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DETERMINING MOISTURE CONTENT OF
GRAPHITE EPOXY COMIPOSITES
BY MEASURING THEIR ELECTRICAL RESISTANCE
by
Avraham Benatarzz
SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE
DEGREE OF
BACHELOR OF SCIENCE INMECHANICAL-ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May, 1981.
GIMassachusetts Institute of Technology
Signature
Certified
of Autho ....................Department
I
by.. . .. . .
of Mech-anical EngineeringMay, 1981
Nam P. SuhThesis Supervisor
A c p t e . -~~~~~~~~~. .. .. ~ ~~// .rmen, Department Committee
MASSACHUSETTS INST1i'UT'EOF Tlr.'OTLOGV -
JUL '7 1981
LIBRARIS,/
1981
Accepted
DETERMINING MOISTURE CONTENT OF
GRAPHITE EPOXY COMPOSITES
BY MEASURING THEIR ELECTRICAL RESISTANCE
by
Avraham Benatar
Submitted to the Department of Mechanical Engineeringon May 13, 1981 in partial fulfillment of the
requirements for the Degree Bachelor of Science inMechanical Engineering
ABSTRACT
The moisture content of graphite epoxy compositescan be used to determine the amount of degradation sufferedby the material due to exposure to humidity environments.The common method used to measure the moisture content ofthese composites is to weigh them; this is sometimesundesirable or impossible. Therefore, a change in anotherproperty which depends on the moisture concentration,overall resistance, may be measured; this can then be usedto determine the moisture concentration.
Unidirectional and multidirectional graphite epoxycomposites were exposed to high temperature and highhumidity (100% RH) environments. Their weight andelectrical resistance were measured. It was found that forboth composites the resistance across the length wasindependent of the moisture content. For the unidirectionalcomposites the normalized change in resistance across thewidth was found to be proportional to moisture concentrationsquared. For multidirectional composites the resistanceacross the thickness was measured in three different ways.The four terminal resistance measurment method was mosteffective because it minimized the contact resistance. Formultidirectional composites the normalized change inresistance across the thickness was found to be proportionalto the moisure concentration.
Thesis Supervisor: Dr. Nam P. Suh
Title: Professor of Mechanical Engineering
-3-
AC KNOWLE DGEMENTS
First, I would like to thank Professor Nam Suh for
his guidance, and for sharing his time and wisdom with me.
My thanks to Dr. Tim Gutoski for many stimulating
discussions, and for his many helpful suggestions.
This project was sponsored by The Boeing Company.
My thanks to Mr. Alan Taylor for his helpful comments. I
would also like to thank Dr. Duk Kim for preparing the
multidirectional composites, and the TELAC group at M.I.T.
for making the unidirectional composites.
I am obliged to many people in the Laboratory for
Manufacturing and Productivity at M.I.T. I would like to
express my appreciation to Fred Anderson, Fred Cote, Bob
Crane, Michael Demaree, John Ford, and Ralph Whittemore;
these lab technicians and instructors helped in the
preparation of samples and instrumentation.
My thanks to my office mates - Richard Okine, Byung
Kim, Myung Moon, Frank Waldman, and Teeraboon
Intragumtornchai.
