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Pergamon

Composires Engmeenng, Vol. 5, No. 9. pp. I177-1 IR6. 1995 Copyright fs: 1995 Elsewer Science Ltd

PrInted in Great Britain. All rights reserved 0961.9526/95 $9.50, IH)

O%l-9526(94) 00106-5

THERMAL CONDUCTIVITY OF COMPOSITE MATERIALS MADE FROM PLAIN WEAVES AND 3-D WEAVES

Yasser Gowayed and Jhy-Cherng Hwang Department of Textile Engineering, Auburn University, Auburn, AL 36849, U.S.A.

(Received 8 September 1994; final version accepted 16 November 1994)

Abstract-In this research activity, thermal conductivity of textile composites made from plain weaves and 3-D XYZ weaves is quantified. Plain weave composites are made from E-glass, KevlaP and AS4 graphite fibers and epoxy resin. 3-D woven composites are manufactured from Toho graphite fibers and epoxy resin. The effect of fiber type and fiber volume fraction on the thermal conductivity of textile composites is investigated.

The fabric Geometry Model is adapted to calculate the thermal conductivity of textile composites. Results using this tool are compared with experimental data and predictions using the Graphical Integrated Numerical Analysis. The analytical approach proved to be a good engineering tool to predict the thermal conductivity of textile composites.

INTRODUCTION

Published literature is rich with investigations of mechanical properties of composites. Fewer accounts are oriented towards thermal properties. Currently, the area of thermal conductivity is getting more attention to expand the applications of composites. Most of the research work in this area is directed towards developing prediction models and experimental work for thermal conductivity of unidirectional and particulate composites, see for example, Rayleigh (1894), Maxwell (1904), Springer and Tsai (1967), Behrens (1968), Donea (1972), Han and Cosner (1981), Brennan et al. (1982), Tzadka and Schulgasser (1983), Tawil et al. (1985), James el a/. (1987) Hasselman et al. (1987) and Havis et al. (1989).

Research oriented towards experimentally quantifying thermal conductivity of various textile composite structures is very limited (Lubin, 1981; Stuart, 1990). Analytical prediction models are also limited and have a high degree of complexity. Dasgupta and Agrawal (1992) introduced an asymptotic scheme to predict the orthotropic thermal conductivity of plain weave composites employing a 3-D thermal resistance network. Also, Gowayed et al. (1995) presented a Graphical Integrated Numerical Analysis Model (GINA) based on hybrid finite element model coupled with a geometrical representation of the fabric preform to predict the thermal conductivity of textile composites with arbitrary preform structures.

In this paper, an experimental investigation of the thermal conductivity of textile composites made from plain weaves and 3-D XYZ weaves is carried out. The effect of fiber type and fiber volume fraction on the thermal conductivity of textile composites is investigated. Moreover, an easy to apply averaging technique (Kregers and Melbardis, 1978; Whyte, 1986; Pastore and Gowayed, 1994) is adapted to calculate the thermal conductivity of textile composites. Results using this tool are compared with experimental data and predictions obtained using the Graphical Integrated Numerical Analysis (Gowayed, 1992; Gowayed et al., 1995).

EXPERIMENTAL WORK

Test apparatus

The thermal conductivity chamber used in this study is a k-Matic 75 thermal conductivity instrument manufactured by Holometrix, Inc. The design of this instrument is in accordance with ASTM Test Method C518 (1985) for steady state heat flux measurements and thermal transmission properties by means of a heat flow meter.

1177

1178 Y. Gowayed and J.-C. Hwang

Movable base plate

Guide rod

Fig. 1. Schematic cross-sectional view of the thermal conductivity testing chamber.

