7

NASA Contractor Report 185307

P55

Optimization of Interface Layers in theDesign of Ceramic Fiber ReinforcedMetal Matrix Composites

I. Doghri, S. Jansson, F.A. Leckie, and J. Lemaitre

University of CaliforniaSanta Barbara, California

November 1990

Prepared forLewis Research Center

Under Grant NAG3-894

IXIASANational Aeronautics andSpace Administration

-(NASA-CR-185307) OPTIMIZATIuN _F INTERFACE

LAYERS IN THE DESIGN OF CFRA, MIC FIBER

r .R, INFORCED MET_%L MATAIX CQMPGSITES Final

R_port (Col ifornia Univ.) 35 p CSCL lid

G3/24

N91-14422

Uncles

0317637

https://ntrs.nasa.gov/search.jsp?R=19910005109 2020-03-19T19:30:25+00:00Zbrought to you by COREView metadata, citation and similar papers at core.ac.uk

provided by NASA Technical Reports Server

OPTIMIZATION OF INTERFACE LAYERS IN THE DESIGN OF

CERAMIC FIBER REINFORCED METAL MATRIX COMPOSITES

I. Doghri, S. Jansson, F.A. Leckie and J. Lemaitre*

Department of Mechanical and Environmental Engineering

University of California

Santa Barbara, CA 93106

ABSTRACT

The potential of using interface layer to reduce thermal stresses in the matrix of

composites with a mismatch in coefficients of thermal expansion (CTE) of fiber and matrix

has been investigated. It was found that the performance of the layer can be defined by the

product of the CTE and the thickness, and that z compensating layer with a sufficiently

high CTE can reduce the thermal stresses in the matrix significantly. A practical procedure

offering a window of candidate layer materials is proposed.

*Visiting Professor from Universit6 Paris 6, LMT Cachan, 61 Avenue du Pr6sident

Wilson, 94230 Cachan, France

INTRODUCTION

Metalmatrixcompositesreinforcedwith ceramicfibersareattractivebecauseof their

high specific stiffnessand strength. Advantagecanbe takenfrom the high temperature

strengthof ceramicfibersandtheductility of themetalmatrix to produceacompositewith

superiorcombinedproperties.However,a thermalmismatchexistsbetweentheceramics

fibersandthemetalmatrix: theceramicshavinga low coefficient of thermalexpansion

(CTE)andmetalshavehighervaluesof CTE. This thermalmismatchinduces stressesin

thecompositewhensubjectedto temperaturechange.Matrix crackinghasbeenobserved

after cooling down from processingtemperatureto roomtemperaturefor brittle matrix

materials[1]. It hasbeenproposedthattheadditionof aninterfacelayerbetweenthefiber

andthematrixcanreducethetensileresidualstressesin thematrix to a level which is low

enoughto avoidmatrixcracking.

Somenumericalparametricstudieshave beenperformed[2], [3] in an attemptto

determinethematerialparameterswhicharemostbeneficialin reducingthermalstresses.It

hasbeensuggestedthattheoptimuminterfacelayer shouldhavea CTE betweenthoseof

the matrix and fiber, with a low allowable modulus and a high layer thickness. A

subsequentsimplifiedanalysiswhichretainsthedominantphysicalfeaturesof theproblem

[4] showedthatacompliantlayer couldnotreducethestressesin thematrix significantly.

However,a layer with a high CTE, compensatinglayer, can reducethe stressesin the

matrixsignificantly. Thepurposeof this studyis to detreminethevalidity of thesimplified

methodandto produceresultswhichareusefulfor design.

The studyis basedon a3 cylindermodel,isolatingonefiber with an interfacelayer

anda matrix layer (Fig. 1). Only monotonic cooling is studied and the variation of the

materials properties with temperature is not considered. In a first part, the results of the

simplified analysis which assumes a rigid fiber and a very thin layer, are recapitulated.

This analysis identifies the properties of an interface layer. In the second part, the

assumptions made previously are released and a complete elastic analysis is performed

assuming that the three materials are isotropic and linearly elastic. A systematic parametric

study is alsoconducted and a practical procedure offering a window of candidate layer

materials is proposed.