I am deeply indebted to Joy David for her constant
support, and for 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. INTRODUCTION 7
A. Background 7
B. Theory 10
II. EXPERIMENTAL PROCEDURES 17
A. Unidirectional Composites 17
B. Multidirectional Composites 17
III. RESULTS AND DISCUSSION 23
.A. Unidirectional Composites 23
B. Multidirectional Composites 23
IV. CONCLUSIONS AND RECOMMENDATIONS 32
Appendices
A. STATISTICAL SUMMARY OF THE EXPERIMENTALRESULTS 34
B. MOISTURE ABSORPTION BY COMPOSITES 37
REFERENCES 41
-5-
LIST OF ILLUSTRATIONS
Figure Page
1. Unidirectional Composite With LongitudenalFibers 9
2. A Reperesentative Volume Element of aUnidirectional Composite 11
3. Multidirectional Composite 14
4. Resistance Measurements of The UnidirectionalSamples 18
5. Resistance Measurements of The MultidirectionalSamples Using Methods 1 and 2 20
6. Jig For Modified Four Terminal ResistanceMeasurement of The Multidirectional Samples 21
7. Standard Four Terminal Resistance Measurementof a Wire 22
8. Change in Resistance Measured Across The Lengthof The Unidirectional Samples Due to Moisture 24
9. Normalized Change in Resistance Across TheWidth of The Unidirectional Samples Due toMoisture 25
10. Change in Resistance Measured Across The Lengthof The Multidirectional Samples Due to Moisture(Measurement Method 2) 26
11. Change in Resistance Across The Thickness(Measured Using Method 1) of TheMultidirectional Samples Due to Moisture 28
12. Change in Resistance Across The Thickness(Using Method 2) of The MultidirectionalSamples Due to Moisture 29
13. Change in Resistance Across The Thickness(Using Method 3) of The MultidirectionalSamples Due to Moisture 31
14. Description of The Boundry Conditions Used inThe Solution of Fick's Equation 38
5.;-P-:>isor-vt i :n A D msortion Values ForUnidirectional And Graphite Epoxy Composites 39
-6-
LIST OF TABLES
Table Page
1. Typical Hygrothermal Properties ofUnidirectional Graphite Epoxy Composites 16
2. Resistance Measurement Across The Length ofThe Unidirectional Samples 34
3. Change in Resistance Across The Width of TheUnidirectional Samples 34
4. Resistance Measurement (Method 2) Across TheLength of The Multidirectional Samples 35
5. Change in Resistance (Measurement Method 1)Across The Thickness of The MultidirectionalSamples 35
6. Change in Resistance (Measurement Method 2)Across The Thickness of The MultidirectionalSamples 35
7. Change in Resistance (Measurement Method 3)Across The Thickness of The MultidirectionalSamples 36
-7-
I. INTRODUCTION
A. Background
The use of graphite epoxy composites is rapidly
growing, especially in the aerospace industry. While in
use, these composites are often exposed to diverse
environmental conditions; specifically, they are exposed to
different temperature and humidity environments which affect
their mechanical properties. It was found that the moisture
content of these composites is related to the change in
their mechanical and physical properties [1]. Therefore, it
is necessary to accurately determine the moisture content of
these composites.
The most common technique used to monitor the
moisture content in composites is by monitoring the weight
of the samples. However, this technique is not effective
when the sample is in a stress loading jig or in operation
on an airplane. Weighing samples that are in operation
requires isolating them from the integral systems; this is
not always possible. In addition, these samples collect
residues such as those produced by the corrosion of the
loading jigs or chemicals from the environment. Weighing
them and assuming that the change in weight is due only to
moisture can lead to erroneous results. Therefore, moisture
measurement should be done indirectly by measuring another
material property that is affected by moisture but is easier
to measure. One such property is the overall resistance of
the composite.
-8-
The overall resistance of a graphite epoxy composite
is due to the contact resistance between touching fibers [2]
and to the number of contact points. Moisture in the
composite causes swelling of. the matrix. The swelling
causes the fibers to separate slightly; this increases the
contact resistance and may even lead to a complete loss of
contact at some points. The increase in the contact
resistance and the decrease in the number of contact points
causes the overall resistance of the composite to increase.
For a unidirectional composite with fibers aligned to
the length (see Figure 1), the swelling affects the width
and the thickness of the composite. The effect of moisture
(swelling) on the length is negligible because it is
constrained by the stiff graphite fibers. Belani and
Broutman [2] correlated the moisture content of graphite
epoxy composites to the change in their electrical
resistance. They found the following correlation:
bWere R(t)
Where
AR_ Wet resistance-Dry resistanceR Dry resistance
AW Wet weight-Dry weightW 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, the resistance
rs.i.anc eh' :in:craes. -Thisis o ' he: f ctt' i-:.s dtn.atthteresistance increases. This is due to the fact that the
-9-
t
_"'V
b --
.....-Ie =
I
Figure 1. Unidirectional Composites diih
Longitudinal Fibers
7.e ,."..~~~~~~~~~~~~~~~·~*-4-~~~~~~~~~~~
-
i
-10-
matrix has a much higher resistance than the fibers.
