DETERMINING MOISTURE CONTENT OF
GRAPHITE EPOXY COMIPOSITES
BY MEASURING THEIR ELECTRICAL RESISTANCE
by
Avraham Benatar
zz
SUBMITTED
IN PARTIAL
FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF
BACHELOR
OF SCIENCE
IN
MECHANICAL-ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May, 1981.
Institute of Technology
GIMassachusetts
1981
Signature of Autho ....................
Department of Mech-anical Engineering
May, 1981
I
Certified by..
.
.. .
.
~~~~~~
Nam
P.
Suh
Thesis Supervisor
Accepted
A cp te
.
-
.. ..
~ ~~//
.
rmen, Department Committee
MASSACHUSETTS
INST1i'UT'E
OF Tlr.'OTLOGV -
JUL '7
1981
LIBRARIS
,/
DETERMINING MOISTURE CONTENT OF
GRAPHITE EPOXY COMPOSITES
BY MEASURING THEIR ELECTRICAL RESISTANCE
by
Avraham Benatar
Submitted to the Department of Mechanical Engineering
on May 13, 1981 in partial fulfillment of the
requirements for the Degree Bachelor of Science in
Mechanical Engineering
ABSTRACT
The moisture content of graphite epoxy composites
can be used to determine the amount of degradation suffered
by the material due to exposure to humidity environments.
The common method used to measure the moisture content of
these composites is to weigh them;
this is sometimes
undesirable or impossible. Therefore, a change in another
property which depends on the moisture
concentration,
overall resistance, may be measured; this can then be used
to determine the moisture concentration.
Unidirectional and multidirectional graphite epoxy
composites
were exposed to high temperature and high
humidity
(100% RH)
environments.
Their
weight
and
electrical resistance were measured. It was found that for
both composites the resistance across the length
was
independent of the moisture content. For the unidirectional
composites the normalized change in resistance across the
width was found to be proportional to moisture concentration
squared. For multidirectional composites the resistance
across the thickness was measured in three different ways.
The four terminal resistance measurment method was most
effective because it minimized the contact resistance. For
multidirectional composites the
normalized
change
in
resistance across the thickness was found to be proportional
to the moisure concentration.
Thesis Supervisor:
Title:
Dr.
Nam P.
Suh
Professor of Mechanical Engineering
-3AC KNOWLE DGEMENTS
First, I would like to thank Professor Nam
My
thanks
for
and for sharing his time and wisdom with me.
guidance,
his
Suh
Dr.
to
Tim
stimulating
many
for
Gutoski
discussions, and for his many helpful suggestions.
This project was sponsored by
My
thanks
Company.
Alan Taylor for his helpful comments.
to Mr.
Duk
would also like to thank Dr.
preparing
for
Kim
I
the
and the TELAC group at M.I.T.
composites,
multidirectional
Boeing
The
for making the unidirectional composites.
I am obliged to many people
Manufacturing
and
Productivity
express my appreciation to Fred
these
Demaree,
Michael
Crane,
lab
technicians
John
and
in
the
Laboratory
I would like to
at M.I.T.
Cote,
Fred
Anderson,
for
Bob
Ford, and Ralph Whittemore;
instructors
helped
in
the
preparation of samples and instrumentation.
My thanks to my office
Moon,
Myung
Kim,
Frank
Okine, Byung
mates - Richard
Waldman,
and
Teeraboon
Intragumtornchai.
I am deeply indebted to Joy David
support,
and
for
for
her
constant
her enormous help in typing this thesis.
Most of all, many thanks to my family, especially Dad
and Mom, for their everlasting support, love, encouragement,
and dedication to education.
-4-
TABLE OF CONTNETS
Section
Page
ABSTRACT
2
ACKNOWLE DGM ENTS
3
TABLE OF CONTENTS
4
LIST OF ILLUSTRATIONS
5
LIST OF TABLES
6
I.
II.
III.
INTRODUCTION
7
A.
Background
7
B.
Theory
EXPERIMENTAL PROCEDURES
17
A.
Unidirectional Composites
17
B.
Multidirectional Composites
17
RESULTS AND DISCUSSION
.A.