In a later study [5] both the interface layer and the matrix are considered to be elastic-

plastic, and the temperature dependence of the properties of the 3 materials is considered.

In addition to the 3 cylinder model, a unit cell of a hexagonal array of the fibrous composite

is defined and finite element computations are performed under several thermal-mechanical

loadings.

NOTATIONS

f fiber

t interface layer

m matrix

j f,/,m

Rj external radius ofj

tt=Rt-Rf layer thickness

Ej Young's modulus of j

vj Poisson's ratio of j

_.j and _j Lain6 coefficients ofj

E_vj Ej

= , }.tj = 2(1+kj (1- 2vj)(l+ v j) v j)

CTE ofj

AT change in temperature

_rj radial stress (6rr) in j

C_Oj hoop stress (o00) in j

Ozj longitudinal stress (Ozz) in j

erj radial strain (err) in j

eOj hoop strain (eO0) in j

ezj longitudinal strain (ezz) in j

_j Mises equivalent stress in j

The radii Rf and R m are related to the fiber volume fraction Cf by the relation

Cf = Rm

1. SIMPLIFIED ELASTIC ANALYSIS

1.1 Stress-Strain Analysis

Ceramics fibers are usually four to five times stiffer than the metal matrix materials.

Hence, in order to simplify the calculations, it is assumed that

Ef >> 1 and ELf >> 1

Em El

The fiber volume fraction, Cf is assumed to be of the same order as the matrix volume

fraction so that

Cf _=11-Cf

For the given assumptions the stiff fiber controls the thermal expansion in the axial

direction of the cylinder model. Hence, the stress distribution in the matrix and interface

layer is governed by a plane strain problem with a fixed inner radius at the fiber interface.

The analysis reveals that the differential CTE's of matrix and fiber, and interface layer and

fiber dictate the thermal stresses. Consequently, the differential CTEs are defined as

AC_m=am-af and Actg=a l-af

The stress distribution in the matrix is given by the plane strain solution for a thick

walled cylinder subjected to an unknown internal pressure p, a traction free outer surface,

and a temperature change AT. Superimposing the solutions given in [6] for an internal

pressure and a temperature change gives the stress distributions in the matrix

(R m / r) 2 - 1

O0m = p(R m / r) 2 + 1

(R m /Rf)2-1

Ozm - p2v m

+ Em A(zm AT

(R m / Rf) 2-1

The highest stresses in the matrix occur at the inner surface of the cylinder, r = Rf. The

von Mises equivalent stress

_ = _/Or2 + O2 + Oz2- OrO0- OrOz- OOOz

can be calculated as

- fr cf -]2 Cf2+l_4Vm( 1 Vm)]_pEmA0_mAT Cf 2[l_2Vm]

Om=,ILpl_--Z ejt3/ - 1-ce

+ [EmA0_ m AT]2} 1f2

The layer is subjected to a pressure in the radial direction resulting from the contact with the

matrix

Crrl = -p

The temperature change AT introduces stresses in the hoop and longitudinal directions due

to the constraint from the fibers. The stresses in the hoop and longitudinal directions are

equal and are the sum of the stresses caused by the pressure and the thermal expansion

O0t = Oz/= V!1 - Vt p + EtA(xtAT

6

The von Mises equivalent stress in the layer is given by

1- v t]EtA_tAT + (1 - 2vt) p

Compatibility in the radial displacement at the boundary between the inner surface of

the matrix and the interface layer is the condition which isolates the value of p which is

found to be

[l+v m]- ttActt l + v tRfAt_ m 1 - v t

P=(l_v 2_I l+Cf Vm J ttEm vtm]Ll_--_f+ -- +1 - Vm RfE t 1- vl

EmA_mAT

1.2 Sensitivi_ Study

1.2.1 Stresses in the matrix

The term EmAOtmAT enters in all the expressions for stress and all results are

normalized with respect to this term. The stresses at the inner radius of the matrix are

shown in Fig. 2 as a function of normalized pressure for a fiber volume fraction Cf = 0.4

in a Ti3A1 matrix with v m = 0.25. It can be seen that a pressure at the interface causes

increased tensile stresses in the hoop and axial direction that could cause matrix cracking,

initiated from defects at the fiber matrix interface.