B. Theory
The governing factor on the overall resistance of
graphite epoxy composites is the contact resistance between
the touching fibers. In general the contact resistance
between two solids is the sum of the constriction resistance
and the film resistance. The constriction resistance is due
to the two solids having contact only at some points,
because of the surface roughness. Thus, the area through
which the current flow passes is less than the apparent
contact area. The film resistance is due to the two solids
being separated at some points by a thin layer of a third
material which has a higher resistivity.
Graphite fibers have a very chemically reactive
surface. So in general they would form a surface layer
which will act as a film when they come in contact. In
addition, most fiber and prepreg manufacturers coat graphite
fibers with an epoxy compatible sizing (usually some epoxy
monomer) for better bonding to the matrix. Therefore, in
the composite the fibers will be separated by a thin film,
which is usually epoxy (see Figure 2). Since the fibers do
not actually contact each other, the constriction resistance
has little, if any, affect on the contact resistance; the
contact resistance is governed by the film resistance.
-11-
Figure 2. A Representative Volume Element of
a Unidirectional Comorosite
-*-·- ·i�?�-� -.. ba-·
;rc� -'d
·'�·��·L3
-··-
VI
-·---
r ·. _�··n�--·-
:··Z "��-r.- -
-- ·· · ·-;
-·-·
�
I'Cti 1I
cl F I F ' ' -';-���i
r
i J-t·ru
1
i-rUrr
I
rY
;·:?s.c�
-' -"
-12-
The film resistance between two materials being
separated by a third is given by the following relation[3]:
·P _S (2)f A,
Where
Rf= film resistance,
f= resistivity of film material, cm
S = film thickness, cm
AC= area of contact, cm
As explained above, most fibers throughout the composites,
as those in Figure 2, will be separated by a thin film,
probably made of epoxy. Swelling of this film due to
moisture will increase its thickness, thereby increasing the
film resistance. The resistivity and area of contact will
remaine approximately the same, because the moisture
concentration in the matrix is small (less than 8%).
Tsai and Hahn[4] show that the dilatation strain is
linearly related to the moisture concentration. The change
in the film thickness is linearly related to the dilatation
strain. And the change in the film thickness is
proportional to the film resistance. Therefore, for
unidirectional composites, which swell in their thickness
and their width, the following correlation is expected:
AR a (At) (b) (3)
where At (the change in thickness) and b (the change in
width) vary linearly with the moisture content. Therefore,
R c ( WN) (4)
-13-
and normalizing gives
~rR d /awl~ (5)R
where R and W are constants. This is in agreement with
correlation found by Belani and Broutman [23.
Similarly, for multidirectional composites only
thickness will be affected by moisture. (See Figure 3.)
length and width of the composite will be constrained by
fiber. Thus, the following correlation is expected:
AR t (6)
And the change in thickness is linearly proportional to
change in the moisture content. Thus,
AR X W (7)
normalizing,
%R ( '6W (8)R W
the
the
The
the
the
It is important to remember that since the strains
are linearly proportional to the change in resistance, then
any strain applied on the sample will also cause a change in
resistance. Therefore, changes in the stresses applied to
the samples will cause changes in the resistance. The
change in resistance due to stress may be subtracted from
the change in total resistance (resistance due to stress
plus resistance due to moisture) in cases where stress
strain relations are linear.