B.
IV.
10
23
Unidirectional Composites
23
Multidirectional
23
Composites
CONCLUSIONS AND RECOMMENDATIONS
32
Appendices
A.
B.
STATISTICAL SUMMARY OF THE EXPERIMENTAL
RESULTS
34
MOISTURE ABSORPTION BY COMPOSITES
37
REFERENCES
41
-5-
LIST OF ILLUSTRATIONS
Page
Figure
1.
2.
Unidirectional Composite With Longitudenal
Fibers
A Reperesentative Volume Element of a
Unidirectional Composite
9
11
14
Composite
3.
Multidirectional
4.
Resistance Measurements of The Unidirectional
Samples
18
Resistance Measurements of The Multidirectional
Samples Using Methods 1 and 2
20
Jig For Modified Four Terminal Resistance
Measurement of The Multidirectional Samples
21
Standard Four Terminal Resistance Measurement
of a Wire
22
Change in Resistance Measured Across The Length
of The Unidirectional Samples Due to Moisture
24
Normalized Change in Resistance Across The
Width of The Unidirectional Samples Due to
Moisture
25
Change in Resistance Measured Across The Length
of The Multidirectional Samples Due to Moisture
(Measurement Method 2)
26
Change in Resistance Across The Thickness
(Measured Using Method 1) of The
Multidirectional Samples Due to Moisture
28
Change in Resistance Across The Thickness
(Using Method 2) of The Multidirectional
Samples Due to Moisture
29
5.
6.
7.
8.
9.
10.
11.
12.
13.
Change in Resistance Across The Thickness
(Using Method 3) of The Multidirectional
Samples
14.
31
Due to Moisture
Description of The Boundry Conditions Used in
The Solution of Fick's Equation
38
5.
;-P-:>isor-vt
i
Unidirectional
A
msortion
D:n
And
Values
Graphite
For
Epoxy Composites
39
-6LIST OF TABLES
Table
1.
2.
3.
4.
5.
6.
7.
Page
Typical Hygrothermal Properties of
Unidirectional Graphite Epoxy Composites
16
Resistance Measurement Across The Length of
The Unidirectional Samples
34
Change in Resistance Across The Width of The
Unidirectional Samples
34
Resistance Measurement (Method 2) Across The
Length of The Multidirectional Samples
35
Change in Resistance (Measurement Method 1)
Across The Thickness of The Multidirectional
Samples
35
Change in Resistance (Measurement Method 2)
Across The Thickness of The Multidirectional
Samples
35
Change in Resistance (Measurement Method 3)
Across The Thickness of The Multidirectional
Samples
36
-7I.
A.
Background
The use
growing,
use,
INTRODUCTION
of
graphite
especially
these
in
composites
environmental conditions;
epoxy
the
are
composites
is
aerospace industry.
often
exposed
rapidly
While in
to
diverse
specifically, they are exposed to
different temperature and humidity environments which affect
their mechanical properties.
content of these composites is
It was found that the moisture
related
to
the
their mechanical and physical properties [1].
change
in
Therefore, it
is necessary to accurately determine the moisture content of
these composites.
The
moisture
most
content
of the samples.
when
the
to
However, this technique
Weighing
samples
monitor
is
not
that
are
in
isolating them from the integral systems;
such
as
In
those
addition,
produced
loading jigs or chemicals from
them
used
the
in composites is by monitoring the weight
not always possible.
residues
technique
effective
sample is in a stress loading jig or in operation
on an airplane.
requires
common
and
the
these
samples
operation
this is
collect
by the corrosion of the
environment.
Weighing
assuming that the change in weight is due only to
moisture can lead to erroneous results.
measurement
should
Therefore, moisture
be done indirectly by measuring another
material property that is affected by moisture but is easier
to
measure.
the composite.
One such property is the overall resistance of
-8composite
The overall resistance of a graphite epoxy
is due to the contact resistance between touching fibers [2]
number
and to the
swelling
causes
composite
points.
contact
of
of. the
contact
resistance
contact
at
this increases
the
and may even lead to a complete loss of
The
points.
some
the
The swelling
matrix.
causes the fibers to separate slightly;
in
Moisture
in
increase
contact
the
and the decrease in the number of contact points
resistance
causes the overall resistance of the composite to increase.