The value of the critical stress for matrix cracking, t_cm, sets an upper limit for the

principal stresses Cr0m, Crzm, and Orm and defines bounds on the pressure p if matrix

failure is to be avoided. The allowable equivalent stress, Oy m, in the matrix defines other

bounds on the pressure. These conditions define a window for the interface pressure, Fig.

2, so that the failure criteria are not violated.

Inspection of the expression of p reveals that the pressure may be reduced by the

introduction of a compliant layer with low modulus which would increase the denominator,

but the second term in the denominator of p is usually sufficiently small to be neglected in

thecalculationsandthepressureis thenlinearlydependenton theparameterAattt . ThisActmR f

effect is demonsuated in Fig. 3 where it can be seen that the influence of Emt-------_tis small.EtRf

Figure 2 shows that the Mises equivalent stress has a minimum for an interface pressure

that is close to zero. The pressure p is zero when

Actttt = (1 + v m) (1 -vt._____._)Aa m Rf 1 + v t

from which it can be deduced that the stresses in the matrix are strongly influenced by the

parameter Act/t/. The results from Fig. 2 and Fig. 3 can then be combined in Fig. 4

where the highest principal stress and equivalent stress at the inner radius of the matrix

cylinder are plotted versus the parameter Actltl/ActmR f.

If the pressure is to be reduced to a minimum, the differential CTE for the layer has to

be Act ! ~6Act m, when tt/Rf = 0.1 For the case of SiC fibers, ctf_- 5 x 10"6/'C in a Ti3A1

matrix, ctm -- 10 x 10 "6, requires that a t ~ 35 x 10 -6. Handbook values [7] of metals with

a reasonably high melting point and high CTE are: silver 26 x 10 -6, hafnium 500 x 10 -6

and copper 17 x 10 -6. It is evident therefore that an interface layer of readily available

materials with high CTE has the potential of substantially reducing thermal stresses in the

matrix.

1.2.2 Stresses in the Interface Laver

The tradeoff for the improved stress state in the matrix is that the thermal mismatch

has to be taken up by the interface layer. The deformation of the layer is constrained in the

hoop and longitudinal direction so that tensile stresses develop in the layer. The highest

principal stress in the interface layer is shown in Fig. 5 as a function of the different

dimensionless parameters defining the problem. The stress is strongly dependent on the

layer modulus, E//E m, and CTE, Actl/Athn, but weakly dependent on the layer thickness

tt/R f. This indicates that the stress is dominated by the constrained thermal expansion,

8

which is givenby thesecondtermin thestressexpression,andis weaklydependenton the

interface pressure,the f'trst term in this expression. The product Aagtt governs the

reduction of stress in the matrix, Fig. 4, and has to have a required value to reducing the

stresses in the matrix to an acceptable level. It can be deducted from Fig. 4 and Fig. 5 that

it is more favorable to have a thick layer and a moderate high layer CTE than a thin layer

and a high layer CTE in order to fulf'fll the requirement of stress reduction in the matrix and

to avoid high tensile stresses in the layer.

2. ELASTIC ANALYSIS

2.1 Stress-strain Analysis

The composite is not subjected to transverse loading and the outer surface of the

compound cylinder is traction free. The thermal loading is axisymmetric with respect to the

z-axis, then the displacement in the transverse plane is radial: Uj(r). The fibers are long

and the stress and strain distributions are constant in the z-direction except at the end

regions which will not be studied here. A generalized plane strain assumption is made: ezj

= constant = ez. The other strains are given by:

ujerj = Uj and e0j = r

and there are no shear strains.

The linear thermo-elastic behavior gives the stresses as

9

Theequilibriumequationsincylindricalcoordinatesgive:

ar + °rJ- °sJ) = 0

which gives the displacement field as

Uj=cjr+D; R_J r

where cj and Dj are constants to be found by the boundary conditions.

order to obtain a finite solution in (f).