Due to thermal expansion, temperature changes also
cause changes in the strains. Tsai and Hahn [4] give
typical values for te coefficient of therial expansion, >Lei,
and the swelling coefficient, i, for unidirectional
-14-
14-
Figure 3. M':vultidirectional
__ :_
C.omposite
-15-
composites. (See Table 1.) They 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
c = moisture concentration
Using these relations, these typical values in the
transverse directions for a moisture concentration, c=0.005
and the temperature change, T=10C, and typical values for
It andS2 from Table 1 gives,
6 ~~T El 67~~(]0)
This means that for some typical temperature changes between
measurements (10°C) and some typical moisture content
(0.5%), the thermal strain is only about 10% of the swelling
strain. Thus, in most applications, the thermal strain may
be neglected. For higher temperature variations, the
thermal strain may be subtracted by assuming the (above)
linear relation without substantial errors.
Table 1
Typical Hygrothermal Propnerties of Un ireti ri-.a
Graphite Epoxy Cormoposites(Taken Fro-, .eferene 4')
P C }>x KiT KTy z ox ay ) 'zg/cmr3 Jl(g-K) W/(m-K) W/(m K) (pmlnm)K (pm/m)/K
1.6 1.0 4.62 0.72 -0.3 28.1
a b K H Ea/R Py z
mm2 /s K m/m m/m
0.018 I 6.51 5722 0 0.44
TOto
OC
177,_ · : . .:- - , ,
z
__ I - -_ - ___ -r --- ·- ·-·---- ·- -------- --
---- -·-------·--
-- ----------------- --
----- ------
...";'.-, ::
---..-..
.�-I--I-···-. - ----
c-----.. �..
.',.2
·
-17-
II. EXPERIMENTAL PROCEDURES
A. Unidirectional Composites
Unidirectional graphite epoxy composites were
prepared by the Technology Laboratory for Advanced
Composites (TELAC) in the Department of Aeronautics and
Astronautics at the Massachusetts Institute of Technology.
Five samples were cut from these 0.015 inch thick
composites; the dimensions were 3/4" by 2". The changes
weight and electrical resistance of these samples were
measured after exposure (for different periods of time) to a
100% RH (relative humidity) and 1000C environment. The
weight and resistance were measured after the samples were
cooled to room temperature. As shown in Figure 4, both the
longitudenal and the transverse resistances were measured
using a Hewlett Packard digital multimeter. Because the
samples 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 prepared
by Boeing Aircraft Company. 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
-
-19-
different lengths of time) in a pressure cooker filled with
water. By using the pressure cooker, it was possible to
expose the samples to both a high temperature (1210C) and a
high humidity (100% RH) environment.
Three different methods were used to measure 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 surface where, the
probes were going to placed, to expose some of the fibers
and then to coat the surface with conductive silver paint.
(See Figure 5.) This was done to minimize the fluctuations
in the resistance measurement.
The second method was a modification of the first.
After each exposure to the high temperature/high humidity
environment, the old silver paint was removed and replaced
with a new coat. This eliminated any effects of the
moisture on the interface between the surface and the silver
paint. (Note - This procedure was used on four samples with
dimensions of 3/16" by 3/4" by 2".)
The final procedure used the four terminals method of
--resistance measurement. Figure 6 shows the jig which was
constructed to perform these measurements. Because the
samples were quite thin, it was not possible to measure the
electrical potential between two points on the thickness.
(See Figure 7.) Therefore, it was assumed that the surfaces
formed two equipotential sheets. Then the potential between
the two surfaces was measured.
-20-
Areas Coated ,ith Conductive
Silver Paint
Figure 5. Resistance Measurements of theMultidirectional Composites Using
Methods 1 and 2
-21-
SAt MLE
.,"'. ::.. .-.J,,; . ., .:,
r1I
Jig For odified Four Terminal Resistance
1
_
-q_
II " fI I~, , -- .. II - _ , - - C, ·~. -I -' .'. -· :
Figure 6.,
-22-
'I
A
Figure 7. Standard Four Terminal Resistance
Measurement of a ire
-23-
III. RESULTS AND DISCUSSIONS
A. Unidirectional Composites
Figure 8 shows the electrical resistance measured
across the length of the samples as a function of moisture
content. As expected, this resistance is independent of the
moisture concentration because it measures the resistance of
the fibers; it is not affected by matrix swelling or
moisture at the interface. The value of the resistance is
high due to the high contact resistance. Having a thicker
sample and coating its end with conductive silver paint
would reduce the contact resistance substantially.