For a unidirectional composite with fibers aligned to
the
(see
length
Figure 1), the swelling affects the width
and the thickness of the composite.
on
(swelling)
constrained
Broutman
epoxy
by
[2]
the
stiff
correlated
composites
resistance.
length
the
to
the
is
The effect of
negligible
the
because
fibers.
graphite
moisture
it
Belani
is
and
moisture content of graphite
change
in
their
electrical
They found the following correlation:
R(t)
bWere
Where
AR_ Wet resistance-Dry resistance
Dry resistance
R
AW
W
Wet weight-Dry weight
Dry weight
It is important to note, here, that even though the increase
in
thickness
increases
the
cross
sectional area through
which the resistance is measured (and thus,
rs.i.anceh'
:in:craes.
-Thisis o '
the
resistance
he:
i-:.s
f ctt'
dtn.atthte
Thisis due to the fact
resistance increases.
that
the
-9-
t
-4-~~~~
_"'V
,."..~~~~~~~~~~~~~~~·~*
.e
7
--
b
Ie
.....-
=
-
I
Figure 1.
Unidirectional Composites diih
Longitudinal Fibers
i
-10matrix has a much higher resistance than the fibers.
B.
Theory
The governing
epoxy
graphite
factor on
the
resistance
overall
of
composites is the contact resistance between
the touching fibers.
In
the
general
contact
resistance
between two solids is the sum of the constriction resistance
The constriction resistance is due
and the film resistance.
to
the
two
solids
having
because of the surface roughness.
which
the
current
contact area.
being
flow
only
contact
at some points,
the
Thus,
area
through
is less than the apparent
passes
The film resistance is due to the two
at
separated
solids
some points by a thin layer of a third
material which has a higher resistivity.
Graphite
surface.
So
fibers
in
have
general
a
they
which will act as a film when
very
chemically
reactive
would form a surface layer
they
come
in
contact.
In
addition, most fiber and prepreg manufacturers coat graphite
fibers with an epoxy compatible sizing (usually
monomer)
for
better
bonding to the matrix.
the composite the fibers will be separated by a
which
is usually epoxy (see Figure 2).
some
epoxy
Therefore, in
thin
film,
Since the fibers do
not actually contact each other, the constriction resistance
has
little,
if any, affect on the contact resistance;
contact resistance is governed by the film resistance.
the
-11-
I'Cti 1I
';-i
-*-·- -.. b ·i?
r
clF'I F'-
a-·
;r
i
J
ru
· -t
c
-'d
1
i-rUr
r
·'
··
-··-
L3
VI
I
-·
--r ·. _··n--
·r
Y
;·:?s
.c
:··Z "r.-
-··
· · ·-;
-- ·
-' -"
Figure
2.
A Representative Volume Element of
a Unidirectional
Comorosite
-12The
being
materials
two
between
resistance
film
separated by a third is given by the following relation[3]:
P ·_S
f
(2)
A,
Where
Rf= film resistance,
cm
resistivity of film material,
f=
S = film thickness, cm
A C = area of contact, cm
As explained above, most fibers throughout
as
in
those
Figure
2,
will be separated by a thin film,
Swelling
epoxy.
probably made of
composites,
the
of
this
due
film
to
moisture will increase its thickness, thereby increasing the
The resistivity and area of
film resistance.
approximately
remaine
the
same,
because
contact
the
will
moisture
concentration in the matrix is small (less than 8%).
Tsai and Hahn[4] show that the dilatation
strain
is
related to the moisture concentration.
The change
in the film thickness is linearly related to the
dilatation
linearly
the
And
strain.
the
to
proportional
unidirectional
change
film
composites,
in
the
film
Therefore,
resistance.
which
thickness
is
for
swell in their thickness
and their width, the following correlation is expected:
AR a
(3)
(At)(b)
where At (the change in thickness) and
b
(the
width) vary linearly with the moisture content.
c R ( WN)
change
in
Therefore,
(4)
-13and normalizing gives
~rR
d /awl~
(5)
R
where R and W are constants.
