 504
Ui 7 DSi55)i
250
6S)
a
J. As, 453(2),
504
L. Dl7-292,
R.
W.,
285(119),
333
Heider; Oem E
lol, 163(92)) 230mm
Heinze, H. D., 23(56), 35, 177(151),
or)
242
Heijboer, J., 139,219,222(9), 235,
2195132077321, 822), 223224320)
224 (321,322), 218(329,342), 219,
224(339)), 252, 219, 222((351), 9253,
224 (366,368), 254,314(254,255)339
,
econ
293(141)
434(176),
334
451
Hillier, K. Ws), 164 (103 h104) ). 240
Lbibyeacl WG Cm
SEO, ssley/Gis)) rls
Bokeepie Ul
VEGAS),
SZ
Hirose,
H.,
Hobbs7e ui.
Hoegberg,
84(37)7
Mi,
Ho,
130
LO4:(lOG)es
ass
171130) | 2415)
314,
B15\(262) peso
H Ae Wayo2,, 94 (63)0 ode
291346) eere
eee
(350) = 253 aman
HO£E,, Nii
591(24)0 505
Hoffman, K. R., 409(79),
446
Hoff,
Hofmann,
W.,
23(62),
35
Holden, G., 59(69), 66,
Aejil 2), BOL GED,
397, 429(39), 444
Holik, Al S1, 301N(@267)\i5
Holliday, li.) 9198s 200.
206, 248, 285(125),
Hansen, J. E., 281(80),
331
Haraday, te, «84\(37)) 33 Olan
RENIN
Gn, SWE)
5 Se
Hardy, G. F., 474(62)507
Hargreaves,
Le,
Homes,
265(16),
Che ONS,
(217s
Homma, T.,
Hopkins,
Horino,
37
109(134),
I.
L.,
217 (CLG),
334,
337
205 (265),
333
328, 302
135
56(4
‘T.,,/83 (21),
114, 116(148),
(25), 236
HOETO;
136,
Mir, mS 91(32))-
(74),
Horsley)
2837
Re
e330
Aw i295
S09
Siler
SHEMCGIIZ)) p S53, SILKS 5 SEO
Hoseman, R., 27(88), 36
——*
Howlett, R. M., 293(152), 334
Hsiao, C. C., 46(11), 62, 52(69),
TS 26.0 (2)
eon
aaa
Hsu, Be, 93(75), Ise
Huelck, V., 122(186), 138, 499(123,
1247 127) 0
Sewbas
Hulse, Ga, 317064), 339
Hunt Belicte (27, (G36)
Po De
Hunt, Jr., R. H., 344(18), 372
Hurst, D. A., 292(138), 3337
Hurst,
Hussain,
S.
J.,
229(388),
M. A.,
255
472(55),
506
Zz
Tannicelli,
Ibaragi,
Ikeda,
T.,
J.,
R. M.,
434(117),
161(81),
59(75),
251, 428(151),
Olle
198(261),
250, 290(128),
450
Heydemann,
P., 22(44),
34
Hill, F..B.,/276(60), 330
Soy
507
455(14,15), 456(14,15),
504, 462(28), 505, 493,
508
iy
Hard miSiey al O41(iO)
eno
Hamada,
Re
LO,
249
pp)
66
418(154),
Hewitt,
480(78),
59 (68),
Herwig He
(29:2)
443
Haldon, Re A.) 222), 225\(3517) 7.253.
Hallie Wien SiehS e224 (341))y e252)
Hall, M. M., 428(155), 450
eWlshin, Wo Cy, ISSO)
ees). DEEN.
329,
Hi,
Hess,
Halalee Wemey aS 02)(2)
E.,
Hendus;
Henny,
H
Hagerup,
adi) Di 20i(70)
Herbert,
Hermann,
Hermans,
255
Soin
204(274),
Helimersy
333,
Guillet, J. E., 104(108),
134
Cwelmem, Co, IOP, MGS),
Per
Gwe i, Wig TOMS),
Bee)
Gulbransen, L. B., 480(76), 507
Gupta, eRe ee, ee aot see)
255s ee
Guth,
246,
Hennig, J., 58(64), 65,
200, 248, 216(301),
nod
Guptay Vie Dies eldaG 14)
bres
(UGS) 24s)
0212718) ees9
Heller, W. R., 228(380),
Hellwege!, Ke ‘His. 207)
INDEX
450
239
452
66, PT
ED)
AUTHOR
INDEX
543
59(68),
PlTersyak=Hiery 926 (69)
85.5),
ils}s) (GLO) ie yy
RACY
66
229(10),_
BES BUSS WI (aleish))
240, 194(204),
195 (204, 215) ; 25 225004, 215)
245, 195 (223),
246
Imada,
K., 198,
2001264),
248
Immergut, E. H., 206(281), 249
Melepactn; Jo ey,
SS
nou,
333
Ms,
LOERER AGE
trie, Fs;
iia pligly, ia
336
28si(89)i
Sol,
re
84(37),
406(45),
445
OUUTano
duve, A.
ONY
IRA
INO}My, Wy pe CESS) 7 sak
ue)
245
Jackson,
P.
Jackson,
Selo
TOS)is
Sms, We die, 18 (6s), 169),
S (2247225) eestor. 204 (102),
S82
ar
MATE,
466(34),
Haplé6éo,
K.,
Die
195,
505
BRP
301(194),
336
SEG),
SE
la,
APM)
danacek, eye lOOK(Gl3i5)i, els
5) 19'5
(CAD PN) , LOVIN
, LS, Os
(220/22)
e220
2Dye l9)
(2200, 246), 291349)
e253
Jansson,
J-F.,
148(65),
238
Jaruzelski, J. J., 409(82), 447
Wenekele Hees C155) 0 oo LS OGL Ola ))e,
229-(10)e, 235, 169%195 ; 197,
222122)
ear
175 (138),
MOS. 2a; 322(215), DNs
(292), 250
Reo
Wucinaca, Mop Ass (ally) 7 Ses)
Wonarin Ge Pelo7 (254)
ees
241,
PRS
Wohnson,)
DOhnsony,
Ui bey
Keweley,)
2 (35)! of am
SO) (LO)
yams 716)
gvohnson,
R.
19'71(233)),,,
H.,
59 (77),
66,
lino
246
Johnson,
R. N., 218, 224(341),
252
TORNSEON
eel) Ley, S487) Sol, SI2K29)yy
373
Johnston, W. V., 26(74),
Jones; Mas oly SS 243)
JOnesy
a>
awe
Loe (Sol
TONES
Ulm
Lie.
O18 (50)
36
ous
coon
nO me hOns.04))7,
250 ols yoda ys 20249) es S8),
416(111,116), 448
li22
445, 422
cO27 s)he
isoo
Kallas ae rmerey mms 60)(910)
2 Ola,
249
248,
=
ASL
Kambour, R. P., 301(205,206),
BOINLOW) , Box (i), SBR
Gepee
64,
352)
177,
RarameecHs
o>
3457)
336,
54(36),
oe
180(148),
WJ,
242
344 (lo,
sae
Kaas Cem Cer msl Ans? 01257) nmsoO
Kardos umn
> (40) moan el ODI lOO)
243, 406(45), 445
ivi Aci
Zool ps Solema7 4
(60) 7 507
Jackson; Gs Bap 119)(176))- 13:8), 285,
289, Sian 35/1. Siz (09)
ems),
Silda SL SpeeslC26N)) S359)
lee
Jackson, do Ba, 1947 195eu" LOACZ07)ie,
240
Jaeckel,
H.,
Tess) 2 (81 5)y, zoey
Kavser,poR <i i207) pued0i7 =Osi,
204(236), 246, 204(274),
Kajiyama, T., 198, 200(264),
222)(S6l)paeeoS
Kargatiy
Jacobs,
De
397(41), 429(41),
(129), 449
J
W.,
64
pier (Cit too 4 los
Passo
E., 361(94),
375
26 5 Pe
PIS)
she!
(USA)
Kani
130
eH 220 (SS)
25>
Ik. - AOD) ~ SE
SS? (ED) | Gy,
B69 (19). 37d. nee
aad
Tey OWNS ey neziO1 (29.9)
es O10
55(40),
R.,
Kainnradis,e
255
M.,
OLOO)
3J.,
Kaelble,
Be, 302),1 3031209) 7 .33)7
es
255
ia
Ike pf) IPyD)
SmEIEy 298(186),
406(57), 445, 414(96), 447,"467 (36)
505, 469(51), 506
TINIE, Von QS
s Zax, 22O(SSy) 5
tO
Mey
Weyer
J.
J.
,
ESAS enip Repeater meet tl) yp eaaal
Shade,
Oper
le), 62, 90, 92(55),
Ike
PASC
aly) er alh) a Sesh
Ishikawa,
Die
Joseph,
K
es. (U7)
a9,
VOPLUNG),s
Joseph,
7%
Karpov, V., 474(61), 507
Kasahara, T., 314(256),
339
Kastnere Say L777 (o>)
2acm
Kato,
ean
Ho) 61 (82) 7) 239) un
Don BI, AOR, SE,
aA. BN US)) eeAe est
372
Kaufman, M., 474(61),
Kauzmann, W., 19(20),
Kawaguchi,
T.,
S337) 9.04
no yz)
507
33, 90(46), 130
246, 222 (358),
195(222),
253
Kawai,
58(61)),,65, 83 (21), 129),
S482) i els
OLSON 25)
256, eano
(296), 250, 283(86), 331
My thy p LON p
Reedy)
DavA
a
Keith,
Hs
D782
Meleh,
Zoo 80), SS
(86),
Sisal
SO),
PSU
PASO TEM)
Keller, Awipe27 (83),
S0, 285) Gal'5)7, 332
Kelley, F. N., 25 (65), 35, 105(103),
Ie
PIGS),
SIO
Kelly, A., 469, 471,CWA
COS (SA)
506,
Kennedy,
Kenyon
480(75),
Wer Distr
Al)
507, 483 (82),
3430),
Si)
LG
5 Lat;
240, 284(105),
Kerner, E. H.,
508
372
25 (27) yn S27
‘sy, SLO (CaleKsy)
387,
XO, Tots 229(113),
332, 489(115), 509
435(20),
443
Keskkula, H., 167(120), 240, 216(309),
251, 294, 319(160), 334, 294, 302,
306, 318(164), 335, 314(260,263),
Epc
hy X=) ere HI
PAON A)
Brac
416(110), 448, 428(153), 450
Khosla,
G.,
116,
ASI.