Figure 9 shows the normalized change in resistance
measured across the width of the sample as a function of
moisture content. The results are in agreement with the
correlation discussed in Section I. It is important to note
that the fluctuation in the resistance between samples was
very high; this 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 electrical resistance measured
across the length of the samples as a function of the
moisture content. As with the unidirectional composites,
the resistance across the length is not affected by the
matrix swelling or the moisture at the fiber-matrix
interface.
Note: Statistics of the experimental data are in Appendix A
-24-
2.0 3,0 I
Resistance (ohms)
Figure 8. Change in Resistance ,.easured Across the Lerth,
of the Unidirectional samples Due to :i->oisture
0
c)
.4
O
a)
0
1.0
.0
1.0
e -,
____1 _ __ __ _I_
I I · _- r · _· · -, ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ --
I -.0 c-- -t--
I - --O --- r
I I I
" 4.0 '
Resistance Chanige, ( )
Figure 9. Normalized Change in Resistance Across the
Width o the Unidirectional marpltes 2ue to
Moisture
4§1.0)
c)
0)
CD4~
0.r 5
-26-
FtO--o
i /1i
I k3" 1.1 .2
Resistance (ohms)
Figure 10. Change in Resistance PMeasured Across the
Length of the 2.^ultidirectional Snples
Due to oisture (Measurement ethod 2)
., 75
4-+)
0do0 .50
+:
.,
.25
_ ___
_
-27-
The resistance across the thickness of the samples
was measured using the three different methods described in
Section II. The normalized change in resistance, as it was
measured by the first method, is presented in Figure 11 as a
function of moisture content. In this case, the line that
best fits the data does not go through the (0,0) point; it
is shifted to the right. This is probably the result of the
moisture environment affecting the interface between the
surface and the conductive silver paint. When the samples
were exposed to humidity at a high temperature, the silver
paint tended to debond from the surface. This increased the
contact resistance, thus making it a function of the time
that the samples were exposed to humidity. The increase in
the contact resistance between the conductive silver paint
and the surface caused the (above-mentioned) shift to the
right.
To minimize the effect of moisture on the contact
resistance, the silver paint was replaced before each
measurement. (See method 2 as described in Section II.) As
shown in Figure 12, this procedure gave the correlation
predicted in Section I. The normalized change in resistance
across the thickness was found to be linearly proportional
to the moisture content. However, it should be remembered
that a contact resistance still existed, and it may have
been significant. The contact resistance may create
difficulties in the practical application of this this
procedure.
To reduce the contact resistance, the four terminal
-23-
5
Resistance Change, 4ABRi
Figure 11. Change in Resistance Across the Thickness
(Measured Using ?,ethod 1) of the ;iultidirectional
Samples Due to ioisture
.3
+I)
r.
00a)
s-f
.1
/
/ I I.0/
I
-29-
Resistance Change, aRR
Figure 12. Change in Resistance Across the Thickness
(Using method 2) of the ultidirectional
Samples Due to 2oisture
-J
0)Ca0
e
0
0a)$4:
.1-,1O
.4.2
.
.1
-30-
method for the measurement of resistance was modified. The
modification assumes that the sample surfaces form
equipotential sheets; this was proven to be an incorrect
assumption. However, within the vicinity of the measurement
points, the electical potential between the two surfaces was
constant. Therefore, the measurements made using this
method are both reliable and accurate. As shown in Figure
13, this procedure also gives the predicted correlation
between the normalized change in resistance and the moisture
content.
The small number of data points (plotted in Figures
10 through 13) is due to the thick samples' slow rate of
moisture absorption; time constraints precluded the
achievement of higher moisture concentrations. For more
information about moisture absorption in graphite epoxy
composites, see Appendix B.