Figure 1 illustrates a cross-section of the testing chamber. The testing chamber is constructed of two parts: a stationary upper section and a movable lower section to accommodate specimens with various thicknesses. The upper section consists of a refrigerated heat sink (HS) separated by insulation (INSl) from a controlled heater plate (CHl) and an aluminum surface plate (SPl). The lower section consists of a heat flow meter (HF) (thermal transducer), with a 10 x 10 cm contact area, to measure the heat flux separated from the lower surface plate (SP2) by a thin layer of thermal insulation (INS2). This is followed by a heater plate (CH2). A thermal-couple (TCl) and (TC2) is installed at both sides of the specimen to measure the heat difference AT.

The refrigerated heat sink is a thermally activated safety switch which serves to inter- rupt the power supply to the heater circuits if, for any reason, the heat sink temperature (TC3) rises above 2C during a test.

On the right side of the test chamber is a linear-motion potentiometer for determining the sample thickness Ax during a test. The potentiometer housing is attached rigidly to the movable lower section. The test chamber is surrounded by insulation to reduce heat transfer to or from the elements in the stack.

Test procedure

The thermal conductivity measurement for different composite samples is carried out by placing the sample between the two surface plates of known temperature. Because of the temperature difference, heat flows through the sample from the hot side to the cold side. The quantity of heat flow through the sample is measured by the thermal transducer. Due to the large size of the heat transducer, the specimen dimensions should be at least 20 x 20 cm to minimize heat loss. The size of the transducer ensures the properties of the composites over the area under consideration. The large size of the sample allows only the measurement of heat conduction through the thickness of the sample. In-plane thermal conductivities are not measured.

The instrument is first calibrated using a specimen with known thermal conductivity. The thermal conductivity k is measured according to the formula:

(1)

where q = heat flow through the sample measured by the thermal transducer (HF), A = area of the sample, AT = temperature difference (TC2 - TCl) across sample thickness Ax.

Thermal conductivity of plain and 3-D weaves 1179

Fig. 2. Micrographic image of balanced plain weave E-glass/epoxy composite with fiber volume fraction of 34.6%.

Fig. 3. Micrographic image of AScl/epoxy composite with fiber volume fraction of 26.8%.


Fig. 4. Micrographic image of Kevlar-49/epoxy composite with fiber volume fraction of 42.7%.

Fig. 5. Micrographic image of 3-D XYZ graphite/epoxy composite with fiber volume fraction of 29.65%.

Materials

Thermal conductivity of plain and 3-D weaves 1181

Plain weaves. The characteristics of the balanced plain weave fabrics utilized in this study are as follows:

?? 2 ends/cm 12k E-glass yarns manufactured by PPG Industries. The E-glass fiber thermal conductivity in the longitudinal and transverse directions, as calculated from unidirectional test results, is 0.50 (W/mC). Composites tested have total fiber volume fractions of: 34.6%, 42.6%, 47.0%, 49.7% and 55.7%.

?? 5 ends/cm 3k AS4 graphite yarns manufactured by BP Chemicals. The thermal conductivities of the fiber (Dasgupta and Agrawal, 1992) are 8.4 (W/mC) along the fiber direction and 0.84(W/mC) in the transverse direction. Composites tested have total fiber volume fractions of: 26.8V0, 37.5%, 47.1%, 54.0% and 55.7%.

?? 12 ends/cm lk Kevlar-49@ fibers manufactured by DuPont. The thermal conductivities of the fiber (Kawabata, 1988) are 3.34 (W/mC) along the fiber direction and 0.212 (W/mC) in the transverse direction. Composites tested have total fiber volume fractions of: 42.7%, 49.7%, 60.7070, 63.5% and 64.5%.

3-D weaves. Three 3-D XYZ woven fabric preforms made from 12k Toho graphite yarns are tested. The thermal conductivities of the fiber (Kawabata, 1988) are 6.69 (W/m%) along the fiber direction and 0.53 (W/mC) in the transverse direction. Composites tested have total volume fractions of 28.77% (V,, = 15.0070, L$,, = 13.44% and V,, = 0.33%), 29.69% (I$, = 13.44%, I$,, = 11.95% and V,, = 4.3%) and 38.0% (5, = 15.6%, V& = 14.0% and vf, = 8.4%).