Kies) die Any 267 me oo (SS) DOD:
Maint, Ig May ASOD) 5 Shs
Rigiael, Weg, My tng 5 SINCE) 5 Bee
Rain eben) 27 S4o)e eo eo
King,
A.
L.,
164(108),
240
KalnciaGon94 melo)51((2.02))pao:
544
AUTHOR
Kinjo, N., 195, 225(230),
Kintsis, T. Ya., 469(49),
Kitagawa,
Klempner,
K.,
D.,
451,
172(135),
216(308),
246
506
241
250,
499(125,128),
Kuramoto,
Kurata,
429(160),
510
Klenany
Sle)
29 41(LO7
ip ooo
Knight,
G. J.,
31(99),
37
41601018)
448
LieI. 5, Ise),
Asi, GIS) 242, 194, 222(205),9245, 222, 229
(52), 253
Kline, J. M. 139(48), 237
Knowles,
J.
K.,
265(13),
K., 212,
395,
Kohn)
416,
M.,
214,
428,
on Uis
217(286),
429(34),
219,(347),
4 L4(94))
444
253
aan
Kojima, K., 285(116), 333
Kolar
el oo (22)
oa Selo Se
215(221), 246
a3
Kollanskyitys elle los Hm209y
216(198), 244
Kolsky, H., 164(103), 240
Komatsu, T., 195, 225(230), 246
KONGO, mateo Sims]O mS 2 0\(250))
ime
338
Koo
mGmaER aS 5:44)
352(45), 374
Koppehele,
132
H.
Koppelmann,
139(57),
253
Koretskaya,
P.,
J.,
T.
as7S pms sie
ania
93, 120(74),
139(12),
237,
a
A.,
235,
219(344,
345),
283(91),
331
Kons alka aaVem Vict mts 4010((5)) 07 nn
Korsukov, V. E., 302,303(221),
337
Kosaka, Y., 187(181),
Kosiyama, K., 47(15),
244
63, 116
(156), 136
za
KoviacsimAn Oey 47 (1920)
165(110), 240
Kragh,
IGZEWES,
A. M., 366, 376
Con Bop SISO),
Gs)
a
SEUS7))
MEN OCI, Abx Me, BOG. eve, ——
Krigbaum, W. R., 111(145), 136,
185(167), 243
2 t;
Krock, R. H., 453, 454, 467, 469,
472, 473(3), 504
Kuenzle, 0., 139(13), 235
Kuhlmann, H. W., 411(88), 447
Kuhn, W., 139(13), 235
a
iC. Je,
283)(90)im
S31
Kuksenko, V. S., 302(208, 209,
221) 7 308(208 7, 209) 221) 337,
Kuphal,
K., 26(71),
204 (236),
246,
36, 197,
204(274),
129
187(29),
236
J., 195(209), 245, 224(370),
254
Kwa, eHell Sata el6( 14S)
elo
Kweiy ele Ka | VOL 38)
iets
5 perSoreLou
194), 244, 216(308), 250, 215,
229(328)e 252), 429)(1O0)e 451,
499 (125,128), 510
S017
249,
Ladizesky,
N.
H.,
202(279),
249
Laka, M. G., 270(35), 329
Lake, G. J., 321(280), 340,
351(37),
373
Lancaster,
JO. Ke, 3597 36177 362(86)),
375
Lanceley,
H. A., 26(73)), 36
Handel
Rewr si, 2 60l0)), 79> e100 109.
TEE CUS) 7 122) 128) 9150) 7266).
2387727 9K(69) 7 S30) 320275) 39,
383(7), 443, 406(63), 446, 419(121)
422(130),
angi
Ger
425(121),
449
S07. (aol 3)iy 376
Langley, N. R., 107(122,123),
174(136,137), 241
hack, Re Ee 62658) pees
Larson,
G.
P.,
Lauis,
L. A.,
448
Lauterbur, P.
414,
430(93),
294(167),
134,
447
335,
416(108),
411(84), 447
458(22), 462,
464(30), 465, 467(36), 469,
474(30), 505, 469(51), 506,
498(114), 509
gee
Lavrentev, V. V., 356(78), 375
Lavengood,
R.
C.,
E.,
Lawrence, R. R., 347(25), 373
Lawton eH «dis 27 Se ab (Ae) eee S30
Lawton, R. W., 164 (2108)., 240)
we
Lazan, B. J., 162(83,84),
239, 350(36),
373
Lazanrelm S348
s52 (33)
S
GLO
(10 7))ee LO SiC)
ligase
191, 193, 209, 216(199), 244,
216(300), 250, 425(140), 450,
ae,
429(161), 451
Krautz, F. G.,)431(167), 451,
479-481(70), 507, 485, 486
(87), 508
aoe
Kravtsov, A. I., 341(2), 372
Kuhre,
137
139,
L
Pied) 2901(130)), SConms Ol,
(200), 336
KOCH el As emec ol eZ S2IG79) ise
Kodama,
Kurz,
116,
83(19),
I.,
328
KOChig
Kodama,
N.,
M.,
Kuriyama,
INDEX
201,
249
EVANS
Uo So7 SO2(AI\,
Leadermany Hes 75), 77 (21)
92)(68)
etsy
Seg
Seeder
159), 162.74)
a8
Lebedinskaya, M. L., 302(218),
Leben, L., 354(57), 374
401(42),
337
3
niet
Lee,
B-L,
Lee,
Lee,
C. C., 434(175),
451
L-H., 462, 465, 474, 486(29),
505
Lee,
W.
3
A.,
21(38),
445
21(39),
SATs
a (99)97
Lees,
J. K., 458(23), 465, 474(23),
505, 480(76), 507
Legge, N. R., 59(69), 66, 217(316),
251, 292, 294(143), 334, 397,
429(39), 444
iw
Le Grand, D. G., 302(211), 337
Lepie; A. Hi, 162 (95), 239) sae
Levreault, R., 56(43), 64, 118(167),
244
119, 137, 189(195),
Levens,
Lewis,
Lewis,
Lewis,
J. A.,
A.
F.,
F.
M.,
R.
B.,
480(79),
139(30),
411(85),
361(95),
507
236
447
376
AUTHOR
INDEX
Lewis),
Ti.
B.,
S824
S83i(5)im
soa,
392, 401(19), 443, 388, 444,
402(43), 403, 735 (43), “15
456, 458(21), 504, 494, 495
(98), 508
hae
Wty; Cle tly SCIEN GID) 4. ZAG
lishe dhs Win. PROS) , Skier
Iiibby, 2. Wa, 434 (177) 452
Lifshrez,
Je
Ma,
162:
163),
422(131),
449
Liska,
ieee
T.
J-
Ils
Be
mp4 25.38)
,449
301(199,200),
307,
343(10),
Gein
D.
372, mS553
376
hloyapeBorA
Lobanov,
As
infopee,,
Co,
HONG
135
30270303220)
Me,
217 (631),
UCI),
337
25200m
222 Ee
Longworth,
Tord,
R.,
Ge,
See
eau,
si(5s)
GED),
BAC) -
ms!
Bor
uss
HOt
os Asie
S O42)
256)
Moteantip
Gon 7 pl SOmete l(a) r, 242
Loveless,
H. S., 44(9), 62:, 348), Spy
S52\(32)
ass
ea
ales) 241
Lubin, G., 308(237),
338
Lucke, K., 228(381),
255
339
Lundstedt,
O. W., 319(268),
Lyons,
J. W., 160(79),
238
Lyons, Wa d., Sol, 352)(40)%, 373)
ByOns; Pe me, LOS (18)i 7 34)
Lovell,
Dn LAS)
E.,
S.
M
McCarthy,
R.
sir,
A.,
339
McCormick,
McCrackin,
Mac Grone;
Sully,
bly) (AGI) 5
Hr
F.
Wis;
L.,
213(43)q,
TAU),
329
329)
a
Ra
K. 7 139 (39),
236)
MeCrumpeNemG eo lee
2 Orel
G7 (IES)ir
240, 186(170), 187(177,178),
Dt, Pols, Oy, 22, APE GID);
229\(Ie1S Npmeeasine 29390) ieZool
395, 424(37), 444
McEvily,
(29),
McGarry,
0f.,
Aw
Jiey
S487,
373
F.
J.,
Spill,
328
443
452
335
ZOD (2) iy,
McGeary,
R. K., 382(4),
MoGisit
Cro Ries 434(177),
McGrath,
J. E., 294(168),
A.
P.,
MacKnight,
W.
J.,
McLean,
29)
373
187(186),
94(80),
244,
2oe(SoW)i azo)
480(74),
J.
445
195(211), 245
e252
D.,
R.,
507
a:
84(31,34),
130,
132
—*
MomManlilian
adjoins, 119 (176) BUSS}
6377939
H. Ji., 48(26),
238
Maeda, Y., 93(76),
132
Maekawa, E., 105(115), 134
McSkimin,
Magagnanal,
Asin
P=
Gin,
A.