-31-
Resistance Change, RM
Figure 13. Change in Resistance Across the Thickness
(Using Method 3) of the Multidimensional
.8
a,
.60C-)
0
t .40
.2
I--, r1 c7 -· 7 r^ * n-I! - -; L ~ ·D .I
-32-
IV. CONCLUSIONS AND RECOMMENDATIONS
An effective method for the determination of moisture
content of graphite epoxy composites is to measure the
change in electrical resistance. For unidirectional
composites, it was found that the normalized change in
resistance across the width is proportional to the moisture
content squared. For multidirectional composites, it was
found that the normalized change in resistance across the
thickness is directly proportional to the moisture content.
In both cases, it was found that the resistance across the
length of the samples was not affected by moisture content.
The presence of contact resistance was found to be
minimized by using a modification of the four terminal
resistance measurement. However, this method requires much
wiring and instrumentation (e.g. 4 probes, volt meter, amp
meter, and division of V/I). 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. Another
way would be to embed accessible fine metal meshes at each
surface. This would allow the measurement of the average
resistance over the piece.
The methoa of res istrne ?.3rasur.nt coul(. also be
-33-
utilized as an inspection technique; it could detect
nonuniformities in the material. The resistance across the
piece is greatly affected by the number of fibers and by how
closely these fibers are packed. These nonuniformities are
reflected in the large variations between the samples'
resistance measurements.
The author recommends that the experiments described
in this thesis be repeated - using the samples embedded with
metal terminals or metal mesh. An investigation upon the
effect of the volume fraction of fibers on the overall
resistance is also recommended. This will aid in the
determination of the proportionality constant of the
correlations found in this paper as a function of the fiber
volume fraction. It will also help to determine if the
above-mentioned method is an effective means of detecting
nonuniformities in the graphite epoxy composite. Finally,
future tests should determine the effects of stress and
temperature upon the resistance. This will permit a more
wide-spread application of these procedures.
-34-
Appendix A
STATISTICAL SUMMARY OF THE EXPERIMENTAL RESULTS
The following Tables present the average values and
the standard deviation of the experimental data.
Table 2
Resistance Measurement Across The Length of The
Unidirectional Samples
avg. of W (;o)
0.00
.41
.53
.78
.84
1.12
S.D. of AW. W0.00
.13
.06
.06
.05
.06
avg of R(A)
3.71
3.67
3.61
3.49
3.55
3.56
S.D. of R
.51
.68
.70
.59
.52
.65
Table 3
Change in Resistance Across the Width of The Unidirectional
Samples
iWv) S.D.YW lta)
0.00
.41
.53
.78
.84
0.00
.13
.06
.06
.05
37.3 15.7
/aR.D.s. D. (RR(l)
29.2
30.4
31.6
33. 5
35.3
S.D. R
11.7
12.9
13.6
13.2
14.6
0.00
.22
.28
.34
.43
0.00
.13
.16
.21
.18
1 12 .06 .51 .1
-35-
Table 4
Resistance Measurement (Methode 2) Across The Length of The
Multidirectional Samples
avg. of a)/)
0.00
.29
.74
.84
S.D. of 4W
0.00
.05
.27
.31
avg of R(%A) S.D. of R
.19 .02
.20
.20
.19
.04
.03
.03
Table 5
Change in Resistance (Measurement Methode
Thickness of The Multidirectional Samples
W(.) S.D. AVw w0.00
.06
.11
.32
0.00
.01
.02
.03
R(~-)
8.05
10.67
11.62
17.38
S.D. R
1.86
