THE MECHANICAL BEHAVIOR OF HIGH
PERFORMANCE POLYMER FIBERS
by
JOHN EDWARD MOALLI
B.S. Civil Engineering
Northeastern University 1987
SUBMITTED TO THE DEPARTMENT OF
MATERIALS SCIENCE AND ENGINEERING
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1992
© Massachusetts Institute of Technology 1992
All Rights Reserved
Signature of Author
Department of Materials
Science And Engineering
May 1, 1992
Certified by
P-f&fesso
ederick J. McGarry
Thesis Supervisor
Accepted by
Linn W. Hobbs
Professor Of Materials Science
Chairman, Departmental Committee on Graduate Students
ARCHIVES
MASSACHUSETTS INSTITUTE
OF TcrwJnl nry
JUL 3 0 1992
UBRAHIES
The Mechanical Behavior of High
Performance Polymer Fibers
by
John E. Moalli
Submitted to The Department of Materials Science and
Engineering on May 1, 1992 in partial fulfillment of the
requirements for the Degree of Doctor of Science.
Abstract
The mechanical behavior of high performance polymer fibers
In order to better characterize the
was investigated.
mechanical properties of these fibers several novel test
methods were developed and improvements were made on older
A device which simplifies fiber cutting for the
ones.
tensile recoil test was constructed.
A new method to
evaluate the transverse strength index of single fibers has
The index is found to be similar among a
been devised.
variety of fibers suggesting that lateral properties depend
more on interfibrillar morphology than interchain properties.
The same instrument can also be modified to perform three
This permitted the
point bending tests on single fibers.
determination of flexural stiffness and compressive modulus.
The compressive modulus is found to be considerably less than
the tensile modulus for most high performance polymer fibers.
Compressive failure of high performance polymer fibers is
Using the
modeled by buckling of fibril structural units.
compressive modulus from three point bending tests, fibril
diameters from scanning electron microscopy and single mode
Euler's
from several methods,
fibril buckling lengths
equation is employed to predict the compressive strength of
experimental
data
is
single
fibers.
Agreement with
reasonable and the model is shown to be especially useful for
predicting relative compressive strength among fibers of
processing
subjected
to different
similar
composition
conditions.
Based
on the
modeling
of
fibril
buckling
initiating
compressive failure, a new method is introduced to improve
compressive strength in which rigid ceramic coatings are
Aluminum oxide coatings
applied to the fiber exterior.
applied by physical vapor deposition are shown to increase
compressive strength well beyond that predicted by a rule of
Alumina coatings also are shown to reduce the
mixtures.
radial thermal expansion coefficient by a factor of two.
Thesis Supervisor: Frederick J. McGarry
Title: Professor of Materials Science and Engineering
2
Dedicated to the memory of my Grandfather,
Luciano Moalli
whose courage and ambition brought my family into this
country, and whose morals and ethics will always be with me.
3
Acknowledgments
I would first like to thank Professor Frederick McGarry whose
guidance, friendship and support made this work possible.
The long discussions, often not related to science, and
constant advice have had an influence on my professional
Many
development and character that cannot be measured.
other faculty members are acknowledged for their input and
limited to:
Professor David
advice,
including but not
Roylance, Professor Michael Rubner, and Professor Peggy Cebe.
For the financial support of Dow Chemical, and the fruitful
Many thanks to
discussions with its employees I am grateful.
Dr. Steve Allen of DuPont for supplying Kevlar® and PPTA
fibers, and for encouraging input on this work.
The staff at MIT has also been instrumental to the completion
machining and design done by Arthur and Steven
of this work:
Rudolph was nothing short of spectacular and my time spent in
Mike Frongillo provided
their lab is most memorable.
microscopy instruction and advice with humor and style that
Rich Perilli's help with PVD and equipment
are unparalleled.
John Martin
rovided
acquisition is greatly appreciated.
(and
The
constant
help
surface
lab.
great help in the
haressment) from Maria Raposo often pushed me over those
barriers we all encounter.
And what would have I done without the UROP's ?
Those who
contributed substantially to this project are: Betty Chang,
Amy Chiang, Maureen Fahey, Francis Lee, Rafy Levine, Troy
Morrison, Rodrigo Rubiano, Shari Schuchmann and Becky Wittry.
The company and friendship of UROP's on other projects is
also recognized: Lynore Abbott, Nate Getrich, Mike Groleau,
Daphne Karydas and Helen Shaugnessy. I would also like to
thank the brothers of Phi Gamma Delta for their friendship.
My fellow graduate students have also provided help and
friendship that was so important: Haskell Beckham, Francois
Billaut, Jeff Carbeck, Mary Chan, Hans Foulger, Sue James,
Sun-Wook Kim, Georgios Margaritis, Susan Noe, Ambuj Sagar,
There are many
Ramnath Subramaniam and the entire PPST clan.
others who are not mentioned but are definitely remembered.
My most special friend, Shari, has provided unselfish love
The happiness and enjoyment she has added to
and friendship.
my life have made MIT much more enjoyable.
Finally, my family must be acknowledged: Mom, Dad, Glenna,
George, Grandma's, Michelle, Dan and Mary Ann, Maria, Pam and
Mike, Andrea and Dave have always been there with support and
Thank you all so much.
love.
4
A bstract .................
.....................
.2
Acknowledgements ..........
.....................
.4
List Of Figures ............
List Of Tables .............
..........................
1 1
Chapter 1. Introduction ......
12
Chapter 2. General Mechanical Behavior of High
Performance Fibers......... ..........................
21
............................
2.1.Anisotropic Elasticit
21
2.1.1.The Cylindric illy Orthotropic Fiber ....... 23
2.1.2.The TransversE ely Isotropic Fiber .......... 24
2.2.Consequences Of Anisc)tropic Elasticity ............ 24
Chap,ter 3. Measurement of Fit Per Mechanical Properties
....
26
26
3.1.Axial Compressive Sti ength ........................
3.2.Transverse Strength.. ............................. 28
3.3.Compressive Modulus.. ............................. 2 9
3.4.Experimental......... .......... ................... 29
3.4.1.Axial Compress;ive Strength ................ 29
3.4.1.1.Recoil Testing ..................... 29
3.4.1.2 .Composiite Testing .................. 32
3.4.2.Transverse Sti:ength ...................... 36
3.4.3.Compressive Mc)dulus ..............
...... 44
3.4.3.1.RectancTular Model .................. 50
3.4.1.2.CirculE ir Model ..................... 54
3.5.Results and Discussic)n
....... ......
...
........ 63
3.5.1.Axial Compresssive Strength ..............
63
3.5.1.1.Recoil Testing .................... 63
3.5.1.2 .Composiite Testing .................. 63
3.5 2.Transverse Str:ength
3.5.3.Compressive Modulus
5
....................... 64
.......................
68
......
.y
Chapter 4.
Modeling of Fiber Compressive Failure
4.1.E .virneP
f Firil
B:llcl
........
n
76
..76
4.2 . 4odeling with Euler Buckling ...................
...
78
4.3.IResults and Discussion .........................
..
88
Chapter 5. Improving Fiber Compressive Strength ......
5.1. lethods of Improvement .........................
5.1.1.Chemical Methods .......................
5.1.2.Rigid Coatings ......................
5.1.2.1.
* . .97
...
97
... .97
..
98
Coating Selection ............. .. .100
5.2 .E Experimental.................................
.. 103
5.2.1.Coating Deposition ..................... ...103
5.2.2.Property Evaluation .................... ... 106
5.3.R Results and Discussion ......................... .. .109
5.3.1.Effect of
5.3.2.Effect of
5.3.3.Effect of
5.3.4.Mechanism
Coatings on Fiber Strength ... .. .109
Coatings on Fiber CTE ........ ...112
Coatings on Flexural Behavior .. .119
of Improvement .............. ...123
5.3.4.1.Rule of Mixtures ................ ...123
5.3.4.2.Lateral Restraint ............... ... 124
5.3.5.Effect of External Stresses on Residual
Strength of Coated Fiber ..................... ...126
Chapter 6.
Conclusions ..................
.............
132
Appendix ...........................................
37
References .........................................
140
6
List
of
Figures
Figure
Page
Figure 1-1.
Aromatic Polymers Spun Into High
Performance Fibers .
..................................
13
Figure 1-2.
SEM Micrograph of Split PBO Fiber Showing
Fibrillar Morphology in Fiber Interior .................... 15
Figure 1-3.
SEM Micrograph of Split PPTA Fiber Showing
Fibrillar Morphology in Fiber Interior .....................
15
Figure 1-4.
SEM Micrograph of Split Polyethylene Fiber
Showing Fibrillar Morphology in Fiber Interior .............
16
Figure 1-5.
SEM Micrograph of Kink Band In PBO Fiber ...... 16
Figure 1-6.
Anisotropy in Mechanical Behavior of High
Performance Polymer Fibers .................................
17
Figure 1-7.
Anisotrcpy in Thermal Expansion Behavior of
High Performance Polymer Fibers ............................
18
Figure 2-1.
Polar Coordinates For A Single Fiber
.......
22
Figure
3-1. Lateral compression of a single fiber
between parallel plates ..............................
30
Figure 3-2.
Schematic of Spike in Load During Tensile
Recoil Testing Caused by Shearing Action of Scissors .......
33
Figure 3-3.
Schematic of spike in load during tensile
recoil testing caused by unsymmetrical cutting.............34
Figure 3-4.
Photograph of FI-RE-CUT device ................
35
Figure 3-5. Schematic of Mini-composite manufacturing
procedure..................................................38
Figure 3-6. Cross section of mini-composite
............... 39
Figure 3-7.
Schematic of lateral splitting test of
single fiber.
............................................ 40
Figure 3-8. Optical Micrograph of Single Fiber Three
Point Bend Specimen
.................................
41
Figure 3-9. Schematic of Instrument Used For Transverse
Testing and Three Point Bending ............................ 42
Figure 3-10. Photo of device used for transverse testing
and three point bending
..................................
7
43
Figure 3-11. Photo of device used for transverse testing
..................................
and three point bending
43
Figure 3-12. Schematic of three point bend device ..........
46
Figure 3-13. SEM micrograph of fiber support block.
Span is about 950 um .......................................
47
Figure 3-14. SEM Micrograph of single fiber being tested
in three point bend configuration .......................... 48
Figure 3-15. SEM Micrograph of single fiber being tested
.......................
in three point bend configuration.
48
Figure 3-16. Rectangular cross-section around the
neutral axis ............................................... 51
Tension-Compression Stress-Strain Diagram
Figure 3-17.
For Material With Unequal Tensile and Compressive Moduli
Subjected to a Bending Moment ..............................
Figure 3-18. Circular Cross-Section
.......................
51
55
Circular Segment .............................
55
Figure 3-20. Compressive Modulus versus Tensile Modulus
for Fibers With Normalized Flexural Rigidities ............
59
Figure 3-21. Flexural rigidity versus compressive
modulus for different cross section ........................
60
Figure 3-22. Normalized bending stiffness for fibers of
different tensile modulus .................................
61
Figure 3-23. Compressive Modulus as a Function of Fiber
Radius for a Measured Flexural Rigidity ....................
62
Figure 3-24. Stress-Deflection plot from compression
..........................
testing of mini-composites
66
Figure 3-25. Load-Deflection plot from three point
bending on single glass fibers .............................
69
Figure 3-26. Load-Deflection plot from three point
bending on single Kevlar® fibers ..........................
72
Figure 3-27. Load-Deflection plot from three point
bending on single Kevlar® 149 fiber. ......................
73
Figure 3-28. Load-Deflection plot from three point
bending on single PBO fibers ...............................
74
Figure 3-19 -
8
Figure 4-1. SEM Micrograph of Single PBO Fiber split
with micromanipulator
.
........................
77
Figure 4-2.
79
Schematic of Simply Supported Column ..........
Figure 4-3. SEM Micrograph of single Kevlar® 49 fibril
from a fiber split with a micromanipulator .................
82
Figure 4-4. SEM Micrograph of sheath of fibrils peeled
from Kevlar® 49 fiber as shown in schematic .
........... 83
Figure 4-5. SEM Micrograph of sheath of fibrils peeled
from Kevlar® 49 fiber. .................................... 84
Figure 4-6.
Method of determination of buckled (arc)
length of single fibril ..................................
86
Figure 4-7. SEM Micrograph of Arrays Of Buckled Rows In
The Skin of a PBO Fiber Which Has Been Peeled Off The
Core .......................................................
87
Figure 4-8. SEM Micrograph of Arrays Of Buckled Rows In
The Skin of a PBO Fiber Which Has Been Peeled Off The
Core .......................................................
87
Figure 4-9. Eulers Curve....
eoee
Figure 4-10. SEM Micrograph of Kink Band Initiating on
Exterior of PBO Fiber....... .f Pits
Along
Kink
Boundary
Q9
J,
... 93
Figure 4-11. SEM Micrograph of Pits Along Kink Boundary
in Plasma Etched PBO Fiber.. .f Pits
Along
Kink
Boundary.
....
94
Figure 4-12. SEM Micrograph of Pits Along Kink Boundary
in Plasma Etched PBO-6 Fiber
....
94
Figure 4-13. SEM Micrograph (of Pits Along Kink Boundary
in Plasma Etched PBO-5 Fiber
....
95
Figure 4-14. SEM Micrograph <of Pits Along Kink Boundary
in Plasma Etched PBO-4 Fiber
95
....
Figure 5-1. Modification of IFibril Model To Consider
Lateral Support By An Elasticc Foundation .................
99
Figure 5-2.
Schematic of FoIrces on Thin Rigid Coating
Applied to Fiber.