(62)y,
205,220 (925),
LAMBS
EE
Magnusson,
B.,
4 ASIC
278(61),
330,
Yu.,
270(35), 329
284(99),
332
Ya.,
52(34), 64,
170(128), 241
Malpass, V. E., 166, 240, 369(118),
376
Mandelkern,
Manny
L.,
23(55),
35,
(94,95),
37
Ueieco
a (L>O)iso 4s
339,
415(99,100),
Margolies,
100(100),1
133
eb elso (55)
Hoshacie
347(25),
S52
329WJ,
130,
He,
A.
F.,
273,
30
1 OZOo)i,
416(99),
447
March,H. W., 48(23), 63
Marcucci, M. A., 362(99),
Wiad
aS 9 (24) p29 0/2 67),
284(25), 329
=
Ven Cen LO4(di06) )l33
Bong
MacKenzie,
Maiors,
I.
Malac,
J.,
Malkin,
A.
Pepe
so (S8)i e230
210, 216(248) , (2477,
86 7) pes 691A),
198, 209,
364 (102),
E. B.,
Z280i(70)) 2 sou
336
Livingston,
McIntyre,
McKee, A. W., 406, 411, 433(53),
McKenna, L. W., 187(186),
244
McLoughlin,
TiN, wo Me) 47 (538) 506
Lindley, P. B., 321(281), 340, 351
(Si), sSies Olle 362(92), 375
Linhardt, E., 56 (46), Gib, BZ
(133), 449, 497 (112), 509
Lipatov, Yu. S., 425(138), 449,
425(139), 450
Lipatova,
J., 225375)
yes
A. D., 216 (295),
250
250
ZUG
16491),
239, 428(145), 450
Lam, mCi (Kewl 221085)
pm138,
McIntosh,
McIntyre,
376
275(44),
47 (U3), 62, 89, 9343),
92(69), 131
WIG, UO GE) o Is, Sus
Mark,
372
(es) 7 BU
Marker,
L., 59(71), 66, 123, 138,
Marin;
335,
217(313),
251, 294(169),
416, 428(106),
448
209
26K 98),
Markerty,. Gey) Lou, Los
244
Bein USM GUE
Markovitz, Ble, LCE:
ASVI)
376
363, 367(100),
Marks,M. E.
290'(126)7333
H or
Markwood,
arLh W
446, 409
Marsden,
J. G. , 409 (80),
(81), 447
509
Marsella,
R. A., 498(116),
Marshall,
I., 300(193),
336
Martin, E. V., 285 (110) ,332
Martin,
G. M., 22(46),
34, ZSi(oo)P,
35
Meret Io. 185 Nay 411(86), 447
25iay 172 (134),
Marvin, R., 139(49),
241
164(101,162,105,106),
Mason,Pan oa
240, LTS 2) LEO 242)
63, 139(61),
Mason,
W. Piece 48(26),
238 T.,
TAL) 5 ASeye alePatatsysp) 5
443
386(13),
445,
V.. La, 406(55),
496(107),
509
448, 499
Matonis, V. A., 416(114),
Masuda,
241,
Matkovich,;
(119),
509
546
AUTHOR
Matsumoto,
A., 216(305),
250
Matsumoto,
T., 386(13),
443
Matsuo,
M., 216(299,308),2.
250,
(B87)
338,
i255
429(160),
Matsuoka,
S.,
451, 499 (125),
510
188,
243,
187,
202(273),
Matsura,
Maus
Moriwaki,
M.,
83(19), 129
Morley,
J. G., See asiaes
508
Mornis;, Et Gey CLULO)),
129
229
SS paesi Or 320(251),
205(180),
248
H., 206-208(285),
nia (eck Oncsa6))n,,
249
ASS
139
Maxwell, B., 104(109), 134,,
(2M) , PRY, 16287Oe
5-53), 163
(87,92,93), 239, 285(111),
BG7.(4)) es Ome
May, Go Bay UOC), 195, 229 (392),
255
Mears,D. R., 270(27-31), 271(30),
329
332
Medaliial,
Ae)
ie,
(406,
411,
413(66),
446, 413(91), 447
Mehan, R. L. 745312) 04
Melchore, J. te 343(15),
Menges,
G.,
Mercier
ule
372
96(85), 132
Pie
Ope Sis 114(40),
Merz,
(Ca New,
Metelskaya,
Meyers
e234) pm 252,
T. K.,
Nii
Oleg
Michno, M.
Mikhayllovi,
Soe
aoe!
474(60),
507
249,
58(60),
395,
Moacanin,
J.,
416,
428,
22(42),
255
Moehlenpah, A. E.,
AST),
32
Moffatt
Mohr,
Ge
Je
elie
Ge,
65,
375)
214,
216 (289)
429(35),
oil) ie 332
504
Mooney,
M., 381,
443
Moone; iG.) Eyes, 2.SuN(Si0))
essa:
MOORE mR
Orsi 910) (516) eon oor
H@): Seta
3
Moreen,
H. A.,
499(121),
509
Morey,
D. R.
7(14)\,
33),0235
(GENO) ac 27708)
SO9K(283)0,
338
—
Morgan, Hise Met, 19191259) ae OOF
248
Morgan,
P.,
354(4),
223,
pae2tsie222640)no
r252) 2221856)
228(365),
254
352(48),
374
294(168),
W.
W.,
335
198(257,
258)i, Luca
Moser, B. G., 383(7),
443
MOSEOVV
Ct
ano)
ees) eee©
(187,188), 336
Mrowca,
B. A., 48(27),
63
Mueller, A., 201(270),
248
Mueller,
E. R., 411(88), 447
Mueller,
F. H., 92(60),
gals
301 (195,196), 336
Muleinisy a Gietn S ecco
ecOLeey
340
Murayama, T., 84(29), 12%,
ZA
A ie7
169(124),
(140), 241
336
Murphy, B. M., 301(203),
508
bb alolehiay he 125¢, 486 (91),
Nagamatsu,
2G
o53)-
ray
K.,
265,
ATS)
6Siy
83,
116
114(23),
129, 114(152),
CIs 2i 156) als
136. 116, 137
Naganuma,
Y.,
M.,
167(121),
100,
Soin
Nakada, O.,
Nakagawa, T.,
240
101(104),
133
eee
Gi6) loo
195, 225230),
246
Nakamura, K., 195, 225(230), 246
Nakanishi, M., 195, 225(230),
246
Nakayama,
Narkis,
C.,
M.,
Nash,
R.
WEIR;
139(32),
406(46),
409(70),
W.,
236
445, _408,
446
=
139(26),
236
Isls Vg A aly (ish) » Sse 262 (5));
B28)
sail (246)
Ssiciun
Natarajan,
Nauton, W.
R., 301(204), 336
J. S., 351, 352(43)i,
Nedexveen,
‘Gad.
139103)
2385)
373
S9
(23) 2361004 OG) 422160) ieee445,
405(68), 409(74), 446
Newmark yy ty Bs), 8431564)Sil
Nelson We,
27/8) (60) SS Olen
Nelson, L. E., 409(79), 446
Nemoto, N., 83(19), 84(27), 129
Nestlen, H., 360(90), 375
na
Newberg, R. G., 293(148,149,152),
Newman, S., 56(42),
T7ONL25)07 2430,
27/3'(49))i7
334
64, 139(33), 236,
88 (19:2) 4 cee
330%) 30.6227)
a3
343
Gay), S72
ee
Nicholails slat, 9265),0 301.3075)
azar
406 (46), 445, 408, 409(70), 446
Nielsen, L. E.,33 -35, 37, 62-66, 128,
131-137, 236-239, 241-245,248250,
252-254, soe, T5290 posal 532,
334, 335, 372, 443-446, 448-451,
a a
S04 05/505 00 nnn
504
Morgan eRe Ul lS 91(40p23 7
OS
LOMO) i 245 eons)
C20)
(G20)
444
34, 229(391),_
AOE) -, Ge4p
4545),
R.,
Jr.,
Nagel eH ay
IS )ipn Soe
J., 498(114),
509
V. K-, 355), 35674),
S.,
M.,
Moseley,
Nagasawa,
Miullowartczr dl e2 90 GUST) mses
Milagin, M. F., 285(113)
, 0332
Mined kOe Gt et and SONGS) tS ONE
Males a Diy Or. 3.91(5)a -2Si/nae
Miller, H. T., 162, 163(94), 239
Mee,
Ie Mop, ACS,
1) 5 BGp
1 LOS) ,,
Sy LOAD) » BAL, USO),
2AL
Miyamoto, K., 83(21), 129
ras
Mayamotoln el e222 Ama 7i(286)e 249
395, 416, 428, 429 (34), 444
Miyata,
D.
Morton,
N
Enh
O5(82)e,. lazy leo (77in7 8).
LEI(78)) 238) U7 ICL29)), 24
DUP, DUS, SUED) , B29, BROOM)
332/294), Sees)
Morrow,
130
INS (UST) 7 WIG, UWI.
Meredith, R., 93(75), 132
Merriam,
INDEX
Ninomiya, K., 100(101-103), 133,
SS UST (GD), BS
GE
Noga, E. A., 431(166), 451,462,
474, 481(27), 505
Nolle,
A. W.,
48(28)63,
, 139(4),
109
465,
235
AUTHOR
INDEX
547
Nordby, G. M.,
Norman, R. H.,
375
Norris,F. H.,
480(77),
355(69),
507
374,
198(251),
we
icuonias
247
NOGtOnN
pure,
Nowick,
Nozakd
Ree
S., 228(380), 255
pC, 2 61299)
25
0 ee
Don Win COMA
mE,
339 A.
238
ion Even
Ny@p
We,
357(82),
Sd,
oi,
317 (263)
USA),
Oberth yA. sEs, 4091(75)7)446,
431(163)),
457
Oberst, H., 194(203),
245, 313(247,
248), 314(247,248),
see 406(51),
TP)
EON)
445, 423(133),
449,
Ochiai, H., 219(348),2
a
OUConnow
DenGe
ain (Le
63, 90, 92(52),
131
Odani mi ym SS.(L9) eee.
