NASA Contractor Report 165632

CSCL 2 3 ~ U n c ~ a s

3 / 3 5 L 7 3 o b

THERMAL EXPANSION PROPERTIES OF COMPOS'PTE MATERIALS

Robert R. Johnson, Murat H. Kural, and George B. Mackey Lockheed Missiles & Space Company, Inc. Sunnyvale, Cal$ornia 94086

Contract NAS1-14887 (Task 17) July 1981

Nat~onal Aeronautics and Space Administration

langley Reseerch Center Hampton. V~rg~nla 23665

FOREWORD

This document was prepared by Lockheed Missiles Space

Company, Inc. (LMSC), P. 0 . Box 504, Sunnyvale, CA 94086,

for the National Aeronautics and Space Administration - Langley Research Center, in compliance with Task Assignment

No. 17, Contract NAS1-14887. This report is intended as a

reference to the thermal expansion properties of various fiber-

reinforced composite materials.

Harold G . Bush is the NASA Contracting Officer's Techni-

cal Representative on this program. The Program Manager

and Project Leader at LMSC are H. Cohan and R . R . Johnson,

respectively.

W€CW,BQ PAGE 8U.NR NOT W

TABLEOF CONTENTS

Pege

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1

FACTORS AFFECTING THE CTE . . . . . . . . . . . . . . . . . . 1

Fiber Volume . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Void Volume . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Layup Angle . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Fabric Skewness . . . . . . . . . . . . . . . . . . . . . . . . 4

Stacking Sequence . . . . . . . . . . . . . . . . . . . . . . 4

Thermal Cycling . . . . . . . . . . . . . . . . . . . . . . . . 5

Temperature Dependence . . . . . . . . . . . . . . . . . . . . 6

Moisture Effects . . . . . . . . . . . . . . . . . . . . . . . . 6

Viscoelasticity . . . . . . . . . . . . . . . . . . . . . . . . . 7

PREDICTION OF CTE . . . . . . . . . . . . . . . . . . . . . . . . 7

CTE by Lamination Theory . . . . . . . . . . . . . . . . . . . 8

Lamina Micromechanics Formulation for CTE . . . . . . . . . . . 11

THERMAL DIMENSIONAL STABILITY AND TUNING FOR ZERO CTE . . 13

Thermal Dimensional Stability . . . . . . . . . . . . . . . . . 13

Tuning Process . . . . . . . . . . . . . . . . . . . . . . . . 15

Novel Approaches to Tuning . . . . . . . . . . . . . . . . . . 19

TESTMETHODS . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Length Measurement Techniques . . . . . . . . . . . . . . . . 20

Electrical Transducers for Displacement Measurement . . . . . . 22

Electrical-Optical Transducers for Displacement Measurement . . 26

Non-Interferometric Methods . . . . . . . . . . . . . . . 26

Interferometric Methods . . . . . . . . . . . . . . . . . . 27

Miscellaneous Optical Methods for Displacement Measurement . . . 29

THERMAL EXPANSION DATA . . . . . . . . . . . . . 29

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0

LIST OF ILLUSTRATIONS

Figure Page

2 1. Variation of CTE of a unidirectional glass fiber laminate with fiber volume.

2. Variation of expansional strain with laminate fiber orientation (from ref. 4).

3. Geometric representation of a laminate.

4. Sensitivity of various laminates to layer orientation 8 .

5. Effect of replacing GY70 fiber with other selected fibers in a unidirectional laminate.

6. Effect of replacing VSB-32 fiber with other selected fibers in a unidirectional layup.

7. Effect of replacing O0 GY7O fiber with other selected fibers in a (9010190) layup.

8. Effect of replacing O0 VSB-32 fiber with other selected fibers in a (9010190) layup.

9. Electromechanical dilatometer.

10. Modified Leit z dilatometer . 11. Laser interferometer and dimensional stability test apparatus.

12. Thermal expansion of Kevlar 49lX904B ( 120 style) fabric.

13. Thermal expansion of unidirectional Boron15505 tape.

14. Thermal expansion of Thornel 3001Narmco 5208 tape (0° fiber direction).

15. Thermal expansion of Thornel 3001Narmco 5208 tape (90" fiber direction).

16. Thermal expansion of AMF 330C ICE339 fabric (T- 300 fiber) (0° warp direction).

17. Thermal expansion of HMF 330C ICE339 fabric (T- SO0 fiber) ( 90° fill direction).

18. Thermal expansion of HMF 330Cl934 fabric (T-300 fiber) (0° warp direction).

19. Thermal expansion of HMF 330C 1934 fabric (T- 300 fiber) ( 90° fill direction) .

20. Thermal expansion of unidirectional HTS- 2 13501- 5A tape (0° fiber direction).

LIST OF ILLUSTRATIONS (Cont . )

Page

4 1 Thermal expansion of unidirectional HTS- 213501- 5A tape ( 90° fiber direction).

Thermal expansion of unidirectional HMSl3501-5A tape (0° fiber direction).

Thermal expansion of unidirectional HMS 13501-5A tape (90° fiber direction).

Thermal expansion of HMSl3501 unidirectional tape (0° direc- tion)

Thermal expansion of HMSl3501 unidilcectional tape (90° di- rection).

Thermal expansion of HMS ICE339 unidirectional tape ( O0 fiber direction).

Thermal expansion of HMS ICE339 unidimctional tape ( 90° fiber direction) . Thermal expansion of HMS1759 unidirectional tape (0° direc- tion).

Thermal expansion of HMS 1759 unidirectional tape (90° di- rection).

Thermal expcansion of HMSI934 unidirectional tape (0° fiber direction).

Thermal expansion of HMS I 934 unidirectional tape ( 90° fiber direction). Thermal expansion of HMSlE788 fabric.

Thermal expansion of unidirectional Thornel- 50 (Pan) IF263 tape (0° fiber direction).

Thermal expansion of GY 7Olepoxy unidirectional tape (0° Piber direction).

Thermal expansion of GY 701X 904B and GY 701 934 unidirec- tional tape (90° fiber direction).

Longitudinal (0°) thermal expansion of P75Sl934 graphitel epoxy Thermal expansion of glass /epoxy tooling material ( 181 cloth laminate).

Thermal expansion of 104 glass scrim cloth.

TABLES

Table

I

v

VI

VII

VIII

Calculated strains in GY701339 [(019O2Is laminate during hy grot hermal cycling

Transformation equations for pK and 6: for the 1;th lamina 11

(0 3/t57. 5 190) laminate CTE sensitivities to lamina pmper-

ties, baseline CTE = 0.41 x ~ o - ~ / K (0.229 x ~ o ' ~ / o F )

Unidirectional fiber lepoxy properties - 60 percent fiber volume

Summary of techniques for length measurement

Coefficient of thermal expansion - epoxy resin systems

Coefficient of thermal expansion - fibrous reinforcements

Coefficient of thermal expansion - unidirectional tape and fabric epoxy systems

THERMAL EXPANSION PROPERTIES

OF COMPOSITE MATERIALS

Robert R. Johnson, Murat H. Kural, and George B. Mackey

SUMMARY

Thermal expansion data for several composite mat -,<als, including generic

epoxy resins, various graphite, boron, and glass fibers, and unidirectional and

woven fabric composites in an epoxy matrix, have been compiled into one compre-

hensive report.

A discussion of the design, material, environmenral, and fabrication properties

affecting thermal expansion behavior is presented. Test met hods and their accu-

racy are discussed. Analytical approaches to predict laminate coefficients of ther-

mal expansion (CTE) based on lamination theory and micromechanics are also in-

cluded.

For space applications, a near-zero CTE is often highly desirable to maintain

the thermal dimensional stability of a structure on-orbit. Although this is easily

achievable with composite materials, it is often at the expense of some structural

efficiency. A discussion is included of methods of tuning a laminate to obtain a

near - zero C TE . Related references that describe these data more extensively are included.

PRECEDING PAGE BUNK NOT

INTRODUCTION

It is well known that the high stiffness and low coefficient of thermal expansion

(CTE) of graphite epoxy, together with its low density, make this material espe-

cially attractive for space applications.

