NISTIR 89-3914

LOW-TEMPERATURE

THERMAL CONDUCTIVITY OF

COMPOSITES:

Alumina Fiber/Epoxy and

Alumina Fiber/PEEK

D. L Rule

L L. Sparks

National Institute of Standards and Technology

U.S. Department of Commerce

Boulder, Colorado 80303-3328

May 1989

NISTIR 89-3914

LOW-TEMPERATURE

THERMAL CONDUCTIVITY OF

COMPOSITES:

Alumina Fiber/Epoxy and

Alumina Fiber/PEEK

D. L. Rule

L. L Sparks

Chemical Engineering Science Division

Center for Chemical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

May 1989

Prepared for, and sponsored in part by.

National Aeronautics and Space Administration

Ames Research Center

Moffett Field, California 94035

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Acting Director

CONTENTS

List of Tables v

List of Figures vi

List of Units and Symbols ix

Abstract 1 Introduction 1 Apparatus 2

Specimens 2

Results 3

Discussion 4

Acknowledgments 5

References 6

Appendix 47

iii

List of Tables

Page

Table 1 Specimen Identification 2

Table 2 Physical Characteristics of Specimens 3

Table 3 Location Index for Figures and Tables of Ail Specimens ... 4

Table 4 Experimental Data for EP-Al-0° 8

Table 5 Coefficients of A(T) for EP-Al-0° 8

Table 6 Thermal Conductivity Values as a Function of

Temperature for Specimen EP-Ai-0° 9

Table 7 Experimental Data for EP-Al-90° 12

Table 8 Coefficients of A(T) for EP-Al-90° 12

Table 9 Thermal Conductivity Values as a Function of

Temperature for Specimen EP-Al-90° 13

Table 10 Experimental Data for PK-Al-l-0° 16

Table 11 Coefficients of A(T) for PK-Al-l-0° 16

Table 12 Thermal Conductivity Values as a Function of

Temperature for Specimen PK-Ai-l-0° 17

Table 13 Experimental Data for PK-Al-l-90° 20

Table 14 Coefficients of A(T) for PK-Ai-l-90° 20

Table 15 Thermal Conductivity Values as a Function of

Temperature for Specimen PK-Al-l-90° 21

Table 16 Experimental Data for PK-Al-2-0° 24

Table 17 Coefficients of A(T) for PK-Al-2-0°. 24

Table 18 Thermal Conductivity Values as a Function of

Temperature for Specimen PK-Al-2-0° 25

Table 19 Experimental Data for Neat-PK 28

Table 20 Coefficients of A(T) for Neat-PK 28

Table 21 Thermal Conductivity Values as a Function of

Temperature for Specimen Neat-PK 29

V
List of Figures

Page

Figure 1 Specimen chamber for "fixed point" compression probe. ... 7

Figure 2 Thermal conductivity of specimen EP-Al-0°.

Experimental data are presented as discrete points 10

Figure 3 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen EP-Al-0°

.

(The horizontal bar indicates the span of temperature

for each run) 11

Figure 4 Thermal conductivity of specimen EP-Al-90°.

Experimental data are presented as discrete points 14

Figure 5 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen EP-Al-90° ... 15

Figure 6 Thermal conductivity of specimen PK-Al-l-0°.

Experimental data are presented as discrete points 18

Figure 7 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen PK-Al-l-0°. . . 19

Figure 8 Thermal conductivity of specimen PK-Al-l-90°.

Experimental data are presented as discrete points 22

Figure 9 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen PK-Al-l-90° . . 23

Figure 10 Thermal conductivity of specimen PK-Al-2-0°.

Experimental data are presented as discrete points 26

Figure 11 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen PK-Al-2-0°. . . 27

Figure 12 Thermal conductivity of specimen Neat-PK.

Experimental data are presented as discrete points 30

Figure 13 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen Neat-PK .... 31

Figure 14 Thermal conductivity of PK-Al-l-0° and PK-Al-2-0°

specimens where heat is flowing parallel to the alumina

fibers 32

Figure 15 Thermal conductivity as a function of fiber volume

ratios for various calculated temperatures (above 40 K)

.

The dashed line shows linear extrapolation taken 33

VI
16

17

18

19

20

21

22

23

24

Thermal conductivity as a function of fiber volume

ratios for various calculated temperatures (below 40 K)

The dashed line shows linear extrapolation taken. . . .

Page

34

Thermal conductivity as a function of temperature for

the EP-Al-0° and the calculated PEEK/alumina curve

( ). Comparison for the same fiber volume fraction.

Note that both scales are logarithmic, which clarifies

the behavior at low temperatures. Compare to Figure 18. . .35

Thermal conductivity as a function of temperature for

the EP-Al-0° and the calculated PEEK/alumina curve

( ). Comparison for the same fiber volume fraction.

Note that both scales are linear, which clarifies the

behavior at high temperatures. Compare to Figure 17 .... 36

Thermal conductivity of the specimens where heat is

flowing parallel to the alumina fibers. The Neat-PEEK

data are also included as a reference. Note that both

scales are logarithmic, which clarifies the behavior at

low temperatures. Compare to Figure 20 37

Thermal conductivity of the specimens where heat is

flowing parallel to the alumina fibers. The Neat-PEEK

data are also included as a reference. Note that both

scales are linear, which clarifies the behavior at high

temperatures. Compare to Figure 19 38

Thermal conductivity of the specimens where heat is

flowing perpendicular to the alumina fibers. The Neat-PEEK

data are also included as a reference. Note that both

scales are logarithmic, which clarifies the behavior at

low temperatures. Compare to Figure 22 39

Thermal conductivity of the specimens where heat is

flowing perpendicular to the alumina fibers. The Neat-PEEK

data are also included as a reference. Note that both

scales are linear, which clarifies the behavior at high

temperatures. Compare to Figure 21 40

Thermal conductivity of the epoxy/alumina fibered data,

both parallel and perpendicular to alumina fibers. Note

that both scales are logarithmic, which clarifies the

behavior at low temperatures. Compare to Figure 24 41

Thermal conductivity of the epoxy/alumina fibered data,

both parallel and perpendicular to alumina fibers. Note

that both scales are linear, which clarifies the behavior

at high temperatures. Compare to Figure 23 42

Vll
Page

Figure 25 Thermal conductivity of the PEEK/alumina fibered data,

both parallel and perpendicular to fiber direction. The

Neat-PEEK data also included. Note that both scales are

logarithmic, which clarifies the behavior at low

temperatures. Compare to Figure 26 43

Figure 26 Thermal conductivity of the PEEK/alumina fibered data,

both parallel and perpendicular to fiber direction. The

Neat-PEEK data also included. Note that both scales are

linear, which clarifies the behavior at high temperatures.

Compare to Figure 25 44

Figure 27 Thermal conductivity of all the specimens tested. Note

that both scales are logarithmic, which clarifies

the behavior at low temperatures. Compare to Figure 28. . .45

Figure 28 Thermal conductivity of all the specimens tested. Note

that both scales are linear, which clarifies the behavior

at high temperatures. Compare to Figure 27 46
List of Units and Symbols

Definition of Symbols

A = thermal conductivity, W/(m»K)

ZiX = mean specimen thickness, m

A = mean specimen area, m^

AT = steady- state temperature difference, K

Unit Conversions

Temperature Tc = Tk - 273 . 15

Tc = (Tp - 32)/1.8

where Tp is temperature in keivins,

Tq is temperature in degrees Celsius,

Tp is temperature in degrees Fahrenheit

Thermal Conductivity 1.000 W/(m»K) = 0.578 Btu/ (hr • f

t» ° F)

= 6.94 Btu«in/(hr»ft^» °F)

Pressure

Force

1.000 Pa = 7.501 X 10 ^ torr

1.000 N = 0.22481 lb force

IX
iv!’-- rr'i

., • “ :* 'j/ii.C' '

wiftl

"7

(

-'

' )• ‘ >.'^' .f,

"A.-.v

x^-

m X[

1. .V

' ^

' ’

' '' rU'\-' .