This is in agreement with
the
correlation found by Belani and Broutman [23.
only
Similarly, for multidirectional composites
thickness will be affected by moisture.
the
(See Figure 3.) The
length and width of the composite will be constrained by the
fiber.
Thus, the following correlation is expected:
AR
(6)
t
And the change in thickness is linearly proportional to the
change in the moisture content.
Thus,
(7)
W
AR X
normalizing,
(8)
%R ( '6W
R
W
It is important to remember that
the
since
strains
linearly proportional to the change in resistance, then
are
any strain applied on the sample will also cause a change in
in
to
due
resistance
the
resistance.
The
due to stress may be subtracted from
resistance
the change in total resistance
plus
in
changes
cause
the samples will
change
changes in the stresses applied to
Therefore,
resistance.
(resistance
moisture)
in
due
to
stress
cases where stress
strain relations are linear.
Due to thermal expansion,
cause
changes
typical
values
and
the
the
in
for
te
swelling
strains.
coefficient
coefficient,
temperature
Tsai
and
changes
also
Hahn [4] give
of therial expansion, >Lei,
i,
for
unidirectional
-14-
1
4-
__
Figure
3.
M':vultidirectional
C.omposite
:_
-15-
(See
composites.
Table
They
1.)
suggest
the
following
linear relations:
Js ~~~~=diOfA~~(9)
where
= thermal strain in the i direction
AT = change in temperature,
6 '=
swelling strain in the i direction
concentration
c = moisture
Using
relations,
these
these
values
in
the
directions for a moisture concentration, c=0.005
transverse
T=10C,
and the temperature change,
It andS2
typical
and typical values
for
from Table 1 gives,
6
El
~~T
67~~(]0)
This means that for some typical temperature changes between
measurements
(10°C)
some
and
typical
moisture
content
(0.5%), the thermal strain is only about 10% of the swelling
strain.
be
Thus, in most applications, the thermal strain may
neglected.
thermal
strain
For
higher
may
be
temperature
variations,
the
subtracted by assuming the (above)
linear relation without substantial errors.
Table
1
Typical Hygrothermal Propnerties of Un ireti
Graphite Epoxy Cormoposites(TakenFro-,
P
C
}>x
g/cmr3
Jl(g-K)
W/(m-K)
W/(m K)
(pmlnm)K
1.6
1.0
4.62
0.72
-0.3
a
b
KH
mm2 /s
Ea/R
K
m/m
6.51
5722
0
0.018
I
KiT
y
KTz
.eferene
ox
ay)'z
(pm/m)/K
28.1
Py z
m/m
0.44
TO
to
OC
177
,_
·
__I -
r
--
:
--
.:-
-_ - ___---
----
----------------
.
·- ·-·---- -- ·-·------·--
----
--
-
,
------
";'....
, ::
------
--..-..
.',
.2
.-I--I-···-.
c-----..
-
----
·
..
z
ri-.a
,
4')
-17II.
A.
EXPERIMENTAL PROCEDURES
Unidirectional Composites
Unidirectional
prepared
by
graphite
the
Technology
Composites (TELAC) in
Astronautics
Five
at
samples
composites;
weight and
the
composites
Laboratory
Department
of
for
were
Advanced
Aeronautics
and
the Massachusetts Institute of Technology.
were
the
epoxy
cut
from
dimensions
electrical
these
0.015
inch
were 3/4" by 2".
resistance
of
these
thick
The changes
samples
were
measured after exposure (for different periods of time) to a
100% RH (relative
weight
and
humidity)
and
the
using a Hewlett Packard
samples
100 0 C
environment.
The
resistance were measured after the samples were
cooled to room temperature.
longitudenal
and
As shown in Figure 4, both
the
transverse resistances were measured
digital
multimeter.
Because
the
were thin, the ends could not be effectively coated
with the conductive silver paint.
Therefore, the resistance
measurement was done by just touching the probes against the
ends, without applying any pressure.
B.
Multidirectional Composites
Multidirectional composites 1/4" thick were
by Boeing Aircraft Company.
prepared
Five samples (again 3/4" by 2")
were cut from these composites.
