Avraham Benatar - DSpace@MIT Home

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



-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


(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


(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


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)


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

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