.

! -.'-.‘j^^'WN,'

<;'^.*'.Vi ;-\ »= n' > u'll^'- '

w;/ "V'v'i^/JiCE^'

'''

' x''

^li’pgvivjLsi

MM

^a*.'

,..o;

f’i'r
Low- Temperature Thermal Conductivity of Composites;

Alumina Fiber/Epoxy and Alumina Fiber/PEEK

The thermal conductivities of poly-ether-etherketone (PEEK) , of alumina fiber in a matrix of PEEK,

and of alumina fiber in a matrix of epoxy, were

determined along with the effects of fiber orientation

and thermal cycling. Thermal conductivity was

measured over the temperature range 4.2 to 310 K using

a steady-state apparatus.

These data are presented and discussed relative to

specimen characteristics. It appears that after

accounting for different fiber fractions in the

specimens, the thermal conductivity of the PEEK

composite material is less than that of the epoxy

composite material in particular temperature ranges.

Key words: alumina-, composite* epoxy,* low temperature;

PEEK* poly-ether-ether-ketone ’, thermal conductivity.

Introduction

Polymer composites reinforced with alumina fibers have the

potential of being excellent thermal- isolation materials for

cryogenic applications. The higher elastic modulus of alumina

compared to the traditional glass fiber will improve fatigue

resistance. Utilization of the thermoplastic matrix material, polyether-ether-ketone (PEEK) , also improves the fatigue performance

compared to that of epoxy resins. PEEK, being a thermoplastic

material, provides attractive advantages for production or fabrication

and can be repaired more readily than thermoset materials.

Both thermal and mechanical behavior of composites to be used in

cryogenic applications are important. The remainder of this paper

deals with experimentally determined thermal conductivities;

mechanical properties are being studied in a parallel NIST program.

1
Apparatus

The system used to perform measurements of thermal conductivity

is a modified version of a previously described "fixed-point"

apparatus [1]. The specimen chamber is shown schematically in figure

1. It allows the thermal conductivity to be determined using fixed

cold-side temperatures of 4 K (liquid helium), 76 K (liquid

nitrogen) , 194 K (mixture of dry ice and alcohol) , and 273 K (mixture

of ice and water) . Measurements were performed by placing the chamber

in one of the temperature-controlled baths and monitoring the power

required to maintain a fixed temperature difference between the top

and bottom blocks. The temperature differences between the hot and

cold blocks were typically 1, 2, 4, 8 , 64 K.

Thermal conductivity measurements of a standard reference

material, SRM 735, [2] indicated a total uncertainty of ± 5%. The la

uncertainty of the composite data being reported is less than ±5%, as

evidenced by the deviation plots. Specimen- to - apparatus thermal

contact resistance may cause the accuracy to be slightly worse for the

composites than for the metallic SRM.

Specimens

The materials studied were supplied by Ronald D. Kriz (Fracture &

Deformation Division, National Institute of Standards & Technology)

.

All of the alumina fibers contained in the epoxy and PEEK specimens

are from a single source. While these fibers are actually composed of

about 85 wt% AI 2 O 3 and 15 wt% Si 02 they will be referred to as alumina

fibers. Neat PEEK is a specimen with no fiber reinforcement material.

All specimens tested were prepared by two private companies. The

specimens and nomenclature are identified in table 1 .

Table 1 Specimen Identification

Specimen

Identification

Comments

EP-Al-0° Epoxy/Alumina heat flow parallel to fiber

direction

EP-Al-90° Epoxy/Alumina heat flow perpendicular to

fiber direction

PK-Al-l-0° PEEK/Alumina heat flow parallel to fiber

direction

PK-Al-l-90° PEEK/Alumina heat flow perpendicular to

fiber direction

PK-Al-2-0° PEEK/Alumina heat flow parallel to fiber

direction

Neat-PK Neat PEEK absent of fibers

2
The specimens were constructed by cementing smaller segments

together with a thin layer of cyanoacrylate adhesive. The laminated

specimens were ground to the shape of a uniform block with parallel

(±0.003 cm) faces. The physical characteristics of the specimens are

given in table 2. An estimate of the fiber content of the specimens

is also given in table 2. These values were determined from

photomicrographs of the specimen plane perpendicular to the fiber axes

(Appendix A)

.

The steady-state measurements were made with a specimen in a vacuum environment of 1.07 x 10~^ Pa (8 x 10~^ torr) . In each case

the specimens had thermally conductive grease and indium foil (76 /xm

thick) on each contact surface to reduce thermal resistance. The load

applied to the specimens, at room temperature, was a constant 4270 N

(960 lb)

.

Table 2 Physical Characteristics of Specimens

Specimen

Identification

Area

cm^

Thickness

cm

Number of

Segments

Alumina Fiber

Volume Ratio

Q,'O

EP-Al-0° 0.5623 0.6359 2 59

EP-Al-90° 1.1909 0.3002 2

PK-Al-l-0° 2.7327 0.8376 4 43

PK-Al-l-90° 3.0067 0.7239 2

PK-Al-2-0° 1.4341 0.8310 4 52

Neat-PK 2.8159 0.6426 2

Results

The thermal conductivities of alumina fiber/epoxy and alumina

fiber/PEEK were measured parallel (0°) and perpendicular (90°) to the

fiber direction. A neat PEEK specimen was also measured. Data were

taken over the temperature range 4.2 to 310 K. Since large

temperature gradients are used and the thermal conductivity as a function of temperature is not simply linear, a thermal conductivity

integral method [3] was used.

The function chosen to fit the thermal conductivity data is

n

A(T) = X ai [in (T+l)]l (1)

1=1

The experimental data, resulting values of aj_, and tabular data of the

function for each of the six specimens, are presented in tables 4

through 21. To obtain proper fits it was necessary to weight some

data. Plots of thermal conductivity and relative deviations, as a function of temperature, are given in figures 2 through 13. For

3 r
convenience, table 3 is an index of the plots and tables for all of

the specimens tested.

Table 3 Location Index for Figures and Tables of All Specimens.

Tables Figures

Specimen Table Table Table Plot Plot

of of of of of

Identification Data Coeff'

s

A(T) A(T) Deviations

EP-Al-0° 4 5 6 2 3

EP-Al-90° 7 8 9 4 5

PK-Al-l-0° 10 11 12 6 7

PK-Al-l-90° 13 14 15 8 9

PK-Al-2-0° 16 17 18 10 11

Neat-PK 19 20 21 12 13

Discussion

Heat Flow Parallel to Fiber Direction

A direct comparison of the thermal conductivities of the

PEEK/alumina composites with those of the epoxy/alumina composite

cannot be made due to differences in the fiber content of the

specimens tested (values listed in table 2) . Because the alumina

fiber material is a better thermal conductor than either matrix

material, an increased fiber content should increase the thermal

conductivity of a specimen. A simple parallel heat flow model was

applied to the PEEK/alumina composites. It was found to be

insufficient for predicting the thermal conductivity in other

composites with different fiber volume ratios.

Figure 14 shows the thermal conductivity for the PK-Al-l-0° and

PK-Al-2-0°. The curves for these two specimens are of similar shape

with a vertical shift between them. The magnitude of this shift is - 17 % and is uniform over the entire temperature range tested. It is

likely that this shift can be attributed to the different fiber volume

ratios of the specimens.

The thermal conductivity is related to the fiber volume ratio in

the PEEK composite materials. Figures 15 and 16 shows this

relationship for a family of temperatures using the data of

PK-Al-l-0°, PK-Al-2-0° and Neat-PK. This relationship may be a good

model for predicting results for other fiber volume ratios in the PEEK

composite materials. A comparison of the thermal conductivity between

the PEEK material and the epoxy material can be approximated. By

utilizing the thermal conductivity- fiber volume ratio relationship, a PEEK-alumina fiber specimen with the same fiber volume ratio as the

EP-Al-0° specimen can be determined. A linear extrapolation of the

4
fiber volume ratio, using the two PEEK- alumina specimens, was used to

determine thermal conductivity as a function of temperature for a fiber volume ratio of 59%. Because the relationship between thermal

conductivity and fiber volume ratios may not be a linear function,

additional experimental data would be required to establish a more

accurate relationship. The resulting calculated curve is compared

with the EP-Al-0° data in figures 17 and 18. From this comparison,

the thermal conductivity of a PEEK/alumina composite is slightly less

than an epoxy/alumina composite of similar fiber volume ratio above

-100 K and below -9 K. The thermal conductivity as a function of

temperature between 9 and 100 K, for one matrix material, does not

differ appreciably from that of the other material.