..........................................
101
Figure 5-3.
Radizal CTE as a Function of Coating Modulus
Generated By Finit:e Element Model .......................... 104
Figure 5-4.
Radizal CTE as a Function of Fiber
Transverse IModu liis Generated By Finite Element Model ......
9
105
Figure 5-5. SEM Micrograph of lumina Coating on PBO
Fiber Applied by Physical Vapor Deposition ...............
107
Figure 5-6. SEM Micrograph of Alumina Coating on Glass
..............
Fiber Applied by Physical Vapor Deposition
107
Figure 5-7. SEM Micrograph of Failed Alumina Coated PBO
Good Adhesion of Coating is Evident............. . .111
Fiber.
Figure 5-8. SEM Micrograph of Failed Alumina Coated PBO
Good Adhesion of Coating is Evident............. . . .111
Fiber.
Ultimate Compressive Strength versus
Figure 5-9.
Alumina Coatina Thickness For PBO Fibers ................ ...
113
Cumulative Distribution Function Of
Figure 5-10.
Ultimate Load For Uncoated and Alumina Coated PBO Fibers
in Tension............................................ ...114
Figure 5-11. SEM Micrograph of Alumina Coated PBO Fiber
Heated In-Situ to 4000 C ................................. ...
Percent Change in Fiber Diameter With
Figure 5-12.
Temperature For Uncoated and Alumina Coated PBO Fibers..
116
... 117
Figure 5-13.
Percent Change in Fiber Diameter With
49
Temperature For Uncoated and Alumina Coated Kevlar
Fibers .................................................. .. .118
For Uncoated and
Load Deflection Plot
Figure 5-14.
Alumina Coated PBO-5 Fibers ............................ ...
121
Figure 5-15.
Load Deflection Plot For an Alumina Coated
...
E-Glass Fiber......................................
122
UCS vs. Coating Thickness: measured data
Figure 5-16.
and values calculated from rule of mixtures........... .....
125
Figure 5-17. Circumferential Cracks in Coating on PBO
Fiber From Tensile Loading ............................ ..... 129
Figure 5-18.
UCS vs. Coating Thickness in PBO Fiber
both Unloaded and After a 60g Tensile Preload .........
UCS vs. Coating Thickness in PBO Fiber
Figure 5-19.
Before and After Heating in Air.......................
.....
130
..... 131
Variation in compressive modulus for PBO
Figure A-1.
fibers of the same lot .................................. 138
Variation in compressive modulus for PBO
Figure A-2.
fibers of the same lot .................................. 139
10
List
of
Tables
Table
Pag
Table 3-1.
Compressive Strength From Tensile
Recoil Test
............................................... 65
Table 3-2.
Compressive Strength of Fibers From MiniComposites .................................................
65
Table 3-3.
Transverse Strength Index for Several High
Performance Fibers ......................................... 67
Table 3-4.
Compressive Modulus for Several High
Performance Fibers ......................................... 71
Table 4-1.
Euler Analysis of Single Fibrils Using
Sheath Peeling and R4 methods ..............................
89
Table 4-2. Euler Analysis of Single Fibrils Using Plasma
Etching Method For Single Mode Buckling Length .............
96
Table 5-1.Mechanical Properties of Alumina
Used For Rigid Coating on Fibers ...........................
108
11
Chapter 1.
High
Introduction
performance
fibers
are
those
described
as
having
strength and moduli many times that of glass fibers.
Almost
since
their inception,
high performance
provoked much excitement:
with
their
benefits
low
for
specific
The
fibers have
their tensile properties, combined
gravity,
structural
applications.
polymer
promise
composites,
performance
of
extraordinary
especially
many aircraft,
in
mobile
missiles,
land vehicles and boats
could be measurably improved by using
structural
with
materials
Unfortunately this has
not
higher
specific
proved out
properties.
in practice;
the
low
compressive strengths of the fibers have severely constrained
their
utility since
relatively
few structural
components
or
systems function exclusively under tension.
Most high performance fibers
polymers.
Figure
1-1:
phenylene
A
are derived from rigid aromatic
few of the more
common ones are illustrated in
poly(p-phenylene benzobisoxazole),
benzobisthiazole),
terepthalamide),
PPTA.
The
PBT;
former
two
PBO;
poly(p-
poly(p-phenyleneare
experimental
fibers while the latter is produced by Dupont under the trade
name Kevlar®.
Extended chain poly
12
(ethylene)
has
also been
N
33~OO~~f
PBO
~
n
t(S9\/S
3PBT
n
H
N
Q
I
NC
H
Figure
1-1.
j
0
Aromatic
PPTA
PPTA
C1
n
Polymers
Fibers.
13
Spun
Into
High
Performance
made into high performance fibers by Allied Signal under the
trade name Spectra®.
The
aromatic polymers form liquid crystalline solutions
in
strong solvents and are dry jet wet spun from these solutions
at low concentrations into fibers.
The alignment of chains
during spinning results in fibers with a high degree of axial
order 1 .
Heat treatment
further
increase
order
aliphatic polymers
chains
and
polymer
good
fibers
under tension
are
and
gel
axial
resultant
a
properties.
spun which results
alignment.
display
is then employed to
All
unique
The
in extended
high
performance
fibrillar
morphology,
illustrated for the above systems in Figures 1-2 to 1-4 which
are SEM micrographs of split fibers.
This
fibrillar
behavior.
morphology
Under axial
leads
to
anisotropic
mechanical
tension, the fibers are very strong
but under axial compression the fibrils buckle and form kink
bands
as
shown in Figure
1-5.
Since the
fibrils
are held
together only by weak secondary forces, the lateral tensile
strength of the
fibers is also low.
also
itself
manifests
behavior:
negative
direction
typically
high
coefficients
and very
in
of
large
Axial chain alignment
anisotropic
performance
thermal
polymer
expansion
positive ones
14
thermal
in
in
the
expansion
fibers
have
the
axial
transverse
SEM Micrograph of Split
Figure 1-2.
Fibrillar Morphology in Fiber Interior.
SEM Micrograph of Split
Figure 1-3.
Fibrillar Morphology in Fiber Interior.
15
PBO
Fiber
Showing
PPTA
Fiber
Showing
SEM Micrograph of Split Polyethylene
Figure 1-4.
Showing Fibrillar Morphology in Fiber Interior.
Figure 1-5.
SEM Micrograph of Kink Band In PBO Fiber.
16
Fiber
-ePW4
*-(
,---
0)-
Excellent
L
·
L
r-
-
III---
Axial Tensioa
_ns
=-
-
0e
Poor
I
I,
L~
_
,,
I
I
.l
.....
.
|_
Ik
i
Axial Compression
4
(
Poor
-?-C
g
,
Is
s-
r
0
*
Transverse Tension
Figure
1-6.
Anisotropy
Performance Polymer Fibers
in
Mechanical
17
Behavior
of
High
-
(
P7
3
-
-1
---I
·
Is
-
-·
-bB
rr
0
+ A T
Fiber Shrinks Axially
And Expands Radially
r
#
f
I
,'
I,
,
4'
Figure 1-7.
Anisotropy in Thermal
High Performance Polymer Fibers
18
Expansion
Behavior
of
direction.
These anisotropic characteristics
are schematized
in Figures 1-6 and 1-7.
The
need to
compressive
correct this
strength,
deficiency,
has
been
chemical
in nature,
increase the
apparent
many efforts to do so have been made.
been
to
for
axial
some time,
and
Principally these have
seeking to provide primary bonding
transversely across the fiber 2 .
The motivating idea was,
and
still is, that if the axially aligned polymer chains could be
crosslinked
in
some
way,
their
failure would be increased.
the
failure
indeed,
fiber
mechanism
resistance
to
compressive
(Implicit is the assumption that
is
by
buckling
of
the
chain
and,
there have been attempts to quantitatively model the
behavior
laterally
this
stabilize
buckling load:
improve.
on
the
changes
in
chain
the compressive
These
Despite
the
basis 3)
attempts
apparent
fiber
and
crosslinks
thereby
strength of
have
not
achievement
compressive
The
of
been
increase
the
very
have
its
fiber would
successful.
crosslinking,
strength
would
been
modest
reported
often at the expense of tensile strength.
This
research
compressive
find a
to
failure
way to
produce
properties.
sought to
in
elucidate
high
with
In Chapter
2,
specific mechanism of
performance
delay it with the
fibers
the
polymer
and
hope of discovering methods
less
anisotropic
an overview of the
19
fibers
mechanical
anisotropic
In order to effectively assess any improvements
presented.
Chapter
them.
properties
mechanical
some
and
of
describes
novel
tensile
testing
the
is
in
developed
to
measurement
of
be
to
fibers
single
including
axial
and
axial
strength
on older test methods are
Improvements
compressive modulus.
made
3
lateral
strength,
compressive
had
methods
properties,
mechanical
evaluate
microstructure
fiber
the
from
resultant
elasticity
techniques
are
developed.
Chapter
4 describes a new method of modeling the compressive
failure
of
high performance
to measured properties.
failure
and
introduces
of
high
a
the
modeling
performance
Chapter
from
polymer
the
fibers
the
Chapter
4,
compressive
using
rigid
5
strength
coatings
on
Effects of rigid coatings on the thermal
expansion behavior of the fibers
highlights
correlates the model
Based on observations of compressive
new method to improve
the fiber exterior.
6
and
fibers
findings
of
suggestions for future work.
20
is also discussed.
the
research
and
Chapter
makes
Chapter 2. General Mechanical Behavior of High
Performance Fibers
2.1. Anisotropic Elasticity
The
fibrillar
performance
structure
polymer
by
covalent
axial
fibers
mechanical behavior.
carried
and
chain
manifests
polar
itself
in
bonds
while
those
coordinate
system,
applied
(transverse or axial loads).
however, if loads on the r and
dissimilar responses.
identically,
the system is
The more general case,
the
fiber
orthogonal
responses
possess
axes.
to
peculiar
If we examine a
one with
fiber will react differently to loads
invoke
high
transversely
r,
0,
and
shown in Figure 2-1, it is not difficult to realize
axes
of
Loads applied axially to the fiber are
are held by weaker secondary forces.
in a
alignment
that the
imposed on the r and z
axes
( radial and hoop) will
the r
ana 0
planes
behave
said to be transversely isotropic.
symmetry
applied
z axes as
It is not entirely clear,
If
though,
These
fiber
is the orthotropic one,
with
two
respect
systems
forces
as
thorough discussion on this topic,
Allen4 .
21
to
three
produce very
described
below.
where
mutually
different
For
a
the reader is referred to
z
0
KN\
r
Figure 2-1.
Polar Coordinates For A Single Fiber.
r=Radial and =Hoop directions.
22
Z=Axial,
2.1.1.
A
The Cylindrically Orthotropic Fiber
completely anisotropic material has
It
constants.
only
9 of
be
can
shown
for the
that
are
constants
these
21 independent
elastic
case
orthotropic
The
independent.
stiffness
matrix then becomes
EI Er Ez 0
Ez 0
Er Eg E
O
Ez EOz E
0
O
0 Goz
0
0
0
and Oz
terms
will produce
indicates
some
then
of the
of
hydrogen
forces
stresses
of
of
the
hoop
indeed
has
direction
these
interactions
system is the result.
23
If the
cylindrically
been
shown
to
sheets 5.
Van
an
be
This
related
Der
covalent bonding;
differ,
forces
on chain
be
to
loads
axial
stiffness would be
axial direction to
of both
in the fiber.
is based
example,
radial direction
bonding,
and the
magnitudes
The presence
application
will
for
(2.1)
radially oriented hydrogen bonded
implies that the
to
GrO
0
system
systems
Kevlar®,
orthotropic.
composed
0
that
radial and hoop
mechanical behavior
only,
0
0
0
0
O0
0
are the principal moduli.
where Eij's
rz
0
0
0
0
O
0
Grz
Waals
as
the
orthotropic
2.1.2.
The Transversely Isotropic Fiber
If mechanical behavior is based on fibril interactions, then
the radial and hoop directions should be indistinguishable
and the stiffness matrix becomes
where K =
exist.
in
Err E 0 Er
Eo Er Er0
Erz E
Ezz
0
0
0O
0
0
0
0O
0
0
0
0
G
0
0
0
G
0
0
0
K
0
0
0
0
0
0
(Err - ErO)/ 2 ,
and
only
(2-1)
5 independent
constants
This type of model does not consider any differences
radial
or
hoop
properties
that
may be
derived
from a
orthotropic
system
skin/core structure in the fiber.
2.2. Consequences Of Anisotropic Elasticity
It
has been shown6 that
a
cylindrically
will produce radial and hoop stresses when an axial load is
applied.
This implies that axial compression on a fiber may
produce transverse tension, a combination of forces that is
obviously detrimental to the
transversely
axial
isotropic
fibrillar structure.
system,
and other directions.
Chapters,
this
research
no
coupling
As will
offers
be
exists
evident
evidence
that
For the
between
in
later
fibril
interactions control mechanical behavior, hence all analysis
are conducted assuming transverse isotropy in the fibers.
24
It
must
structure
Kevlar®)
constant
also
be
pleated
in
anisotropy
depending
on
the
fibers
compressive moduli.
would
may
sign
have
supramolecular
fiber
the
result
can
Specifically,
matrices
the
example
(for
that
recognized
sheet
arrangement
in
single
of
a
the
different
in
elastic
applied
tensile
load.
and
This would imply that separate stiffness
have
to
be
compressive loadings.
25
compiled
for
tensile
and
Chapter 3.