Much data currently exist as the result of thermal expansion tests on graphite,

Kevlar , boron, and glass fibers. Properties of composites, including unidirec-

tional and woven fibers in epoxy, as well as some heat resins, are presented

here, This document summarizes thermal expansion data cbtained from published

literature, as well as unpublished data from the LMSC data bank.

Factors that affect the thermal expansion properties are discussed briefly,

and a related set of references that more extensively describe the influence of

these factors is presented.

Use of commercial products or names of manufacturers in this report does not

constitute official endorsement of such products or manufacturers, either ex-

pressed or implied, by the National Aeronautics and Space Adn~inistration

FACTORS AFFECTING THE CTE

The requirement of thermally stable space structures has led to the selection

of fiber-resin con~posite materials to achieve a near-zero CTE. A number of fac-

tors affect the thermal dimensional stability of a laminate, and there is some ques-

tion as to how close to zero CTE a laminate may be fabric'hted. Reference 1 pre-

sents the results of a rather thorough study of 29 test samples from one batch of

pseudoisotropic GY7OIX-30 material. Extension of the CTE data to a large sample

indicated a 3 sigma statistical variation of close to 0.10 x ~ O - ~ / ~ F (0.18 x ~ o - ~ / K ) . " . . Another analytical study (ref. 2) , ' e h includes material elastic constant^ , layup r ql

V ' n Y .We angle, material thickness, and input CTE data, indicates that for practical lami-

:A, .. nate designs, it is not feasible to specify a CTE less than 20.05 x 10 -6pF $" - ~. (0.09 x 10'~lK). This section contains discussions of the following factors

which affect the laminate CTE : fiber and void volumes, layup angle, fabric skewness, stacking sequence, thermal cycling, temperature dependence, moisture effects, and material viscoelasticity .

Fiber Volume

The dependence of CTE on fiber volume is illustrated in fig. 1 for a unidirec-

tional llayup. These curves were calculated based on formulas given in ref. 3. A s

seen in this figure, at approximately 60 percent fiber content, the longitudinal

I I 1 1 0 0.2 0.4 0.6 0.8 1.0

Fiber volume fraction (Ref. 3)

Figure 1. - Variation of CTE of a undirectional glass fiber laminate with fiber volume.

UHZGiNAL PAGE IS W POOR QUAWTY

CTE is virtually unaffected by any changes in the laminate fiber content. In the

case of transverse CTE, the sensitivity is more pronounced. In terms of angle ply

laminates comprised of several layers, the effect of fiber volume variations on the

thermal expansion behavior of the laminate may not be negligible.

Void Volume

The direct effect of voids on the CTE of composite laminates is small within the

bounds of practical manufacturing requirements ( 1.5 percent max . void volume).

However, the presence of voids can indirectly affect the CTE of a laminate by

initiating microcracks in the resin. Voids in the resin also tend to increase the PO-

tential moisture content of the laminate. Both the microcrack and moisture effects

are discussed in separate sections.

Layup Angle

One of the main advantages of laminated fiber reinforced composites is that mech-

anical and thermal response of the composites can be tailored directionally to satisfy

desiv- requirements. This is accomplished by varying the orientation of each layer

in a systenaatic manner to reach the desired effect. Figure 2 shows the variation

of C'FE utlidirectional and 2 8 angle laminates with fiber crientation (ref. 4 ) . The

composite CTE can exceed the thermal expansion properties of single layers at cer-

tain angles for the 28 angle laminates. This >hh:nomenon is predicted by laminate

theory and also substantiated by tests.

The sensitivity of the composite CTE to variations from the intended fiber ori-

entations can be severe. Although manufacturing tolerances for the layup angles

are typically +3O, this practice can lead to serious CTE deviations for dimension-

ally critical structures. For example, a 5* deviation in the layup angle for the

angle ply luminate shown in fig. 2 at approximately 8 = 4 5 O will cause almost an order of magnitude change in the value of the CTE of the laminate. Although

this is an extreme case, it nevertheless points out the degree of sensitivity of

certain classes of laminates to the change in the layup angle.

9, Fiber Direction

Figure 2. - Variation of expansional s t r a h with laminate fiber orientation (from ref. 4 ) .

Fabric Skewness

Woven laminae have become quite popular for use with structural composites.

The effect of fabric skewness is to render the lamina monoclinic (one plane of sym-

metry). Thus, the lamina will display two axial coefficients and an 'itdependent

coefficient of thermal shear strain. Such laminae make it i~npossible to fabricate a

symmetric laminate. The behavior of unsymmetric laminates is well known. Woven

laminae should be handled with great care to avoid the inducement of +dbric skew-

ness (e. g. , avoid pulling a fabric on the bias).

Stacking Sequence

In general, if a laminate is symmetric and orthotropic (three mutually perpendic-

ular planes of elastic symmetry), the coefficients of free thermal sfXain are not a *

function of stacking sequence. The presence of coupling response between bending

and extension behavior in an unsymmetric laminate will generally increase the co-

efficients of thermal strain (expansion or contraction), because the effective lami-

nate stiffnesses have been decreased. However, the laminate coefficients,of thermal

curvature are inversely proportional to laminate thickness and can be controlled by

increasing the number of laminae within the laminate. For couplec! laminates, the

cmfficients of thermal strain usually remain quite large compared to their sym-

metrical counterparts.

It is well known that if an unsymmetric laminate is restrained to closed geometry

or zero curvature (e.g. , cylindrical tubes or the unsymmetrical facings used to

fabricate a symmetric laminate sandwich structure), the general response will ap-

pear as if the laminate was symmetric. However, for truly sensitive desig?' ap-

plications involving CTEs , the reliability of this approach is questionable (ref. 5) . For example, if a tubular member of (03/+45)T stacking sequence is fabri-

cated to satisfy a particular design, the tube will not warp, bend, or bow as the

closed geometry of the tube satisfies the symmetry condition. However, because

in-plane symmetry conditions are not met in the wall, the tube will 'exhibit a ther- mal shear strain that will take the form of tubular twisting when exposed to ther-

mal environments. If the tube i s proposed to support an antenna, the deleteri-

ous effect of thermal shear strain is obvious. Thus, for msitive thermal expon-

sion designs, although unsymmetric laminates can be usec , they must be used

with great care.

Thermal Cycling

Thermal cycling is well known to have a significant effect upon the lam in at^!

CTEs. A s shown in refs. 5 , 6 , and 7 , the primary influence of thermal cycling is

to induce resin microcracking. When microcracking occurs, and as it progresses,

the laminate becomes partially decoupled , both thermally and mechanically. Resin

degradation proceeds gradually at first, and then somewhat more rapidly, and

can be detected by changes in the laminate thermal response. For single material

laminates, the value of the laminate coefficient of expansion drifts toward the uni-

directional CTE value of the material. This drift depends on many factors, in-

cluding materials, rate and number of thermal cycles, temperature extremes,

mechanical load level, and layup angle. For example, the drift of the CTE

of a cross-plied HMS laminate with (0/802/0)T layup cycled between -250°F and ':, \

250°F (116 K m d 394 K ) '.a!, been observed to stop after nine cycles. Laminates '

with more gradual change iayer orientations usually take much longer to /'

stabilize.

Temperature Depender. .: e

It is a common practice to report the CTE of materials as a single quantity;

these values are often used by designer, and analysts in the same manner. This

practice may precipitate significant errors in composite design because of the

temperature dependence of the thermal expansion behavior of composite materials.

This temperature dependence is mainly caused by the mechanical and physical

changes in the resin system. For this reason, the CTE values should be obtained

from thermal expansion test data for the specific design temperature range. The

CTE is a calculated value which is the slope of the thermal strain-temperature

curve between two temperatures, This temperature dependence may be ubserved

on lntlny of the curves presented later in this document.