Offenbach, J. O., 116(155),
136
Ogawa, Y., 58(61), 65, 216(296), 250
Ogihara, S., 1l6(157)j, 136, 161(82),
239
S.
M.,
317(265),
OhitayaMere2 24670)
254)
Okajima, S., 202(272),
248
Okano), .Ke 7) 185)(160)),. 242000
Oleesky,
S.
S.,
454(5),
339
504
Oliphant, W. J., 89, 92(42),
130, 162(96), 239
Oost
Sop
Maley, DEAI(25)/,
EUG GES) ip
161(81,82),
USPC) 5 BAW, P72 (E35);
1,
SSA,
BME),
ae,
so,
35G,
15932) 236,
AN,
241, 386(13), 443
Geis, Ws Asa SS, BAM,
avs
O'Reilly, J. M., 22(43), 34
Orlova;mteeP
ye (SS NpE coe.
Orowan,
E., 297(182),
O'Shaughnessy,
M. T.,
IAG),
WAGs),
Oswald, H. J.,
ashy
335
84,
290(131),
92(30),
333
OM Toole; edi) Ley Sol 44)
pests.
351, 352(45), 374
Otto, H-W., 313(252), 338
ONS, We, SoGheyys S77
Qutwater ~ ore
506
Owen,A.
Owens,
Oyane,
Ul.
J.,
M.,
OMAlveeiis
Parikh,
Onpm469,0
202(278),
354,
285(116),
Mon
RYO
ali
N. M.,
Parrish,
285(121),
M.,
Parsons,
D.,
G.
B.,
479(68),
507
We;
E.,
S56 (772) 7 oD
22(46),
34; 9
Sa (Ni)
Pe
Be,
Wie
Wan
Coie
eo
247,
SOs
(143,144),
750
cee
Pechhold, W., 223(364), 254
Pegoraro, M., 113, 114(149), 136
Penn ReaWer So pekabo
ee
wagae, On SGA). Gop. Aan),
428(150),
Aan
450
aon
Peterlin, A., 27(85), 36, 281(75-77),
2835
—27 re S007) Sol 05
(2227223)ie Sou,
a
Petersen, J., 225(374), 254
Wea, Dy Bi, SRAM),
Cues 455,
A644 93\(1'4)p a5 040) eee
Petker, I., 473(57),
506
Petrie) (Sa) He, OS
(1 2)pes4
456,
Rezdin tz, Gene elo 43 2)r 234
Maple, Co, LOSGUG), LS TALL) AMG USS, AB, 225(229), 246
Philippoff,
Phillips,
(89),
Piggott,
Pinchbeck,
W.,-
139)(56),
D. C.,
508
Mor.
P.
484,
9409),
H.,
237
485(86),
5001,
353(56),
(69) 45
PRUE Wo p SOTO),
486
484(85),
374,
433
508
S06
Pizzirani,
G., 224(369), 254
Plueddemann,
E. P., 409(79),
446
Blazelkiwe Dismiwtee evils)iy) sOSi Esa UOO)) i
130), 108),
VO9 (131),
135; 139(14),
265)
Polmanter,
4701041),
249
wet
li7i (USS)
io
IG
We
Say
kei
pena2
COGO)p 3S
120(180),
dele
Pomeroy,
C. Do
Porod,
G., 27(80),
POnter
333
puye,
aad
Payne, A. R., 162(88-90), 163(88-90),
164(88-90), 239, 280(71-72), 331,
357(82), 375, ot
406(65), 446, 428
Pon Ge
356(63), 374
LACS)
333
sk Cayy 270 (37 \rars29
ny
tos (76, ©4 5a
Pacers Ony eMac, 62214 5),
Patterson,
Di, 198i(254)i 9
Be
ez
499(121),
V.
PAGICY 7 eOveeS
Paieny
pen.
wwe
Ns
AOA)
Parkhomenko,
Port)
D. K.,
NOS
W., 139(53
eS 47.(27))\ >
(UO) 7 MSA,
O
Ohlberg,
C.
Bascoe;
MS
Passaglia,
0(30), 62
So)
Painter,
PalmMpmWemE
en
Rowles
uRmGermee
Pregun,
S. E.,
Prestridge,
E.
372)
Zoo)
eos
L(sSo) m2b2
308(243),
338
B., 413(92),
447
Ozaki,
M.,
100,
101(104),
133
Prevorsek,
Ozawa,
Y.,
187,
188(182),
244
SHayihy Sey) 5 Ss}
PxicenmG.1,1k2
29) (co)
meeo>
iaankeryy ay Jon- 2677) yms0i 283 (95),
Prins, W., 100(98),
133
rae
Wey tla Sek (Sy)
Pees
Pilla O ee iliien | 4-21 (50) pu .O
Dbkopoy Sy oie a PECs
msi
Pyankov, G. N., 341(6),
372
12
Padawer,
G. E., 496(109),
509
Padden, F. J., 27(86), 36, 281,
ZOAGS)i
Cosh moO!
Pac
Kea Die
AO
—S2) ime vl SO),
329
Pagano, Os Naa CHBICED rs ZACSer
Pagano,
N. J., 462(28, 31), 464(31),
505
Pyrkov,
L.
D.
138
36
5 43)(13)i75
M.,
416(108),
C.,
290(131),
294(167),
448
333
335,
332)
548
AUTHOR
R
Rogers,
E. A.,
270(37),
329,
198,
202(235),
292, 306(145), 334
Rabjohn, N., 278(58), 330
Radcliffe, S. V., 270(33,38), 329
Rademacher, H. J., 93(77), 132
Radford, K. C., 406(58), 445
esi (205) oso)
Rae teem
Ranby, B., 225(374), 254
Ranchoux, R. J. P., 292, 294(144),
334, 415(103), 448
Ranney, M. W., 411(83), 447
Rasmussen, D. H., 195(211), oe
Raumann,
Rel,
197,
G.,
246
Rawson,
290(130),
F. F.,
1},
Bon
ENC) 5 IPC), Tes,
198 (64), 238, 18770201, 215,
2es (1TI 246 nile?
217, 222)
S5
(186), 244
Read, R. M., 47(21), 63
Reddish, W., 219(343), 252
Reding, bye Pe, 25327)
mobile,
Reed
Reed,
224(371),
254
ea
Regeta,
Rehneryyd
(162), 451
D. R., 90(49,50), 91, 92
(49,50), 131
Remaly, L. S.,281, 283(81), 331
B.,
27(78),
M.
O.
W.,
Saba,
36
359(85),
375
Rider, D. K., 384(98), 332
Rider, J. G., 285(114,115), 287
_,
§114) 7 332, 290)(130)), 333)
Rieke; Ji. Kay201, 202), 2291(269)),
238
V.
R.,
469,
470(47),
Ripling, E. J., 17(18),
(187,188), 336
Riser,
G. _R., 343(13),
Roark,
R.
Rivlin,
R.
S.,
J.,
Robertson,
R.
L.
506
298
372
E.,
M.,
337
118(170),
137,
Robinson,
A. E.,
406(64),
248
195
446
236, 219,
222850) 258)
Roder, T. M., 281(80), 331
Rodriquez, F., 139(20), 235
Roe,
Roe
J.
M.,
139,
187(29), 236
R.
81,
129,
msa6,,
448,
337
294(159),
415102)"
421(128),
229(383), 255
381(2), 442
Rend
LLIN DAaS\e 136, wl85 (1167),
243
Roelig, H., 139(46), a8
Roesler, F. C., 297(177), 335
G.,
187,
215(324),
gra,
334
449
aes
198,
206(174),
251
219,
ds 7a)
Lion
Lab
138, 409(78), 446
Sadowsky, M. A., 306(231), 338,
472(55), 506
e
Sahu, S., 406(59), 409(59), 445
St. Lawrence, W. F., 406(62),
446
St. Pierre, Li. Es, 4250137), 440m
Saito, M., 187(181), 244
ca
SalleevaGay
\eea
Sallveriy Es, O.,,. 1284105) 9 S52
423(132), 449, 497(111), 509
Samuel's, (R= Ji-eLOSi(252) 5 227mm
Sands, A. G., 414(94), 447 _
R. H., 188(190), 244
Sasaguri,
(2267 227224
(226n22
7)NAG
284, 318(104), 332, 314, 319,
-320(259), 339, 428 (157), 451
Robinson, D. Wa» 13935),
C.,
J.,
R.,
243,
Sardar,
62
198-200(260),
428(145),
317 (265) 7 359)
K.
Sabitay
Sands,
321(276),340
44(8),
302(215,216),
Robeson,
33,
239,
Ss
Richmond, P. G., 406, 414, 422,
425(44), 445, 496(102), 508
Riddell, M. N., 351(44), 373, 351,
_
352(45), 374
Riley,
Mier
334
Ryan, J. D., 363; 367 (200), 376
RY.ZhOVi7) NiewiGer) 341) (2)igee 12
188(190), 2h a
Rempel, R. C.
Rhode--Liebenau, Wo, BB((Gily
pySs:
M.
ROtH
162-164(91),
EE mEe oe L2S)
Rovatti, W., 434(175), 451
Roylance, D. K., 305(224,225),
Rudakov, A. P., 341(1), 371
Rudd, R. F., 96(83), 132
Rugger, G., 496(101), 508
ROUSey
Russell,
Rutgers,
Reid,
Rhodes,
J.