Measurement of Fiber Mechanical
Properties
3.1. Axial Compressive Strength
As
described previously,
rigid rod polymer
axial compressive strengths;
measure
this.
Most
of
them mark
failure
strength
is
low
by
the
onset
of
They include the elastica loop
matrix shrinkage 8 and beam bending
compressive
have
several methods are available to
visible kink band formation.
test 7,
fibers
calculated
3 9
.
,
In these tests
from the product
of the
tensile modulus and the critical strain for kinking, thus it
is assumed that the fiber behaves in a linear elastic fashion
to
compressive
moduli
are
uncertainty
axial
failure and that
identical.
so
a
compressive
more
These
assumptions
direct
strength
the tensile and compressive
cause
measurement
is desirable.
tension
to
various
levels
and then
single
The tensile
test developed by Allen is such a method1 0 .
in
of
substantial
cut
surface and cause compressive
recoil
Fibers are loaded
and the
recoil stresses created from tensile failure reflect
grip
fiber
damage in the
elastic
from the
fiber.
is assumed that no damping occurs during reflection
It
such that
the magnitude of the resulting compressive stress is equal to
the tensile stress
determined by
at
failure.
fracturing a
The compressive
number
of
tensile
strength is
specimens
at
different stress levels to find the minimum value which just
26
initiates
tensile
kink
band
failure
at
formation.
different
Obviously
stress
this
levels
requires
and
several
cutting techniques have been developed for the purpose.
include
spot
etching,
heat
cutting,
mechanical damage,
and scissor cutting 1 0 .
the
is
first
undesirable
shearing
a
poor
increases
action.
symmetrical
gives
three
in the
A
new
accurate
applied
localized
Reproducibility in
scissor
device
cutting of the
more
and
prior
They
cutting
induces
stress because
has
been
of the
developed
for
fiber during recoil testing which
assessment
of
the
axial
compressive
strength.
Another
method
compressive
fiber
have
may
be
strength is by using
is available,
compression
which
which
to
evaluate
composites.
If
fiber
sufficient
a high quality composite can be made and
tested.
been
used
The
composite
shown to
must
substantially
strength in unidirectional composites.
be
free
reduce
of
voids
compressive
Fiber alignment must
also be perfect as strength and modulus decrease rapidly with
increasing misalignment of fibers.
If these
met,
can
the
fiber
compressive strength
micromechanical
disadvantages.
differential
theories,
Among
the
thermal
perfect alignment.
fiber
compressive
method
latter
are
shrinkage
Poisson's Ratio effects,
of
a
conditions are
be calculated using
which
matrix
effects,
has
hardening
many
and
differential
specimen end friction and difficulty
Also
failure
it is very difficult
details
27
in
such
to monitor
assemblages,
compared to a single fiber specimen.
methods
are
desirable
as
they
Nonetheless, composite
provide
properties during end use applications.
has
been
developed
which
allows
for
data
for
fiber
Hence, a new method
the
construction
of
highly aligned void free composites for compression testing.
3.2. Transverse Strength
The
transverse
very low.
strength
Several
by
produces
strength of rigid
rod polymer
researchers have measured the
lateral
tension
compression
on
the
of
midplane
procedure is shown in Figure 3-1.
test
which
Such
is
fiber
are
condition
is
tend
which
Furthermore,
fiber
crushing
developed
forces
the
at
to
to
of
the
Therefore,
opening mode
polymer
a
test
which
This
by
frictional
low
load
unless
lateral
state,
attenuation
all
of
a
strength.
in
the
In order to avoid such
has been
forces
deformation.
stress
desirable to perform lateral testing on
fibers.
transverse
fiber.
during
assumed
of
determine
is
A major deficiency of this
the
nature
also
fiber1 1
single
fiber base
exacerbated
exact
difficult
the
change
is
a
and the resultant
elastic constants are known.
it is
fibers
the
fiber
effects
free standing
developed
in which
an
crack is propagated axially in high performance
fibers.
The
crack
initiation
force
measure of a transverse fiber mechanical property.
28
provides
a
3.3. Compressive Modulus
The most
modulus
comnon
is
technique
with
for
evaluating
unidirectionally
fiber compressive
reinforced
thermosetting polymer matrixl 2,
usually with a
13
composites,
.
The fiber
modulus is calculated through application of micromechanical
theories
to
composite
disadvantages
as
properties,
mentioned
a
method which has
previously.
Other
researchers
have used cantilever bending on large diameter fibers
500
um)
to
calculate
fiber
compressive
many
modulus1 4.
(250 To the
authors knowledge, no such flexural tests have been performed
on
high
performance
polymer
fibers
which
typically
have
.;
diameters
from
development
of
10
a
um to
single
20
um. This
fiber three
research presents
point
bending
test
the
for
evaluation of fiber compressive modulus.
3.4. Experimental
3.4.1.
Axial Compressive Strength
3.4.1.1.
Recoil Testing
The analysis of the tensile recoil test has been presented by
Allen1 0 .
Since
zero
attenuation
of
the
reflected
wave
is
desirable and the amplitude of the reflected wave is given by
(Pm Cm- Pf cf)
(PAe +ncm
f cf)
29
(3.1)
__
*
s __
wI
S
I
-u,-....,
-
iber -
-- -- -- - - - ,,
Parallel Plates
- - -
,
,
,
- ,
E'/////////////////////
A--
P
Figure 3-1. Lateral compression of a single fiber between
parallel plates.
30
where the wave velocity, ci is
ci
Pi
and E is the modulus and p is the density, it is obvious that
the fiber and gripping medium must have different impedances.
This
is
readily
accomplished by placing the -fiber ends
in
epoxy resin which typically has modulus values 40 to 80 times
less than that of the fiber.
The epoxy is used to mount the
fibers onto cardboard tabs, the center of which is a hole of
the desired gauge length.
The fiber/tab assembly is placed
in a tensile testing machine
(Instron 4505 with 2000 g load
cell at 20 g full scale load) and gripped.
The edges of the
tab are then cut away such that only the fiber is loaded.
The most
difficult part
of the test
is
finding a suitable
method to cause tensile failure in the fibers.
is not done with great care,
applied load will occur.
large increases
If breaking
(spikes) in the
If the spikes are too large, the
test is invalid because the exact stress state in the fiber
becomes unknown.
surgical
scissors
problems
exist
Although some researchers have
can
provide
with this
shearing action,
and as
reasonable
technique.
found that
reproducibility,
The blades
cut by a
shown schematically in Figure
3-2,
this imposes a twist on the fiber causing an increase in the
applied load.
Another problem arises when the blades do not
cut symmetrically: both blades do not come in
31
contact with
the fiber at the same time. The fiber is displaced laterally,
as
in Figure 3-3,
shown
which
also causes a spike in the
Both of these effects are more pronounced as the fiber
load.
modulus increases.
To
remedy
these
(FIber-REcoil-CUTter)
shown
in Figure 3-4.
a
was
a photograph
made,
device
named
problems
FI-RE-CUT
of
which
is
It employs scalpel blades mounted on
blocks which are supported by linear bearings.
The blades
avoiding any shearing action.
The blocks
remain co-planar,
are connected to a drive rod with opposing left
and right
handed threads; when the rod is rotated it brings the blades
together
smoothly at
The entire device is
a uniform rate.
mounted on a micrometer substage which facilitates precision
centering
of
the
fiber
between
the
blades
and
prevents
unsymmetrical cutting.
3.4.1.2.
Composite Testing
The method developed for composite manufacture, similar to
that of Piggot 13
is a pultrusion technique. Four inch lengths
of fibers were cut and placed on top of a small wire.
After
a sufficient number of fibers were in place the wire was
looped over the fibers which were pulled by the wire into a
hollow glass tube of 20 mm diameter.
A smaller glass tube (5
mm) lined with rubber was then placed over the wire just
above the fibers.
Next, epoxy resin (Dow Tactix 123) was
32
I
I
C.__.
Tensile
Force
Time
Figure 3-2.
Schematic of Spike in Load During Tensile
Recoil Testing Caused by Shearing Action of Scissors.
33
I
I
II
-
I
I
I
I
I
CO ;fL
Tensile
Force
Time
Figure 3-3.
Schematic of spike in load during
recoil testing caused by unsymmetrical cutting.
34
tensile
S.
Figure .- 4.
Photograph
of
FI-RE-CUT
35
device.
poured into the
(Figure
assembly
glass
small
placed
3-5)
the resin
degassing,
tube over the
large
tube and
a
in
fibers and the entire
After
oven.
vacuum
soaked fibers were pulled through the
Void free,
cured.
high
fiber volume
fraction composites were produced using this method.
A cross
section of a typical composite is shown in Figure 3-6.
Composites were cut to 12.5 mm lengths with a diamond saw in
a specially designed jig to ensure that specimens ends were
Specimens
parallel.
loaded
were
unsupported,
end on,
in
direct compression in an Instron 4505 at a crosshead speed of
Teflon was placed between the loading platens and
1 mm/min.
the specimen ends to minimize frictional end constraints.
Transverse Strength
3.4.2.
The poor lateral
integrity of rigid rod polymer fibers makes
that
a
fiber
of
It was observed
from handling.
them susceptible to damage
cross
circular
could
section
easily be
flattened with tweezers or other instruments. Then if the end
was split,
the force
transverse strength.
required could give some
idea of the
Using a micromanipulator , one end of a
fiber which is a few centimeters in length is flattened.
vee
shaped
segment
is
removed
defining
two
A
ligaments
(usually this operation is easily performed on the rigid rod
polymer
fibers
because
of
their
high
orientation
and
directionality; with other less oriented fibers such as nylon
it may be more difficult).
This whole procedure is sketched
36
in Figure 3-7 and, experimentally,
made with a micromanipulator.
in
Figire
3-8.
The
extremely small and
loads
such specimens have been
An optical micrograph is shown
involved
in
splitting
difficult to measure.
fibers are
To determine the
critical crack propagating force an instrument which operates
with dead weights has been constructed;
in
Figure
3-11.
3-9 and photographs are
The operation
notched fiber
is
movable grip
(it
is
quite
placed in a
a
given
schematic is shown
in Figures
simple:
fixed grip
3-10
and
one ligament of
the
and the
is necessary to keep the axis
specimen approximately perpendicular to the
the
two grips
and the
weighing
splitting of the fiber).
movable
supported
weights
grip
shaft.
are
is
The
placed.
a
of the fiber
line defined by
to ensure successful
The moveable grip is supported by a
gas bearing which eliminates
the
cable,
other in
a
friction effects.
cable
running
cable ends
at
[Since
loads
the
a
over
Attached to
a
bucket
gas
in
required
bearing
which
for
the
crack
propagation are in the milligram range, the gas bearings are
critical:
frictional forces
in conventional bearings easily
exceed the loads of the test.]
testing, the entire device is
end
causing
Weights
are
position.
the
movable
added
until
To balance the system before
slightly elevated on the right
grip
the
to
displace
movable
grip
is
to
in
the
a
left.
neutral
Then the fiber is inserted into the grips and more
weights are added until the fiber splits.
37
The entire test
I
Rubber Tube
Small Glass Tube
Wire
Resin
Fibers
I
Large Glass Tube
lubber Stopper
Fiaurna
*-
procedure.
ouIIleUman C
Ot
Mini-composite
38
manufacturing
Figure 3-6. Cross section of mini-composite showing good
distribution of fibers and fiber volume fraction of 50
percent.
39
+I
I
A
B
C
Figure 3-7.
Schematic of lateral splitting test of single
fiber.
a) Flattening of. fiber end b) Creating notch in
flattened portion c) Pulling ligaments apart d) Propagating
crack
40
D
Ig
Figure 3-8. Optical micrograph of single fiber which has
been flattened and then had a notch created in it using a
micromanipulator.
41
Vz
0
-g
z
£b
hn
0
b
c
-
rq
,.c
a
c
I3
Go
Lt
p
xE
U) ,
0a
p0
"dU
I -I.4
rl ,.
Figure 3-10. Photo of device
testing and three point bending.
used
Figure 3-11. Photo of device used
testing and three point bending.
43
for
for
transverse
transverse
procedure
is
observed with
an optical
measured on
and
accurate
a
easy
chemical
to
diameter of the fiber split,
the
balance
which
Their
value,
use.
equipped
The incremental weights
with a closed circuit video system.
are
microscope
is
inexpensive,
divided
by the
provides a number to represent
lateral integrity of the fiber:
the opening mode axial
crack initiating force, normalized by diameter.
In recognition of the fact that this test does not measure
the true transverse tensile strength
of micro fracture toughness test)
(it is actually a kind
this number has been named
the Transverse Strength Index (TSI).
Compressive Modulus
3.4.3.
The apparatus also can be used for single fiber three point
bending tests. The fixed grip is replaced by a fiber support
A hooked probe is attached to the movable grip.
block.
A
fiber is placed on the platform with the hooked probe beneath
it.
When weights are added to the bucket the hooked probe
loads the
with
a
fiber at
video
its midpoint.
micrometer
and
Deflections are measured
kept
small
so
that
linear
behavior occurs.
A schematic of the bending device is given
in Figure 3-12.
A micrograph of the fiber support block is
shown in Figure 3-13 and micrographs of a fiber being loaded
are given in Figures 3-14 and 3-15.
44
If the angle of rotation of the fiber,
small,
then
the
basic
differential
(Figure 3-12),
equation
for
is
bending
holds:
2
ax2
EI
(3.2)
where 6 is the deflection, x is the distance along the fiber,
M is the bending moment, E is the modulus and I is the moment
of inertia.
The equation of the load deflection curve can be
derived by double integration of equation 3.2
p=48EI 8
L3
(3.3)
where P is the load and L is the span.