The weight
and
resistance
changes were measured after the samples were placed (for
-
Figure 4.
Resistance Measurements of the
Unidirectional
3Samples
-19with
different lengths of time) in a pressure cooker filled
By
water.
using
pressure cooker, it was possible to
the
expose the samples to both a high temperature (1210 C) and
a
high humidity (100% RH) environment.
Three different methods
were
used
measure
to
the
electical resistance of the samples across the width and the
thickness.
In all of the methods, Hewlett
Packard
digital
multimeters were used.
The first method was to file the
probes
were
going
surface
to placed, to expose some of the fibers
and then to coat the surface with conductive
(See
where, the
silver
paint.
5.) This was done to minimize the fluctuations
Figure
in the resistance measurement.
The second method was a modification
After
each
a
new
coat.
first.
to the high temperature/high humidity
exposure
environment, the old silver paint was removed
with
the
of
This
eliminated
any
and
replaced
effects
of the
moisture on the interface between the surface and the silver
(Note - This procedure was used on four samples with
paint.
dimensions of 3/16" by 3/4" by 2".)
The final procedure used the four terminals method of
-resistance
measurement.
constructed to
samples
perform
Figure
these
6 shows the jig which was
measurements.
the
were quite thin, it was not possible to measure the
electrical potential between two points
(See
Because
on
the
thickness.
Figure 7.) Therefore, it was assumed that the surfaces
formed two equipotential sheets.
the two surfaces was measured.
Then the potential between
-20-
Areas Coated ,ith Conductive
Silver Paint
Figure 5.
Resistance Measurementsof the
Multidirectional Composites Using
Methods
1 and 2
-21-
SAtMLE
.J,,;
"'. :..:.,
_
r1I
.-
.:,
.,
-q_
.
1
Figure 6.,
Jig For
III~, ",
odified Four Terminal Resistance
fI --
..
II
-
_
,
-
. -I -' .'. ·
-
- :
C,
~
·
-22-
'I
A
Figure 7.
Standard Four Terminal Resistance
Measurement of a
ire
-23III. RESULTS AND DISCUSSIONS
A.
Unidirectional Composites
Figure 8 shows
across
the
content.
the
electrical
resistance
measured
length of the samples as a function of moisture
As expected, this resistance is independent of the
moisture concentration because it measures the resistance of
the fibers;
moisture
at
it
is
not
affected
the interface.
by
matrix
and
coating
its
or
The value of the resistance is
high due to the high contact resistance.
sample
swelling
end
Having
a
thicker
with conductive silver paint
would reduce the contact resistance substantially.
Figure 9 shows the normalized
measured
across
the
moisture content.
width
change
in
of the sample as a function of
The results are
in
correlation discussed in Section I.
agreement
high;
this
was
with
the
It is important to note
that the fluctuation in the resistance between
very
resistance
samples
was
probably the combined result of the
rough method of measurement, the lack of
conductive
silver
paint, and the non-uniformity between the samples.
B.
Multidirectional Composites
Figure 10 shows the
across
the
length
moisture content.
the
resistance
matrix
swelling
of
electrical
the
As with
across
or
the
the
the
samples
resistance
as
a function of the
unidirectional
length
moisture
measured
composites,
is not affected by the
at
the
fiber-matrix
interface.
Note:
Statistics of the experimental data are in Appendix A
-24-
____1
_
_I_
__
__
-.0c-- -t-
I
0
1.0
-
c)
.4
O
a)
0
0
I - --O --- r
.
I
,
1.0
I
~~ ~ ~I
-
2.0
~
~
~
~ II
3,0
~ · ~
I
_- er -, ·
-
"
_·
4.0
·
-
'
Resistance (ohms)
Figure
8.
Change in Resistance,.easured
Across the Lerth,
of the Unidirectional samples Due to :i->oisture
4§1.
0)
c)
0)
CD
4~
0
.r
5
Resistance Chanige,
Figure 9.