Heat Flow Perpendicular to Fiber Direction

The thermal conductivities of the specimens tested with the heat

flow perpendicular to the alumina fibers are shown in figures 21 and

22. A crossover occurs at -23 K between the Neat-PK curve and the

PK-Al-l-90° curve. Further study is required before an explanation of

this effect can be suggested. The heat transfer characteristics may

be further complicated by anisotropy in the PEEK material itself. The

importance of this effect has yet to be determined.

Thermal Cycling of PEEK Composite

After initial tests were conducted on one of the original

PEEK/alumina specimens (PK-Al-l-0°) it was thermally cycled. This

experiment was done to determine if the conductivity of the PEEK

composite material is affected by strains induced due to repeated

thermal cycles. The specimen was cycled 25 times between room

temperature and liquid nitrogen temperature (one of these cycles was

to 4 K) and retested as before. Thermal conductivity was measured

with the heat flow parallel to the fiber direction only. No effect on

thermal conductivity due to this thermal cycling was detectable within

the total experimental uncertainty (± 5%) outlined above.

The remaining figures are various comparisons giving additional

perspectives . Logarithmic and linear presentations of the data are

given to highlight the behavior of conductivity over ranges of both

high and low temperatures.

Acknowledgments

The authors wish to recognize B. J. Filla and J. G. Hust for

their contributions in developing the apparatus and automating the

control and acquisition features of this system. R. D. Kriz was

primarily responsible for acquiring the specimens. Materials and

fabrication were due to the efforts of I.C.I. Americas, Inc.,

Structural Composites Industries and Sumitomo Corporation.

5
References

[1] Hust, J. G., Arvidson, J., "Thermal Conductivity of Glass

Fiber/Epoxy Composite Support Bands for Cryogenic Dewars,"

Internal Report No, 275.03-78-2, National Bureau of Standards,

Boulder, Colorado (1978).

[2] Hust, J. G., Sparks, L. L. , "Thermal Conductivity of Austenitic

Stainless Steel, SRM735, from 5 to 280 K," Nat. Bur. Stand.

Special Publication 260-35 (1972).

[3] Hust, J. G., Lankford, A, B,, "Comments on the measurement of

Thermal Conductivity and Presentation of a Thermal Conductivity

Integral Method," Int'l J. of Thermophysics 3 , No, 1, 67-77

(1982) .

6
Figure 1 Specimen chamber for "fixed point" compression probe.

7
Table 4 Experimental Data for EP-Al-0

Average

Temperature

Kelvin

Thermal

Conductivity,

W/(m-K)

5.132 0.025

6.154 0.027

8.189 0.035

12.314 0.055

20.940 0.116

38.727 0.280

76.522 0.597

77.043 0.596

78.088 0.615

80.180 0.628

84.376 0.659

92.820 0.723

109.892 0.840

192.557 1.300

193.119 1.368

194.235 1.333

196.478 1.348

200.974 1.343

210.038 1.363

228.463 1.402

273.716 1.527

274.280 1.487

275.412 1.501

277.681 1.509

282.233 1.541

291.435 1.558

310.207 1.647

Table 5 Coefficients of A(T) for EP-Al-0°

^1 9.4838610E-02

a2 -1 .4612297E-01

^3 1.1101024E-01

34 -4.5386804E-02

^5 9.5660835E-03

^6 -7.1230263E-04

8
Table 6 Thermal Conductivity Values as a Function of Temperature

for Specimen EP-Al-0°

T A(T) T A(T) T A(T) T A(T)

Kelvin W/(m-K) Kelvin W/(m-K) Kelvin W/(m-K) Ke Ivin W/(m-K)

4.1000 0.0234 9.1000 0.0364 51 .0000 0.381

1

110.0000 0.8646

4.2000 0.0235 9.2000 0.e3o8 52.0000 0.3903 120.0000 0.9318

4.3000 0.0237 9.3000 0.0372 53.0000 0.3996 130.0000 0.9947

4.4000 0.0238 9 . 4000 0.0377 54 . 0000 0.4088 1 40 . 0000 1 .0537

4.5000 0.0239 9.5000 0.0381 55.0000 0.4180 150.0000 1.1088

4.6000 0.0241 9 . 6000 0 . 0385 56.0000 0.4272 160.0000 1.1602

4.7000 0.0242 9 . 7000 0.0389 57.0000 0.4363 170.0000 1 .2081

4.8000 0.0244 9.8000 0.0393 58 . 0000 0 . 4454 180.0000 1 .2526

4.9000 0.0245 9.9000 0.0398 59.0000 0.4545 190.0000 1 .2940

5 . 0000 0.0247 10.0000 0.0402 60.0000 0.4636 200.0000 1 .3322

5.1000 0.0248 1 1 .0000 0 . 0448 61 .0000 0.4726 210.0000 1 .3675

5.2000 0.0250 12.0000 0.0499 62.0000 0.4816 220.0000 1 . 4000

5.3000 0.0252 13.0000 0.0554 63.0000 0.4905 230.0000 1 .4298

5.4000 0.0254 14.0000 0.0612 64.0000 0.4995 240 . 0000 1.4571

5.5000 0.0256 15.0000 0.0674 65 . 0000 0.5084 250.0000 1 .4820

5.6000 0.0258 16.0000 0.0739 66.0000 0.5172 260.0000 1 .5044

5.7000 0.0260 17.0000 0.0807 67.0000 0.5260 270.0000 1 .5247

5.8000 0.0262 18.0000 0.0877 68.0000 0.5348 280.0000 1 .5428

5.9000 0.0264 1 9 . 0000 0.0950 69.0000 0.5435 290 . 0000 1 .5588

6.0000 0.0267 20.0000 0.1025 70 . 0000 0.5522 300 . 0000 1 .5728

6. 1000 0.0269 21 .0000 0.1103 71 .0000 0.5609 310.0000 1 .5849

6.2000 0.0271 22.0000 0.1182 72.0000 0.5695 320.0000 1 .5952

6.3000 0.0274 23.0000 0.1263 73.0000 0.5780 330.0000 1 .6037

6.4000 0.0276 24 . 0000 0.1345 74 . 0000 0.5866 340 . 0000 1 .6105

6.5000 0.0279 25.0000 0.1429 75.0000 0.5951

6.6000 0.0281 26.0000 0.1514 76.0000 0.6035

6.7000 0.0284 27.0000 0.1600 77.0000 0.6119

6.8000 0.0287 28.0000 0.1687 78.0000 0.6203

6.9000 0.0290 29.0000 0.1776 79 . 0000 0.6286

7 . 0000 0.0293 30 . 0000 0.1865 80 . 0000 0.6369

7. 1000 0.0295 31 .0000 0.1954 81 .0000 0.6451

7.2000 0.0298 32.0000 0.2045 82.0000 0.6533

7.3000 0.0301 33.0000 0.2136 83.0000 0.6614

7 . 4000 0.0304 34.0000 0.2227 84 . 0000 0.6695

7.5000 0.0308 35.0000 0.2319 85.0000 0.6776

7.6000 0.0311 36.0000 0.2411 86.0000 0.6856

7.7000 0.0314 37.0000 0.2504 87.0000 0.6935

7.8000 0.0317 38.0000 0.2597 88.0000 0.7015

7.9000 0.0321 39.0000 0.2690 89.0000 0.7094

8.0000 0.0324 40 . 0000 0.2783 90 . 0000 0.7172

8. 1000 0.0327 41 .0000 0.2877 91 .0000 0.7250

8.2000 0.0331 42.0000 0.2970 92.0000 0.7327

8.3000 0.0334 43.0000 0.3064 93.0000 0.7404

8.4000 0.0338 44.0000 0.3158 94.0000 0.7481

8.5000 0.0342 45 . 0000 0.3251 95.0000 0.7557

8.6000 0.0345 46.0000 0.3345 96.0000 0.7633

8.7000 0.0349 47.0000 0.3438 97.0000 0.7708

8.8000 0.0353 48.0000 0.3531 98.0000 0.7783

8.9000 0.0357 49 . 0000 0.3625 99 . 0000 0.7857

9 . 0000 0.0361 50.0000 0.3718 100.0000 0.7931

9
THERMAL

CONDUCTIVITY,

W/m4 6 10 20 40 60 100 200

TEMPERRTURE, K

Figure 2 Thermal conductivity of specimen EP-Al-0°.