Integration of equation 3.2
gives the angle
of rotation of
the fiber
6 =
P
L2
16 E I
If
is
large
(tan
0),
then
derive equation 3.3 is not valid.
the
(3.4)
analysis
employed to
Typical fiber diameters in
the three point bend test are 10 - 30 um.
The span is 800 -
1100 um and loads
5 mN.
typical
rotation
values
is
are usually less than
entered
into
sufficiently
equation
small
analysis.
45
to
3.4,
employ
With such
the
basic
angle
of
elastic
P
Figure 3-12. Schematic diagram of three point bend device
46
Figure 3-13. SEM micrograph of fiber support block.
about 950 um.
47
Span is
Figure 3-14. SEM Micrograph of single
tested in three point bend configuration.
fiber
being
Figure 3-15. SEM Micrograph of single fiber being
Deflection
tested in three point bend configuration.
is about 100um.
48
Equation 3.3 assumes that all deformation is due to flexure
only;
shear effects are not
considered. Modified for shear
deformation, equation (3.3) becomes
p=48EI 6( 1+
where d is
)(3.5)
the fiber diameter and G is the shear modulus.
Typical values of G are about two orders of magnitude less
than E
um
8.
and
However, since the span in this case is about 950
the
fiber
diameter
is
typically
comparison of equation 3.3 and 3.5
10
show that
to
20
um,
shear effects
are negligible for this particular testing geometry.
Equation 3.3 cannot be solved directly for the modulus as the
moment
of
unknown.
neutral
one,
inertia
with
respect
to
the
neutral
axis
is
When the tensile and compressive moduli differ, the
axis
and
the
of the
fiber shifts
expression
for the
away
from the
fiber
centroidal
bending
stiffness
becomes:
(EI)f =EcI + ETIT
(3.6)
Where the subscripts f, c and T refer to fiber, compression
and tension.
The moment of inertia for each of the latter
two is with reference to the displaced neutral axis and the
magnitude of its displacement
from the centroidal one is a
function of the relative magnitudes of Ec and ET.
Thus, if ET
is known from another test, a tensile one, then Equation 3.6
49
but the algebra involved in
contains only one unknown, Ec,
for Ec
an expression
obtaining
becomes
quite
complicated,
especially if the beam cross section is circular rather than
Such
rectilinear.
the
is
case
many
with
fibers,
so the
details of the solution are presented below.
In working out the solution for the anisotropic beam, a fiber
with a circular cross section, it was also of interest to see
how well this could be approximated by a rectilinear cross
either a square circumscribed about the circle
section,
one
or
This was motivated by the relative
inscribed within it.
simplicity of the squares analyses.
Recalling equation 3.6, since If=It+Ic, 3.6 can be simplified
to:
EfIf = (Et - E) It + EcIf
With the
flexural
rigidity measured
(3.7)
from the three
point
bending test and the tensile modulus evaluated from a tension
test,
we can
solve
3.7
for
the compressive modulus
if the
appropriate moments of inertia are known.
3.4.3.1
If
the
Rectangular Model
cross
section
of
the
fiber
is
rectangle which circumscribes the circle
moments
of
inertia
for
the
50
three
approximated
(Figure 3-16),
rectangular
by
a
the
sections
b =2r
...w
~~~~~~~~~~
F_
-
l
""
_1
-
I
--
I
II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
h 1
Neutral Axis
A
h =2r
w
-
-
-
,
d
_
..
I .
Centroidal Axis
..
.
h2
I
Figure 3-16.
axis
r
L
Rectangular cross-section around the neutral
G
£2
e
Figure 3-17.
Tension-Compression Stress-Strain Diagram For
Material With Unequal Tensile and Compressive Moduli
Subjected to a Bending Moment
51
(total section, compressive section and tensile section)
can
be found by the parallel axis theorem (3.8) and the equation
for the moment of inertia of a rectangle around its centroid
(3.9):
I, = I,,x + Ad 2
where
Ixc
(3.8)
Ix is the moment of inertia of a section about axis x,
is the centroidal moment of inertia of the section and A
is the area.
For rectangular shapes
Ix = bh
12
(3.9)
Thus,
the
for the moment of inertia of the cross section around
neutral
section
,
axis,
It,
If,
and the
the moment
moment
of
section around the neutral axis,
If 4
of
inertia
inertia
of the
of the
tensile
compressive
Ic we obtain:
+ 4r2 d2
3
(3.10)
It=
24r(r-d)3
(3.11)
2r + d
Ic=
3
(3.12)
shift
measured,
another method
the
is
beam
in
the neutral axis,
Since the
subjected
must be
to
a
used to
positive
52
d,
cannot be
determine
bending
directly
it.
If
moment,
for
equilibrium the
shaded
two
areas
stress-strain
Hence
curve (Figure 3-17) must be equal.
at C =
the
under
c E2
2
2
(3.13)
From Hooke's Law
:
(Ft = Etl
ac= Ec2
£1 = -hl
E2 = -Kh
(3.14)
also :
2
(3.15)
where K is the curvature.
(3.15) into equation
Substituting equations
(3.13),
(3.14) and
gives:
E t h2 = Ech
(3.%6)
Which can also be expressed as:
=(r+d d = d 2 +2rd + r2
Et =
Ec
h2
(r-d)2
d2 -2rd+r
2
(3.17)
Collecting terms, gives:
53
1
2
E
+2)rd+t-
1)r2=0
(3.18)
Solving equation 3.18 for d, using the quadratic
formula,
yields:
fp+
(3.19)
(note that the root selected is the one for which
Substitution
of
equations
(3.10)-(3.12)
and
d < r)
(3.19)
into
equation (3.6) gives the flexural rigidity :
EfIf=21
3
4
(Et-E)( 1- z) +3E(
3
1+ 3z2)
(3.20)
where
Appropriate+
can be used to evaluate
(3.20)
Appropriate numerical methods can be used to evaluate (3.20)
for Ec.
3.4.3.2
Circular Model
The same analysis as applied to a rectangular section can be
applied to a section which is circular (Figure 3-18).
54
h
xis
Figure 3-18.
Circular Cross-Section
dis
0
Figure 3-19 - Circular
55
Segment
For a circle:
If=
4
+
r4z 2
(3.21)
For
It we
use a circular segment
(Figure 3-19).
Applying
the parallel axis theorem we find that
It=4
(2a8Asin6a
+ sin 2a)(1 + a-2sin3acosa)_
sin o- cos
sin 2a)
a 9 2a
+ (2 2 ~~ic~~
[ 6a-4- sin
sin2orIJ
3 sin
(3.22)
Where:
a = cos-1 dr = Cos- z
(3.23)
Substituting
(3.21)
-
(3.23)
into
(3.7)
we
arrive
at the
expression for the flexural stiffness of an anisotropic beam
with a circular cross section
Ef If E - E)
sin
+ a2 -sin
2a1
T(2a-si
· 8sin
cosaa
a
9 2a -sin
sin2a
r2(2a - sin 2a[
,
-c o s o a)
2
L %6o[a 3 sin 2o
}
+E4t4+
(3.24)
56
4Z2)
Again, appropriate numerical methods can be used to evaluate
Equation 3.24 for Ec.
A
validity check
of the analysis
is
shown
in Figure 3-20.
Here each curve represents a single value of the normalized
bending
stiffness,
(EI)f/r 4 ,
and shows how the tensile and
compressive moduli vary as the stiffness
The
curves
are
symmetrical about the
remains constant.
450 diagonal as
they
should be, hence the validity check.
Figure
3-21
compressive
shows
modulus
a
plot
for
circumscribed square is
of
flexural
different
rigidity
cross
versus
sections.
seriously in error and while
The
it
is
not shown, the inscribed one is also; the magnitudes of the
errors
change,
depending
on
analyzed, but they are always
square cross section having
the
particular
significant.
the
fiber
being
In contrast, a
same area as
the
circular
cross section gives a nearly identical solution, at least for
the case presented.
How broadly this equivalence
can
be
generalized or extended is not known, but for the fibers of
interest
it seems to be a good approximation.
Figure 3-22 shows the fiber compressive modulus as a function
of the
fiber
normalized bending stiffness,
radius.
plotted:
Curves
for
two
(EI)f/r4 , where r is the
fiber
tensile
moduli
are
124 GPa (18 Msi) is typical for Kevlar® 49 and 276
57
GPa
(40 Msi)
section
represents PBO.
fibers
expressions
and
shown.
both
Both refer to circular cross-
can
This
be
fit
presentation
by
the
of
polynomial
the
analysis
is
convenient for interpreting experimental measurements made on
fibers: to obtain a
measured value of
compressive modulus one simply takes
(EI), divides
into the expression
of
this
Figure 3-22 does imply one very sensitive
whole
compressive modulus:
to the
approach
to
magnitude
Use
of
measurement
a
fiber's
errors in the fiber diameter are raised
of
the
is
radius
an
SEM
error
is
recommended.
associated
for
a
with
shown in Figure 3-2315:
can
lead
to
almost
uniform
cross
section
The
potential
improper
radius
a 0.5 um difference in
100
compressive modulus in some cases.
need
determining
fourth power, so accuracy in this measurement is very
important.
the
and substitutes it
derived from the tensile modulus of the
fiber of interest.
feature
by r4
it
the
percent
error
in
This also emphasizes the
in
the
analysis
invoked.
For a more detailed description of error sources in the three
point
bending
Finally,
a
test
the
validity
reader
check
on
is
referred
the
three
to
Appendix
point
bend
I.
test
procedure was made:
glass fibers which are isotropic and well
characterized were
tested.
the
identical
glass
fibers
A
measured flexural modulus
to
the
tensile
indicate a satisfactory testing process.
58
modulus
for
would
400
0
300
0
X
200
rI
100
V.
OP
0
0
100
200
300
'400
Tensile Modulus (Gpa)
Figure 3-20. Compressive Modulus versus Tensile Modulus for
Fibers With Normalized Flexural Rigidities Typical of Kevlar®
(11.8) and PBO(13.4).
59
Comparison of Anisotropic
Section Models
- -
2.5
2.0
a
rIM
0
rW4
e4
'ircumscribed Square
[qual Areas
Circle
1.5
C
1.0
0.5
0.0
0
50
100
150
Ec (Gpa)
Figure 3-21. Flexural rigidity versus
for different cross section
60
compressive
modulus
ran
5WU
250
co
CL
200
t =
276 Gpa (40 Msi)
c = 124 Gpa (18Msi)
150
Q0
Sm
100
C0
Et = 124 Gpa
50
Et = 276 Gpa
0
0
5
10
15
(EI)f / r ^4
Figure 3-22.
20
25
(Pa x ElO)
Normalized bendingq stiffness for fibers of
different tensile modulus.
61
300
I
m
200-
r0
r-
100
_=
-r
--
I--
W1
o
0u
04.0
I
I
I
5.0
6.0
Radius
.
-
.
7.0
(microns)
Figure 3-23. Compressive Modulus as a Function of Fiber
Radius for a Measured Flexural Rigidity, EI, Typical of PBO
Fibers.
62
3.5. Results and Discussion
3.5.1.
Axial Compressive Strength
3.5.1.1.
Recoil Testing
It has been found that using FI-RE-CUT the
success rate
for
correctly cutting fibers is nearly 100 percent for Kevlar
49
and
about
fibers,
80
percent
compared
respectively,
compressive
for
with
using
PBO and
about
other
80
other
stiff
percent
methods.
and
Typical
strength from the tensile recoil
experimental
30
percent,
values
of
test are
the
given
in Table 3-1.
3.5.1.2.
Composite Testing
A typical Stress - displacement curve for a mini-composite is
given
in
onset
of nonlinear behavior.
Figure
3-24.
Specimen failure
is
defined
as
the
This is also marked by visible
failure in the composite by formation of a global kink band.
Compressive
strengths
mixtures
approach
exhibited
linear
for
fiber failure
were
which
obtained using
assumed
behavior well
(this was
that
a
simple
the
beyond the
epoxy
strains
rule
of
matrix
required
verified by compression testing
neat epoxy samples).
The
results
are
in
for PBO and Kevlar®
reasonable
agreement
with
63
fibers,
single
given
fiber
in
Table
3-2
compressive
The Kevlar®
strengths obtained from tensile recoil testing.
are
values
also
manufacturer 1 6.
similar
caused
by
the
reported
those
by
the
The increase in fiber compressive strengths
composite data over
from
to
increased
those from recoil testing may be
support
lateral
provided by
the
matrix to the composite fibers.
Transverse Strength
3.5.2.
Table
3-3 presents
the results
from lateral testing.
The
various PBO fibers listed have the same composition but were
The difference in the
processed under different conditions.
transverse strength index (TSI) between these fibers indicate
in processing
that the TSI can be used to evaluate changes
exists
any
relationship between TSI and fiber compressive strength.
It
parameters.
It
does
not
appear
that
there
is interesting to note that PBO-1 and Kevlar® 49 have similar
TSI
values.
strength,
one
If
the
would
TSI
were
expect
the
based
on
Kevlar®
intermolecular
49,
a
polyamide
capable of hydrogen bonding, to have a higher value than PBO.
Since this
is
properties
are
intermolecular
lateral
not the
more
case,
likely
strength.
(and compressive)
one can conclude that
based
Hence,
on
interfibrillar
attempts
strength by
at
than
improving
introducing primary
valence bonding in the transverse direction
64
lateral
(interchain) will
Table
3-1.