2.10
2.02
3.25
1) Across The
S D. .%
0.00
.08
.14
.21
0.00
.34
.47
1.19
Table 6
Change in Resistance (Measurement Methode 2) Across The
Thickness of The Multidirectional Samples
0.00
.33
.38
S.D. Ww
0.00
.01
.01
R(-)
1.15
1.42
1.50
S.D. R
.27
.27
.35
AR
0.00
.25
.31
S. D. -q
0.00
.08
.04
1.62 .3558 .02 .432 .14
-36-
Table 7
Change in Resistance (Measurement Methode 3)
Thickness of The Multidirectional Samples
Wae) s.D. at R(4) S.D. R _-
0.00 0.00 2.63 .46 0.00
.48 .04 6.15 1.33 1.32
.60 .05 7.98 1.69 2.02
.95 .05 12.19 2.52 3.82
Across The
S.D. R
0.00
.13
.20
.17
-37-
Appendix B
MOISTURE ABSORPTION BY COMPOSITES
Moisture absorption of graphite epoxy composites may
be modelled using Fick's equation [5] (See Figure 14):
C D zc (11)
where
c=moisture concentration
t=time, seconds
D=moisture diffusion coefficient, mm /sec
Assuming that the moisture diffusion coefficient is only a
function of temperature, as well as assuming that the
initial conditions and the boundary conditions are (See
Figure 14)
c=c. for O<x<h and t<O
c=c, for x=O and x=h and t>O
then, Crank[6] gives the following solution to Fick's
equation
CO. .- I P , ) .- )'C;,_o = 1-- S-2 / ____( h(12
where o
c = average moisture concentration in the composite.
Shen and Springer [7] correlate Equation 2 and experimental
data. (See Figure 15.)
- 38-
Co
- c4 --- h
N%- -70 IN.
x
z
Fi ure 1. eo ;i . non of -ti.oe ouidiry on ditirons s:cd
in the Solution of Fick' s Equation
c.o C.
-39-
0.8
-1I
03
0.6
G4
0.001.
Figure 15.
CO * .fiha h 0.It^ aI/h}
4I .- l
.0
Comparison of Analytical And Measured
Moisture Absorption And Desorption
Values For Unidirectional And W/4
Graphite Epoxy Composites.
(Taken From Reference 5)
Grophile T- 300-- Fiberile 1034
(vf 0.65 to068)
o ; / <~~AnlyticalAbsorplion and Desorplion
,, ,,, 1111 1 I Itll I I I I I 1
n - . A__I I I ............ J ..
UIJ I ...... I I I I I I -
----!II
i
I
I
OE .i I [ E I I J I W I ! · I I ] I I Z i & ~ M ![ I ~~~j
-40-
Tsai and Hahn [41 give an empirical formula for
finding D as 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.
C 0 .0/8 (14)
where
0=relative humidity, %
By using Equations 2 and 3, it is possible to determine the
time required for a sample to reach a given fraction of
equilibrium moisture concentration. For example, for a
sample 0.25 inches thick, the time t /2 for which
(Z-cO)/(c.-c )=l/2 at a temperature T=373°K (100°C) is
t /2 =16 days. (15)
And for the same conditions, t /=39 days and t q4 0=70 days.
This gives an estimate of the time required to perform the
experiments described in this thesis.
-41-
REFERENCES
1. Shen, C.H. and Springer, G.S., "Effects of Moisture andTemperature on the Tensile Strength of CompositeMaterials," Journal of Composite Materials,Vol. 11, 1977, pp. 2-16
2. Belani, J.G. and Broutman, L.J., "Moisture InducedResistivity Changes in Graphite - ReinforcedPlastics," 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 Hahn, H.T., Introduction To CompositeMaterials, Technomic Publishing Co., Inc.,Westport, Connecticut, 1980
5. Springer, G.S., "Environmental Effects on Epoxy MatrixComposites," Composite Materials: Testing andDesign (Fifth Conference), ASTM STP 674, 1979,pp. 291-312
6. Crank, J., The Mathematics of Diffusion, Second Edition,Clarendon Press, Oxford, 1975
7. Shen, C.H. and Springer, G.S., "Moisture Absorption andDesorption of Composite Materials," Journal ofComposite Materials, Vol. 10, 1976, pp. 2-20