Epoxy resin. Ciba-Geigy Araldite epoxy resin and HY 956 hardener are used as the matrix. The mixing is carried out at room temperature with a ratio of 4 : 1 resin : hardener. The measured thermal conductivity for pure matrix is 0.196 (W/mC).

Composite manufacturing. Fabrics were manually placed in a 38 x 30 cm mold and impregnated with epoxy resin. The composite plates were cured in a compression molding machine at 80C for two hours and then post cured at 120C for one and a half hours. Composite plates were then cut to 25 x 25 cm for thermal conductivity testing. Micrographical images of balanced plain weaves E-glass/epoxy, AS4/epoxy, Kevlar- 49/epoxy composites are shown in Figs 2, 3 and 4, respectively. A micrographic image of a 3-D XYZ graphite/epoxy composite is shown in Fig. 5.

THEORETICAL ANALYSIS

The Fabric Geometry Model , or the Stiffness Averaging Technique, was originally developed (Kregers and Melbardis, 1978; Whyte, 1986; Pastore and Gowayed, 1994) to predict the elastic properties of textile composites. The basic idea behind the Fabric Geometry Model is to treat the fibers and matrix as a set of composite rods having various spatial orientations. Each composite rod represents a reinforcing system. The local stiffness tensor for each of these rods is calculated and rotated in space to fit the global composite axes. The global stiffness tensors of all the composite rods (i.e. reinforcing systems) are then superimposed with respect to their relative volume fraction to form the composite stiffness tensor.

In the current research activity, this approach is adapted to predict the thermal conductivity of textile composites. The analysis steps are illustrated in Fig. 6.

The first step in the analysis is to calculate the local thermal conductivity tensor for each reinforcing system. The local conductivity tensor could be represented as follows:

k 11 k,, k,, K local =

[ I

k21 k 22 k23 (2)

k 31 ka ku

where k, = symmetric conductivity tensor in the i and j directions (i, j = 1,2, 3).


I input Material Properties Thermal conductivifies and Volume fractio For Each Reinforcing System

Direction cosines

Calculate Transfromation Matrix T

JI Calculate Global Thermal Conductivity

For Each Reinforcing System

K global

JI

Calculate Thermal Conductivity of Composite

K composite

Fig. 6. Analysis steps for conductivity predictions using a Modified Fabric Geometry Model.

A large number of unidirectional micro-level thermal analysis models, used to calculate Kj,j, do exist in archived literature (Bruggeman, 1935; Springer and Tsai, 1967; Behrens, 1968; Hashin, 1979). The authors utilized the model developed by Behrens (1968) due to the large experimental verification data available in literature to support this model.

The next step is to transform the local thermal conductivity tensor Klocal for each reinforcing system to fit the directions of the composite global axes. This is done utilizing the transformation relation:

K global = T- Kloca, T (3)

where Kgtobat = global thermal conductivity tensor for the composite rod, T = transformation tensor of direction cosines. T could be represented as:

1; 1; 13

T = rnt rni rn:

[ I

(4)

nT n: n:

The formulation of the transformation matrix depends on the direction cosines li, mi and n, (i = 1,2, 3). These direction cosines may be observed as components of unit basis vectors associated with the fiber axis. A pseudo-code is presented in Pastore and Gowayed (1994) to calculate Ii, mi and Q.

Finally, the composite thermal conductivity matrix K,somposite is calculated by super- imposing the global conductivity tensor for each reinforcing system Kgloba, with respect to its relative volume fraction as follows:

K composite = ! Kglobal,i ei i=O

(5)

where Kglobal,i = global conductivity of reinforcing system i, 19~ = relative volume fraction of reinforcing system i and N = total number of reinforcing systems.