Experimental data are presented as discrete points.

10
Figure 3 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen EP-Al-0°.

(The horizontal bar indicates the span of temperature

for each run)

.

11
Table 7 Experimental Data for EP-Al-90

Average

Temperature

Kelvin

Thermal

Conductivity

W/(m-K)

4.630 0.014

5.140 0.016

6.169 0.019

8.273 0.027

12.610 0.047

21.908 0.103

41.595 0.231

76.552 0.427

77.103 0.427

78.208 0.434

80.427 0.444

84.890 0.465

93.923 0.499

112.346 0.563

192.620 0.801

193.241 0.806

194.484 0.808

196.977 0.811

201.987 0.819

212.081 0.827

278.117 0.926

283.123 0.937

293.259 0.961

306.262 0.962

Table 8 Coefficients of A(T) for EP-Al-90°

^1 -4.7747384E-02

a2 9.8421893E-02

^3 -6.4348531E-02

34 1.7615317E-02

^5 -1 .4383095E-03

12
Table 9 Thermal Conductivity Values as a Function of Temperature

for Specimen EP-Al-90°

T A ( T ) T A ( T ) T A ( T ) T

Kelvin W/(m-K) Kelvin W/(m-K) Kelvin W/(m-K) Ke Ivin

4. 1000 0.0128 9. 1000 0.0288 51 .0000 0.2868 110.0000

4.2000 0.0131 9.2000 0.0292 52.0000 0.2927 120.0000

4.3000 0.0133 9.3000 0.0296 53.0000 0.2986 130.0000

4 . 4000 0.0136 9 . 4000 0.0300 54.0000 0.3045 140.0000

4.5000 0.0139 9.5000 0.0304 55.0000 0.3103 150.0000

4.6000 0.0142 9.6000 0.0309 56.0000 0.3161 1 60.0000

4 . 7000 0.0144 9.7000 0.0313 57.0000 0.3218 170.0000

4 . 8000 0.0147 9.8000 0.0317 58.0000 0.3275 180.0000

4 . 9000 0.0150 9 . 9000 0.0321 59.0000 0.3331 1 90 . 0000

5 . 0000 0.0153 1 0 . 0000 0.0326 60.0000 0.3387 200 . 0000

5. 1000 0.0155 1 1 .0000 0.0371 61 .0000 0.3443 210.0000

5.2000 0.0158 12.0000 0.0419 62.0000 0.3498 220.0000

5.3000 0.0161 13.0000 0.0471 63.0000 0.3553 230.0000

5 . 4000 0.0164 1 4 . 0000 0.0524 64.0000 0.3607 240.0000

5.5000 0.0166 15.0000 0.0580 65.0000 0.3661 250.0000

5.6000 0.0169 16.0000 0.0638 66.0000 0.3714 260.0000

5.7000 0.0172 17.0000 0.0697 67.0000 0.3768 270.0000

5.8000 0.0175 18.0000 0.0758 68.0000 0.3820 280.0000

5.9000 0.0178 1 9 . 0000 0.0819 69 . 0000 0.3873 290 . 0000

6 . 0000 0.0181 20 . 0000 0.0882 70 . 0000 0.3924 300 . 0000

6. 1000 0.0184 21 .0000 0.0946 71 .0000 0.3976 310.0000

6.2000 0.0187 22.0000 0.1010 72.0000 0.4027 320.0000

6.3000 0.0190 23.0000 0.1075 73.0000 0.4078 330.0000

6.4000 0.0193 24.0000 0.1140 74.0000 0.4128

6.5000 0.0196 25.0000 0.1206 75.0000 0.4178

6.6000 0.0199 26.0000 0.1272 76.0000 0.4227

6.7000 0.0202 27.0000 0.1338 77.0000 0.4276

6.8000 0.0205 28.0000 0. 1404 78.0000 0.4325

6.9000 0.0208 29 . 0000 0 . 1 470 79 . 0000 0.4373

7 . 0000 0.0211 30 . 0000 0.1536 80 . 0000 0.4421

7. 1000 0.0215 31 .0000 0.1602 81 .0000 0.4469

7.2000 0.0218 32.0000 0.1668 82.0000 0.4516

7.3000 0.0221 33.0000 0. 1734 83.0000 0.4563

7 . 4000 0.0225 34 . 0000 0. 1800 84 . 0000 0.4609

7.5000 0.0228 35.0000 0.1865 85.0000 0.4656

7.6000 0.0232 36.0000 0.1930 86.0000 0.4701

7.7000 0.0235 37.0000 0.1995 87.0000 0.4747

7.8000 0.0239 38.0000 0.2060 88.0000 0.4792

7.9000 0.0242 39.0000 0.2124 89.0000 0.4836

8 . 0000 0.0246 40 . 0000 0.2188 90 . 0000 0.4881

8.1000 0.0249 41 . 0000 0.2252 91 .0000 0.4925

8.2000 0.0253 42 . 0000 0.2315 92.0000 0.4968

8.3000 0.0257 43.0000 0.2378 93.0000 0.5012

8.4000 0.0260 44 . 0000 0.2441 94.0000 0.5055

8.5000 0.0264 45.0000 0.2503 95.0000 0.5097

8.6000 0.0268 46.0000 0.2565 96.0000 0.5140

8.7000 0.0272 47 . 0000 0.2626 97.0000 0.5182

8.8000 0.0276 48.0000 0.2687 98.0000 0.5223

8.9000 0.0280 49 . 0000 0.2748 99 . 0000 0.5265

9.0000 0.0284 50.0000 0.2808 100.0000 0.5306

A(T)

W/(m-K)

0.5699

0.6063

0.6401

0.6714

0.7004

0.7274

0.7524

0.7756

0.7972

0.8173

0.8359

0.8531

0.8691

0.8838

0.8975

0.9101

0.9217

0.9323

0.9421

0.9510

0.9592

0.9665

0.9732

13
THERMAL

CONDUCTIVITY,

N/mFigure 4 Thermal conductivity of specimen EP-Al-90°,

Experimental data are presented as discrete points.

lA
Figure 5 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen EP-Al-90°.