( )
Normalized Change in Resistance Across the
Width
o
the Unidirectional
Moisture
marpltes 2ue to
-26-
_
.,
___
75
FtO--o
4-+)
0do
0 .50
+:
.,
.25
_
i
/1i
I k3" 1
.1
.2
Resistance (ohms)
Figure 10.
Change in Resistance PMeasured Across the
Length of the 2.^ultidirectionalSnples
Due to
oisture
(Measurement
ethod 2)
-27The resistance across the thickness
was
of
the
samples
measured using the three different methods described in
Section II.
measured
The normalized change in resistance, as it
by the first method,
is presented
function of moisture content.
best
in Figure
In this case, the
was
11 as a
line
that
fits the data does not go through the (0,0) point;
is shifted to the right.
moisture
environment
This is probably the result of the
affecting
the
interface between the
surface and the conductive silver paint.
were
exposed
When
resistance,
contact
samples
thus
This increased the
making it a function of the time
that the samples were exposed to humidity.
the
the
to humidity at a high temperature, the silver
paint tended to debond from the surface.
contact
it
The increase
in
resistance between the conductive silver paint
and the surface caused the (above-mentioned)
shift
to
the
right.
To minimize the effect of
resistance,
the
measurement.
shown
in
silver
Figure
the
12,
this
replaced
the
contact
before
each
As
procedure gave the correlation
The normalized change in resistance
thickness was found to be linearly proportional
to the moisture content.
However, it should
that
a
contact
resistance
been
significant.
The
difficulties
was
on
(See method 2 as described in Section II.)
predicted in Section I.
across
paint
moisture
in
the
be
remembered
still existed, and it may have
contact
practical
resistance
application
may
of
create
this this
procedure.
To reduce the contact resistance, the
four
terminal
-23-
.3
+I)
r.
00
a)
s-f
/
.1
I
/
/
I
I
.0
5
Resistance Change,
4AB
Ri
Figure
11.
Change in Resistance Across the Thickness
(Measured Using ?,ethod 1) of the ;iultidirectional
Samples Due to ioisture
-29-
-J
0)
C
a0
e
0
0
a)
$4
:
.4
.2
.
.1,1
O
.1
Resistance Change, aR
R
Figure 12.
Change in Resistance Across the Thickness
(Using method 2) of the
Samples Due to 2oisture
ultidirectional
-30-
method
for the measurement of resistance was modified.
modification
assumes
equipotential
assumption.
that
sheets;
the
this
sample
surfaces
The
form
was proven to be an incorrect
However, within the vicinity of the measurement
points, the electical potential between the two surfaces was
constant.
method
Therefore,
are
the
measurements
made
both reliable and accurate.
13, this procedure
also
gives
the
using
this
As shown in Figure
predicted
correlation
between the normalized change in resistance and the moisture
content.
The small number of data points (plotted
10
through
moisture
13)
is
of
higher
information about
Figures
due to the thick samples' slow rate of
absorption;
achievement
in
time
constraints
moisture
moisture
composites, see Appendix B.
precluded
concentrations.
absorption
in
the
For more
graphite
epoxy
-31-
.8
a,
.6
0
C-)
0
t
.4
0
.2
Resistance Change,
Figure 13.
R
M
Change in Resistance Across the Thickness
(Using Method 3) of the Multidimensional
r1c7-·7
I--,
-I!
-
r^~
-; L
D
*
.I ·
n
-32IV. CONCLUSIONS AND RECOMMENDATIONS
An effective method for the determination of moisture
of
content
in
change
was
it
composites,
found
that
the
to measure the
unidirectional
For
resistance.
electrical
is
composites
epoxy
graphite
normalized change in
moisture
resistance across the width is proportional to the
For
squared.
content
multidirectional composites, it was
found that the normalized change in
thickness
across
resistance
the
is directly proportional to the moisture content.
across
In both cases, it was found that the resistance
the
length of the samples was not affected by moisture content.
The presence of contact resistance was
minimized
by
using
a
resistance measurement.
modification
meter, and division of V/I).
be
the four terminal
However, this method requires
and instrumentation (e.g.
wiring
of
to
found
much
4 probes, volt meter, amp
In order to
avoid
this,
the
author recommends that when the piece is produced, two small
metal plates (or more than two for averaging over the piece)
should
be
embedded
in
the
two surfaces of the material.