To summarize, the strains are given by

We have Df = 0 in

tzj = ez = constant

The stresses are defined by

(Yrj = 2(_,j + IJ.j)cj + _tje z - 21.tj Dj - (3_Lj + 2l.tj)otjAT

_0j = 2(_,j + IJ.j)cj + _.je z + 2l.tj Dj - (37Lj + 2[J.j)otjAT

Ozj = 2_Ljcj + (_,j + 2l.tj)e z - (3_,j + 21J,j)o_jAT

10

The strains and the stresses are uniform in the fiber. The axial strain is constant in the

whole composite and the axial stresses are uniform in (t) and (m). The Mises equivalent

stress _j is defined by

1 ¢_ +_-_l/,_o0_/_Io0_-oz_/_+/o,_o,AR" 4=4 {3I ) 2}

The six unknown cf, c/, D/, c m, D m and e z are determined by the following conditions:

Uf = Ug at r = Rf

U t = U m at r = R !

arf = ¢_rl at r = Rf

(_rl = _rrn at r = R l

crrm = 0 at r = R m

Rm 2 2_2_: J' O'zjrdr=0:=_RfOzf+(Rt R2)_zZ+(R2m-R2)Ozm=0

0

The linear system obtained is given in Appendix I.

Since crrm(R m) = 0, the stresses in the matrix can also be written as

... .mOm[X/e/ JOem=2 m°m[a+I 121

11

azm = 2_m[Dm - Cm + ez]

It is reasonable to assume that D m > 0 (because this gives a compressive arm and a tensile

_0m). in this case, it is obvious that the minimal hoop stress is obtained for D m = 0,

which gives grm = 0 and a0m -- 0, i.e. a uniaxial lonotudinal stress state. This result was

confirmed numerically (see Section 2.3).

2.2 Sensitivity Study

The properties of the interface layer are defined by the four parameters: E I, v t, a t

and t t. A sensitivity study was conducted in order to measure the influence of each of

these parameters on the reduction of the residual stresses in the matrix. As a conclusion to

this study, a procedure allowing the choice of candidate interface layer materials is

proposed in Section 2.3.

The fiber and the matrix are def'med by the following data

Fiber: SiC (SCS6)

Ef = 360 GPa, vf = 0.17, af = 4.9 x 10-6/'C

Matrix: Ti3A1

E m = 75.2 GPa, v m = 0.25, a m -- 11.7 x 10-6/'C

The radii Rf and Rm are related to the fiber volume fraction by

Cf = L_m) = 40.5%

The characteristics of the fiber and the matrix were kept constant but the parametric study

can be readily applied to fibers and matrix with other properties.

The range of interface layer parameters were chosen as follows:

12

69<E I<517 GPa

4<_xt<30 xl0-6/°C

0.028 < tt < 0.28

Rf

The Poisson's ratio of the layer v! was kept constant: vg = 0.3.

To study the impact of the interface layer, a reference state was defined which

corresponds to the state of stresses in the matrix in a 2 cyclinder without the layer. The

stresses in the 3 cylinder model have been normalized with the reference stresses. The

stresses in the layer and matrix are given at the inner radii.

2.2.1 Influence of the Young's Modulus E_ (ct/, tg fixed)

The results of the sensitivity study have shown that in the range 69 + 200 GPA, the

value of Eg has little influence on matrix stresses (Fig. 6a). fiE/= 200 + 517 GPA, then

(Fig. 6a).

if otg < 10 x 10-6/°C, the value of 5m is again independent of the value of E !

if o_t > 10 x 10-6/°C, the increase of E l may reduce the stresses in (m) but

increase the stresses in (t) to unacceptable values (see Fig. 6a and 6b).

For the remaining of this study, we will choose E l < 200 GPa. This is not too

restrictive because an important property of the interface layer is a high value of CTE (see

discussion in section 1.2) so that the layer is likely to be a metal for which the Young

modulus is usually lower than 200 GPa.