15
Table 10 Experimental Data for PK-Al-1-0

Average

Temperature

Kelvin

Thermal

Conductivity

W/(m-K)

4.628 0.013

5.138 0.014

6.160 0.017

8.250 0.024

12.508 0.041

21.525 0.088

40.611 0.203

40.625 0.205

76.542 0.406

77.085 0.411

78.173 0.419

80.354 0.431

84.743 0.455

93.635 0.501

111.841 0.590

192.617 0.944

193.233 0.937

194.467 0.939

196.941 0.942

201.921 0.955

211.988 0.975

232.568 1.015

273.769 1.119

274.390 1.126

275.630 1.124

278.119 1.129

283.131 1.146

293.267 1.173

305.906 1.196

Table 11 Coefficients of A(T) for PK-Al-l-0°

ai 1.2517495E-01

32 -2. 1465594E-01

^3 1.5127037E-01

a4 -5.2639361E-02

^5 9.2557441E-03

^6 -6.0375954E-04

16
Table 12 Thermal Conductivity Values as a Function of Temperature

for Specimen PK-Al-l-0°

T A ( T ) T A ( T ) Kelvin W/(m-K) Kelvin W/(m-K)

4. 1000 0.0124 9. 1000 0.0267

4,2000 0.0125 9 . 2000 0.0270

4 . 3000 0.0126 9.3000 0.0274

4 . 4000 0.0127 9.4000 0.0278

4 , 5000 0.0129 9.5000 0.0282

4.6000 0.0130 9 . 6000 0.0286

4.7000 0.0132 9.7000 0.0290

4 . 8000 0.0133 9.8000 0.0294

4 . 9000 0.0135 9.9000 0.0298

5 . 0000 0.0137 1 0 . 0000 0.0302

5 . 1000 0.0139 1 1 .0000 0 . 0344

5.2000 0.0141 12.0000 0.0388

5.3000 0.0143 13.0000 0.0432

5 . 4000 0.0146 14.0000 0.0479

5.5000 0.0148 15.0000 0.0526

5 . 6000 0.0150 16.0000 0.0575

5.7000 0.0153 17.0000 0.0625

5.8000 0.0156 18.0000 0.0675

5.9000 0.0158 1 9 . 0000 0.0727

6 . 0000 0.0161 20 . 0000 0.0779

6.1000 0.0164 21 .0000 0.0833

6.2000 0.0167 22.0000 0.0887

6.3000 0.0169 23.0000 0.0942

6.4000 0.0172 24 . 0000 0.0997

6.5000 0.0175 25.0000 0.1053

6.6000 0.0178 26.0000 0.1110

6.7000 0.0181 27.0000 0.1167

6.8000 0.0185 28.0000 0.1224

6.9000 0.0188 29 . 0000 0.1282

7.0000 0.0191 30 . 0000 0. 1341

7 . 1000 0.0194 31 .0000 0.1399

7.2000 0.0198 32.0000 0.1458

7 . 3000 0.0201 33.0000 0.1518

7 . 4000 0.0204 34 . 0000 0.1577

7.5000 0.0208 35.0000 0.1637

7.6000 0.0211 36.0000 0.1697

7.7000 0.0215 37.0000 0.1757

7.8000 0.0218 38.0000 0.1818

7.9000 0.0222 39.0000 0.1878

8.0000 0.0225 40 . 0000 0.1939

8.1000 0.0229 41 .0000 0.2000

8.2000 0.0233 42.0000 0.2061

8.3000 0.0236 43 . 0000 0.2122

8.4000 0.0240 44.0000 0.2183

8.5000 0.0244 45 . 0000 0.2244

8.6000 0.0247 46.0000 0.2305

8.7000 0.0251 47 . 0000 0.2366

8.8000 0.0255 48 . 0000 0.2427

8.9000 0.0259 49.0000 0.2488

9 . 0000 0.0263 50.0000 0.2548

T A ( T ) T A(T)

Kelvin W/(m-K) Kelvin U/(m51 .0000 0.2609 1 18.0000 0.5903

52.0000 0.2670 120.0000 0.6386

53.0000 0.2731 130.0000 0.6845

54.0000 0.2792 140.0000 0.7282

55.0000 0.2852 150.0000 0.7697

56.0000 0.2913 160.0000 0.8090

57.0000 0.2973 170.0000 0.8463

58.0000 0.3033 180.0000 0.8816

59 . 0000 0.3093 190.0000 0.9151

60.0000 0.3153 200 . 0000 0.9466

61 .0000 0.3213 210.0000 0.9764

62.0000 0.3273 220.0000 1 . 0045

63.0000 0.3332 230.0000 1 .0310

64.0000 0.3392 240.0000 1 .0559

65.0000 0.3451 250.0000 1 .0792

66.0000 0.3510 260.0000 1.1011

67.0000 0.3569 270.0000 1.1216

68.0000 0.3628 280.0000 1 . 1 408

69.0000 0.3686 290 . 0000 1.1586

70.0000 0.3744 300 . 0000 1.1751

71 .0000 0.3803 310.0000 1.1904

72.0000 0.3861 320.0000 1 .2046

73.0000 0.3918 330.0000 1 .2176

74.0000 0.3976

75.0000 0.4033

76.0000 0.4091

77.0000 0.4148

78.0000 0.4204

79.0000 0.4261

80 . 0000 0.4317

81 .0000 0.4373

82.0000 0.4429

83 . 0000 0.4485

84 . 0000 0.4541

85.0000 0.4596

86.0000 0.4651

87.0000 0.4706

88.0000 0.4760

89.0000 0.4815

90.0000 0.4869

91 .0000 0.4923

92.0000 0.4976

93.0000 0.5030

94 . 0000 0.5083

95 . 0000 0.5136

96.0000 0.5189

97.0000 0.5241

98 . 0000 0.5294

99.0000 0.5346

100.0000 0.5398

17
THERMRL

CONDUCTIVITY,

W/mFigure 6 Thermal conductivity of specimen PK-Ai-l-0°.

Experimental data are presented as discrete points.

18
Figure 7 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen PK-Al-l-0°.

19
Table 13 Experimental Data for PK-Al-1-90

Average

Temperature

Kelvin

Thermal

Conductivity

W/(m-K)

4.627 0.008

5.136 0.009

6.160 0.012

8.232 0.018

12.506 0.033

21.522 0.068

40.280 0.141

76.536 0.260

77.071 0.257

78.143 0.261

80.292 0.265

84.607 0.276

93.302 0.296

98.107 0.308

192.582 0.470

193.162 0.461

194.327 0.463

196.667 0.471

201.362 0.477

210.844 0.487

230.137 0.502

273.738 0.553

274.325 0.544

275.510 0.573

277.856 0.547

282.589 0.551

292.145 0.560

311.721 0.593

Table 14 Coefficients of A(T) for PK-Al-l-90°

ai 3.5119232E-03

a2 7.4568227E-03

^3 -1 .0401511E-02

34 4.4786925E-03

^5 -4. 1507969E-04

20
Table 15 Thermal Conductivity Values as a Function of Temperature

for Specimen PK-Ai-l-90°

T A ( T ) T A ( T) T A ( T ) T A(T)

Kelvin W/(m-K) Kelvin U/(m-K) Kelvin W/(m-K) Kelvin W/(m-K)

4.