301201) 307,
447, 416(115),
V. P., 341(6), 372
7 296(175)),, 3355) 1431
Richardson,
293(154),
A.,
Ross,
Rusch,
Mem
aesai(24) ysl
P. E., 301(204), 336
132
376
Roller, M. By, 139\(28),7m236)
Rollmann, K. W., 56, 57(50), 58
Gir By Wi, M35 2ODp ALG
(199), 244, 216(300), 250, 429
(161), 451
Romans, J. B., 473(58), 506
Ropte, E., 59(68), 66
Rosen, B., 297(181), 335
Rosen, B. W., 453(1), 469, 503, 455
(8,17), 469(17), 504, 469(43),
472(54), 506
Rotem, A.,
450
333
448
96(84),
369(117),
P.,
Rohall,
418(119),
Z.,
L.
Rogovina,
S.,
Rabinowitz,
INDEX
D.,
283(87))7
Satake,
Sato,
Sato
Sato,
(97)
270(33),
K.,
K.,
329) 9)
116(157),
331
292142),
S16)
45,
136,
334,
362
AlGhOl),
447
My, 205em206 (260)
4 0 samen
Ue osiry lls LL (25)oor
84(38), 130
A>
Y.,
394, 444
Sailer, J. A., 19(24),, 34. 221a7,
EG ip USGI, Gan EOL Cpxcia))
SO) 2169) esee“162 (96), 239,
187 (171, 173-175), 198, 206 (174),
2USi (UTE)
229(171),
243,
215
(323,324), 219(323), 222324) ,
25.07) 2U7(335), 252), 222352)
B55) 229(352), 253, 229 (386),
255, 260(2), 328, 270(28,30,31),
271(30),
329, 343(11),
372
AUTHOR
INDEX
549
Saunders,
De Wis peel Ope e207
9) >) 238),
L977 198, 202(235),
246, 198(247),
24,
202((269), 248)
Se
Sherrard-Smith,
Savkin;,
W753, 54)
Sd (Loo) eee:
212, 214, 217(286), 249, 219
(347), 253, 285 (Gig) pmsesr
395, 416, 428, 429(34), 4
Shindo, H., 219 (348), 253
a
Shinohara, Y., 216(303),
250
Shishkin Neer 2o Sills) masse
Shito, N., 205, 206(280), 249
Shooter, aKeven coui(cl)) Sv bm
V..
G.,
356(76),
375
SazhinpeB-mle e217 (S30)
mao 2
Schael, G. W., 354-356(65),
374
Schaffer,
.M.
Cs.)
Schaffhauser,
278(58)),
R.,
(22), 8322
Schallamach,
A.,
Schell;
Wa
te
Terr. jp e22 (3602),.254
vie e209 (838)p
225(357)),,
Schilein
347
64,
353 (53,54), 355\(72),
SIE) SMF 433(172,173),
359, 374,
451
Schatzkije
330mn
53(37),
252m 222,
253)
Hey)
<a
LOSi(217i
235,
177(151),
PA)
Schmitt,
(164),
335,
35,
222,
242,
302,
306 (212),
soe
337
7 oli
242
Schonhorn, H., 188(191,194),
244
Schoppee, M. M., 265(10),
328,
301 (1:97))
74336)
Schrager,
M.,
Schreyer,
351,
G.,
352(42),
58(64),
65,
216(301),
esol
131, 157(69-71), 158(69,70),
238, 393(31), 444, 406, 422(60),
Schwertz
EF.
Schwippert,
406(61),
SCOEG,
Wal
Aw,
G.
372
SOO,"
oO
Scott, W. W., 139(39), 236
371,
Semenov,
N. A., 341(1),
372
Sen,
J. K.,
Sendeckyj,
Senshu,
K.,
162(97),
G.
P.,
84(32),
446
422(60),445,
446
Rey
411(74),
s43tll)7,
A.,
341 (2) 7
239
455(12,18),
130,
S.
Ra
139(58),
94(63),
LOSS)
A.,
Ney
as 5,
425142),
3 91(38)),
450
23670
237
me
113,
LL6(1L48),
136
mE 651(9) VmZe
SEraLini
is Le
Sergeyev,
V. A., B41N(5) 77 37.
Sergeyeva,
L. M.,
Sewell,
J. H., 21(38),
34
52,
Shapery,
R. A., 435(180),
504
114,
508 M. G., 89, 92(45), wes
130,
Sharma,
R.,
409(76),
446
Sillwood, J. M., 487(93), 508
Simeoni, R., 177, 180, 181(149),
242
Simha, 22(41,42), 34 TOSI),
134, 218(338), 2 52, 222,
2251(357) eee:
Simon, R. H. M., 100(98), 133
Simunkova,
E.,
Sinnott,
K.
255
336
Skinner,
J.,
Skelton,
Schwaneke,
A. E.,
139(26),
236
Schwarzl,
F. R., 17(10),
33,7
92(59),
409,
449
Kee
Shreiner,
Shro£&,
(183),
373
250, 428(154), 450
Schultz md Me wo cle2 O5i(81))
445, 406(61),
419(122,124),
Shibayama,
Shuttleworth,
CPLR
PINOYEY
J. A., 294,
302,306,
SchnedlpmGeymesi(S 6)
92,
Shteding, M. M., 341(4), 372
Shtrikman, S., 387(21), 443 —
245
Schmid, R= 231(62))7 35) ae
Schmidt, H., 96(85), 132
Schmidt, P. G., 285(119)
Schmieder,
K., 23(56),
G47 13978 W897) 2197)
K.,
Alpe
Slonaker,
244,
265(10),
W.,
M.,
D.
I.
332
139(15),
188(189),
D.
S.
Skinner,
Slinyakova,
284(99),
M.,
351,
235,
328,
301(197)
352\(41),
(209),
F.,
104(108),
303(208),
Smallwood,
H.
M.,
337
386(15),
443
Smith, J. C., 139, 198, 204(31),
236
Smat hima
mekcmdie mel Islas
5)ye 136,
185(167), 243
SmichieRa Ra 2O ey 302 (146), 334
Smith, @. U.,205, 267, 268(21),
328, 267(22-24), 268 (22-24),
278-280(24), 329, 278(61),
406, 409
B30 280670), So
(52), 445,
Smolluky
419,7 425(121), 449
68), LL9(3)ie 128
Gumi
Ts
474(60),
Soliman,
F.
1.,
283(91),,
331,
507
Y.7;
479(71),
507
Solomon,
D. H., 181(156,158),
Soney
deni
S 02197) i mesiao!
92(73)
162(97), 239, 406 (62) , 446
Js, 293(154);,, 334
Shaw, R., 139(6), 235
Shen, M. C., 19(34,35), 34, 26(74), 36
84(26), 129, 107(121), 111, 134,
USiZiy
373
434(175),
451
451
B., 431(164),
Slonimskii,
G. L., 96(84),
Slutsker,
A. I., 302(208),
Sogollova,
487(94)
187
229(389),
Sookne, A. M., 273(41,42),
352(47),
374
Southern,
Beis
oo Co),
oid)
Speerschneider,
C.
J.,
Spence,
J., 198(244),
247
Spencer,
R. S., 19(29);)34
Sperling,
L. H., 122(186),
122(184),138, 195(216-218),
197(218),
245, 219(346), 253,
422(129),
44
Sherman, M. A.,
OLS 37235) 7 292
(U3887L35)inesss
Spurlin,
H.
Stachurski,
197,
204,
Stainsby,
138,
510
M.,
290(126),
SSIS
Z. H., 187(187),
244,
198, 200,
205275)
D.
329,
433(174),
Sharp, T.
499(122-124,127),
242
F.,
204(238),
24
eso
139(21),
236
451
AUTHOR INDEX
550
Tanaka,
T., 181(156),
242,
ZL
ZAT iy 253
Tarnopol'skii,
Yu. M., 469,
Sittaritay, wie) Me, 499(126),
510
State
she oO C1243)i 338
Starkweather,
Jr.,
H. W.,Bo
(80,84),
Statton,
SS25
ZOIGi2)i 36
3
03210)
Soir
A. J.,
2229)
17(10),
33,
HESOV 2
azo!
Stearns,
C.
A.,
139(48),
237
SEGAENS
pn
ots
OACe
SS) ir
Stephenson,
Ce
S.,
Stern, D.,
He,
s4 (27a);
409(80),
47(21),
446,
BUS)
409(81),
63
Sternberg,
E., 306(231),
338
Stevens,
D., 496, 497(106),
Stockmair,
W.,
Stockton,
USiGie
167(116),
F. D.,
240
54(38),
64, 111(142)
LS 5166) pe 43
Stowell
Bazin,
SiEPAEEOn,
(Ra
47(LSn,
Ar,
63
), 240, 306
e651LiO
(229)Fa sow.
Strauch,
O.
R.,
414(95),
447
Street, K. N., 480(75),
507
Strella, S., 17(16), 33, “139 (36), 236
306 (227,228), 337, ~308(240),
338
Strong, J. D., 195(216,217),
245,
ZIO(S46)0 25S
SEGUI
Ley Cee Earl,
Se) sey
E5869),
238, 224(368),
254, —393\(31)> 344
44,
406, 422(60),
445, 406(61),
446,
419(122),
449 —
Sumner,
J. K.,
Sutherland,
T.
284(98),
332
H., 19(26),
Sutton,
453(1),
W.
H.,
469,5
453(2), 504, 469, 505
Suzerki, Y., 110(139),135
Suzukay,eever ele 7.597 el5.4.) ieee
Sviridyonok,
A. I.,
Swanson,
373
Sweeny,
Swift,
Di.