Moisture Effects

The dimensional stability nf composites is highly affected by exposure to com-

plex hygrothermal histories. Moisture causes swelling and plasticization of the

resin system. The swelling phenomenon alters internal stresses, thus causing a

dimensional change in the laminate. Coupled with plasticization of the resin sys-

tem, t, . rmanent dimensional changes of lip to 30 percent have been observed in

laboratory experiments after exposure to complex hygrothermal histories (ref. 8).

The importance of moistlire on the thermal expnnsion behavior of graphitelepoxy

composites is denanstrated in a study reported in ref. 9. The data snc-vn In

table I , .-.xtracted from the reference, demonstrate that dimensional changes

caused by a temperature change of 118OF (339 K ) are 2.09 P C , wliich is much

less than the dimensional change due to moisture exposure (38.4 CI c ) . It is there-

fore important to account for nroisture effects in assessing dimensional changes

due to thermal effects,

TABLE I. - CALCULATED STRAINS IN GT701339 [(0/90)21,

LAMINATE UURING HYGROTHERMAL CYCLING

Sequential hygrothermcll history I Moisture content, percent water

I After exposure to 75OF ( 297 K) / 95 percent RH I ; for one year

After heating to 160°F (344 K) for 20 minutes

After cooling to 7S°F (297 K) from 193OF (362 K) stress-free temperature

1 After desorbing at 125OF (325 K) for 128 days ] 0.0 1 7.22

I After cooling to 75OF (297 K) I 0.0 I 8.11

0.0

Viscoelasticity

2.09

A s stated above, changes in the internal stresses due to moisture and thermal

environment can result in significant dimensional changes in composite laminntes.

Internal stress levels also change due to the viscoelastic phenomenon called the

relaxation of the resin system. In the true sense, relaxation of the internal stresses

is a continuous process even without any mechanical, thermal, or moisture excur-

sions. This process is usually minimized by placing fibers in the direction where

dimensional stability is required. Graphite fibers are known to have negligible

viscoelastic behavior.

PREDICTION OF CTE

The analytical methods used in the prediction of CTZs are presented in the

following paragraphs. This review includes formulations based on lamination

theory and the micromechanical approach. A more complete presentation of analyti-

cal methods discussed here can be obtained from the references listed later in this

document.

Successful prediction of laminate thermal properties by the lamination theory is

highly dependent on defining accurate mechanical and thermal properties of indi-

vidunl layers. In almcst all cases, this is accomplished by testing unidirectional

laminates. The micromechanical approach, where prediction is based on the

7

properties of constituent materials, is seldom used because of several factors.

These factors include unavailability of constituent material properties, uncertain-

ties in fiber data. and the inability of the micromechanical approach to define the

i:ansverse properties of the unidirectional laminate with high accuracy.

CTE by Lamination Theory

Classical lamination theory is based upon the concepts of linear ~nieotropic

elasticity. Beceuse of the stress and deformation hypotheses tt ~t are an insepar-

able p ~ r t of c l~ssical lamination theory, a more correct name would be classical

thin lamination theory , or even classical laminated plate theory . Strictly speaking,

this theory is valid only for a solid homogeneous continuum, which is subjected to

homogeneous boundary conditions. The approach and background for this

method are well developed in refs. 4. 7 . and 10 through 12.

The general constitutive equation for a laminated plate is given by:

This expression is used to relnte the laainate mechanical s t ress resultants nnd - stress couples. Ni and Mi . to t h e lnminnte middle surface strains and curvatures. - t- * and K i m . The laminatc thermal stress resultants and stress couples are de- i fined for n state of uniform (i.e. , homogenous) temperature e h ~ ~ i g e :

N -K -K s v T = AT C '* i K= 1 Qij ( lj [ z K - z K - l ] Thermal forces

A T N K K , MT = -- Gij lz;( - Z K - l ] Thermal moments

1

where.

* T ~ ~ ~ ~ ~ ~ ~ ~ ~ is usually defined crs the stress free temperature for the laminate,

8

The laminate atiffneee matrices are R~RO def'ined:

Extensional l~tiffheesea

N -I< " Bil

1 Coupling stifmeaaes = 112 Qij Z - ZK-, K= 1

N 3 ] Bending stiffheases Dii = 113 [ZK - ZK,l K=l

The geometric representation of 8 lami~lnte i s depicted in f i ~ . 3 . Both the

l ~ m i n ~ t e nnd lnmina thicknesses ( h and hli) mav be defined thmugh tne use of the

following equntion :

2*:>

T ( X I /- Lamina number

- li Note that Q~ snd a are e~pressed in terms of the laminate coordinate sys- i j K tem. The equations necessary to obtnin the trnnsformed lamina st ifhessea (q,, )

'J nnd tra~iaformcd coefficients of free thcrmRI strain ( 6 ) are given in table 11.

Tlrese trnnsformnttons nre linear and homogeneous. The invariant forms of the

equntions shown in tnbie I1 wem first given by Tsni nnij Pagan0 ( m f . 13) in the

9

case of 0 !! , and Halpin and Pagano (ref. 14) in the case of . Note that the 11

equations given in table I1 are sufficient to describe the transformation relation-

ships for orthotropic laminae. This is a special, but highly practical, case. \.

- K TABLE 11. - TRANSFORMATION EQUATIONS FOR 0; AND 0

FOR THE K~~ LAMINA

where : U1 = 118 (3Q11 + 3Q22 + 2Q12 + 4666)

U2 = 1!2 (Qll - Q22) W1 = 112 ( Q1 + 5)

-K For Q!! : U g = 118 (Ql l + QZ2 - 2Q12 - 4666) Forai : 11 W 2 = 112 ( 5 - a2)

U4 = 118 ( e l l + Q2, + 6Q12 - 4Q66)

r)

Sin4 OK

0

0

0

0

u 3

-u3

0

0

0

Sin2 OK

0

0

0

0

112 u2

112 U2

0

0

W2

Cos2 OK

U 2

-U2

0

0

0

0

W2

0

Term

-K Qll -K

22 -K

12

'!6 -K

16 -K

26 -K CY 1 -K &2

9 6

C O S ~ OK

u 3

U;

-"3

-"3

0

0

0

0

0

Rotation invariant

1

"1

u 4

0

0

W1

W1

0

To determine the laminate coefficients of free thermal strain (expansion,

contraction, o r shear) and free thermal curvature (bending o r twisting), the m e -

chanical s t ress resultants and stress couples must be equated to zero:

If equation (9 ) is now substituted into equation (1) and both sides of the

resulting equation are divided by AT, the desired solution is obtained :

where : - ,* i (y = -

i AT 1,aminate coefficients of free thermal s t rAin

-* I( X = -

i AT L~minclte coefficients of free thermal curvature

Equation (10) can now be used directly and solved by any algebraic method.

including e *;rix inversion.

1,aminn Micromechanics Formulation for CTE

There nre two bnsic approaches to the micromechanics of composite materials

(ref. 7 ) :

( 1) Mec ' , inics of materitlls

( 2 ) ' "asticity.

Tlit. mechanics of materials approach embodies the usual concept of vastly

s'-iplifying assumptions regarding the hypothesized behavior of the mechanical

system. The elasticity approach mny include ( 1) bounding (variational) tech-

nic,ues. ( 2 ) exnzt solution, and ( 3 ) approximate solutions.

Irrespective of the micromechanical approach used, the usual restrictions on

the composite material are :

Lamina

Macroscopically homogenous

Linearly elastic

Macroscopically ort hot ropic

Initially stress- free

Reinforcement - Resin

liomopneous Homogeneous

Linearly elastic Linearly elastic

I sot ropic Isot mpic

Regularly spaced

Perfectly aligned

Although the expressions given in the literature for lamina CTEs vary, the

results of Schapery (ref. 3) are widely quoted. The equation for the longitudinal

CTE takes the form :

where :

EF = Fiber modulus

Em = hlntrix modulus

cu = FiberCTE F

CYm = Matrix CTE

L ' F B L ' ~ = Volume frnctiol.~

This equation is quite practical and is suitable for preliminary design. Similarly,

the transverse CTE can be ~pproximtlted by (ref. 3):

However, care must be exercised in using this equation. I t is at best an ap-

proximation.