1

000 0.0073 9.1000 0 . 0200 51 .0000 0.1805 110.0000 0.3370

4.2000 0.0075 9.2000 0.0203 52.0000 0.1839 120.0000 0.3572

4.3000 0.0076 9.3000 0.0207 53.0000 0.1872 130.0000 0.3760

4.4000 0.0078 9.4000 0.0210 54.0000 0.1905 140.0000 0.3936

4 . 5000 0 . 0080 9.5000 0.0213 55.0000 0.1937 150.0000 0.4100

4.6000 0.0082 9 . 6000 0.0217 56.0000 0.1970 160.0000 0.4254

4.7000 0.0083 9.7000 0.0220 57.0000 0.2002 170.0000 0.4399

4.8000 0.0085 9.8000 0.0224 58.0000 0.2033 180.0000 0.4535

4.9000 0.0087 9.9000 0.0227 59.0000 0.2065 190.0000 0.4663

5 . 0000 0.0089 1 0 . 0000 0.0230 60 . 0000 0.2096 200.0000 0.4784

5.1000 0.0091 1 1 .0000 0.0266 61 .0000 0.2127 210.0000 0.4897

5.2000 0.0093 12.0000 0.0303 62.0000 0.2157 220.0000 0.5005

5.3000 0.0095 13.0000 0.0341 63.0000 0.2188 230.0000 0.5106

5.4000 0.0097 14.0000 0.0380 64.0000 0.2218 240.0000 0.5202

5 . 5000 0 . 0099 15.0000 0.0420 65.0000 0.2248 250.0000 0.5292

5.5000 0.0101 16.0000 0.0461 66.0000 0.2277 260.0000 0.5378

5.7000 0.0104 17.0000 0.0501 67.0000 0.2307 270.0000 0.5459

5.8000 0.0106 18.0000 0.0542 68.0000 0.2336 280.0000 0.5535

5.9000 0.0108 19.0000 0.0584 69.0000 0.2365 290.0000 0.5608

6 . 0000 0.0111 20.0000 0.0625 70.0000 0.2393 300 . 0000 0.5676

6. 1000 0.0113 21 .0000 0.0666 71 .0000 0.2422 310.0000 0.5741

6.2000 0.0115 22.0000 0.0708 72.0000 0.2450 320.0000 0.5803

6.3000 0.0118 23.0000 0.0749 73.0000 0.2478 330.0000 0.5861

6.4000 0.0120 24 . 0000 0.0790 74.0000 0.2506 340.0000 0.5915

6.5000 0.0123 25.0000 0.0831 75.0000 0.2533

6.6000 0.0126 26.0000 0.0872 76.0000 0.2560

6.7000 0.0128 27.0000 0.0913 77.0000 0.2587

6.8000 0.0131 28.0000 0.0953 78.0000 0.2614

6.9000 0.0134 29 . 0000 0.0994 79.0000 0.2641

7 . 0000 0.0136 30 . 0000 0 . 1 034 80 . 0000 0.2667

7. 1000 0.0139 31 .0000 0.1073 81 .0000 0.2693

7.2000 0.0142 32.0000 0.1113 82.0000 0.2719

7 . 3000 0.0145 33.0000 0.1152 83.0000 0.2745

7 . 4000 0.0147 34.0000 0.1191 84 . 0000 0.2771

7.5000 0.0150 35.0000 0.1230 85.0000 0.2796

7.6000 0.0153 36.0000 0.1268 86.0000 0.2821

7.7000 0.0156 37.0000 0.1306 87.0000 0.2846

7.8000 0.0159 38.0000 0. 1344 88.0000 0.2871

7.9000 0.0162 39.0000 0.1381 89.0000 0.2895

8.0000 0.0165 40.0000 0.1418 90.0000 0.2920

8.1000 0.0168 41 .0000 0.1455 91 .0000 0.2944

8.2000 0.0171 42.0000 0.1491 92.0000 0.2968

8.3000 0.0174 43.0000 0.1527 93.0000 0.2992

8.4000 0.0177 44 . 0000 0.1563 94.0000 0.3015

8.5000 0.0181 45 . 0000 0.1599 95.0000 0.3039

8.6000 0.0184 46.0000 0.1634 96.0000 0.3062

8.7000 0.0187 47 . 0000 0.1669 97.0000 0.3085

8.8000 0.0190 48 . 0000 0.1703 98.0000 0.3108

8.9000 0.0193 49 . 0000 0. 1738 99 . 0000 0.3131

9.0000 0.0197 50 . 0000 0.1772 1 00 . 0000 0.3153

21
THERMAL

CONDUCTIVITY,

W/mFigure 8 Thermal conductivity of specimen PK-Al-l-90°.

Experimental data are presented as discrete points.

22
4 6 10 20 40 60 100 200

TEMPERRTURE, K

Figure 9 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen PK-Al-l-90°.

23
Table 16 Experimental Data for PK-Al-2-0

Average

Temperature

Kelvin

Thermal

Conductivity

W/(m-K)

5.134 0.016

6.157 0.019

8.200 0.028

12.419 0.050

21.195 0.108

39.561 0.243

76.530 0.494

77.058 0.488

78.120 0.494

80.247 0.509

84.515 0.534

93.129 0.589

110.632 0.691

110.639 0.693

192.582 1.117

192.582 1.116

193.159 1.081

194.320 1.080

196.648 1.091

201.328 1.107

210.770 1.129

230.056 1.185

273.735 1.261

274.321 1.269

275.492 1.265

277.841 1.272

282.563 1.285

292.104 1.316

311.595 1.378

Table 17 Coefficients of A(T) for PK-Al-2-0°

^1 1.9787333E-01

a2 -3.4326128E-01

^3 2.3817078E-01

34 -8.0759153E-02

^5 1 . 3746504E-02

^6 -8.8121097E-04

24
Table 18 Thermal Conductivity Values as a Function of Temperature

for Specimen PK-Al-2-0°.

T A ( T ) T A ( T ) Kelvin W/(m-K) Kelvin W/(m-K)

4. 1000 0.0135 9.1000 0.0321

4.2000 0.0136 9.2000 0.0326

4.3000 0.0137 9 . 3000 0.0331

4.4000 0.0138 9 . 4000 0.0336

4.5000 0.0139 9 . 5000 0.0342

4.6000 0.0141 9 . 6000 0.0347

4.7000 0.0143 9.7000 0.0352

4.8000 0.0145 9 . 8000 0.0358

4 . 9000 0.0147 9.9000 0.0363

5.0000 0.0149 10.0000 0.0368

5.1000 0.0151 1 1 . 0000 0.0423

5.2000 0.0154 12.0000 0.0480

5.3000 0.0157 13.0000 0.0538

5.4000 0.0160 14.0000 0.0597

5 . 5000 0.0163 15.0000 0.0658

5.6000 0.0166 16.0000 0.0719

5.7000 0.0169 17.0000 0.0781

5.8000 0.0172 18.0000 0.0844

5.9000 0.0176 19.0000 0.0908

6.0000 0.0179 20 . 0000 0.0973

6.1000 0.0183 21 .0000 0.1039

6.2000 0.0187 22.0000 0.1105

6.3000 0.0191 23.0000 0.1172

6.4000 0.0195 24 . 0000 0.1239

6.5000 0.0199 25.0000 0.1307

6.6000 0.0203 26.0000 0.1375

6.7000 0.0207 27.0000 0 . 1 444

6.8000 0.021

1

28.0000 0.1514

6.9000 0.0215 29 . 0000 0.1583

7.0000 0.0220 30.0000 0.1653

7.1000 0.0224 31 .0000 0.1724

7.2000 0.0228 32.0000 0.1795

7.3000 0.0233 33.0000 0.1866

7 . 4000 0.0237 34.0000 0.1937

7.5000 0.0242 35.0000 0.2008

7.6000 0.0247 36.0000 0.2080

7.7000 0.0251 37.0000 0.2152

7.8000 0.0256 38.0000 0.2224

7.9000 0.0261 39.0000 0.2296

8.0000 0.0266 40 . 0000 0.2368

8.1000 0.0270 41 .0000 0.2440

8.2000 0.0275 42.0000 0.2512

8.3000 0.0280 43.0000 0.2585

8.4000 0.0285 44.0000 0.2657

8.5000 0.0290 45.0000 0.2729

8.6000 0.0295 46.0000 0.2802

8.7000 0 . 0300 47.0000 0.2874

8.8000 0.0305 48.0000 0.2946

8.9000 0.0310 49 . 0000 0.3018

9.0000 0.0316 50.0000 0.3090

T A ( T) T A ( T ) Kelvin W/(m-K) Kelvin W/(m-K)

51 .0000 0.3162 110.0000 0.7012

52.0000 0.3234 120.0000 0.7567

53.0000 0.3306 130.0000 0.8091

54.0000 0.3378 140.0000 0.8587

55.0000 0.3449 150.0000 0.9054

56.0000 0.3520 160.0000 0.9494

57.0000 0.3592 170.0000 0.9908

58.0000 0.3663 180.0000 1 .0295

59.0000 0.3733 190.0000 1 .0658

60.0000 0.3804 200.0000 1 .0998

61 .0000 0.3875 210.0000 1 .1314

62.0000 0.3945 220.0000 1.1608

63.0000 0.4015 230.0000 1 .1881

64.0000 0.4085 240.0000 1 .2133

65 . 0000 0.4155 250.0000 1 .2366

66.0000 0.4224 260.0000 1 .2580

67.0000 0.4293 270.0000 1 .2775

68.0000 0.4362 280.0000 1 .2952

69.0000 0.4431 290.0000 1 .3113

70.0000 0.4499 300.0000 1 .3257

71 .0000 0.4568 310.0000 1 .3384

72.0000 0.4636 320.0000 1 .3497

73.0000 0.4703 330.0000 1 .3595

74 . 0000 0.4771 340 . 0000 1 .3678

75.0000 0.4838

76.0000 0.4905

77.0000 0.4972

78.0000 0.5038

79.0000 0.5105

80 . 0000 0.5170

81 .0000 0.5236

82.0000 0.5301

83.0000 0.5367

84.0000 0.5431

85.0000 0.5496

86.0000 0.5560

87.0000 0.5624

88.0000 0.5688

89.0000 0.5751

90 . 0000 0.5814

91 .0000 0.5877

92.0000 0.5939

93.0000 0.6001

94.0000 0.6063

95 . 0000 0.6125

96.0000 0.6186

97.0000 0.6247

98 . 0000 0.6308

99 . 0000 0.6368

100.0000 0.6428

25
THERMAL

CONDUCTIVITY,

N/mFigure 10 Thermal conductivity of specimen PK-Al-2-0°.