L.,
Dig
H.,
iWJ.;
Temple,
R. B., 198(250), 247
Terada,
H., 187, 188(182), 244
Tetelman,
A. S., 484, 485(86), 508
Tetreault,
Reds, 215(329)" 252
Thedinin Wiel elt ey 354-356 (65),
374
Theocoris,
P. S., 84(36),130
Thomas,
A. G.,
321(276, 277, 279-281),
340, 361, 362(92),
375, 416(112;
113), 418(118),
448
Thomas,
D. A., 96(86),
E32;
122(186),
138, .499(123,
124,
510
THOMAS
Wis ls Reo Or 436(179), 4452
Thomas,
L. S., 290,
ZO2HMS 6), 333
12.
Thomas,
1b.
His,
SDC,
Thomas,
R.
L.,
481(81),
508
Thompson,
A.
248,
Uvawevaays
198,
300(193),
Thomson,
507
Thorner
B.,
J.
Jen
B.,
375
491,
*225:(256)),
505,
480(79),
336
467,
Ae,eZe(70))
1stypy AMC N7A))
35
34,
423(134),
SOFT GEUS)) 5 0)
cal)
Piew Hele
Hi 82) ny 36!
Timoshenko,
S., 121(182),
(Lis) Fess 5y0s65)snG
ToOboliskya ASmLUea iGnie 3377
39,
64,
494(97),
20477,
56(49),
65,
2337),
59(70),
597,
Sigil ©) pO Seo
444
242
20S (G44)
242, 185(164,165),
243, 198(246),
247, 217(314),
20 E29 ASD
301 (199,200),
307(199,200),
336,
347 (21,22), 372, 429(159),
451
an
356(66), 374,
367 (104),376
53(37),
64, 84(26),_
Toggenburger,
R.,
273,
330
maid
Dabow7 De, SOs
Sle
856,077),
Stig eSODF
Okita ya Neelso
Takahashi,
Tompa, |A. S., 279(65),
330
Toor,
H. Le, ZI0K27i
ses.
Trachte,
Keen oliver, AS,
AR
301,
328
OS
M.,
4 (22) ype odie
Takahashi, Y., 216(294), 250
Takano, M., 200(266), 248
Takashima,
A., 386(13),44
Takayanagi,
M., 58, 59(65),
66,
139(60)
7230) USts 18s, 225:
(185), 244, 198, 200(264),
2S, PANES) 5 285, SOCON -
445,
429(158),
451
Takemoto, Ty, Ll4,ile(l52))),
116 (158), 137
Takemura,
(152),
T.,
136
114(152,153),
Takeuchi’,
(As) 202)(272)),
248
Tanaka,
H., 216(305),
250
449,
75, 76, 79, 128, 84(26,28),
84 (31, 33), 34) mo ON47)i eLsior
132, 105 (118), LOTCL21
eee
345
US (AO 1419) els Sy LESG47)ye laiom
(B55)
9 (47a
SG eel eh
cin
343,
Kona, 393(28),
Ss ADISy- 181(158),
R.
Di
338
Stein
Re Sip li (S157),
TRIS MENT)
IESG, abies, |be)
(245,246,251),
247,
331, 416(105), 448
Sterman,
447
A.
Taylor,
283(96),
O.,
sO 27
Staverman,
506
107(120), 134
366, 376
Taylor,
Ge. Rz; 278-280 (59), 330
Payor
iso ez
25, 26(66), 35
faylor,) Ra Ba, 84(26),
129
Teitel'Baum,
B. Ya.,
341(3), 372
Teltavcr
Dis
yy (esi, 33, 311(246),
Tawn,
331
W.
136,
116
(6)
333
mez o or
a
290 (132)),
307(6),
Trayer, Ga Wan 4.8123) 63
Tregear, G. W., 294(170), 335
WaAMWerWe, Whe Wo Cop MS, WOOTGAD)~
ZO2M 277) 2 4o) 275 (57), 390
Trementozza!,)
\OMmeAc
1217/3149) wSSO
Dza
=a
Trivisonno, N. M., 139(48), 237
Tsai, S. W., 388, 444, 455(7,13),
456(13), 504, 760(25), 462(25,31),
464(31), 466(25), 505
Tschoegl, N. W., 122(185), 1387, 422
(131),
Tsuge,
K.,
449
187,
188(182),
24
AUTHOR
INDEX
551
Tsunekawa,
Y.,
285(116),
333
PSUS
Mey
SOO 119) > Se
Tugjnman,
GC. As Fe, 187(184),
W
244
Gewbeeps lig. lig p PPG) 5 SEO
is
TuBwey
ose Gs ps OS OS),
C57 (20),
240), 216(309)7
251, 314 (258,260),
S9( 258;
A235
32012260),
260)
3))0,
339,
0.
Turner,
L. B.,
293(149),
334
Hhbb aver
I
Ban “salaispy
Turner,
Se;
IO0K(53) 7a oly, 92(61),
92(53),
94(66),
TLAN(62) 5 UG:
Usd, 92, 94(71)), abe shae(Gha
yy. 5
120(181),
1387, 479(69),
152
n,
W.
R.,
469(42),
Weedon
Uematsu,
Uematsu,
Uemuna,
Wenoye
SS
<<
SU 97S 20(250)
185(161), 242
LESS), Be
Mo,
L287 (si),
69(L19)
p
yes
ore
3137
Es,
Yop
244
S77
Updegraff,
I. H., 344(18),
372
Ushirokawa,
M.,
83,
113,
L425)",
129,
Utracki,
84(38),
Ge
130
LOSi(laen) > 134
Valentine,
R. H.,
109 (U34) 7 135
Van Brederode,
R. Avr
3'9\(20)
e235,
Vanderbilt,
B. M., 409(82),
447
Van der Wal, Cc W.,
139(23),_
236,
406, 422(60),
445, 406(61),
446
van Duijkeren,
M. P., 224(368), 254
Van Holde,
K., 90,92(48),
130
van HOOEN
Haye Oe
OL
BOS) is
330
Van
Kerpel, R. G., 229 (383), 255
van
Schooten,
Je, Pakeyy PREG, SITS 3)%,
330
Van Vilack,
L.« H.,
ae
Van Wazer,
J. R.,
160(79),
Vasilieko,
Ya. P.,
ree
Vernon),
2.7) 229'(388) 7 255)
238
49
Vickers7, H. He, 355(70)
7374
Veith, A. G., 361(94),
375
Vincent,
Pee Leg e024),
92O5i13))),
328, 301(198),
336, 308(235,
ZAI)
SOI 2857245) iy ol aoe:
(235), 338
G.
V.,
52(34),
64,
POL
2 8) ip 2a,
SO DoD OA) iy
375, 406(48),
445
mye 2542)450
Vokulonskaya,
I. I.,
Volkova,
T. A., 425(142),
450
Voyutskit,
(Ss Say
340(4)%)
3i2)
139(14),
23
Vrancken,
M. N.,
54(61),
Vroom,
W. L., 270(36),
329,
374
R.,
, 187, 188(182),
37 3114(256)), 339
3201(259) F339)
314, 319,
428(157),
451
Wagner,
H. L., 474(62),
Wagner,
M. P., 474(63),
Wales, M., 283(90),
331
Walker,
R. W., 355(75),
375
View, ats Nails Is
BeOGlRy
DINGS) p PSA, seta
406, 414, 422, 425(44),
496(102),
508
Wallach,
M.
L.,59(75),
Walters,
M.
H.,
4285)
A.,
66,
450)
362(98),
425(135),
Aes,
ae”
44
as
ZA AS E2))iy
376
449 _
Warburton,
B., 314, 330087), 339
Ward,
I. M., 39(4), 62, 92(72),
132,
187 (187), 244, 197(237,238),
198 (237-239,254),
200(238),
201
(237), 202237),
204238),
247,
202\(276,278,279) 7 204 (275), 205
(275), 249, 225(373),
254, 265,
300(14), 3:
328, 270(37), S20); 285
(2207, 1227123),
2901(122),1:29)) , 300
(120,192), 301 (192), 336
Warfield,
R.
Wargin,
Vv
Vinogradov,
E.
Wambach,
Uechberrelter,,
Ke, 23(51,52)),
35,
BSG) 5 ein alah, AUSKOn GIS)
i
25
Y., 84 (37),
244, 222(354),
Wagner,
25a)
506
U
242
Wada,
R.
W.,
V.,
270(34),
279(64),
329
330
Warnaka,
G. E., 162,
Warren,
R. F., 229(388),
Warrick,
E. L.,
411(84),
447
Warshavsky,
M., 290(132),
333
Waterman,
H. A., 48(25),
63, 139 (62),
238,
198,
254
Waters,
204(262),
N. E.,
36705),
Watson,
Watson,
M.
W.
239 Dy
Watts,
Weaver,
Webb;
Cs,
A.
D.
352(38))7,
Bil;
E.,
Be wSse)
188(190),
oOo
A.,
(E20)
R.
(6) Feo
37
104(108),
F.,
366,
(89),
252
244
eine
1134
Weusr en (ose bays nln
o/A)ee Spr
2367229392)
eo)
Welner, S., 23, 24(59),
35)
Wen, BP. R., 89, 92:(45) 7) 130
Westover,
224 (368),
372
(9),
162-164
109,
135,,
T.,
F.,
Reo
Weems,
Soyby
376343
248,
13922),
270(36),
a)
LS O40
5 5)ir ZSiliy
R. Es,
217 (332), Zoe
BEGLOA)
Weyland, H. G. pp
ZO2 ZT Yip 249,
White,
E. F. ..
336
BOM C203),
Wetton,
White,
J.