2.2.2 Influence 9f the CTE 0t__(E l, tg fixed)

The results show that generally the matrix equivalent stress _m decreases

considerably as at increases. However as illustrated in Fig. 7, the stresses reach a

minimum after which they increase again with increasing otl.

The decrease of _m is more pronounced if the fixed thickness tl is high as is evident

13

from Fig. 7.

In all thecases_ < 1: the addition of the interface layer does reduce the residual(_ref

stresses in the matrix.

2.2.3 Influence of the Thickness tI (E l, a t fixed)

The results are qualitatively the same as for al; i.e. in general _m decreases as tt

increases (see Fig. 8).

2.2.4 A (70nveni_nt Parametric Representation

The conclusions of the above sensitivity analysis are in agreement with those of the

simplified analysis [4] described in section 1. That analysis lead naturally to the graphical

representation given in Fig. 4. In the analysis it was shown that the important layer

parameter which affected the matrix stress is Aatt l. This graphical representation is used

to present the results of the sensitivity study and they are given in Fig. 9. These results

were generated using E t -- E m = 75.2 GPa, and they are nearly the same for all values of

E l lower than 200 GPa. The representation proves to be very useful since all the factors

influencing the matrix stresses can be presented in one graph. Also shown in Fig. 9 are the

results of the simplified analysis. The complete analysis predicts lower stresses than those

from the simplified analysis, which is not surprising since the full analysis avoids

assumptions which imply constraint.

The range of x t Aattl= was limited to the domain of allowable pressure (def'medAO:mR f

in Fig. 2 and 3). The minimum value of _m corresponds to x t - 0.65. If x / > 0.65, it

was found that the radial stress in (m) becomes tensile and the hoop stress compressive

((rrm > 0, (_0m < 0, (_zm > 0). Layers such that x l > 0.65 are over-compensating layers.

2.3 A Convenient Procedure to Choose Candidate Layer Materials

The interface layer is defined by 4 parameters: E l, v l, a t and t l. In the sensitivity

study we kept the Poisson's ratio of the layer constant: v t = 0.3 and we found that it is

14

reasonableto taketheYoungmodulusof the layerin thisrange: Eg= 69÷ 200GPa. So

wekeptEl -- 69 GPa = constant.

The matrix stresses can be readily calculated using Fig. 9. However, using this form

requires further effort when making selection of the interface layer. This procedure is

developed to deal with this situation. The axes used in the proposed graphs are the

thickness of the layer and the CTE of the layer. The ratio of the matrix Mises equivalent

stress with and without the layer is determined, and the graph shown in Fig. 10 then

presents contours of constant reduction factor. Similarly in Figs. 11, 12, 13 the reduction

factors for the damage stress, tensile hoop stress and tensile axial stress are plotted in an

identical manner.

Reduction of the Mises __uivalent stress-

It has been noticed that _Cr-----L-fand _t_---L'tdecrease if tx t decreases. So, for a givent_ref (Tref

stress reduction inthe matrix (i.e. a given contour in Fig. 10) one can choose tzt such that

_ does not exceed a certain value to avoid layer cracking. The rnin. value of _ was(Sref 6ref

found to be = 0.387 (see shaded line in Fig. 10). This contour was also found to

correspond to a uniaxial longitudinal stress state in the matrix (see remark at the end of

section 2.1).

Reduction of the Damatze Eouivalent Stress

In the same way that the Mises equivalent stress is related to the distorsion energy, a

so-called damage equivalent stress [8] is related to the total elastic energy and is defined by

6" = _ (1 + v) + 3(1 - 2v) _

1where (r H = "2"(Tkk"

3

15

One notices the presence of the triaxiality ratio c--_-H which is known to be a main feature in(1

i_ailure.

The contours of Fig. 11 can be used in the same way as those of the Mises stress.