RESULTS AND DISCUSSION

Plain weaves

Tables l-3 and Figs 7-9 show out-of-plane thermal conductivity test results and standard deviations, predictions using the modified FGM, detailed in the previous section,

Thermal conductivity of plain and 3-D weaves

Table 1. Experimental results and analytical predictions for out-of-plane thermal conductivity in (W/mC) for plain weave E-glass/epoxy composites

1183

Volume fraction (Q)

Experiment Prediction

Mod. FGM GINA

34.6 0.269 f 0.002 0.268 0.214 42.6 0.299 + 0.005 0.289 0.295 47.0 0.313 f 0.005 0.30 0.308 49.7 0.337 + 0.009 0.307 0.316 55.7 0.378 f 0.032 0.327 0.336

Table 2. Experimental results and analytical predictions for out-of-plane thermal conductivity in (W/m(Z) for plain weave AS4/epoxy composites

Volum(+fjaction 0


Mod. FGM GINA

26.8 0.288 + 0.027 0.291 0.304 37.5 0.336 f 0.028 0.338 0.353 47.1 0.373 + 0.028 0.387 0.41 I 54.0 0.441 + 0.01 0.426 0.456 55.7 0.453 + 0.005 0.437 0.469

Table 3. Experimental results and analytical predictions for out-of-plane thermal conductivity in (W/m(Z) for plain weave Kevlar-49/epoxy composites

Volume fraction (%)


Mod. FGM GINA

42.7 0.236 + 0.001 0.264 0.268 49.7 0.246 + 0.01 I 0.276 0.28 60.7 0.260 f 0.023 0.293 0.299 63.5 0.268 f 0.018 0.298 0.304 64.5 0.272 + 0.013 0.299 0.306

I ??Experiment

-Mod. FGM *-_* GINA

0.45

T

25.0 35.0 45.0 55.0 f Fiber Volume Fracttan (%)

Fig. 7. Experimental results and analytical predictions for out-of-plane thermal conductivity vs volume fraction for plain weave E-glass/epoxy composite.


0.50

0.45

o^

5

$ o&l

i 0.35 E

{

h 0.30 L 0

0

0.25

0.20 L i !5.(

1

??Experiment W Mod. FGM -GINA

1

) 35.0 4j.o d.0

Fiber Volume Fraction (%)

Fig. 8. Experimental results and analytical predictions for out-of-plane thermal conductivity vs volume fraction for plain weave AWepoxy composite.

??Experiment W Mod. FGM -GINA

0.20 25.0 35.0 45.0 -55.0 ~ L

Fiber Volume Fraction (%)

Fig. 9. Experimental results and analytical predictions for out-of-plane thermal conductivity vs volume fraction for plain weave Kevlar-49/epoxy composite.

and results from the Graphical Integrated Numerical Analysis (GINA) (Gowayed et al., 1995) for E-glass/epoxy, AS4/epoxy and Kevlar-49/epoxy test specimens detailed in section on materials, respectively.

The crimp angles used in the modified FGM and GINA approaches as taken from the micrographical images for E-glass, AS4 carbon and Kevlar-49 balanced plain weaves are 2.8, 5.0 and 11.3, respectively. The number of finite element divisions for GINA is 16 subcells.

Tables l-3 and Figs 7-9 show that the out-of-plane thermal conductivity of plain weaves increases with the increase of fiber volume fraction. The degree of this increase could also be attributed to fabric crimp angle, value of fiber thermal conductivities, ratio

Thermal conductivity of plain and 3-D weaves

Table 4. Experimental results and analytical predictions for out-of-plane thermal conductivity in (W/mC) for 3-D XYZ Toho graphite/epoxy composites

1185

Volume fraction @J)


Mod. FGM GINA

28.77 0.3 17 rtr 0.024 0.267 0.274 29.69 0.396 + 0.019 0.394 0.398 38.0 0.43 + 0.041 0.544 0.480

of fiber thermal conductivity along the fiber axis k,,, to that transverse to the fiber axis k f,t, and ratio of fiber thermal conductivities (kf,,, kf,,) to matrix thermal conductivity. The AS4/epoxy composite exhibits a pronounced increase in thermal conductivity (57%) with the increase in fiber volume fraction between 26.8% and 55.7%. This is mainly attributed to the high kf,, and the 5.0 crimp angle of this fabric. On the other hand, Kevlar-49/epoxy composites exhibited the least increase in thermal conductivity although they had the highest crimp angle of 11.3. This is due to the low thermal conductivity in the transverse fiber direction.