248,
W.,
198,200,205,206(265),
285(125),
White,P. L.,
333
499(120).,
509
Whitman,
R. D., 215(327),
251,
224(371),
254
SieMl
Whitenevy Uren SueneeZOls, 28279),
Whitney,
J.
ASS (11)),
M.,
504
39,
40(2), 62,
552
AUTHOR
Whitney, J. W., 198(242), 247
Whittaker, R. E., 280(72), 331
Wright,
Wiederhorn,
N.,
Wiinikainen,
R.
Wu,
B75
Wiktorel
Wrzesien,
113,
119(147),
136
A., 359, 363(88),
Wijga,P. W. O.,
mR U3
275(55),
ly
251,
373
Amie.
BO,
52 (4)
Williams,
A.
Williams,
G.,
Williams,
205).
2197
J.,
L.,
499(121),
esr)
509
129,
118779201,
Winans
Rene
OOS
23 Nps oS
Witnauer,
Ga Pi, 343\(13)), sov2y
847\(27)) 7)873
ae
Witsiepe, W. K., 217(318), 251
eReS.5)
43I(27)1
Gs
~—ee
Woerner, S., 223(364),
254
Wohlnsiedler, H. P., 344(18),
Wohrer,
509
Woltmik.
L. C.,
A),
406(55),
23(56)),)
372
445,
35),
496(107),
56(44.45)),
64, 139 "189, Bie), PAA POM) , Beis,
177 (251). 242, 187 (184), 189 (196),
215(184), 219,222,225(184), 244
Wolfe, J. M., 92(72), 32
vo
WolockyLenecO0(s3)135)he2o2
135)
SSO eZ ORS)
Wolstenholme,
W.
E.,
372
Woodhams,
465,
D. E.,
162(85),
R.
431(166),
474,
509
Woods, D. W.,
241, 198,
Woodward,
A.
T.,
481(27),
19(24),
D.
19(27),
B.,
P.,
34,
225(376),
29, 36
21(40),
HS} 5
34,
x
Xanthos,
M.,
498 (117),
509
¥.
PS I(B2)
Kix,
e250
H., ois) tena) (348),
253
Yamazaki, H., 369(119), SLT
Yanko nie mAvs a2) 3147) eo
eS
Vannas
mele
L 2.5 (240)
5
Yano, O., 222(354), 253
Yanovsky, Yu. G., 406(48), 445
Wes)
5 Cn, SLE), Sa
Yavorsky, P., 139(50), 237 |
Yeh; G. Sin, 367 (El), S69KEE7)) 5 Sao
Wie Ave ee42 Sil Sep) a9
ees
Vii)
Paeepeeligl4(clesdh) moar
Yokoyama, T., 206-208(285), 249
Yorgiadis, A., 162(84), 239, 350
(36)b 8373
ars
Yoshino, M., 139(60), PRY BS
(387), 255
Yoshimura, N., 58(59), 8, ZG ZIT) ae
250), 293)(150)),, 334, ~428, 429
Tis2), 450
Yoshi:tomi,.
‘De
116 (152),
137
YOUNG HEC aun
Young, D. W.,
334
ATS)
136, 116
63), 114,
63,
(158,159),
27 8i(60) aass0
293(148,149,152),
(lec
1307,
239,
347(20),
451,
505,
462,
498(117),
acon
56(41), 64, 170(126),
204, 225 (256), 248
E.,
Wyman,
508
509
ese4
84(35),
308(243), 338
=o
Wolter, F., 411(88), 447
Wood, L. A., 26(67), 35, 108(128ASO)
5
ne
Woodbrey, J., 195(209), 245, 224(370),
ces
254
Woodford,
F.,
Yamamoto,
Yamamura,
374
PU, BND, B22, 2H) » LES,
ANG, BINS) 7) LEZ
Williams, J. L., 343, 344(16), 372
Williams, M. C., 84(29), 129
Williams, M. L., 76(10), 79, 100,
UOMGLS Va L415)
22) 2870 50
(GO7C7) pn 7 2166)in 2S87 422) (130)u,
449
Williams, M. L., 297(184,185), 336,
302, 303(220), 305(224,225), 337
Witte,
Wuerstlin,
Wunderlich,
INDEX
249
487(92),
496(108),
BAW(Prey) ;
354-356(65),
81(17),
A.,
T.,
m222(319)0,
222(OS0) > 253,
B.
T.
202(277),
254
330
Wilchinsky, Z. W., 198(249), 247
Wiley, R. H., 19(23) ,34
Wilkes, G. L., 123, 138, 416(105),
448
Wilkinson, C. S., 139(47), 237,
162(86), 239, 347(20), 372
Wildibousn,
H.,
34,
224
De
25 Us (Ql NS) 5 Ouaee229 (1711,
194 (205, 206), 215(205), 222 (205,
206), 245, 201, 202(267), 248,
2 Tee O8 23) yee lel (SSORSSNie
222201886) i255
WORE Ws Iho, SUS,Aye
Work, J. L., 56(47), 64
Wrasidlo, W., 167(114), 240, 217, 218,
*
2291(83'4) 252)
Z
Zahradnikova,
A.,
Zakrevskyi,
V. A.,
ZO
S49)\e 253
302, 303'(221)) 7
SB
Zaks peviaen Bare 302(218),
33
Zapas), lie
L395 0), 237
Zapp, R. L., 361(96),
376
Zaukelies,
D. A.,
383 (Bey
i
Zelinger,
J.,
58(62),
33
65, , 216(298),
250, 284(99),
332
Zhurkov,
S. N.,
302 (208, ZUR 22)
310/3'(208,221) , 337
Ziemianski,
L. P., ~411(83),
aa7,
DUNNEy eA Mie, 29'0\(1-29)) e330 ee
Zilvar,
Zimm,
Zikek,
Vici
B.
oo te
H.,
P.,
S8i(62) emo,
250 P.
I.,
H.
M.,
Zubov,
Zupko,
So 2KA
6) a maid
76), 128
425(142),
188(193),
ove
216 (298),
450
244
SUBJECT
A
Abrasion,
materials
definition,
39
Anisotropy of fiber
40, 454, 519
Antiplasticization,
ASTM
Craze
cracks,
SOU, 430
Crazing
stress-strain
tests,
effects
creep,
effect on,
96, 122
Creep
biaxial,
121
359
Anisotropic
standards,
composites,
B
100
Block polymers
creep of, 121
modulus
of,
of,
By.
208,
394
modulus-temperature
stress
dependence
of,
87
temperature,
effect of,
84 tests,
4, 67
thermal
treatments,
94
curve,
aes
solvent
WAP,
effects,
PAUSY
428
stress-strain
292,
tests
Crosslinking
creep,
effect on, 106
dynamic properties,
effect
modulus of rubbers,
176
on,
415
Branching
viscosity,
effect
on,
104
of
Coefficients
friction,
of
353
thermal
filled polymers,
Cold-drawing,
282,
expansion
dynamic
487
modulus,
interrelation
to, 182
stress-strain
tests,
274,
280
434,
299
theory of,
299
Complex moduli,
12, 139
Composite materials,
379,
creep of, 418,
479
dynamic
422
mechanical
hardness
of,
distortion
431, 481
impact strength
interfacial
temperature
of,
430, 483
effect
adhesion,
of,
thermal expansion,
thick interlayers,
Cracks,
295
433
factors,
434,
497
513
of,
499
392,
465
stress relaxation of, 421
stress-strain
tests,
405,
wear of,
Conversion
filled
of,
405,
on,
Damping
advantages
and disadvantages,
creep,
relation
to, 158
definitions,
12
fatigue
life, effect on, S}5)1L
of,
409, 471, 483
interpenetrating networks,
strength
effect
181
D
properties,
modulus
of,
387,
454
particle size,
effect
properties,
174
106
453
433
heat
on,
stress relaxation,
effect on,
stress-strain
tests,
274
Crystallinity,
26
creep and stress relaxation,
effect on,
111
(e
Coefficient
157
effect of, 118
crosslinking,
effect of, 106
crystallinity,
effect of, 11l
fiber-filled composites,
479
models,
70
molecular weight,
effect of, 95
Nutting equation,
78, 89
orientation,
effect
of, 149
polyblends,
121
pressure,
effect of, 93
Biaxial orientation,
264, 290
definition,
42
Blends of molecular weights,
properties
281
on,
block polymers,
121
composites,
418, 479
conversion to dynamic properties,
copolymers and plasticization,
195
3
dynamic
428
INDEX
polymers,
487
422
interrelations,
16
mechanisms,
147
molecular weight effects,
171
rolling
friction,
correlation with,
stress relaxation,
relation
to,
41]
159
swelling ratio,
Damping peak
465
142
effect
of,
shift with frequency,
143
Deflection temperature under
341, 345
Dewetting,
409,
Distribution of
Wisi ausy:
553
483
relaxation
IWS)
load,
times,
354
554
SUBJECT
Distribution
of
retardation
times,
(ap BSS
Dynamic mechanical
instruments,
139
Dynamic mechanical properties,
1l
chemical heterogeneity of
copolymers,
190, 209
composite materials,
422
copolymerization,
effect of,
189
crosslinking,
effect of, 174
crystallinity,
effect of, 181
molecular
weight
effects,
stress amplitude effects,
temperature and frequency
143
history
time-temperature
effects,
161
effects,
165
superposition,
conversions,
Fracture
mechanics,
Fracture
theory,
Priction,
factors
E
intermolecular
Failure envelope,
268
Fatigue,
348, 480
fiber-filled composites,
480
Fatigue life, 349
damping,
effect
on,
351
Fatigue tests, 348
Fiber-filled composites,
453
ereep of, 479
fatigue,
480
heat distortion temperature,
impact strength,
483
dependence,
modulus of, 454
randomly oriented fibers,
474
strength of, 465
strength of laminates,
474
stress-strain
tests,
465
thermal expansion,
487
Filled polymers,
379
354
forces,
polymers,
of,
effect
433
stress,
effect of, 344
Heat distortion
tests,
18,
Hertz
hardness,
365
Hookes'
law,
341
10
E
Impact
strength,
composites,
308,
430,
erystallinity,
483
430,
483
effect
of,
317
properties,
correlation
fiber-filled
with,
320
composites,
instruments,
308
notches,
effect of,
orientation,
effect
polyblends,
309
of,
483
314
318
temperature,
effect of,
313
Impact tests,
17
Indentation
tests,
363,
365
Interlaminar
shear
strength,
473
Interpenetrating
network
composites,
Inverted
499
composites,
481
459
394
K
Kinetic
theory
elasticity,
of,
modulus-temperature
58
Heat distortion temperature
annealing,
effect of, 343
fiber-filled composites,
481
filled polymers,
431
dynamic
143
¥
angular
353
affecting,
Hardness,
363
Hardness
of composites,
157
48,
416
on,
298
296
Glass transition,
515
copolymerization,
effect of, 26,
crosslinking,
effect of, 23, 177
molecular weight dependence,
22
plasticizers,
effect of, 25, 193