References 15 through 20 contain additional information on micromechanical

methods and CTEs.

THERMAL DIMENSIONAL STABILITY AND TUNING FOR ZERO CTE

!

This section discusses the thermal dimensional stability of laminated structurtis,

including the tuning of laminates to obtain a near-zero CTE with a minimum effect

upon structural efficiency. 'I

Thermal Dimensional Stability

Factors affecting the CTE of a composite were discussed previously. Other

factors include chemical and physical changes in the resin due to aging and solar1

physical radiation. It is significant to note that even during a CTE test under lab-

oratory conditions, the test specimen is not free from some of these effects, sug-

gesting that the measured thermal strains in reality are the sum of strains caused

by di.fferent effects. Perhaps the most significant design criterion for composite structures requiring

extreme dimensional stability is the determination of the specific mechanical and

phy~iical environmental spectrum the structure wi l l go through during its lifetime.

Once the environmental conditions are known, mechanical, physical, and thermal

beb'avior of the composite structure can be determined using analytical and experi-

mental techniques.

A s the starting point, the designer selects the material and laminate configu-

rations. Stiffness, strength, and CTE requirements determine the type of fi-

brous materials used in the structure. By determining the number of layers and

properly orienting them, one can achieve a near-zero CTE laminate that will satisfy

both the stiffness and strength requirements. Usually, there is more than one

laminate configuration that will satisfy the preliminary requirements. For better thermal dimensional stability, the most likely laminate to succeed is the one that

is least sensitive to changes affecting the CTE of the laminate.

A somewhat similar approach has been suggested and shown in refs. 2 1 and 22.

A study was conducted on general (Oil?8)s laminates to establish a configuration

with a zero CTE that also satisfies the required mechanical properties. Results are shown in fig. 4.

Laminates with (012 8Is, (02/i8), , and ( 0 3 / 2 81, layups satisfy'the zero CTE

requirements for a specific 8. Also, the sensitivity of laminates to ply orientation

Design point sensitivity

o. 8 4 0.01 3ldeg \

Ply orientat~on, + 0, deg

Figure 4. - Sensitivity of various laminates to layer oi'ientation 8.

decreases with an increase in angle. For example. the slope of the expansion

curve with the ( 0 3 / t O) , layup is smaller than for the other two laminates men-

tioned above at zero CTE ; thus , less sensitive to changes in angle 8 . However, as

angle @ gets larger, the shear stiffness of the laminate diminishes. To counteract

this tendency, a 90° ply is added to the (03/+76)s laminate. The resulting lamin-

ate, (031 257.5190) . provides longitudinal extensional stiffness behavior nearly S

similar to the (03/278!b laminate, but i ts shear stiffness is doubled. Results of

computations for the two laminates are shown below:

Once a particular configuration is chosen, further sensitivity studies may be

performed to establish the dimensional stability of the laminate as influenced by

Material and layups

HMSl934 (03/?76)s

HMSl934 (03/+57. 5/90),

G x ~

(x 10 '~ /9 )

0.229

0.229

Msi

1.15

2.31

(x I O - ~ / K )

(0.41)

(0.41)

E X

(GPa)

(7.8)

(15.7)

Msi

- 16.6

14.4

(GPa)

(112.8)

(97.8)

other factors. A typic81 CTE sensitivity study is shown in table 111. In each case,

the baseline layer properties are increased 10 percent to obtain their effect on the

composite CTE.

TABLE 111. - (03/?57.5/90)s LAMINATE CTE SENSITIVITIES TO LAMINA

PROPERTIES, BASELINE CTE = 0.41 x IO-~!K (0.229 x ~ O - ~ I O F )

Tuning Process

The tuning of 8 composite structure to obtain a nesr-zero CTE with a minimum

effect on structural efficiency is not an easy task. Most conventional methods to

drive or tune the CTE of the laminate to zero levels, such as changing the layups

with different CTE characteristics, will usually result in a sacrifice of structural

efficiency. '

Theoretically, one of the most effective methods to achieve tuning without

sacrificing the structural efficiency is to replace a percentage of the laminate

fibers with an equally stiff but different CTE material. Results of a study show-

ing the effect of adding boron, silicon carbide (Sic) , FP (A1203), aluminum, or

steel fibers to replace a percentage of graphite fibers in an epoxy laminate are

shown in figs. 5 through 8. Specifically, laminates of VSB -32 pitch and GY 70

fibers in an epoxy resin were examined. Results are shown in figs. 5 through 6

for unidirectional laminates and in figs. 7 and 8 for (90/0/ laminates.

Material properties used in the analysis are given in table IV.

i

Lamina properties

E22

12

'32 -.-

Change in laminate CTE

(x ~ o ' ~ / ~ F )

-. = -0.056 (lO%)Ell -- = +!).048 ( 10%)EZZ

a(CTE) = +0.001 ( 10%)G12

3 = +o.o2g (10%) a1

a = +0.052 ( 10%)crz

(X I O - ~ / K )

-0.10

+0.09

0.002

0.05

0.09

1 o6

too i i E" r

0 0 - P -

1 I I 1 9 5 90 85 80 75

Craphite fiber ( 8 )

Figure 5 . - Effect of replacing GY70 fiber with other selected fibers in a unidirectionol laminate.

Sic- N FP

I

. 0.1 CTE - 200 2

W Aluminum

G. 2

Craphite f iber , (t)

Figure 6 . - Effect of replacing VSB- 32 fiber with other selected fibers in a unidirectional layup.

Aluminum

400 P

CT E 0 .2 300

0 .2 o0 plies 0.020 In. (0 .51 mm) thick

0 . 4 ' I I I 1 I

9 5 90 85 80 7 5

O0 Graph i te f ibe r . (%)

Figure 7 . - Effect of replacing 0 GY 70 fiber with other selected fibers in a (9010190) layup.

x 10 6

1.8

1 .6-

1.4- O S 8 - N

% 1.0- W

0.4 0.6- 0 . - 0.7

O0 plies 0.020 ~ n . (0 .51 mm) thlck w 0.2-

0 - -7-1-- 9 5 93 8 5 80 7 5

0' Craphi te f iber , (\)

Figure 8. - Effect of replacing 0 VSB-32 fiber with other selected fibers in a (9010190) layup.

For G Y 70 (fig. 5) , approximately 20 to 22 percent of the graphite must be

replaced with boron. S ic , or FP to achieve a zero CTE. This is accomplished

with almost no reduction in the specific modulus of elasticity for boron and about

a 5 percent decrease for Sic.

Only about 7 or 8 percent of boron or Sic is required to obtain the zero CTE

in unidirectio:kal VSB-32 graphite epoxy (fig. 6). A very small decrease in spe-

cific stiffness is obtained as a result of using S ic , and a small increase in specific

stiffness is achieved with boron fibers.

Steel and aluminum fibers were introduced for comparison pupposes. When

used to leeplace the VSB-32 fiber, 6 percept of the steel fibe- i c ~aequired as com-

pared to 7 or 8 percent with boron or Sic. The decrease ir, - :fit modulcs of

elasticity is approximately 9 percent.

Similar results were obtained for a ( 9010190) laminate in which each of the

90" plies is 0.003 in. (0.076 mm) thick and the O0 or longitudinal ply is 0.020 in.

(0.51 mm). For this portion of the study, a percentage of the O0 fibers was re- placed by the hybrid fiber. These results are shown in figs. 7 and 8. In fig. 7,

note that the replacement of about 1 2 or 13 percent of the GY70 fiber with SiC or

boron will produce a zero CTE. The specific modulus of elasticity will decrease

from 563 x lo6 to 551 x 10 @ (143 to 110 for the boron or SiC lbmlin . 3

replacement.

For the VSB-32 fiber (fig. 8). the CTE of the (90/0P90) materip1 is very ciose

to zero. The addition of any replacement fibers will make the laminate CTE posi-

tive. It should be pointed out that the VSB-32 is still developmental. Any devel-

opmental increase in fiber modulus will make this (019010) laminate negative: the

addition of boron or Sic fibers will make the CTE of the laminate zero and alrn

provide an increased stiffness. Ea An examination of the Tgiven in table IV indicates that an efficient proce-

dure for tuning a laminate with a negative CTE is to select fibers with a high

positive Ealp for partial replacement of :he O0 fibers, and vice versa.