These plates should be accessible from the outside, and they
should
be
in direct contact with the graphite fibers.
The
plates can then be used as electric terminals which would be
used
for
moisture measurements with an ohm meter.
way would be to embed accessible fine metal meshes
surface.
This
would
Another
at
each
allow the measurement of the average
resistance over the piece.
The methoa of resistrne
?.3rasur.nt
coul(.
also
be
-33utilized
as
an
inspection
technique;
nonuniformities in the material.
it
could
detect
The resistance across
the
piece is greatly affected by the number of fibers and by how
These nonuniformities
closely these fibers are packed.
reflected
in
the
large
between
variations
are
the samples'
resistance measurements.
described
The author recommends that the experiments
in this thesis be repeated - using the samples embedded with
metal terminals or metal mesh.
effect
of
the
volume
resistance is
also
determination
of
An
fraction
recommended.
the
upon
investigation
of
fibers on the overall
This
will
proportionality
aid
in
the
constant
of
the
correlations found in this paper as a function of the
volume
fraction.
It
will
also
in
temperature
upon
means
detecting
of
the graphite epoxy composite.
future tests should determine
the
the
resistance.
fiber
help to determine if the
above-mentioned method is an effective
nonuniformities
the
effects
of
Finally,
stress
and
This will permit a more
wide-spread application of these procedures.
-34Appendix A
STATISTICAL SUMMARY OF THE EXPERIMENTAL RESULTS
The following Tables present the average
values
and
of
The
the standard deviation of the experimental data.
Table
Resistance
Measurement
2
Across
The
Length
Unidirectional Samples
of W(;o)
avg.
S.D.
of AW
S.D.
avg of R(A)
.W
of R
0.00
0.00
3.71
.51
.41
.13
3.67
.68
.53
.06
3.61
.70
.78
.06
3.49
.59
.84
.05
3.55
.52
1.12
.06
3.56
.65
Table
3
Change in Resistance Across the Width of The
Unidirectional
Samples
iWv)
/aR.D.
s. D. (R
S.D.Y
R(l)
S.D. R
0.00
0.00
29.2
11.7
0.00
0.00
.41
.13
30.4
12.9
.22
.13
.53
.06
31.6
13.6
.28
.16
.78
.06
33. 5
13.2
.34
.21
.84
.05
35.3
14.6
.43
.18
1 12
.06
37.3
15.7
.51
.1
W lta)
-35Table
4
Resistance Measurement (Methode 2) Across
The Length of
The
Multidirectional Samples
avg.
of
a)/)
S.D.
of 4W
S.D.
avg of R(%A)
of R
0.00
0.00
.19
.02
.29
.05
.20
.04
.74
.27
.20
.03
.84
.31
.19
.03
Table
Change in Resistance
5
(Measurement
Methode
1)
Across
The
Thickness of The Multidirectional Samples
W(.)
w
S.D. AV
w
R(~-)
S.D. R
S D.
0.00
0.00
8.05
1.86
0.00
0.00
.06
.01
10.67
2.10
.34
.08
.11
.02
11.62
2.02
.47
.14
.32
.03
17.38
3.25
1.19
.21
.%
Table 6
Change in Resistance
(Measurement
Methode
2)
Across
The
Thickness of The Multidirectional Samples
S.D. W
w
R(-)
S.D. R
AR
0.00
S. D.
-q
0.00
0.00
0.00
1.15
.27
.33
.01
1.42
.27
.25
.08
.38
.01
1.50
.35
.31
.04
58
.02
1.62
.35
.432
.14
-36Table
Change in Resistance
7
(Measurement
3)
Methode
Across
The
Thickness of The Multidirectional Samples
Wae)
s.D.
at
R(4)
S.D. R
_-
S.D. R
0.00
0.00
2.63
.46
0.00
0.00
.48
.04
6.15
1.33
1.32
.13
.60
.05
7.98
1.69
2.02
.20
.95
.05
12.19
2.52
3.82
.17
-37Appendix B
MOISTURE ABSORPTION BY COMPOSITES
Moisture absorption of graphite epoxy composites
may
be modelled using Fick's equation [5] (See Figure 14):
D
C
zc
(11)
where
c=moisture concentration
t=time, seconds
D=moisture diffusion coefficient, mm /sec
Assuming that the moisture diffusion coefficient is
function
of
temperature,
initial conditions and
the
as
well
as
boundary
assuming
conditions
only
a
that the
are
(See
Figure 14)
c=c. for O<x<h and t<O
c=c,
then,
for x=O and x=h and t>O
Crank[6]
gives
the
following
solution
to
Fick's
equation
CO.