Compressive Strength From Tensile Recoil Test
Fiber
Compressive Strength
[MPa(Ksi)]
PBO-1
PBO-2
PBO-3
PBO-4
PBO-5
PBO-6
Kevlar® 29
Kevlar® 49
172
414
152
324
227
165
365
379
Table
+ 5
4
+ 6
± 5
+ 6
± 6
+ 10
± 10
f
(25)
(60)
(22)
(47)
(31)
(24)
(53)
(55)
3-2.
Compressive Strength of Fibers From Mini-Composites
Fiber
Compressive
[IPa (Ksi)
PBO-1
Kevlar~ 4 9
220
448
65
11
13
Strength
(32)
(5)
800
600
400
r2
200
0
0.00
0.10
0.20
0.30
Displacement (mm)
Figure 3-24. Stress-Deflection plot from compression testing
of mini-composites
66
Table 3-3.
Transverse Strength Index for Several
High Performance Fibers
Fiber
Designation
Fiber
Diameter
(um)
Transverse
Strength Index
[N/m (lb/in)]
Spectra
Kevlar® 49
PBO-1
PBO-3
PBO-4
PBO-5
PBO-6
35
12
24
16
17
24
27
349
519
491
272
278
285
339
±
±
±
±
±
±
±
44
42
47
21
24
15
38
(1.99)
(2.96)
(2.80)
(1.55)
(1.59)
(1.63)
(1.93)
Note: PBO-2 was not included in this study as an insufficient
quantity of it was available for TSI evaluation.
67
be
ineffective
unaffected.
interactions
interfibrillar
will
be
This has been the case in several studies5Z.
Compressive Modulus
3.5.3.
Figure
as
3-25
shows
the
single glass fibers.
results
for
three
point
bending of
Since the glass fibers are isotropic,
equation 3.3 can be solved directly for Ef.
using a least squares analysis line fit
This is done by
to the load data .
The slope of the line of the load - deflection curve is then
given by
Slope = 48 E I
L3
(3.22)
which is solved for E since I and L are known.
The result
is an average flexural modulus of 75.8 GPa (11 Msi) which is
in
good
agreement
with
literature
values
for
the tensile
modulus of E-glass.
Figure 3-26 shows flexural data for Kevlar® fibers. The least
squares fit for the Kevlar® 149 fibers uses the first three
data points only as the fibers exhibited non-linear behavior
at
higher loads as
shown
in Figure 3-27,
result of kink band formation.
most
likely as
a
Figure 3-28 shows the three
The difference in the slopes
point bending for PBO fibers.
of the curves comes from the variation in fiber diameter.
68
Vetrotex Glass P103-24
h
Am~.
in
1.50e-3
Z
1.QOe-3
T,oi
011
Pk
5.o0e-4
0.00e+O
O.00e+O
1.00e-5
2.00e-5
Deflection
3.00e-5
(m)
Figure 3-25. Load-Deflection plot from three point bending
on single glass fibers
69
the
Using
modulus
values
analysis
for
described,
several
are
fibers
of tensile moduli
the
values
given
in
employed in the
of
compressive
Table
All
3-4.
calculations
are
those provided by the manufacturers.
Tensile moduli were not
explicitly measured in this study.
As can be seen,
in all
cases the values of the compressive modulus are less than the
and in one instance, greatly so.
tensile ones
While there
has arisen the assumption that the two should be equal3
The microstructure
fact just the opposite is to be expected.
of these
chains
fibers
are
probably
is highly
is
not perfect
and while the polymer
fibrillar
the
oriented along
in
fiber
nor uniform.
axis,
the
Thus,
alignment
at the
chain
level, a pull will tend to improve the alignment and a push,
to reduce
have
and
it.
It
is also clear if the molecules involved
a non symmetric potential well that different tensile
compressive
limit
absolute
microstructure
tension, will
moduli
of
zero
will
be
expected,
strain.
Further,
exhibits a pleated sheet1 7
open and flatten,
when compressed,
except
the
in
the
Kevlar®
form which, under
becoming stiffer,
whereas,
it will fold more closed and decrease in
stiffness.
Another
interesting
feature
of
the
data
sensitivity of the compressive modulus.
is
the
apparent
The two PBO cases,
while identical in composition, underwent somewhat different
processing in the fiber drawing stage and this was reflected
70
Table 3-4.
Compressive Modulus for Several High Performance Fibers
Fiber
PBO-1
PBO-2
Kevlar® 29
Kevlar® 49
Kevlar® 149
Assumed
Tensile
Modulus, Et
[GPa(Msi)]
Compressive
Modulus, Ec
[GPa(Msi)]
Ratio E/Et
276 (40)
276 (40)
96 (14)
124 (18)
179 (26)
40
240
90
90
55
0.15
0.87
0.94
0.73
0.31
71
(6)
(35)
(13)
(13)
(8)
____
5.000e-4
0 Kevlar 49
O Kevlar 49
o Kevlar 49
4.000e-4
ZCu
3.000e-4
o
Kevlar 149
O
Kevlar 149
O
Kevlar 149
0
,-
2.000e-4
1.000e-4
O.000e+O
0.00e+0
2.00e-5
4.00e-5
Deflection
6.00e-5
8.00e-5
(m)
Figure 3-26. Load-Deflection plot from three point bending
on single Kevlar® fibers
72
Kevlar 149
Z
o
0~
C
0.OOe+0
2.00e-5
4.00e-5
6.00e-5
8.00e-5
Deflection (m)
Figure 3-27. Load-Deflection plot from three point bending
on single Kevlar® 149 fiber.
73
_
Ads_
1.00e-3
8.00e-4
Z
6.00e-4
co
4.00e-4
2.00e-4
.00e+0
O.00e+O
1.00e-5
2.00e-5
3.00e-5
4.00e-5
Deflection (m)
Figure 3-28. Load-Deflection plot from three point bending
on single PBO fibers
74
in
the
compressive modulus
values.
By other methods, the
microstructural
and morphological
changes
difference
be
the
revealed
can
that
the
explored,
two
mechanical properties;
but
fibers
accompanying the
simple
had marked
bending
test
differences
this was confirmed by differences
in
in
compressive strength behavior also (Table 3-1).
Some other interesting three point bending experiments can be
envisioned:
experimentation
with
shorter
spans
which
will
produce significant shear deformations is being conducted; it
may be possible to determine the shear modulus directly in
this manner.
Finally, another feature of the single fiber bending test is
proving
to
failure.
can
be
be
interesting:
its
use
to
study
compressive
Bending fibers until visible kink band formation
a
strength.
useful
method
for
determination
of
compressive
The current loading geometry makes this difficult,
however, because the loading probe is located at the point of
maximum stress and tends to make kinks difficult to see.
A
four point bending configuration would be more suitable for a
compressive strength test and it is under development1 5.
75
Modeling of Fiber Compressive Failure
Chapter 4.
4.1. Evidence of Fibril Buckling
It
is well known that high performance polymer fibers fail in
by
compression
described
kink
a
as
band
buckling
microstructural scales:
formationl8,3 .
failure
on
Kinking
has
been
different
several
Deteresaet a1 3 developed a model for
kink formation based on the buckling of single polymer chains
while
Cohen
buckling
and
Thomasl 9 described
The
entity.
former
microfibrils
model
concludes
as
the
that
the
compressive strength should be equal to the shear modulus and
although this has not proven to be the case, data exists that
show a
correlation between
linear
recognized
the
fibril
as
the
the
buckling
two.
Although
entity,
the
they
latter
researchers made no attempt to model the compressive strength
of fibers as a
discussed
viable
function of fibrillar microstructure.
fibril
mechanism
buckling but
to
explain
concluded that
similarities
in
it
Kumar 20
was
not
a
compressive
strength among PBO fibers with different tensile moduli.
Figure 4-1
split
with
is a SEM micrograph of a PBO fiber which has been
a
micromanipulator
; the
fibrillar
the fiber is evident on the split surface.
76
structure
of
The rear surface
Figure 4-1. SEM Micrograph of Single PBO Fiber split
with micromanipulator.
77
of the
fiber is in compression and kink bands have formed.
buckled
These kinks have propagated through the fiber and
fibrils are also visible on the split surface.
evidence
(along with that from others1 7 ,1 8 ),
Such visible
which is clearly
indicative of fibril failure within the kink, has motivated
by fibril buckling
modeling of compressive failure
in this
research.
4.2. Modeling with Euler Buckling
The most simple model for buckling is that given by Euler 2 1.
a column is defined as the
The critical buckling load for
load applied to the column which, when
column
not
to
return
to
its
original
removed, causes
position.
At
the
loads
higher than the critical value, the column becomes unstable
and will collapse by bending. Examining Figure 4-2,
see that
greater
this
than
will occur when
the
restoring
the applied moment
moment
(M).
EI
i =-M
ax2
(4.1)
Setting this equal to the external moment gives
EI
2y +Py=O
ax2
78
(P*y) is
Assuming
deformations, the internal moment, M, is given by
(4.2)
we can
small
x
x
P1
P
x
IX
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
a
I
I,
Y
Figure 4-2.
y
Schematic of Simply Supported Column
79
Y
which
is
a
second
order
homogeneous
linear
differential
equation and can be solved to yield
p = n 2 X 2 EI
L2
(4.6)
where n is the number of half sine waves or buckling modes.
The smallest value of the buckling force is given when n=l,
Obviously, no lateral loading of the fibril is considered in
the
Euler
analysis.
transversely
This
isotropic
implies
(Chapter
exists between axial and radial
orthotropic
stress
system could have
develop
on
the
fibrils
2)
that
and
that
stresses.
substantial
as
a
the
fiber
no
is
coupling
A cylindrically
lateral
consequence
tensile
of
axial
compressive loading, and the critical buckling load would be
greatly reduced.
With respect to fibril buckling, the parameters necessary for
prediction
of
critical
buckling
loads
are
the
fibril
compressive modulus, Ec, the fibril moment of inertia, I, and
the fibril single mode buckling length L.
The compressive modulus is obtained from single fiber three
point
bending tests
described
in
Chapter
3.
Here
it
is
assumed that the individual fibrils have the same compressive
80
The fibril moment of inertia is
modulus as the bulk fiber.
given by
4
where no shift in the neutral axis is considered for axial
fibril
The
loading.
is
diameter
found
by
splitting
individual fibers and measuring the diameters with an SEM. A
typical micrograph is shown in Figure 4-3.
The single mode buckling length for a single
found
in a
number
of
different
ways.
The
fibril can be
first
has
been
performed on Kevlar® 49 fibers and entails peeling a sheath
of fibrils from the fiber as shown in Figure 4-4.
The high
curvature at the peel point causes the fibrils to buckle.
micrograph
composite
Figure 4-5.
of
a
sheath
of
fibrils
is
given
A
in
The single mode buckling length L, or arc length
of the buckled fibril, is easily calculated by measuring the
chord length,
chord as
2b,
shown
in
and the departure,
Figure
4-6.
,of the arc from the
Using this
method on
10
different buckled Kevlar® 49 fibrils from Figure 4-5 gives an
average buckled length of 1510 nm with a standard deviation
of 224 nm.
Another method for determination of the buckled length has
In this process a section of
been employed on PBO fibers.
the skin is peeled from the fiber.
In PBO, the skin buckles
in regular arrays as shown in Figures 4-7 and 4-8.
81
4-3.
SEM Micrograph of single Kevlar®
Figure
fibril from a fiber split with a micromanipulator.
82
49
Peel
(
00-0000Compression
Surface
iber
Figure 4-4. SEM Micrograph of sheath of fibrils
peeled from Kevlar® 49 fiber as shown in schematic.
Buckling of fibrils in high curvature region is
evident.
83
Figure 4-5. SEM Micrograph of sheath of
Kevlar® 49 fiber.
84
fibrils
peeled
from
This
R4t
effect
Kevlar® fibers.
skin
buckle
seems
to
be
more
prominent
in
PBO
than
If it is assumed that the fibrils behind the
over
the
same
length
periodic spacing of the R4 effect
as
the
skin
then
the
can be used as the single
mode buckling length.
The buckling length can also be determined by plasma etching
of
previously
DeTeresa
compressed
et.al
that
fibers.
fibers
It
which
are
formation and subsequently placed in
or
reversal
0 2 CF
4
of
plasma,
kinks8 .
small
If these
pits
appear
shown in Figure
4-11.
failure
causes
an
increase
buckled
region
is
etched
formation.
The
Since
diameter
in
shown
compressed
to
by
kink
tension show unfolding
fibers
are etched with an
at
kink
the
fibril
a
the
length of the buckled fibril.
been
boundary
22
as
fibrillation during compressive
at
of
has
higher
pits
are
surface
rate
area,
the
causing
pit
indicative
of
the
Since the ultimate pit size is
a function of etchant and exposure time, this method can only
be
used
qualitatively
for
comparison
of
fibers
exposed
to
similar conditions.
t This is called the R4 effect since it was first observed by
an undergraduate research student: Rodrigo R. Rubiano's
Ripples.
85
'I
R
b
NJ
I] II
0
1
L
ii
A
e
R=
2+ b 2
26
.4
L = R * 20
= sin- b
R
Figure 4-6. Method of determination of buckled (arc) length
of single fibril.
86
Figure 4-7. SEM Micrograph of Arrays Of Buckled Rows
In The Skin of a PBO Fiber Which Has Been Peeled Off
The Core.
Figure
4-8. Same as Above, Higher Magnification.
87
4.3. Results and Discussion
Table 4-1 presents the results of the Euler buckling analysis
applied to
Kevlar@
49
and
PBO
fibrils.
The
single
mode
buckling length was found by the sheath peeling and R4 method
for
Kevlar®
strength
is
and
PBO
respectively.
calculated
strength by the
ratio
The
fiber
by multiplying
of
fiber to
the
fibril
compressive
single
area
fibril
(number of
fibrils).