Novel Approaches to Tuning

Some rather innovative techniques have been developed by researchers to

obtain near-zero CTE laminates, or structural configurations. A tunable end-

fitting principle for struts is described in ref. 23.

Another novel approach to the tuning of composite struts is described in

ref. 24. In particular, a ttdual-alijha" concept is described in detail and a

"variable-alpha" method is also briefly presented. The dual-alpha strut method

is a relatively simple concept, which enables the attainment of a specific expansiv-

ity from parts whose as-cured CTE variability exceeds the design allowables.

This method uses a laminated construction t1.d exhibits expsns i~ tties along a

htrut length that are different from one another on either side of a transition zone

length. In this manner, the expansion charrccteristics on either side of a trdnsi-

tion zone bound the desired end-item expaneivity. A11 final tuning :i.e., CTE

adjustment ) is then accomplished in the as-post -cured condition, thus accounti~g

for most material and process variables (e.g. , fiber volume). Tuning is accom-

piiskcd usiiig the as-cured material only. Addition?' parts or t rning "spacers,"

which are usually of a different material and therefwe different tharmd diffusiv-

ity , are not required. This thto-.i tends to enhance the thermal stability of the

structure when subjected to transient thermal environments.

TEST METHODS

This section presents a brief discussion of the various test methods and

techniques used to determine the c~mposite CTE. The determiriation of CTE re-

quires an approach that uses both length arid temperature measurement tech-

niques. The quality of the CTE data is directly dependent upon the accuraqr

and resolution polential of the equipment utilized. Since composite materials, as

a class, may e ~ h i b i t both very low and very high CTE values, it is often judicious

to use combinations of test methods in the pursuit of a cost-conscious data-

generation test pian. Wolff (ref. 25) provides an excellent and comprehensive

discussion of composite CTZ test techniques. Much of this discussion has been

extracted from this reference.

Length Measurement Techniques

Table V (formulated frc .r refs. 25 and 26) provides a surnmpry of the general

metrological groups and dimensional measurement techniques in accordance with

their principles of operation. The accuracy of each method covers wi2e limits and

2 0

TABLE V. - SUMMARY OF TECHNIQUES FOR LENGTH MEASUREMENT

Contact, no contact,

or s m d l gap, < 10-

A. Electrical transdrcers

7

Accuracy' or

range (%I

5 ld7 (0

( r )

lo'10

10-

1%

0.01%

3 %

R a n g e , m or A E (%)

Measurement technique

Contact

Contact

Small gap

Small gap

Contact

Contact

Small gap

Contact

20%

1%

10-

10-

los5

3

1 0 ' ~

10-

Resistance strain gages

Semiconductor strain gages Capacitance

LVDT (dilatomc+ers )

Electronic gages

Resistance transducers

Variable impedence

Variable reluctance

Resolution, E or ( m )

( r )

lom9 (c)

lo'11

10-

10-

10-

transducers - optical

3% lo2

10-I

lo -2

10-

l om3

10-

10-

10%

-1%

-1%

B : Electrical

10-

0 .5%

0.1%

5 x

10-

lo-*

1 0 ' ~

(1 ) Non-interferometric

Autocollimator

Fiber optics

Optical levers

S ' :ale beam shadowing Scanning beams

Detector arrays

Photoelectric

No contact

Small gap

No contact

No contact

No contact

I No contact

Small gap

No contact

Contact

Contact

No contact

3 x 10' *

2 x 1 0 - ~

10-

10-

10' No contact

1 0 ' ~ No contact

micmscope I l o 9

( 2) Interferometric I Michelson

Fabry - Perot

Fizeau

Holographic

Speckle

Moire

10- a

1 i? - 7

10-

TABLE V. - Concluded

C . Miscellaneous optical

i s , in general, a function of e q ~ p m e n t modifica:ions, accessories, andlor the in-

genuity of the particular designer or user of the apparatus. Several methods suit-

able for linear displacement measurement on composite materials are described in

the following paragraphs. Where possible, a primary consideration for a test tech-

nique is the elimination of contacts to the test sample or structure ( e . g., see

ref. 25 and table V ) .

no contact, o r small gap,

. .

Electrical Transducers for Displacement Measuremenl

Measurement '

technique

No contact

No contact

No contact

Resistance strain gages are attached to the test sample by adhesive bonding.

These gages are then used to determine the average strain (AL/LD) over a small

area ( i . e. . gage area). Multiple gages can be employed to monitor displacements

at multiple sites or in multiple directions, and to provide a temperature compensated

circuit in a Wheatstone bridge unit. This approach is particularly useful for com-

posite materials if sufficient care is taken to conipare identical gageladhesive sys- 22

Range, m Or ($1

Resolution, (m)

lo'10

10-

1%

10-

. Telemicmscopes

Dial gages

Air gage

Micrometers

Accuracy, m o r

range ($1

>log5

.

Venier scales

Profile projectors

Micrometer slides +

10'~

10'

3

Diffraction patter^ analysis

Ellipsometry

Spatial filtering

1

10‘

10'

10-I .

10'~

10- lo - 7 - 10

3

8 x

1 0 ' ~ -

2 I contact I No contact

. 1 :i:i 1 -: Small gap -

tems on a reference material ( e . g. , fused silica, in the same bridge circuit).

Potential problems with the use of these resistance s t r d n gages include gage vari-

ability, local stiffening of thin sections, moisture, adhesive post cure effects, elec-

trical heating, lead wires, and cwntact resistances. Further comments . including a

brief discussion of s~.miconductor strnin gages. can be obtained from refs. 25 and

27.

Cap~.citance methods, or capacity cell methods, can d s o be used to determine

the composite CTE. The principles of operation involve the use of parallel plate

condensers. The capacitance changes of these plates can be measured as the fre-

quency changes of an LC oscillator circuit, where the plate spacing is proportional

to the cheinge in frequency. Calibration is required using identical sample materials

on the capacitance cell /plate system. This technique is essential!^ a differential

one, as described in ref. 25. requiring knowledge of the cell position (upper capac-

itance plate) during any r u ~ l . Possible sources of error for capacity cell methods

include edge capacitance effects. parallelism, sample sizes and shapes, and the time

required to stabilize temperatures and record readings.

Linear Variable Differential Transformers (LVDTs) are used widely RS a stan-

dard contact met hod for determining relative length changes. In practice, voltage

is induced in the secondary winding of the transformer by the position of the axial

core of the transducer. Commercial instruments (ref. 25) usually have n dc oili-

put proportional to the axial core position relative to the electrica! center. Rlany

dilatometers operate with LVDTs as the sensing elenlent that is attached to a

pushrod placed against an espanding sample in a furnace. Dilatornetera using

LVDTs are marginally useful for low CTE nlaterials because of contacting errors ,

friction, aligpment. and tempernture effects on the LVDT itself. However, LVDTs

have potentially infinite resolution, since the signal output is limited only by the

ability to measure dc voltages. and the vibration stability of the core within the

LVDT. Sources of error associated with the use o!' LVDTs and dilatometers, in

addition to those mentioned above, include the power supply, recording instru- ? " ,

, . ments, and the standard (e. g. . qut~rtz) used to calibrate the LVDT-dilatometsr i"' . system.

The majority of the LVDT-dilatometer test data given later in this report were

obtained with the electrical (LVDT) -mechanical (quartz pushrod) system shown in

fig. 9. The basic approach is described in ref. 26 (ASTM method of rest 228-71).

Electrc sensor

l nvar bracket

Quartz outer tube

l nsulation

mechanical (LVDT) Quar.2 inner (pusk. rod)

Sample

Heater

Cooling

tube

coils

Figure 9. - Electmrneuhanical dilatometer .