C;,_o =
where
1-- I S-2
.-
P
/, )
.-
____(
)'
h(12
o
c = average moisture concentration in the composite.
Shen and Springer [7] correlate Equation 2 and
data.
(See Figure 15.)
experimental
- 38-
-
c.o
-
c4 --
C.
Co
h
7
N%- - 0
IN.
x
z
Fi ure 1.
eo
;i . non of -ti.oe ouidiry
onditirons
in the Solution of Fick' s Equation
s:cd
-39-
n
..
I I
i
W
I
[
E
II
I
!J
I
·
I
I
I
]
............
I
J
I
-
A__
.
Z
&
i
OE.
4IM
~
![
.-
I
I
l~~~j
GrophileT- 300
0.8 --
Fiberile 1034
0.65 to068)
(vf
-1
I
0.6
03 G4
I
o/ ;
<~~Anlytical
Absorplion and Desorplion
!II
UIJ
-
---I
0.001.
Figure 15.
,,
......
1111
,,,
I
I
I
1
I
Itll
I
CO t^
* aI/h}
.fiha
h
I
I
I
I I I 1
I
0.I
i .0
Comparison of Analytical And Measured
Moisture Absorption And Desorption
Values For Unidirectional And
Graphite Epoxy Composites.
(Taken From Reference 5)
W/4
-40Tsai and Hahn
finding
D
as
[41
give
an
empirical
formula
for
a function of temperature for graphite epoxy
composites.
D=6.51 exp(-5722/T)
(13)
where
T=absolute temperature, OK
They [4] also give a formula for estimating the
equilibrium
moisture concentration for graphite epoxy composites.
0 .0/8
C
(14)
where
0=relative humidity, %
By using Equations 2 and 3, it is possible to determine
time
required
for
a
equilibrium moisture
sample
0.25
inches
sample
to reach a given fraction of
concentration.
thick,
the
the
For
time
example,
t /2
for
for
a
which
(Z-cO)/(c.-c )=l/2 at a temperature T=373°K (100°C) is
t /2 =16 days.
And for the same conditions, t /=39
This
gives
(15)
days and t q4 0=70
days.
an estimate of the time required to perform the
experiments described in this thesis.
-41REFERENCES
1.
of Moisture and
Shen, C.H. and Springer, G.S., "Effects
Temperature on the Tensile Strength of Composite
Materials,
of Composite
Journal
Materials,"
Vol. 11, 1977, pp. 2-16
2.
"Moisture Induced
Belani, J.G. and Broutman, L.J.,
Reinforced
Changes in Graphite Resistivity
Plastics," Composites, Vol. 9, N. 4, October 1978
3.
Holm, Ragnar, Electric Contacts Theory and Application,
Fourth Edition, Springer - Verlag New York Inc.,
New York, 1967
4.
Tsai,
S.W.
and
Materials,
Hahn, H.T.,
Introduction
Technomic Publishing
To
Composite
Inc.,
Co.,
Westport, Connecticut, 1980
5.
Springer, G.S., "Environmental Effects on Epoxy Matrix
Materials: Testing and
Composite
Composites,"
Design (Fifth Conference), ASTM STP 674, 1979,
pp. 291-312
6.
Crank,
7.
Shen, C.H. and Springer, G.S., "Moisture Absorption and
Desorption of Composite Materials," Journal of
J., The Mathematics of
ClarendonPress,
Composite
Oxford,
Diffusion,
Second
Edition,
1975
Materials, Vol.
10,
1976,
pp.
2-20