It is clear that the predicted load for compressive failure
overestimates
the
measured one.
A
number
of
reasons
are
available to explain this:
1)
The
size
of
the
fibril
is
not
single
valued.
Actually a distribution of fibril diameters exists.
2) The
compressive deformation
in
the
fibrils
is
not
elastic as assumed in the Euler analysis. The analysis
is based on
long
stability considerations and is valid for
slender
columns.
The
slenderness
ratio
of
fibrils is very low, on the order of about 20 - 25.
the
(The
slenderness ratio is the length of the column ,L,divided
by the radius
of gyration ,R, of the cross section in
the plane of
buckling).
ratio
which
above
The
Eulers
value of
formula
estimated by
R)min
=i\
88
UCs
the
slenderness
applies
can
be
Table 4-1.
Euler Analysis of Single Fibrils Using
Sheath Peeling and R4 methods.
Fiber
Fibril
Diameter
(nm)
Kevlar 49 160±20
PBO-1
220±30
Calc.
Measd
Fibril
Length
(nm)
Comp.
Modulus
(GPa)
Compress
Strength
IMPa)
Compress.
Strength
(MPa)
1510±220
1400±200
90
40
620+205
620±276
345±35
207±35
Note: Measured Compressive Strength From Tensile
(Fiber Diameters: Kevlar® 49=12um, PBO-1=18um)
89
Recoil.
which conservatively assumes that non -linear behavior
For Kevlar® and PBO
occurs after compressive failure.
this
value
is
50.
about
Examination
of
4-9
Figure
indicates that the Euler analysis will overestimate the
compressive
strength
for
typical
fibrils.
This
overestimation is derived from the fact that crushing is
also involved in fibril failure.
In order to consider
this type of behavior, the compressive stress - strain
curve for a single fibril/fiber would have to be known.
The
agreement
observations
is
of
the
with
model
encouraging:
it
other
postulates
experimental
that
the
kink
band initiates on the fiber surface, where the low degree of
lateral support leads to small critical buckling loads. Kink
bands do start on the fiber surface as can be seen in Figure
4-10.
Perhaps the best use of the model is in the investigation of
processing variations on the mechanical properties of a fiber
of given composition.
One such study was conducted on four
types of PBO fibers, each subjected to different processing
conditions.
O2CF 4
plasma
length.
The fibers were simultaneously subjected to an
for 20 minutes
to obtain the
fibril buckling
Figures 4-11 to 4-14 are SEM micrographs of the pits
created from plasma
The
etching.
similar to kink lengths
lengths of the pits
are
in PBO fibers measured by others 2 3.
90
Split fibers were used to measure fibril diameters.
presents
the
results
aforementioned
uncertainty
(section 3.5.3),
are
given on
of
the
in
analysis.
the
plasma
Due
The
to
etching
the predicted fiber compressive
a ranked basis only.
Table 4-2
the
method
strengths
fibril peel
and R4
methods measure actual buckling entities and hence are more
accurate.
Nonetheless, the relative measurement provided by
the plasma etching is effective:
compressive
strength
is
in
the predicted rank
excellent
agreement
in the
with
the
measured one, indicating the merit of the model.
Despite the fact that the model is useful in ranking ultimate
compressive
strength
of
single
fibers,
its
utility
in
determining the absolute ultimate compressive strength may be
limited.
fibril
To
improve the model
compressive
fibril-fibril
for axial
stress--strain
interactions,
lateral
would require knowledge of
and the
interaction, Szo.
items would allow for more
behavior,
the
nature
of
compliance coefficient
Identification of these
exact modeling of these complex
systems.
91
---5000
4000
u
3000
0
1000
0
0a0
o
0
20
40
60
80
100
Slenderness Ratio
Figure 4-9 Eulers Curve for Fiber with Compressive Modulus
of 89.5 GPa
92
4-10 SEM Micrograph
Figure
Exterior of PBO Fiber
93
of
Kink
Band
Initiating
on
Figure
4-11.
SEM Micrograph of Pits
Boundary in Plasma Etched PBO Fiber.
Along
Figure 4-12. SEM Micrograph of Pits Along
Boundary in Plasma Etched PBO-6 Fiber.
Kink
94
Kink
SEM Micrograph of Pits
4-13.
Figure
Boundary in Plasma Etched PBO-5 Fiber.
Along
Figure 4-14. SEM Micrograph of Pits Along Kink
Boundary in Plasma Etched PBO-4 Fiber.
95
Kink
Table 4-2.
Euler Analysis of Single Fibrils Using Plasma
Etching Method For Single Mode Buckling Length.
Fibril
Diameter
Fibril
Length
Measured
UCS
Measured
Rank in
Predicted
Rank in
Fiber
(nm)
(nm)
[MPa (ksi) ]
UCS
UCS
PBO-3
PBO-4
PBO-5
PBO-6
220
230
180
250
590
350
360
660
152
324
214
165
4
1
2
3
4
1
2
3
96
(22)
(47)
(31)
(24)
Chapter 5. Improving Fiber Compressive Strength
5.1. Methods of Improvement
5.1.1.
As
Chemical Methods
discussed
in
Chapter
4,
several
researchers
have
recognized that buckling of polymer chains 3 or fibrils 19
is
responsible for the compressive failure
in high performance
polymer fibers.
the introduction
Others predicted that
of
lateral covalent bonding between chains would delay buckling
and improve the compressive strength.
introduced
flourene
moieties
Bhattacharya et. al.
into
Poly(p-phenylene
benzobisthiazole) (PBT) fibers 2 for lateral crosslinking while
Chuah et. al.
crosslinked PBT copolymers via labile methyl
groups 2 4. Both
studies
compressive strength;
reduced' because
showed
minimal
improvement
in
in fact, the axial tensile strength was
of the
reduction
in packing ability.
The
lack of improvement from interchain crosslinking is further
indication
that
compressive
fibrillar morphology,
properties
are
governed
by
thus a method to laterally reinforce
the fibrils was sought.
97
5.1.2.
Rigid
Coatings
Examination of the model developed in
section 4.2
indicates
that lateral restraint of a column will increase its critical
buckling load.
elastic
If the model is modified to include
support,
as
shown
in
Figure
5-1,
the
lateral,
critical
buckling load is2 5
PI, -2 EI n 2
L2
where
is
the
other variables
modulus
are as
of
+
n2n4 E
the
elastic
given previously.
(5.1)
foundation
and
all
By choosing a high
modulus material for the foundation, the buckling load can be
increased by
n2Ei
percent.
00
Note, however that by increasing
condition at which Pn=
(5.2)
there is a
< Pn=2 i.e
1+
=4+
4 EI
p
4/x4 E
(5.3)
=4
'4 EI
(5.4)
Thus if only stability is considered, the maximum increase in
single mode buckling strength is 500 percent.
initiates on the fiber exterior where
98
Since kinking
X
t
Figure 5-1.
Modification
of Fibril
Model To Consider
Lateral Support By An Elastic
Foundation. Each spring has a
spring constant k.
The modulus of the foundation,
, is
given by
i = k /
b
99
the
lateral
support
is
minimal,
application
of
a
rigid
coating to the fiber surface should increase the compressive
strength.
5.1.2.1.
Coating Selection
Equation 5.1
indicates that any material of finite modulus
applied
the
to
strength.
fiber
should
increase
its
compressive
However, the coating itself also carries an axial
load so a high modulus is desirable to prevent buckling of
it.
Strength
of
materials
calculations
indicate
that
the
coating will carry an axial load given by
Pc = applied *
EfA
ECA +
)
(5.5)
EfAf
where P is force, E is the modulus, A is the cross sectional
area
and the
fiber.
are
subscripts
This shows
desirable
for
that
c and
f refer to the
coating and
coating materials with high moduli
lateral
support
(equation 5.1)
but
they
will acquire a higher proportion of the applied axial forces
which may lead to their premature buckling.
A schematic of some of the forces on the coating is given in
Figure 5-2.
The lateral forces come from fibrils attempting
to buckle and the hoop forces are derived from the lateral
expansion of the fiber.
If the coating and the fiber have
different thermal expansion coefficients, residual
100
Axial Force From
A1
T
-- d
aLU.U
,A
Hoop Force From
Poisson Effects
Lateral Force
From Kink B
Figure 5-2.
Schematic of Forces on Thin Rigid Coating
Applied to Fiber (Fiber Not Shown).
101
stresses will result from temperature excursions.
These
forces are given by
p=(a1
a
is
by
and
fiber
the
either
coefficient,
AT
as
is
the
defined
can be found by dividing
sectional
cross
coating
or
are
subscripts
the
appropriate stress
The
previously.
expansion
thermal
temperature
in
change
the
(5.6)
EAf
EAcP
where
AT
1
Xj
area.
To
coating materials with thermal expansion
minimize the stress,
coefficients similar to those of the fiber are desirable.
Good adhesion
for
necessary
the
fiber
and the
the coating
between
reinforcing concept
to be
surface
effective.
is
If
the outer fibrils are not constrained and can start to bend,
they
support
from
the
fiber
if
only
coating
the
Similarly,
buckle.
will
two
the
lateral
derives
are
adhered.
well
Absent good adhesion, the coating idea is not effective.
A
rigid coating also reduces the
thermal
expansion
40
greater than
is
so
low,
the
(CTE)
ppm/ 0 C.
high
fiber radial coefficient of
is
which
the
Since
modulus
very
large,
fiber transverse
coating
restrains
Finite element calculations performed by Jao2
fiber
with
thickness
of
a
transverse
modulus
1 percent of the
of
4
GPa
the
modulus
fiber.
show that for a
and
fiber diameter the
102
typically
a
coating
radial CTE
is
significantly reduced with high modulus coatings.
results are
reduction
shown in Figure
in
transverse
will
not
higher
radial
CTE
modulus.
It
also
by
the
be
reduced
fiber
element
5-3.
modulus
calculations
is
in
a
strong
5-4
rigid
coating
even
of
that
direction.
that
shows that the
function
indicates
that
show
Figure
if
These
the
the
fiber
axial
because
of
CTE
the
Finally,
finite
coating
cracks
the
axially at
450 intervals around the fiber circumference, the
radial
increases
CTE
only by
a
few percent
if
the
coating
remains well adhered to the fiber surface.
5.2. Experimental
5.2.1.
Coating Deposition
High modulus
physical
ceramic coatings
vapor
(PVD)
were
deposition
applied
to
techniques
fibers
as
using
outlined
in
United States Patent 502125827.
The PVD process is unique in
that
high
melting
point
the
polymer
substrate
it
permits
materials
deposition
without
of
subjecting
appreciable temperature
differentials.
beam evaporator with special
fixtures
A
for
A1 2 0 3 )
most
The
literature 2 8
of the
bulk
are
study was
properties
given
of
in Table
Temescal
used.
aluminum oxide
alumina
5-1.
to
electron
designed to rotate the
fibers for uniform coating deposition was
used
ceramic
The
ceramic
(alumina or
obtained
from
The properties
the
listed
are for crystalline a-alumina which was the evaporant source.
103
60 -
I
_
_
meter
0
50
E'
40d
30
.I
0
.
200
I
.
I
400
.
600
800
Coating Modulus ( Gpa )
Figure 5-3.
Radial CTE as a Function
Generated By Finite Element Model.
104
of
Coating
Modulus
70
60
.
s
--
--
-
O
50 -
5U
1-1
0
U
40 -
30 -
"a
20 -
r Diameter
Coating Modulus = 414 upa
10
IP
.1
· ··
.1
10
1
--
10
Fiber Transverse Modulus
-1 00
1000
( Gpa )
Figure 5-4.
Radial CTE as a Function of Fiber Transverse
Modulus Generated By Finite Element Model.
105
However,
X-ray
was
deposited material
indicated
studies
diffraction
that
of
SEM observations
amorphous.
the
the
coatings showed they are homogeneous and uniform both axially
(Figure 5-6).
(Figure 5-5) and circumferentialy
Figure
5-6
shows
frozen
in
liquid
glass
the
was
to
produce
the
illustration
coating thickness on
The
to prepare.)
which
fiber
fiber was used for this
placed adjacent to
slides
fractured
and
nitrogen
is easier
it
glass
coated
alumina
(A glass
surface shown.
because
an
fibers during deposition
was used to measure the coating thickness on the fibers.
glass
provided
slides
a
on
substrate
flat
which
a
The
Dektak®
profilometer was used to measure the thickness.
5.2.2.
Property Evaluation
The
compressive
the
tensile
fibers
were
strength of
recoil
bending test.
The
with
radial
fibers
Flexural
test.
determined
coated
the
thermal
evaluated by
was
of
coated
three
point
properties
single
fiber
observed by
expansion was
using a hot stage in an SEM and measuring the change in fiber
diameter with heating.
Fibers were dried under vacuum prior
to testing to avoid dimensional
No
composites
were
made
with
changes from water expulsion.
coated
thousands of fibers required for a
be
coated by
the
fibers
106
the
many
single specimen could not
batch electron beam process
times periods.
as
in
reasonable
Figure 5-5. SEM Micrograph of Alumina Coating on PBO
Fiber Applied by Physical Vapor Deposition.
Coating
is Smooth and Homogeneous.
Figure 5-6. SEM Micrograph of Alumina Coating on Glass Fiber
Applied by Physical Vapor Deposition.
Coating is Uniform
Around Fiber Circumference.
107
Table 5-1.