The apparatus shown in fig. 9 uses a specimen 12.00 fl.010 in. long and 1-in.

wide. Prior to measurements, the samples are preconditioned in the apparatus for

124 hours at 210 flO°F (372 +6K) with a dry helium purge. Each specimen ir then

subjected to two individual cycles during testing, since it is recognized that CTE

tends to change with humidity and thermal history. The largest such changes

usually occur during the first cycle.

Other dilatometric CTE methods used to generate the LVDT-dilatometer test

data include the Netzisch ciilntometer, modified Leitz dilatometer (fig. lo) , ez' t k

dilatometer used in a thermornechaiiilidd analyzer (TMA) .

Level sensor

-- Calve. prism

Figure 10. - Modified Leitz dilatometer.

The Netzsch dilatometer system basically consists of a fused silica stand and

pushrod between which the test sample is inserted. The movement of the pushrod

is transmitted to an iron core at the top of the rod that changes the inductance of

25

a transducer, thereby detuning a balanced ac bridge circuit, the rectified

output of which is proportional to the specimen afspiacement.

The modifled Leitt dilatometer system shown in fig. 10 ia a mechanical-

optical type method. This instrument is a typical quartz tube dilatometer in which

the relative distance between ends is transmitted to the remrding system by

quartz rods tkat contact each end of the specimen. Relative movement of the

quartz rods is transmitted to a rotatable prism by a mechanical lever system

that magnifies the specimen displacement. A light beam projected through the

prism passes through a lens system that further magnifies the displacement.

Specimen size is restricted only by the size of the dilatometer. An unmodified

pushrod type Leitz dilatometer is described in ref. 28.

The use, description, and explanaticn of the TMA method is well stated in

ref. 29. This method is not recommended for measurements of low CTE materials,

as the basic restrictions on specimen size alone may introduce a rather large per-

centage of error. Finally, electronic gages are often used for gage block compara-

tors. These gages represent an extension of LVDT - type sensors with exceptional

care taken to ensure accuracy and repeatability of readings.

Electrical-Optical Transducers for Displacement Measurement

Non-Interfernmetric Methods. - Auto collimaters use collimated light beams to - detect small angular displacements of a reflecting surface area as small as

3 3 x 10 m in diameter. A sensitivity of 0.01 arc sec corresponds to a strain of

-4.8 x lo'* m /m. This is achievable only with the use of electronic sensors. Visually, only strains of can be detected (ref . 25). These instruments are

suitable for monitoring the distortions of large structures for straightness or

flatness.

Fiber optics bundles provide a noncontact method to provide optical measure-

ments over distances of lo-' m . The use of fiber optic methods can produce res-

olutions comparable to LVDTs (ref. 25). An advantage of this approach is that

light beams can be diverted to reach otherwise inaccessible locations.

Interfernmetric Methods. - The interfernmetric method has been recommended

by the ASTM (ref. 28). Its upper temperature of application is determined by

the optical parts of the interferometer (e. g. , 1,000 K for vitreous silica). The . various interfernmetric methods are described in refs. 25, 28, 29, 30, and 31.

An interferometer recombines the two or more parts of a split light beam into

a third beam whose intensity varies sinusoidally as the optical path length differ-

ences, relative to one (reference) beam, change by multiples of the wavelength ( A ) .

The advent of the laser (laser interferometer) has provided the increased coher-

ence needed to permit the widespread use of this approach for a variety of dimen-

sional testing applications.

There are many types of interferometers, but thermal expansion measurements

mainly employ the original Michelson interferometer (two-beam), and the Fabry-

Perot and Fizeau interferometers (multiple reflections). It is fairly easy to count

intensity variations, or fringes, as a sample expands or contracts when subjected

to thermal excursions. This implies an immediate resolution potential of m . For low expansion materials, however, fringe interpolation techniques are re-

quired. These include analysis of volt~ge outputs from photodiodes or photo-

multip!iers, polarization and phase modulation techniques, and analysis of photo-

graphic plates (e. g. , microdensitometry). Values of A1100 - X 11000 are

presently the state of the art.

The Michelson interferometry method provides a measure of the relative dis-

placement of the two reflecting surfaces. Figure 11 (extracted from ref. 25)

represents n geometrical arrangement applicable to the study of hollow structures

(e. g. , tubes) . Fabry-Perot il~terferometry met hods require contact, but offer

higher resolution potential than tne Michelson approach. Fizeau interferometry

(usually restricted to small samples) normally yields equal thickness circular

fringes of very large radii of curvature (Newton's rings) depending on the con-

tour of the reflecting surfaces.

Principal disadvantages of interferometris methods include the exposure of the

measuring equipment to test environments, requirement of highly specialized, ex-

pensive equipment and difficu:ties , such as variation of air sources (e. g. , changes in index of refraction),and target perturbations which can obliterate the

time devoted to careful test setups.

Class bell jar

Damping a

Mgure 11. - Laser interferometer and dimensional stability test apparatus.

Timer printer

2- . - Control data

computer analysis

4

- 1 I

Chart - recorder i

Miscellaneous Op kal Methods for Displacement Measurement

Another important method ia the diffraction pattern analysis which has been

used to determine the CTE of E and S glass fibers. A laser beam illuminates the

test object directly, resulting in a far-field diffraction pattern which is analyzed. I

When the diffracted light is collected with a lens, the pattern formed at its focal

length is equivalent to the Fourier transform of the test object. Further comments 1 can be found in ref. 25, I

Other methods, described sufficiently elsewhere, are not covered here.

(See refs. 25, 26, 28, 29, and 30. ) In general, the telemicroscope met hod is

directly applicable for CTE determinations of fibers, whereas, for example, dial gages (coupled with dilatometers as discussed in ASTM D-696, ref. 32) are suit - able for the CTE determinations of resins, or very high CTE laminates.

THERMAL EXPANSION DATA

This section presents a summary of data relating to the CTE of fibrous cam-

posite materials. The CTE of reinforce~ilrrlts and some resin systems are included

in addition to the fiberlepoxy data. The data presented were obtained as a result

of a literature search, and these data have been supplemented with properties from the LMSC data bank. Fibers and resins that are no longer available were

eliminated during the screening process.

The properties are presented in two formats. Tabular values of the CTE

are listed for various temperatures as available from the literature. In addition, plots of free thermal strain (i.e., ALIL) as a function of temperature are also presented as they are available. In some cases, the data have been replotted

in an effort to achieve some consistency in the presentation. In other cases, the curves have been reproduced as they occurred in the original presentation.

Tables VI and VII list CTE values for various neat resin systems and fibers,

respectively. Fiber materials include K-evlar- 49, boron, graphite, and glass. Table VIII is a list of available composite thermal test data for unidirectional

fibers and woven fabrics in epoxy matrix. Each table alm includes test methods with which the CTE values have been obtained, and the origin of data (i.e.,

references ) .

TABLE V1. - COEFFICIENT OF THERMAL EXPANSION - EPOXY RESIN SYSTEMS

Plots of free thermal strain as a function of temperature for various uni-

directional and fabric composites are given in figs. 12 through 38. These plots are useful in determining the CTE of a lamina for a temperature range.

that is not included in the tables. The value of the CTE is obtained by deter- nining the slope of the curves between two temperatures.

Resin

Nmmco 2387

3M PR 279

Ferro CE-3305

Temperature, K

200 250 300 350 400 x 1 0 - ~

200 - .

100 - 0 ' $

A - - d

-100 - - - -

-200 - - (Union - -

- 300 -100 0 100 ' 200 300

Temperature, O F

Temperature

Carbide

O F

RT 350

RT 350

68-212

Figure 12. - Thermal expansion of Kevlar 49lX904B (120 etyle) fabric.