For all practical purposes, GINA and FGM provide a very good estimate for out-of- plane thermal conductivity of the plain weave composite. For E-glass/epoxy and AS4/ epoxy composites, the results are within the experimental error limits. For the Kevlar/ epoxy composite, the percentage of error is around 12%.

A non-linear increase in the thermal conductivity is observed with the increase of fiber volume fraction of plain weaves. This could be attributed to the high compaction of fibers at high volume fractions resulting in increased yarn packing factor. Moreover at high fiber volume fractions, yarns from different fabric layers could touch and form a heat flow passage reducing the adverse effect of fiber/matrix interface on thermal conductivity values. Both the modified FGM and GINA do not account for non-linearity because the micro-level thermal analysis available in literature, and utilized in these models, do not consider such phenomena. The E-glass/epoxy and the AS4/epoxy plain weave composites exhibited a higher degree of nonlinearity than the Kevlar-49/epoxy plain weave composites.

3-D XYZ weaves

Table 4 provides out-of-plane thermal conductivity test results, predictions using the modified FGM and results from the Graphical Integrated Numerical Analysis (GINA) (Gowayed et al., 1995) for 3-D XYZ Toho grahite/epoxy weaves. The input for modified FGM and GINA is taken from the micro-graphical images. The number of finite element divisions for GINA is 16 subcells.

Results in Table 4 indicate that the out-of-plane thermal conductivity of the graphite/ epoxy composites increases with the increase of the fiber volume fraction in the out-of- plane direction. This is attributed to the high thermal conductivity along the graphite fiber axis as compared with the thermal conductivity transverse to the fiber direction and the thermal conductivity of the matrix. Consequently, increasing the volume fraction of fibers oriented in the out-of-plane direction (V,,) increased the thermal conductivity of the composite.

As calculated from Table 4, the average error in predictions using GINA is around 8% and the average error for modified FGM predictions for the same samples is 14%.

CONCLUSIONS

In this study, an experimental program is carried out to quantify the out-of-plane thermal conductivity of three types of balanced plain weaves, E-glass/epoxy, AS4/epoxy and Kevlar-49/epoxy composites and 3-D XYZ graphite/epoxy woven composites. In the balanced plain weave composites, a non-linear increase in the out-of-plane thermal conductivity of the composite is observed with the increase in fiber volume fraction.


Moreover, the out-of-plane thermal conductivity of the 3-D weaves increased, as expected, with the increase in the fiber volume fraction in the out-of-plane direction.

The Fabric Geometry Model (FGM), a versatile tool used as a first hand estimate to predict the stiffness of composite materials, is modified to predict the thermal conductivity of textile composites. Results from the modified FGM are compared with a hybrid finite element approach Graphical Integrated Numerical Analysis and experimental analysis.

The modified FGM is able to predict the thermal conductivity of textile composites with simple preform structures (i.e. plain weaves and 3-D XYZ weaves) with a degree of accuracy comparable to that of more complex model, such as the Graphical Integrated Numerical Analysis. Both models are not able to predict the non-linear increase of the out-of-plane thermal conductivity of the plain weaves with the increase in fiber volume fraction. The accuracy of the modified FGM is not tested for more complex textile structures, such as 3-D braids or 3-D angle interlock weaves.

Acknowfedgemenls-The authors would like to thank Pratt Kt Whitney, NASA Lewis and the National Textile Center for partial funding of this research activity. Also, they would like to thank Feng Chia University of Taiwan for providing the 3-D XYZ fabrics.

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