Mechanical Properties of Alumina
Used For Rigid Coating on Fibers
Modulus Of Elasticity
372 GPa
(54 Msi)
Compressive Strength
2.4 GPa
(350 Ksi)
Tensile Strength
207 MPa
(30 Ksi)
Coefficient of
Thermal Expan-sion
7 ppm/°C
.... .. .. .. . . .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
108
5.3. Results and Discussion
Effect of Coatings on Fiber Strength
5.3.1.
A range of coating thicknesses was applied to both single PBO
49
and Kevlar®
fibers
29
.
strength
ultimate compressive
The
versus coating thickness for PBO is given in Figure 5-9.
A
fit
linear
well
correlates
to
the
line
the
strength
compressive
almost exactly to the
extrapolates back
and
data
strength of the
PBO
is more than doubled with a coating thickness of 8000 A.
SEM
in Figures
5-7
of
micrographs
and
failed coated fibers are given
Kink
5-8.
compressive
The
of the uncoated fiber.
are
bands
In fact, the
coating and the excellent adhesion is apparent.
adhesion
was
so
engineering
traditional
adhesion was not
polymers
to
unique
were made to
attempts
good that
to
be
certain
and
acrylonitrile
that
good
fibers.
poly-methylmethacrylate,
polywas
adhesion
poly-ethylene:
of
A study was initiated to investigate
excellent in all cases.
the
more
flat plates
Alumina .coatings were successfully applied to
styrene
coat
high performance polymer
poly-styrene, poly-carbonate,
failed
the
beneath
discernible
source of the adhesion and preliminary secondary ion mass
spectrometry
indicate
alumina
that
and
conclusive
interface
and
x-ray
primary
the
as the
caused
bonding
valence
polymers.
minute
The
volume
analytical
between
existed
studies
fraction
difficulties.
109
data
spectroscopy
photoelectron
of
were
not
the
fully
ceramic/polymer
It
is
suspected
that
the
atomic
oxygen which is
known
to be
present
electron beam evaporation of alumina 3 0 is responsible
during
for
he
formation of primary bonds.
The
improvements
not
as
in compressive strength for Kevlar®
consistent
Kevlar®
fibers
strength
and
as those observed for PBO.
would
other
show
times
large
almost
determined that the reason for the
poor adhesion between the
Sometimes the
increases
none.
49 were
in
compressive
Eventually
it
was
inconsistent behavior was
fiber and
coating.
Morgan
31
et al
found large amounts of residual sulfur and sodium in Kevlar®
while
Penn3 2
confirmed
the
et
al
found
presence
of
stearic
and
palmitic
sulfur
and
sodium
acids.
by
a
We
neutron
activation study.
The stearic and palmitic acids are used as
lubricants
processing
weak
during
boundary
layer
coating adhesion.
were
obtained
from
on
the
and their
fiber
presence
surface
PPTA fibers made without
DuPont
indicate that improvements
and
the
limited
which
110
a
inhibits
such lubricants
data
in their compressive
similar to those observed in PBO.
creates
obtained
strength are
Figure
Fiber.
5-7. SEM Micrograph of Failed Alumina Coated PBO
Good Adhesion of Coating is Evident.
Figure 5-8. SEM Micrograph of Failed Alumina Coated PBO
Fiber.
Good Adhesion of Coating is Evident.
111
Since
the
rigid
existed that,
ceramic
coating
in tension,
failure
of the
occur.
The data
fiber.
is
brittle,
some
concern
its fracture would cause premature
Figure 5-10
shows
indicate no significant
that this
does not
difference between
the two.
Well adhered rigid ceramic coatings significantly improve the
compressive
strength of PBO fibers.
This improvement
is not
accompanied by a decrease in tensile strength as was found in
the
other
studies
cited2 ,2 4 .
It
has
also been
observed by
Chang3 3 that cracking in the coating caused by tensile loading
or
by thermal
compressive
cycling
strength
does
not
provided
degrade
the
the
improvement
coating
remains
in
well
adhered.
5.3.2.
Effect of Coatings on Fiber CTE
Uncoated fibers and coated fibers
250 C to 400 ° C
at about
were heated in a
SEM from
250 C/min. A micrograph of a
coated
fiber at
4000 C is
given in Figure 5-11. The axial cracking is
a
of
large
result
critical
thickness.
be used to
the
cracking
radial
expansion of
temperature
This cracking
is
the
dependent
fiber;
the
on
coating
at elevated temperatures
can also
indicate adhesion:
a poorly
adhered coating will
show a single axial crack and spall free while a well adhered
one will give multiple cracks, while remaining in place.
112
600
I
4
500
S
;-
Ut
w
400
D
*
rA
300
._W
r>
C6
E
4)
200
14-
100
0
2000
4000
6000
8000
10000
Coating Thickness (A)
Figure 5-9.
Ultimate Compressive Strength versus Alumina
Coating Thickness For PBO Fibers.
113
--
A
1.0 '
0
O
A
0.8O
=1
a0
eC
0
0.60
.0
O Uncoated
A Coated
O A
[]
0.4-
C:
0
[]
0]
0.2-
0.0 I
60
[]
~-
.
i
-
80
Ultimate
.
--
1 00
Tensile
--
--
L-
120
s
140
Load (g)
Figure 5-10.
Cumulative Distribution Function Of Ultimate
Load For Uncoated and Alumina Coated PBO Fibers in Tension.
114
Figure 5-12 presents the percent change in fiber diameter for
PBO fibers, both uncoated and coated with 6000A (3% of fiber
All data were fit linearly by the least
diameter).
The slope
method.
radial CTE in ppm /
in
radial
CTE
by a
coated fibers at
of the lines m, divided by 100,
C.
squares
is the
The coated fibers show a reduction
factor
of
2.
begins
Cracking
the
in
about 250 ° C, but no substantial deviation
finite
in expansion is observed, in good agreement with the
element predictions.
Figure 5-13 presents the percent change in fiber diameter for
Kevlar® 49 fibers both uncoated and coated with 3500A (3% of
fiber diameter).
The more than three fold decrease in radial
CTE is more dramatic in the Kevlar® system.
Since less axial
cracking was observed in the Kevlar® system its adhesion was
worse
than
that
of
the
PBO.
This
indicates
that
good
adhesion is not as critical in reduction of radial CTE's as
it
is
for
improvement
of
compressive
strength.
It
is
encouraging to observe that a problem long associated with
high performance polymer
fibers,
large radial
solved by the application of rigid coatings.
11
CTEs,
can be
Figure 5-11. SEM Micrograph
Fiber Heated In-Situ to 4000 C.
of
116
Alumina
Coated
PBO
7
6
5
cm
=so
4
.0
3
2
B0
0
0
100
200
300
Temperature (
400
500
600
C)
Figure 5-12.
Percent Change in Fiber Diameter With
Temperature For Uncoated and Alumina Coated PBO Fibers.
(m=slope).
117
3
L(
2
Cu
*-i
.0J
0
100
200
Temperature (
300
C)
Figure 5-13.
Percent Change in Fiber Diameter With
Temperature For Uncoated and Alumina Coated Kevlar
49
Fibers. (m=slope).
118
400
5.3.3.
The
Effect of Coatings on Flexural Behavior
presence
neutral
EI.
axis
This
of
of
a
high
a
modulus
beam will
produces
lower
material
increase
its
deflections
the
flexural
behavior.
determine the
transformed
coated
shows
fiber
The
in-situ
flexural
rigidity
for
uncoated and coated with 8000 A of alumina.
of
from
the
same
the
load.
load-deflection plot for PBO fibers
Figure 5-14 is a flexural
rigidity
distant
increase
modulus
of
the
can
the
The increase in
improvement
also
coating
be
used
by use
of
in
to
a
section method in which the coating is virtually
transformed into a mechanically equivalent area of the fiber.
Recognizing
that
the
axial
force
on
the
coated
fiber
section must be zero it follows
.
ydA + Ef
ydA =O
(5.7)
If n, the modulus ratio, is defined as
n=Ec
Ef
(5.8)
then equation 5.7 can be rewritten as
nydA+
ydA=O
(5.9)
119
cross
where A
is
area and
Equation 5.9
remains
is the
y
distance to
the neutral axis.
indicates that the position of the neutral axis
unchanged
multiplied by n.
single material
if
each
area
element
of
coating
the
is
the coated fiber can be modeled as a
Hence,
(fiber) with a moment of inertia
I
(d+ 2 n t)4
64
(5.10)
where d is the fiber diameter, and t is the coating
thickness.
The anisotropic nature of the high performance polymer fibers
creates uncertainties in the appropriate fiber modulus to be
used
in
equation
involved:
5.8
since
three
different
Et,fiber,Ec,fiber and Ecoat.
Instead,
moduli
three
are
point
bend tests were conducted on coated glass fibers since glass
is an isotropic material.
A plot of the load-deflection data
for a 24 um diameter E-glass fiber is given in Figure 5-15.
From the slope of the linear fit,
inertia from equation 3.22
known.
ratio
we can find the moment of
since the modulus and span are
Equation 5.10 can then be
since the
coating
thickness
solved for the modulus
is
known.
Using this
method, the in-situ modulus of the coating was found to be
310 GPa (45 Msi) to 345 GPa
(50 Msi) which is in reasonable
agreement with the modulus of the bulk material ( 372 GPa [54
Msi])
reported previously.
120
A
~
A
4.u0e-3
3.00e-3
O Uncoated
O Coated
2.00e-3
o
Pk
1.00e-3
0.00e+0
0.00e+0
1.00e-5
2.00e-5
Deflection
Figure 5-14.
Coated PBO-5
Load Deflection Plot
Fibers. (m=slope).
121
3.00e-5
4.00e-5
(m)
For Uncoated and Alumina
0.003
0.002
Z
3-
0so
L,
ex
0.001
0.000
.00e+O
1.00e-5
2.00e-5
Deflection
3.00e-5
(m)
Load Deflection Plot For an Alumina Coated EFigure 5-15.
Glass Fiber. (m=slope).
122
5.3.4.
The
Mechanism of Improvement
motive
restraint
for
of
the
the
rigid
outer
coating
fibrils
was
and
compressive strength of the fibers.
to
provide
thereby
lateral
increase
the
It is possible, however,
that the high modulus coating simply takes load away from the
fiber thus
rule
of
allowing the
mixtures
system to
(ROM) type
of
sustain
a
behavior.
higher
This
load;
a
alternate
explanation of its action had to be explored.
5.3.4.1.
Rule of Mixtures
Equation 5.5
345
GPa
shows that for a coating of 4000A thickness
Modulus
on
compressive modulus
of the load is
the
fiber
thickness
is
it
occurring.
a
fiber
20
um
increased
coating.
by
unlikely
more
that
Alternatively,
it
a
Since the
than
80
ROM
type
levels
5.5,
The
load
either
analysis
required
the
thickness.
study
fiber
70
GPa
strength of
percent
of
at
was
chose
coating properties
to
reach
or
the
the
ultimate
coating
for
a
Figure 5-16 displays the results:
123
Using
examine
stress
coating
and then
stress
given
is
coating
follow a ROM.
conducted to
this
behavior
in the fiber and in the coating for different
moduli.
the
an
and
is possible to find a
modulus value such that the system does
equation
diameter
(typical of PBO) approximately 29 percent
borne by the
is
of
and
found
level
in
coating
measured values
of coated fiber ultimate compressive
(On the figure, the coating
generated by using equation 5.5.
modulus, Ec,
and strength,
The analysis shows
GPa.)
Sc,
strength and the data
are given for each line
in
that in order to obtain behavior
similar to that which was measured, the coating must have a
950
of more than
modulus
strength of 3.8 GPa
GPa
the
represented by
set
These are much higher than
(551 Ksi).
Much closer to the known values
their known, in-situ values.
is
and a compressive
(138 Msi)
the
triangle
(A),
which
is
This casts
below the experimentally measured data.
far
strong
doubt on the relevance of the simple rule of mixtures to the
system; either a more complicated rule is required ,
true action
of
the
coating
against
constraint
is
to provide
buckling.
The
the
latter
or the
stabilizing
appears
more
probable.
5.3.4.2.
Lateral Restraint
Implementing
is
hypothesis
restrains
a
model
difficult.
kink
controls),
to
then
formation
the
validate
If
we
until
the
lateral
assume
it
appropriate
fails
model
the
coating
(coating
failure
that
would
be
a
shell supported on
foundation.
This shell would be loaded as in Figure 5-2.
also attempt
to model
the
thin
interior by an elastic
cylindrical
could
its
restraint
outer
fibrils
as
We
columns
supported by an elastic foundation as depicted in Figure 5-1.
124
--bUU
500-
0
Ec--551 Sc=2
A
Ec=345 Sc=2x
Ec=950 Sc=3.8
Measured Values
X
0
X
X
x
x xM
CL
a
400
"
E*-A
200-
0XX 00 00
D
xx
00
00000 00A
A
xAA
0
O"AAA
100
0
2000
4000
0
0000
0
AAAA
6000
8000
10000
Coating Thickness (A)
Figure 5-16.
Ultimate Compressive Strength vs. Coating
Thickness: measured data and values calculated from rule of
mixtures (Ec=Coating Modulus, Sc=Coating Compressive
Strength) Units:Gpa
125
Unfortunately,
magnitudes
since
of the
the
lateral
restraint
forces
conditions
imposed
by the
and
the
kinks
are
unknown, predicting the coated fiber behavior based on these
models
would
assumptions
degenerate
play
out
into
in
the
seeing
now
results.
It
the
starting
would
not
be
conclusive.