Glass transition temperature,
18
chemical
structure,
relation to,
curve
Einstein
coefficient,
381, 391,
458, 459
Elastic modulus
anisotropic materials,
39, 454,
49
519
composite materials,
387,
454
conversion
factors,
513
definition,
9
dynamic,
12, 143
isotropic materials,
39, 387
measurement
of, 43
rubber
theory,
176,
275
temperature,
effect of,
Entanglements,
97, 271
347
Foams
modulus
of,
394
stress-strain
tests
Graft
relation to, 160
Dynamic mechanical
tests,
11
Dynamic properties to creep
conversions,
158
Dynamic properties to stress
modulus,
temperature,
INDEX
496
G
150
viscosity,
relaxation
Flex
composites,
170
orientation,
effect of, 197
plasticizers,
effect of,
189
polyblends,
block and graft
polymers,
208, 428
thermal
Flake-filled
of
rubber
1767)
275
L
Laminates,
strength of,
Logarithmic decrement,
definition,
14
474
193
20
205
SUBJECT
INDEX
555
M
Master
curves,
JUNBF L227
jz
SOpeeC Siac Onl Ode,
oO aml 2
26S
Packing
fraction,
381
Penetration
softening
mcdel,
68
POU s lS
Maxwell
Melting
copolymerization,
19 3
molecular weight,
plasticizers,
Modeis,
68, 70,
Molecular
dynamic
170
creep,
effect
of,
30
effect
effect of,
of,
Sp
30
AES)
148,
rheology,
on,
effect
definition,
orientation,
Polyblends
258
weight
properties,
effect
347
inversion
394, 428
Poisson's
ratio
Phase
creep
effect
83,
on,
on,
97
Polymers,
40,
Retardation
454,
effect
of,
NY Oya BUD
kinetic
theory of,
measurement
of, 43
394
Modulus
of block polymers,
454, 491
of composites,
387,
Modulus
errors
in, 401
effect of, 402
thermal
stresses,
of filled polymers,
387
Modulus
effect of, 39/3)
392
particle
size,
effect of,
viscosity,
relation to, 386
of foams,
394, 416
Modulus
394
of inverted composites,
Modulus
of
polyblends,
394
Modulus
of ribbon-filled composites,
Modulus
adhesion,
curves,
effect
209
58,
of,
56
Non-Newtonian suspensions,
384
Nutting equation,
78, 89, 158
stress
relaxation,
Lg
properties,
effect
impact strength,
effect on,
effect on,
Poisson's
ratio,
stress-strain tests, effect
75
71,
75
490
Ss
Scratch
resistance,
359,
362
Secondary glass transitions,
215
liquids and plasticizers,
195, 219
Shear modulus of filled polymers
388
341
Softening
temperature,
definition,
dependence
9
of
Stress
concentrators,
Stress,
definition,
9
stress
296
294
87
Stress dependence of creep,
Stress relaxation,
5
121
block polymers
and polyblends,
composites,
421
conversion to dynamic properties,
157
copolymers
O
Ont,
dynamic
70,
times,
relaxation,
92
Strength,
theory of,
56
N
Orientation
creep and
times,
moduli of, 491
strength of,
493
Rolling
friction,
354
Rubber elasticity,
kinetic
theory of, 176,
275
Strain
crystallinity,
effect of, 54, 181
molecular
weight,
effect of, 5a
polyblends,
292,
structure,
Rheology,
95, 380
suspensions,
380
Ribbon-filled composites,
Strain,
48
58
block polymers,
copolymerization effect of,
effect of, 52
crosslinking,
plasticization,
on,
of,
R
205
491
Modulus- temperature
chemical
curve
yall
519
interfacial
120
of,
121
modulus
of,
394
modulus-temperature
58
stress-strain
tests
805), 0415
Relaxation
definition,
9
fiber- filled composites,
forces,
10, 42
effect
182
relation,
intermolecular
temperature,
composites,
dynamic properties of, 208,
428
impact strength of, 318
95
stress relaxation,
effect on,
95, 101
stress-strain
tests,
effect
ony, 271
viscosity,
effect on,
97
Modulus
conversion factors,
513
crosslinking,
effect on,
176
crystallinity
of,
in
effect
on,
197
314
120
on,
285
and
plasticization,
effect of, 118
crosslinking,
effect of, 106
crystallinity,
effect of, 111
model
for,
68
molecular weight,
effect of, 101
orientation,
effect of, 119
pressure,
effect of, 93
strain dependence of, 92
temperature,
effect of, 84
thermal
treatments,
94
556
SUBJECT
Stress relaxation
tests,
5,
Stress-strain models,
258
Stress-strain
tests,
5, 257
block and graft polymers,
branching,
effect of, 274
composite materials,
405,
compression
and
shear,
67
292,
Tt
415
465
crystallinity,
effect of, 274,
failure envelope,
268
fiber-filled composites,
465
filled polymers,
405
ribbon-filled composites,
493
rubbers,
275
spherulites,
effect of, 282
temperature,
effect of, 262
Superposition principles,
77, 79
Boltzmann,
77
Suspensions,
rheology
79,
267
of,
380
superposition,
79
Toughness,
definition,
258
Transcrystallinity,
188
Vv
283
275
280
flexural,
261
foams,
416
heat treatments,
effect of, 283
hysteresis,
correlation with,
280
molecular weight,
effect of, 271
morphology,
effect of, 281
orientation,
effect of, 285
plasticization,
effect of, 283
polyblends,
292,
305, 415
pressure,
effect of,
270
rate of testing,
effect of, 265
time-temperature,
Tearing,
320
Time-temperature
260
copolymerization,
effects
of,
crosslinking,
effect of, 274,
INDEX
Vicat softening
Viscosity
temperature,
complex,
13
conversion
factor,
dynamic
13,
properties,
160
514
relation
molecular weight,
effect
plasticizers,
effect of,
shear rate
Viscosity of
shear
347
on,
to,
97
104
dependence,
160
suspensions,
380
modulus,
relation
to,
386
Viscoelasticity
definition,
2
molecular
theories,
76
WwW
Wear,
359
composites,
433
W-l-P Superposition,
USO LZ
19),
S20
LO),
Y
Yielding,
theories
of, 299
Young's modulus,
definition,
9
\\ \\\
about the book...
The mechanical properties of polymers and composites are responsible for their extraordinary versatility —ranging from soft elastomers to rigid materials—and thus their industrial
importance. This two-volume set is the first up-to-date work to offer a discussion on the
mechanical properties of polymers that is basic enough for students and newcomers to the
field to understand. However, at the same time, it contains ample detail to interest the
polymer specialist.
The first volume outlines the general mechanical behavior of polymers in reference
to
environmental and structural factors. Emphasis is placed throughout on general principles,
useful empirical rules, and practical equations. The specific behavior of numerous common
polymers is also detailed. The second volume deals with the mechanical behavior of a wide
variety of composites including particulate-filled polymers, fiber-filled materials,
foams
and high-impact polymers and polyblends. Problems are included throughout the
book so
that the reader can test himself on his comprehension of the material. Most of the
subject
matter has been class-tested by the author at Washington University. A selective
bibliography has also been provided.
This book is an ideal text for advanced students in the fields
of polymer chemistry and
materials science. It is also a practical reference for polymer
chemists, design engineers,
materials scientists, and fabricators who are working with
all types of polymer plastics,
rubbers, and composite materials.
about the author...
LAWRENCE
E. NIELSEN is Distinguished Science Fellow at
Monsanto
Company and
Affiliate Professor of Materials Science at Washin
gton University in St. Louis, Missouri.
Dr. Nielsen has been with Monsanto in various Capacit
ies since 1945 and has been in the
Corporate Research Department in St. Louis for
the last 11 years. His research interests
encompass the mechanical properties of polyme
rs and composites, the relationship of
structure to mechanical properties, rheology, and
transitions in polymers. He has published
about 100 technical papers on these topics and
is the author of the book, Mechanical
Properties of Polymers.
Dr. Nielsen received his A.B. (1940) from
Pacific University, his M.S. (1942) from
Washington State University, and his Ph.D.
(1945) from Cornell University. He engag
ed
in postdoctoral studies at Harvard University
from 1952 to 1953. Dr. Nielsen is a Fellow of
the American Physical Society and a membe
r of the ACS, the Society of Rheology,
the Fine
Particle Society, the Glaciological Society,
and the Arctic Society of North America.
Printed in the United States of Ameri
ca
ISBN: 0-8247—6208-—8
marcel dekker, inc./new york - basel