Experimental data are presented as discrete points.

26
Figure 11 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen PK-Al-2-0°.

27
Table 19 Experimental Data for Neat-PK

Average

Temperature

Kelvin

Thermal

Conductivity

W/(m-K)

4.629 0.012

5.140 0.013

6.167 0.016

8.263 0.024

12.583 0.039

21.553 0.067

76.525 0.147

77.050 0.150

78.100 0.151

80.205 0.155

84.420 0.158

92.888 0.165

109.955 0.178

192.553 0.226

193.109 0.238

194.221 0.242

196.444 0.240

200.909 0.242

209.898 0.243

228.143 0.246

273.711 0.264

274.273 0.269

275.398 0.268

277.652 0.270

282.180 0.272

291.313 0.277

309.916 0.288

Table 20 Coefficients of A(T) for Neat-PK

ai 1 .0636976E-01

a2 -1.6340006E-01

^3 9.4941322E-02

a4 -2.4117988E-02

^5 2.8797748E-03

^6 -1.3025208E-04

28
Table 21 Thermal Conductivity Values as a Function of Temperature

for Specimen Neat-PK.

T A ( T ) T A ( T ) Kelvin W/(m-K) Kelvin W/(m-K)

4. 1000 0.0108 9. 1000 0.0271

4.2000 0.0110 9.2000 0.0275

4.3000 0.0111 9.3000 0.0279

4 . 4000 0.0112 9 . 4000 0.0283

4.5000 0.0114 9.5000 0.0287

4.6000 0.0116 9.6000 0.0291

4.7000 0.0118 9 . 7000 0.0295

4 . 8000 0.0120 9.8000 0.0299

4 . 9000 0.0122 9.9000 0.0303

5 . 0000 0.0124 10.0000 0.0307

5.1000 0.0127 1 1 .0000 0.0347

5.2000 0.0129 12.0000 0.0387

5 . 3000 0.0132 13.0000 0.0425

5 . 4000 0.0135 14.0000 0.0462

5 . 5000 0.0138 15.0000 0.0498

5.6000 0.0140 16.0000 0.0533

5.7000 0.0143 17.0000 0.0566

5.8000 0.0147 18.0000 0.0598

5.9000 0.0150 1 9 . 0000 0.0629

6 . 0000 0.0153 20.0000 0.0659

6.1000 0.0156 21 .0000 0.0688

6.2000 0.0160 22.0000 0.0716

6.3000 0.0163 23.0000 0.0743

6.4000 0.0166 24 . 0000 0.0769

6.5000 0.0170 25.0000 0.0794

6.6000 0.0173 26.0000 0.0818

6.7000 0.0177 27.0000 0.0842

6.8000 0.0181 28.0000 0.0864

6.9000 0.0184 29.0000 0.0887

7 . 0000 0.0188 30 . 0000 0.0908

7.1000 0.0192 31 .0000 0.0929

7 . 2000 0.0196 32.0000 0.0949

7 . 3000 0.0199 33.0000 0.0969

7 . 4000 0.0203 34.0000 0.0988

7.5000 0.0207 35.0000 0.1006

7.6000 0.0211 36.0000 0. 1024

7.7000 0.0215 37.0000 0. 1042

7.8000 0.0219 38.0000 0.1059

7.9000 0.0223 39.0000 0.1076

8.0000 0.0227 40.0000 0.1092

8.1000 0.0231 41 .0000 0.1109

8.2000 0.0235 42.0000 0.1124

8.3000 0.0239 43.0000 0.1140

8.4000 0.0243 44.0000 0.1155

8.5000 0.0247 45.0000 0.1169

8.6000 0.0251 46.0000 0.1184

8.7000 0.0255 47.0000 0.1198

8.8000 0.0259 48.0000 0.1212

8.9000 0.0263 49.0000 0.1225

9 . 0000 0.0267 50.0000 0.1239

T A ( T ) T A ( T ) Kelvin W/( m - K ) Ke Ivin W/( m - K ) 51 .0000 0. 1252 1 10.0000 0.1801

52.0000 0.1265 120.0000 0.1871

53.0000 0.1277 130.0000 0.1938

54 . 0000 0. 1290 140.0000 0.2003

55.0000 0.1302 150.0000 0.2065

56.0000 0.1314 160.0000 0.2124

57.0000 0.1326 170.0000 0.2182

58.0000 0. 1338 180.0000 0.2239

59 . 0000 0. 1349 1 90 . 0000 0.2293

60 . 0000 0. 1361 200 . 0000 0.2347

61 .0000 0.1372 210.0000 0.2399

62.0000 0.1383 220.0000 0.2450

63.0000 0. 1394 230.0000 0.2499

64.0000 0 . 1405 240.0000 0.2548

65.0000 0.1415 250.0000 0.2596

66.0000 0.1426 260.0000 0.2642

67.0000 0.1436 270.0000 0.2688

68.0000 0. 1446 280.0000 0.2733

69.0000 0.1457 290 . 0000 0.2777

70.0000 0. 1467 300 . 0000 0.2821

71 .0000 0. 1476 310.0000 0.2863

72.0000 0. 1486 320.0000 0.2905

73.0000 0. 1496 330.0000 0.2946

74.0000 0.1505 340 . 0000 0.2986

75.0000 0.1515

76.0000 0.1524

77.0000 0.1534

78.0000 0.1543

79 . 0000 0.1552

80 . 0000 0.1561

81 .0000 0.1570

82.0000 0. 1579

83.0000 0.1587

84.0000 0. 1596

85.0000 0. 1605

86.0000 0.1613

87.0000 0.1622

88.0000 0.1630

89.0000 0.1639

90.0000 0.1647

91 .0000 0.1655

92.0000 0.1663

93.0000 0.1671

94.0000 0.1679

95.0000 0.1687

96.0000 0.1695

97.0000 0. 1703

98 . 0000 0.1711

99 . 0000 0.1719

100.0000 0.1726

29
THERMRL

CONDUCTIVITY,

W/mFigure 12 Thermal conductivity of specimen Neat-PK.

Experimental data are presented as discrete points.

30
Figure 13 Relative deviations of the experimental and calculated

thermal conductivity integrals for specimen Neat-PK.

31
THERMRL

CONDUCTIVITY,

W/mO PK-RL-1-0 A PK-flL-2-0

TEMPERATURE K

Figure 14 Thermal conductivity of PK-Al-l-0° and PK-Al-2-0°

specimens where heat is flowing parallel to the alumina

fibers

.

32
THERMAL

CONDUCTIVITY,

N/mO 330 K A 250 K 200 K V 150 K

O 100 K + 75 K X 50 K

0 10 20 30 40 50 60

FIBER VOLUME FRPCTION X

Figure 15 Thermal conductivity as a function of fiber volume

ratios for various calculated temperatures (above 40 K)

.

The dashed line shows linear extrapolation taken.

33
THERMRL

CONDUCTIVITY,

N/mO ^0 K

O 7.5 K A 30 K + 5.0 K

20 K X ^.1 K V 10 K

0 10 20 30 ^0 50 60

HBaR volume ERPCTION X

Figure 16 Thermal conductivity as a function of fiber volume

ratios for various calculated temperatures (below 40 K)

.