K

450

4 50

293-373

CTE

data 1

Test method

LVDT Dilatometer

LVDT Dilatometer

LVDT Dilatometer

- - -

h0-qap

2 7 38

25 7 0

35.8

Source

Ref. 33

Ref. 33

Du Pont

: r ~ O - ~ / K

(48.6) ( 68.4)

(45) (126)

(64.4)

TA

BL

E

VII

. - C

OE

FF

ICIE

NT

O

F T

HE

RM

AL

EX

PA

NS

ION

-

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IBR

OU

S

RE

INF

OR

CE

ME

NT

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Te

st M

eth

od

Tel

ern

icro

sco

pe

Un

kn

ow

n

1 Te

l~m

icro

sco

pe

Un

kn

ow

n

Dif

frac

tio

n

pa

tte

rn

Dif

frac

tio

n

pa

tte

rn

Un

kn

ow

n

1 Un

kn

ow

n

Un

kn

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So

urc

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Po

nt

Ref

. 33

I Her

cule

s, I

nc

.

Cel

anes

e, I

nc.

Ref

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1 0 w

ens-

Co

rnin

g

Ref

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Un

ion

Carbide

Ref

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Rei

nfo

rcem

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Kev

lar-

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Bo

ron

AS

HT

S

HM

S

GY

70

E-G

lass

S - G

lass

S- 2

-Gla

ss

Pit

ch (

P7

5S

)

Pit

ch

(95

msi

)

Pit

ch

(50

rns

i)

Th

orn

el

50

(PA

N)

OF

32 t

o 2

12

212

to 3

92

392

to 5

00

RT

RT

RT

RT

RT

RT

RT

RT

-300

to

+30

0°F

RT

RT

RT

Te

mp

era

ture

K

27

3to

37

3

37

3to

47

3

473

to 5

33

89

to

422

x ~

o-~

/.F

-1.1

-2

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-2.8

2.7

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3

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2.8

3.1

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CT

E x

10

-~

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4

4.86

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1

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5.58

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III.

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abri

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Kev

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Dir

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eg

ree

s

0 0 0 0 90

90

90

90 0 90 0 90 0 90 0 0 0 0 0 90

90

Ter

np

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-11

0 t

o 2

12

-11

0 t

o 2

12

-31

9 t

o 2

48

0 t

o 1

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68 t

o 2

12

-31

9 t

o 2

48

194

to 3

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0 to

151

68 t

o 2

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68 t

o 2

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RT

RT

-65

to1

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-65

to1

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72

100

200

300

350 72

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ure

K

194

to 3

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194

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78 t

o 3

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to 3

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1 1 ' AST

M D

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i

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36

i \ ) Ref.

38

1

- -

8 0 b rl

E 6 m 6 . . ccc +I ccc

8 uu d S 2 / 0--

B QD CY CY k k

5 I Q,

E 3 0 3 C, C

X * N Q n

a C; L2 3 4

w 6 '

al k 3 ' a k al a 5 Q, t3

- x -.

(O

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&

0 - 3 - 4 O + @ =

0 ' tr

N N I 0 I I I t-

(I)

(O 0 Q, b Q, Q) (3 (*: d ( o N Q o ~ o v ) ( o ~ o o o ~ * ~ - o ~ ~ ~ N N P I C I ) ~ . d i 4 A & $ d h ' d o ' d n ' d d d o d d G m n

4 e U e 3 d N N 1 I N I N c 3 CU C Y m H

-

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a- n 3 I-

g g g g o o o a o o o a m U J g o g ~ 3 ~ ~ % 8 S

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m * V) \

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s 5 : ~ 8 o w 0 - m a (O s m O N 9:

a \ a ua V) % %

nd = y g %

& 0 0 0

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x U CI c.c w

I

* O

O d Q O ~ m m N ~ O O m b O o d 4 d W V ) V ) . . L c . ~ : , e ; ; d ; d ; d A r ; d d d o o d d i ~ x d d , d d d 1 4 1 4 1 4 4 4 d d d - w ~ ) p l - ~ ~ ) r n o o 0 O W * (O ~ ) m m a ~ ) m m 1 n t - ~ r - u , 9 r r m m c u m m c ) m - P w ~ ~ a a - P m m

CY CY *, C, 0 0 s O S S B S 8 2 B e 0 e + - Q1 r n ( O ~ c o ( O ( O ~ . 4 d + ~ ~ b Q I Q ) 0 0 I n ( 0 0 Q b ~ 1 0 (D ( O ~ . ( d Q ) Q , Q ) r n Q ) Q , Q ) c t , o , d d Q 1 o o , o Q ) e N m + m d m c ~ m m o o c u a o ~ ~ m c u c ~ w ~ c u c u * -

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TA

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00

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. 41

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.5

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1 Unknown

1 Hexcel

arp*

-

.f , * , , , o O ~ ; / O 5

(Ref. 44)

-100 0 100 200 300 400 Temperature, O F

Figure 13. - Thermal expansion of unidirectional Boron I5505 tape.

Figure 14 . - Thermal expansion of Thornel 3001Narmco 5208 tape (0° fiber direction).

Temperature, K x 300 350 400 450

(Ref. 43)

60

40

4 \

4 20 a

0

-20 0 50 100 150 200 250 300 350 400

Temperature, O F

1 1 1 1

Heating - ---- Cooling / M -

- -

- r - 0 .-/

- I I I 1 I I I -

Temperature, K

x 10i6 200 I 350 I 400 I I 450

---Cooling 1st cvcle

=! II q 1000- -

, (Ref.

- 1 0 0 0 ~ 1 I I 1 I I I 1 50 100 150 200 250 300 350 400

Temperature, O F

Figure 15. -- Thermd expansion of Thornel 3001Narmco 5208 tape (90° fill direction).

- c Temperature, K

(Ref.

Temperature, OF

Figure 16. - Thermal expansion of HMF 330C ICE339 fabric (T - 300 fiber) ( O0 warp direction).

Temperature, K X 200 250 300 350

Ref. 45)

-100 -50 0 50 100 150 200

Temperature, O F

Figure 17. - Thermal expansion of HMF 330ClCE339 fabric (T - 300 fiber) (90° fill direction).

Temperature, K x lo-6 280 2 90 300 31 0

Figure 18. - Thermal expansion of HMF 330C 1934 fabric (T-300 fiber) (0° warp direction).

Temperature, K x lo-6 280 290 300 310

60 -- 1 1 I 1

40 - 20 -

A o r \

- -;(Ref. 36)

-60 ' 1 1 I 1 I I 30 40 50 60 70 80 90 100

Temperature, O F

Figure 19. - Thermal expansion of HMF 330C I934 fabric (T-300 fiber) (90° fill direction).

Temperature, K -

Temperature, O F

Figure 20. - Thermal expansion of unidirectional HTS-213501-5A tape (0° fiber direction).

Data )

Temperature, K X lo-6 200 250 300 350

1000 - - 0.

i -1 Q -1000 - -

-2000 - - ( LMSC - unpublished data)

- 4000 I 1 1 I I 1 I I 1 . -200 -100 0 100 2 00

Temperature, OF

Figure 21. - Thermal expansion of unidirectional HTS- 2/3501- 5A tape ( 90° fiber direction) .

Temperature, K x lo+ 120

150 2 00 250 300 350 400 I i 1 I I I .

- -

- - 40 - -

J \

- J

- Q O h

- - -40 - , ( LMSC

unpublished - I 1 I I data)

- *O -2:o

1 1 1 1 1

- 100 0 100 200 300 Temperature, O F

Figure 22. - Thermal expansion of unidirectional HMS / 3501- 5A tape (0° fiber direction).

Temperature, K x 1 0 - ~ : 50 200 250 300 350 400

2000 - 1000 -

0 - A \

J -1000 - - a

-2000 - - W S C

- unpublished data)

-200 -1 00 0 100 200 300 Temperature, O F

Figure 23. - Thermal expansion of unidirectional HMS / 3501- 5A tape ( 90° fiber direction) .

Temperature, O F

x 1 0 - ~ Temperature, K 280 290 300 310

Figure 24. - Thermal expansion of HMSI3501 unidirectional tape ( O0 direction).

20 I 1

I I . 16 ,- -

Temperature, K

x lo-6 280 290 300 310 I I 1

Ref. 36)

-600 1 I I 1 1 1 I 30 40 5C 60 70 80 90 100

Temperature, O F

Figure 25. - Thermal expansion of HMSl3501 unidirectiond tape ( 90° direction) .