At this point
the
it is believed that the correct explanation of
coating effect
compressive
There
is
is
its
buckling.
abundant
mechanism
is
crosslinking
stiffening of the
This
derives
evidence
fibril
between
that
kink bands at
fiber
coating
coating
a
stiff
functions
temperature
excursions
reinforcement
dimensions
even
action
of
essential to
fibrils.
its
Good
function,
it
localized,
adhesion
since
it is
why
failure
chemical
The
surface of the
delays
tensile
crack
factors.
ineffective.
surface
though
is very
is
is
or near the
on the
may
several
compressive
which
chains
buckling initiates
and
the
buckling,
polymer
from
surface against
it.
The
preloading
extensively;
or
the
consistent with the
of
the
coating
is
attached to only one
side of the fibril rather than entirely surrounding it.
5.3.5.
Effect of External Stresses on Residual Strength of
Coated Fiber
Since the coating is brittle, in work done by Chang3 3
cracked extensively,
to
near
its
either by loading the
breaking
point
or
126
by
fiber
heating
it
it was
in tension
such
that
significant
differential
thermal
expansion
occurred.
The
fibers used PBO with a baseline compressive strength of about
80 Mpa as measured by the tensile recoil method.
were coated with various uniform thicknesses
pulled
to
about
80%
of
their
breaking
The
fibers
of ceramic and
load,
producing
uniformly spaced circumferential cracks as shown in Figure 517.
Then
results
data,
these
shown
the
improvement
in
were
tested
Figure
in
5-18.
tensile
Within
precracked
fibers
as
uncracked ones,
did
thicker coatings.
the
recoil
with
scatter
the
same
showed
the
the
of
the
strength
especially
with the
Though cracked, the coating remained well
adhered to the fiber, with no spalling evident, and the width
of the
crack
cracks was very small,
width
buckling
same
is
much
fibril
order
elements
of
less
elements
buckling
remain
of the order
than
in
the
fibrils
observed by
by
cracks.
This suggests that
it
elements
that
which
observed
A
length
PBO observed by us
constrained
we
15,000
of 2500 A.
is
but
This
of
the
on the
others 2 3.
The
the
coating
the
larger scale buckling
control
despite
the
the
compressive
strength.
Using coated fibers
exposed
to
minutes
in
elevated
air.
No
from the
same population,
temperatures:
special
steps
150 0 C
fibers to
rates
contract
number were
2500 C
and
accompanied
specimens were simply removed from the oven.
the
a
cooling;
127
30
the
Heating caused
axially and expand radially,
different from the ceramic coating,
for
and the
both at
result was
a series of axial cracks as seen in Figure 5-11.
occurred and the
radial thermal
cracked coating
expansion
of the
continued to
fiber.
No spalling
inhibit
When these
the
fibers
were tested in tensile recoil, the compressive strengths were
nearly the same as for the uncracked coated fibers as shown
The axial cracks were narrow, about 2500 A,
in Figure 5-19.
and followed a circuitous path on that scale
they were
irregular
not
perfectly straight.
path
apparently
The
combined
of dimension;
small
to
gap and the
preserve
constraining action of the coating on the fibril elements.
128
the
Figure 5-17. Circumferential Cracks
PBO Fiber From Tensile Loading.
129
in
Coating
on
___
uu
---
2
100
*050
0
2000
4000
Coating Thickness
6000
8000
(A)
Figure 5-18.
Ultimate Compressive Strength vs. Coating
Thickness in PBO Fiber both Unloaded and After a 60g Tensile
Preload.
130
200 . I
-
--
--·
---- [
0
a
A
150[
O
aqa
100-
A
0
U
0
A
I"
Uncylcled
Preheated to 150 °C
Preheated to 250 °C
E
I
0
'
2000
I
4000
Coating Thickness
'
I
I
6000
8000
(A)
Figure 5-19. Ultimate Compressive Strength vs. Coating
Thickness in PBO Fiber Before and After Heating in Air..
131
Chapter 6.
Conclusions
have been developed to evaluate the mechanical
New methods
fibers.
polymer
high performance
of
properties
A
device
which simplifies recoil testing by symmetrical cutting of the
fiber was made and it gives a more accurate measurement of
Load spikes created by non-
the axial compressive strength.
symmetric cutting are nearly eliminated in Kevlar® fibers and
greatly reduced for PBO fibers.
To evaluate the transverse strength of single fibers,
was
developed in which an
opening mode
a test
crack is propagated
axially in the fiber. The crack initiation force normalized
by the
fiber
diameter provides a
fiber mechanical property.
The loads
weights
was
an
force
which
instrument
Gas
constructed.
involved are extremely
To determine critical crack
small and difficult to measure.
propagating
measure of a transverse
operates
were
bearings
with
used
on
dead
all
translational parts to minimize frictional forces.
Because
the
tensile
test
does
not
measure
the
true
transverse
strength the numbers obtained have been termed the Transverse
Strength
changes
the
TSI
Index
(TSI).
The
TSI
in processing parameters.
and
the
fiber
can
used
to
evaluate
No relationship between
compressive
132
be
strength
is
evident.
Values
TSI
the
of
strong
with
fibers
for
obtained
(aramids) are similar to those without
intermolecular bonding
(PBO) suggesting that the lateral properties are more likely
based on interfibrillar than intermolecular strength.
A
fibers. Load deflection curves
single
three point bending of
enables
apparatus
testing
the transverse
to
modification
are generated by adding incremental weights and measuring the
deflection
corresponding
Analysis
video micrometer.
a
with
shows that shear effects are minimal and basic elasticity is
section
were
derived.
numerically
tested to
for
the
They
and
check
are
were
High
ones.
were
and
in
of
excellent
The
to
for Kevlar®
conditions:
it
149
is
conditions
from
0.15
tensile
PBO
0.31.
showed
to
moduli
is
29 Ec/Et
fibers
The ratio of
Future
bending
to
with it
compressive failure, thus
work
A
133
for
of
different
Ec/Et
should
Kevlar®
ranged
focus
on
four point bending
a single fiber can be tested
replacing the
test.
processing
under
ratios
shorter spans to examine shear effects.
test has been developed;
to
0.94 while
processed
similar effects:
0.87.
sensitive
is
values
compressive
had
moduli that were less than their tensile ones.
compressive
were
agreement with the
fibers
performance
fibers
device.
the
both
solved
glass
Isotropic
performance
glass modulus
published
complex
graphically.
the
moduli
tensile and compressive
different
with
cross
a material of circular
for bending of
The equations
valid.
cumbersome
recoil
fiber compressive
modeling of
The
of
buckling
fibrils
the
has
been
behavior through a
simple
The
fibril
successful.
diameters are determined from SEM observation of fibers split
The
a micromanipulator.
with
of the
assumed to be that
point
bend
fiber as obtained from the
fibril
The
test.
compressive modulus
fibril
buckling
have
lengths
is
three
been
determined in several ways: plasma etching, buckled peels and
the
strength but it
in
The
effect.
R4
of
fibers
overestimates
model
compressive
fiber
is useful in ranking the compressive behavior
the
same
composition
to
subjected
processing
variations which alter their fibrillar morphology.
coupled with the observation of external kink band
The model,
initiation,
be
could
suggested
improved
When
coatings.
physical
using
by
that
was
applied
improvement
compressive
from about
to
the
deposition,
strength improved significantly.
coating thickness
fiber
application
the
alumina
vapor
the
of
rigid
exterior
fiber
surface,
the
fiber
compressive
linear with
The increase is
1000 A
strength
The observed
to 8000 A.
exceeds that predicted by the rule
of mixtures,
indicating that the coating does restrain fibril buckling and
does not
also
simply carry load away from the fiber.
reduces,
thermal
by
a
factor
of
2,
the
radial
The coating
coefficient
expansion of the high performance fibers.
of
Cracks in
the coating from tensile preloading or from high temperature
134
exposure
do
not
significantly
degrade
the
improved
compressive performance.
Further work should be done to examine effects of different
coatings
(of
both
higher
and
lower
moduli)
compressive, flexural and thermal characteristics.
135
on
fiber
Appendix
Error In Single Fiber
Bending Experiments
136
The
for
potential
bending experiments is
in
deflections
to
related
3-23,
Figure
moment
the
dependent
on
quickly.
Hence,
it
is
It
measured accurately.
fiber
section of the
critical
is
is
error but,
sources
of
largest
is
is
which
errors
in
the
propagate
fiber diameter
the
imperative that
also
are
order
fourth
tend to
that the
is
cross
This can
length.
uniform along its
as
fiber
properties
flexural
the
small
point
Inaccurate measurements
inertia
of
diameter,
the
the
Since
evaluation.
diameter
are both
three
fiber
single
the
significant.
load
and
in
exemplified
in
error
be a significant problem in experimental fibers made in batch
A
processing.
caused by
which
nonuniform cross
shows
of PBO
the
for
the
same
SEM:
their
test
minimized
and
useful
of
fibers
length
the
data.
single
For
a
reader is referred to
shows
group
is
given
the
fibers
of
in Figure A-i,
been
omitted.
calculated
fiber
It.is
three
thorough
137
series
large
and
compressive
been
they have
The
compressive
section
scatter
is
modulus
evident then, that careful
point
discussion
[15].
is
calculated
after
a
for
nonuniform cross
with a
have
statistically significant.
execution
the
The scatter
lot.
error
potential
of
calculated compressive modulus
Figure A-2
screened in an
over
sections
from the same
fibers
unacceptable.
modulus
illustration
good
bending
on this
can
yield
topic
the
1__
4UU
350300pi
V
250-
;
200-
~0~~0
S
00
*
;0
0
150$00
0
50
o00
2
I
I
I
4
6
8
10
I
I
I
I
12
14
16
18
20
Test Number
Figure A-1.
Variation in compressive modulus for PBO fibers
of the same lot.
included..
Fibers with nonuniform cross sections are
138
IAA
4UU
350_J
300-
-
250-
0
o-_
150
·
a
0
0
·
S
5
6
I
100x
200 -
0
1
2
3
4
7
Test Number
Figure A-2. Variation in compressive modulus for PBO fibers
of the same lot.
Fibers with nonuniform cross sections have
been omitted..
139
References
1
Chatzi, E.G.
and Koenig, L.J.,
26, 229 (1987)
2
Bhattacharya S., Chuah, H.H, Dotrong, M., Wei, K.H.,
Wang, C.S., Vezie, D., Day, A., Adams, W.W., Procs.
A.C.S. Div. Poly. Mats. Sci. and Eng., 60, 512 (1989)
3
Deteresa, S.J., Porter, R.S., and Farris, R.J.,
Sci., 20, 1645 (1985)
4
Allen, S.R., PhD Thesis, UMASS, 1983
5
Dobb,M.G., Johnson,D.J., and Saville,B.P, J. Polym.
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6
Likhnitskii, S.G, Theory of Elasticity of an Anisotropic
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7
Sinclair, D.J.,
8
Deteresa, S.J., Allen, S.R., Farris, R.J., and Porter,
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9
Deteresa, S.J., Porter, R.S., Farris, R.J.,
Sci., 23, 1886 (1988)
10
Allen, S.R.,
11
Phoenix, S.L.,
934 (1974)
12
Bazhenov, S.L., Kozey, V.V
Sci., 24, 4509 (1989)
13
Piggot,M.R.,
14
Freeston, W.D.,
15
Fahey, M.
16
Kevlar 49 Data Manual, Dupont
J. Appl. Phys.,
J. Mat. Sci.,
Polym.-Plast. Tech.,
21, 380
22, 853
and Skelton, J.,
(1950)
J. Mat.
(1987)
Text. Res. Jour. ,44,
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J. Mat.
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140
J. Mat.
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(1980)
(1972)
17
Dobb, M.G., Johnson, D.G., and Saville, B.P., J. Poly.
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18
Dobb, M.G.,Johnson,D.J.,and Saville, B.P., Polymer, 22,
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19
Cohen, Y., and Thomas,E.L., Macromolecules,21,433(1988)
20
Kumar,S., SAMPE Quart., Jan. 1989
21
Van den Broek, J.A., Amer. Jour. Phys.,
22
Pit formation during plasma etching was first observed
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an adhesion study.
23
W.W. Adams and D.L. Vezie,
1991
24
Chuah, H.H, Tsai, T.T, Wei, K.H., Wang, C.S.,
Arnold,F.E.,
Procs.
A.C.S. Div. Poly. Mats. Sci.
and Eng., 60, 517 (1989)
25
S.P. Timoshenko, J.M. Gere, Theory of Elastic Stability.
McGraw Hill, New York (1961)
26
Jao, S., Studies of Interface Properties and Influence
of Fiber Coating In Composite Materials, PhD Thesis,
MIT, (1989)
27
US Patent 5021258, F.J. McGarry, June 1991
28
HandBook Of Materials Science, V2, CRC Press, 1975
29
Spectra polyethylene fibers from Allied Signal were also
coated with Alumina.
Adhesion to Spectra was
excellent.
Spectra fibers were not evaluated for
compressive strength however because their irregular
cross section makes stress calculations very cumbersome.
30
Skvortsov, N.N., Skeber, V.A., Ustinov, Y.K., and
Yalyshko, S.V., Sov. J. Opt. Tech., 56 (7) 1989
31
Morgan, R.J., Mones, E.T., Steele, W.J.,
S.B., Polym. Prepr., 21-2, 264 (1980)
32
Penn, L. and Larsen,
(1979)
F.,
4 9 th
15-4,309(1947)
EMSA proceedings, 1040,
and Deutscher,
J. Appl. Polym. Sci., 23, 59
141
33
Chang, B., Effects of Temperature and Tensile Loading on
The Compressive Strength Of Ceramic Coated Poly(pphenylene benzobisoxazole) Fibers, BS Thesis,MIT, (1991)
142