The dashed line shows linear extrapolation taken.

34
THERMAL

CONDUCTIVITY,

W/mO EP-RL-0

Figure 17 Thermal conductivity as a function of temperature for

the EP-Al-0° and the calculated PEEK/alumina curve

( ). Comparison for the same fiber volume fraction.

Note that both scales are logarithmic, which clarifies

the behavior at low temperatures. Compare to Figure 18.

35
THERMAL

CONDUCTIVITY,

W/mO EP-flL-0

0 50 ]00 150 200 250 300 350

temperrture: k

Figure 18 Thermal conductivity as a function of temperature for

the EP-Al-0° and the calculated PEEK/alumina curve

( ). Comparison for the same fiber volume fraction.

Note that both scales are linear, which clarifies the

behavior at high temperatures. Compare to Figure 17.

36
THERMRL

CONDUCTIVITY,

W/mO EF-RL-0 A PK-RL-I-0 C PK-RL-2-0 V nert-pk

TEMPERATURE K

Figure 19 Thermal conductivity of the specimens where

flowing parallel to the alumina fibers. The

data are also included as a reference. Note

scales are logarithmic, which clarifies the

low temperatures. Compare to Figure 20.

heat is

Neat - PEEK

that both

behavior at

37
THERMAL

CONDUCTIVITY,

W/mO EP-flL-0 A PK-RL-I-0 PK-RL-2-0 V NERT-PK

0 50 100 150 200 250 300 350

TEMPERRTURE K

Figure 20 Thermal conductivity of the specimens where heat is

flowing parallel to the alumina fibers. The Neat-PEEK

data are also included as a reference. Note that both

scales are linear, which clarifies the behavior at high

temperatures. Compare to Figure 19.

38
TIIERMRL

CONDUCTIVITY,

W/mC EP-RL.-90 A PK-RL-I-90 G NERT-PK

Figure 21 Thermal conductivity of the specimens where heat is

flowing perpendicular to the alumina fibers. The Neat-PEEK

data are also included as a reference. Note that both

scales are logarithmic, which clarifies the behavior at

low temperatures. Compare to Figure 22.

39
THERMRL

CONDUCTIVITY,

N/mO CF-RL-90 A PK-RL-1-90 NERT-PK

Figure 22 Thermal conductivity of the specimens where heat is

flowing perpendicular to the alumina fibers. The Neat-PEEK

data are also included as a reference. Note that both

scales are linear, which clarifies the behavior at high

temperatures. Compare to Figure 21.

40
THERMRL

CONDUCTIVITY,

N/mO EP-RL-0 A EP-flL-90

Figure 23 Thermal conductivity of the epoxy/aiumina fibered data,

both parallel and perpendicular to alumina fibers. Note

that both scales are logarithmic, which clarifies the

behavior at low temperatures. Compare to Figure 24.

41
THERMRL

CONDUCTIVITY,

W/mO EP-flL-0 A EP-RL-90

0 50 100 150 200 250 300 350

TEMPERRTURE K

Figure 24 Thermal conductivity of the epoxy/alumina fibered data,

both parallel and perpendicular to alumina fibers. Note

that both scales are linear, which clarifies the behavior

at high temperatures. Compare to Figure 23.

42
THERMRL

CONDUCTIVITY,

N/mO PK-flL-1-0 A PK-RL-1-90 PK-flL-2-0 V NERT-PK

temperrture: k

Figure 25 Thermal conductivity of the PEEK/aiumina fibered data,

both parallel and perpendicular to fiber direction. The

Neat-PEEK data also included. Note that both scales are

logarithmic, which clarifies the behavior at low

temperatures. Compare to Figure 26.

43
THERMAL

CONDUCTIVITY,

W/mO PK-RL-1-0 A PK-RL-1-90 PK-RL-2-0 V NERT-PK

TEMPERRTURE K

Figure 26 Thermal conductivity of the PEEK/alumina fibered data,

both parallel and perpendicular to fiber direction. The

Neat-PEEK data also included. Note that both scales are

linear, which clarifies the behavior at high temperatures.

Compare to Figure 25.

44
JIIERMnL

CONDUCTIVITY,

N/mO lP-RL-G

O PK-RL-2-0

A l=-RL-90 * NlRT-PK

PK-RL-1-0 V PK-RL 0

Figure 27 Thermal conductivity of all the specimens tested. Note

that both scales are logarithmic, which clarifies

the behavior at low temperatures. Compare to Figure 28.

45
THERMAL

CONDUCTIVITY,

N/mO EP-RL-0 A E^-flL-90 PK-flL-1-0 V PK-flL-1-90

O PK-RL-2-0 + NlRT-PK

temperrture; k

Figure 28 Thermal conductivity of all the specimens tested. Note

that both scales are linear, which clarifies the behavior

at high temperatures. Compare to Figure 27.

46
Appendix

I I 100 /i,m

PK-Al-l-0° photomicrograph. A larger

section was used to determine the fiber

volume ratio of 43%.

47
100

PK-Al-2-0° photomicrograph. A larger

section was used to determine the fiber

volume ratio of 52%.

48
w

3^

m

EP-Al-0° photomicrograph. A larger section

was used to determine the fiber volume ratio

of 59%.

49
FORM NBS-1 14A (REV. 1 1-84)

U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. PubI ication Date

BIBLIOGRAPHIC DATA

SHEET (See instructions)

REPORT NO.

NISTIR 89-3914 May 1989

4. TITLE AND SUBTITLE

Low-Temperature Thermal Conductivity of Composites

Alumina Fiber/Epoxy and Alumina Feber/PEEK

5, AUTHOR(S)

D.L. Rule and L.L. Sparks

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8 . Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

National Aeronautics and Space Administration

Ames Research Center

Moffett Field, California 94035

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT ( A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here)

The thermal conductivities of poly-ether-ether-ketone (PEEK), of

alumina fiber in a matrix of PEEK, and of alumina fiber in a matrix of

epoxy, were determined along with the effects of fiber orientation and

thermal cycling. Thermal conductivity was measured over the temperature

range of 4.2 to 310 K using a steady-state apparatus.

These data are presented and discussed relative to specimen characteristics. It appears that after accounting for different fiber fractions

in the specimens, the thermal conductivity of the PEEK composite material

is less than that of the epoxy composite material in particular temperature

ranges.

12. KEY WORDS (S/x to twelve entries; alphabeti cal order; capitalize only proper names; and separate key words by semicolon s) alumina; composite; epoxy; low temperature; PEEKy poly-ether-ether-ketone;

thermal conductivity

13. AVAILABILITY

Uni imited

I I For Official Distribution, Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, DC

20402.

Order From National Technical Information Service (NTIS), Springfield, VA 22161

14. NO. OF

PRINTED PAGES

60

15. Price

< .

'.: ": ' -^ /’

: V /

'^.^, '^^.V -:VSt--:v?f; ' : "

' -w. ' :'."

. ''''i'll /%Wa

- "'.

. • f'

’*-y^ ^

.-/v

•: TV V-*,.. _:,.»

• ^ ' • ^/,V 'V- „; '

''';i'\'' '

till

?V »

’•i.,;.u

.,

'

^_, »«*• ' ::-':Xr^'<

' ^^^' ''1

.

''

> f'-'fj ’ 1^- • "'

•

•'•'} I* i'

*;T(

,

• •».* ;?j * It. I * \}inff\il'«i‘'"' f f

>.' '^. . ' r'

•;. ,f>t^ t^''i i

' :'

;‘

' "

'

, ,;,^ IS

>T- r"^ j, t .A^^*).***i-‘f’'<^>''

i r >- '>'^ •

?•'- 5 , »-Lf r ‘--f <>•

; >

<r

•

n •; ‘ \<'i •;.=•^.>.

. '.Vl t !. ^^

' i",

'

-*

• iUfJi

.r-f ' : t'.

.

*">»

'

" ^

“

-r

' ’5

'

i\




IR 89-3915

RESTRICTED