(Ref.

- 100 - 50 0 50 1 00 150 2 00 Temperature, O F

Figure 26. - Thermal expansion of HMSlCE339 unidirectional tape (0° fiber direction).

Temperature, K

2000 -

1000 -

-1000 - - - - (Ref. 45)

-4000' 1 1 1 1 1 I -100 -50 0 50 100 150 200 . . .

Temperature, OF

Figure 27. - Thermal expansion of HMS 1 CE339 unidirectional tape ( 90° fiber direction).

x 1 0 - ~ Temperature, K 28U 300 310

20 ,-,

(Ref

30 40 50 60 70 80 90 100

Temperature, O F

Figure 28. - Thermal expansion of HMSl759 unidirectional tape (0° direction).

30 40 50 60 70 80 90 100

Temperature, OF

Figure 29. - Thermal expansion of HMSl759 unidirectional tape (90° direction).

- Temperature, K

( Ref,

Temperature, O F

Figure 30. - Thermal expansion of HMSI934 unidirecticnal tape ( O0 fiber direction).

45

Temperature, K x lo-6 280 2 90 300 310

600 1 I I I I

Figure 31. - Thermal expansion of HMSl934 undirectional tape ( 90° fiber direction) .

Temperature, K

150 200 250 300 350 400 2 00

Fill direction

-

J 1 l l l l l a l l l .

( LMSC unpublished dab)

Temperature, O F

Figure 32. - Thermal expansion of HMS lE788 fabric.

Temperature, K 150 200 250 300 350 4001

- - - - -

-20 - -40 -

-200 -100 0 100 200 300

Temperature, O F

Figure 33. - Thermal expansion of unidirectional Thornel-50 (Pan) IF263 tape (0° fiber direction).

Temperature, K X 1 0 - ~ 200

2 50 300 350 400 160 1 450

1 1 I I I

Identical results for GY 701X904B and GY 701934 -

- -

- - -

- 120 -80 -40 0 40 80 120 160 203 240 280 320 Temperature, O F

Mgure 54. - Thermal expansion of GY 701epoxy unidirectional tape ( O0 flber direction) .

LMSC data 1

Temperature, O F

unpublished

Figure 35. - Thermal expansion of GY701X904B and GY 70/934 unidirectional tape (90° fiber direction).

Temperature, K 150 200 250 300 350 900

250 0'

(Ref. 35)

Figure 36. - Longitudi,lal (0°) thermal expansion of P75S 1934, graphite /epoxy.

Temperature, O F

Figure 37. - Thermal expansion of glasslepoxy tooling material ( 181 cloth laminate) .

Temperature, K

I I I I I I 100 150 200 250 300 350

Temperature, O F (Ref. 33)

Figure 38. - Thermal exparlsion of 104 glass scrim cloth.

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151831, General Dynamics Corporation, August 1978.

Kural, M. : Sensitivity Analysis for CTE of a Graphite Epoxy Laminate.

LMSC S /I- 1791, September 20, 1978.

Schapery . R. A. : Thermal Expansion Coefficients of Composite Materials

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Ashton, J . E. ; Halpin, J . C. ; and Petit, P. H. : Primer on Composite

Materids: nnalysio. Progress in Materials Science Series, 'rol. 111,

Technomic Publishing Co. , Inc. , 1969.

Geiler , D. E. : Analysis, Test , and Comparison of Composite Material

Laminates Configured for Low Thermal Expansion. Proceedings of 28t h

Annual Technic~l Conference, Reinforced Plastics /Composites Institute,

The Society of the Plastics Industry, Inc. , 1973.

Fahny , A . A. ; nnd Cunnington, T . G. : Investigation of Thermal Fatigue

in Fiber Composite Materials. NASA-CR-2641, July 1976.

Jones, R . hl . : Mechanics of Composite Materials. Scripta Book Company,

1975.

hlauri. R . E. ; Crossman. F. W . ; nnd Warren, W . J. : Assessment of

Moisture Altered Dimensional Stability ot' Structurttl Composites.

Proceedings of 23rd N~tional SAMPE Symposium, May 1978.

Crossmnn, F. W . ; and Flaggs, D. L. : Dimensional Stability of Composite

Laminate During Environmental Exposure. Proceedings of the 24th

National SAMPE Symposium, May 1979.

Dong. S. B. ; Pister , K . S. ; and Taylor, R . L. : On the Theory of

Laminated Anisotropic Shells and Plates. J . Aero, Sci. , 28, 969, 1962.

Reissner. E. ; and Stavsky, Y . : Bending and Stretching of Certain Types . of Heterogeneous Amlotropic Elastic Plates. J . Applied Mechanics, 28,

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Tsai , S. W . : Introduction to Mechanics of Composite Materials, Part

I1 - Theoretical Aspects. AFML-TR- 66- 149, Air Force Materials

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Tsai , S. W . ; and Pagano, N . J . : Invariant Properties of Composite

Materials. AFML-TR-67- 349, March 1968.

Halpin , J. C. : and Pagano, N . J. : Consequences of Environmentally

Induced Dilatation in Solids. AFML-TR- 68- 375, December 1969.

Chamis, C. C. ; and Sendecky , G . P. : Critique on Theories Predicting

T hermoelastic Properties of Fibrous Composites. J. Comp . Material, 2,

332, 1968.

Ishikawa, T. : Thermal Expansion Coefficients of Unidirectiont~l Composites.

J. Comp. Material, 12, 153, 1978.

Bradstreet, S. W . ; and Davis, L. W . : Prediction of Thermal Expansion in

Simple Solids and i ts Control in Structural Composites. AIP Conf. Pmc.

No. 3, 1971.

Wakashima, K . ; Otsuka, M. ; and Umekawa, S. : Thermal Expansion of

Heterogeneous Solids Containing Aligned Ellipsoidal Inclusions. J. Comp.

Material, 8, 391, 1974.

Rosen , B . W . : and Hashin, 2. : Effective Thermal Expansion Coefficients of

Composite Materials. Int . J. Eng. Sci. , vol. 8, pp. 157, Pergamon Press,

1970.

\Yang. A. S .D . ; Pipes. R. B . ; and Ahmadi , A. : Thermoelastic Expclnsion of

GraphiteIEpoxy Unidirectional and Angle Ply Composites. ASTM STP 580,

1975.

Design, Fabrication and Test of a Graphite /Epoxy Metering Shell (GEMS).

NASA-CR-143870. Final Report (June 1973 - April 1975). April 19.

1975.

Arnts, J r . . C . W . : Structural Design of Space Telescope. Transportation

Engineering Journal of ASCE , pp. 363. hlay 1976.

Nelson, P. T. : Strut with Infinitely Adjustable Thermal Expansivity and

Length. NASA TR1- X- 3274, August 1975. (Ninth Aerospace Mechanisms

Symposium, October 17- 18, 1974. )

Nelson, P. T . ; and Krim, 1\1. H . : A Thermally Int.rt Cylindrical Truss

Concept. NASA Tbl-X- 3377, pp. 275. Part I , 3rd Conference on

Fibrous Composites in Flight Vehicle Design, April 1976.

Wolff , E. G. : Measurement Techniques for Low Expansion Materials.

Materials and Processes - In Service Performance, vol. 9, National

Sampe Technical Conference Series, October 1977.

ASThl Method of Test, E228 - 71, for Linear Thermal Expansion of Rigid

Solids with a Vitreous Silica Dilatometer. 1971 Book of ASTM Standards,

Part 31. Freeman, W . T . ; and Campbell, M . D , : Thermal Expansion Characteristics

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STP 497, ASTM, pp. 121-142, 1972.

Fitzer , E . : Thermophysical Properties of Materials. North Atlantic Tmaty

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Standard Method of Test for Coefficient of Linear Thermal Expansion of

Plastics. ASThl Method of Test, D-696, 1980.

Advanced Composites Design Guide. A i r Force Flight Dynamics Laboratory,

vol . IV , January 1977.

Dow , N , F . ; and Rosen , B . W . : Zero Thermal Expansion Composites of

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