The same remark about the decrease of (r_ and a_ when a t decreases applies also. If we

compare the contours of the Mises and the damage equivalent stresses, we find that:

i) In the "upper" region of the plane defined by a t = 30 x 10 -6/°C, t-L = 0.28Rf

(I mand --¢- = 0.387 (shaded line) the criterion based on the reduction of the Mises stress is

(lref

a bit more severe than the second one, i.e. for a given point (_Lf,c_tl we have

(lref (lref

ii) In the remainder region, the criterion based on the reduction of the damage

equivalent stress is a bit more severe than the In'st one. The reason is the following.

ill

The calculations have shown that (Sref _=_Fref, so

--..-¢- < _ _ <(_ref _ref

so, the triaxiality ratio in the matrix is

1 "upper"<- in the region i)3

> _1 in the remainder region ii)3

Reduction of the H(X)p Stress

It appears that the reduction of the hoop stress in (m) is much more important than the

reduction of the Mises stress. The hoop stress can actually be decreased to a zero value,

which is shown by the shaded line in Fig. 12. This line corresponds also to the min. Mises

16

stress and to a uniaxial z-stress in the matrix. In the "upper" region defined by the shaded

line as previously, the hoop stress in (m) becomes compressive: _0n_ < 0. This region

corresponds also to x! > 0.65, as defined in section 2.2.4.

R_duction of the Lon_tudinal Stress

It appears that the reduction of azm is smaller than the reduction of _m or O0m. The

shaded line (_m minimal and C0m = 0) gives Ozm = 0.6. A lower reduction cannot bet_zrcf

expected and if the reduction of t_zm is a concern, then the window of candidate layer

materials is reduced as shown by comparing Fig. 13 to the previous figures.

CONCLUSIONS

The thermal mismatch between the fiber and the matrix has to be taken up by the

interface layer and can subject it to high stresses if the Young modulus of the layer is high.

If this modulus is taken in a certain range, common to most metals, then the layer

performance is defined by the product of the CTE and the thickness.

A compensating layer with a sufficiently high CTE has the potential of reducing the

thermal stresses in the matrix significantly. Both the CTE and the thickness of the layer can

be adjusted in order to keep the stresses in the layer under a certain level. The maximum

hoop stress in the matrix can be reduced substantially but the axial stress in the matrix is

less affected by a layer. This implies that compensating layers can be expected to be very

successful in preventing cracking in composites where predominantly radial cracking is

observed in the matrix, but that while axial stresses can also be reduced, this reduction is

less dramatic.

Graphs have been produced which are simple to use. From Figs. 10 to 13, the

reduction in stress for any value of layer CTE and thickness are readily determined. The

absolute values of matrix stress can be easily determined by reference from another diagram

(Fig. 9).

17

J

E

J

!

I

_1 _I

I

i-

÷ ÷

E

S

E

v

EN

I If I

I I

_1_ _1_

!

I('-,I

E I _

e,l _1

! 1

I

!

-t-t

-1

e_

I

! !

e4

-t+

I

I !

It'-,I

_1 -_! i

E

÷

'____.,'_! -_

I

! 1

+

-1

+

II

!

It",,I

! !

u

I

I

t-',i

II

18

REFERENCES

[1] Brindley, P.K., Bartolotta, P.A. and MacKay, R.A., "Thermal and Mechanical

Fatigue of SiC/Ti3AI+Nb," 2nd HITEMP Review, NASA CP-10039, paper 52,

1989.

[2] Ghosn, L.J. and Bradley, A.L., "Optimum Interface Properties for Metal Matrix

Composites," NASA TM-102295, 1989.

[3] Caruso, J.J., Chamis, C.C. and Brown, H.C., "Parametric Studies to Determine the

Effects of Compliant Layers on Metal Matrix Composite Systems," NASA TM-

102465, 1990.

[4] Jansson, S. and Leclde, F.A., "Reduction of Thermal Stresses in Continuous Fiber

Reinforced Metal Matrix Composites with Interface Layers," submitted for

publication, 1990.

[5] Doghri, I. and Leckie, F.A., "Elasto-plastic Analysis of Interface Layers for Fiber

Reinforced Metal Matrix Composites," submitted for publication, 1990.

[6] Timoshenko, S.P. and Goodier, J.N., "Theory of Elasticity," McGraw-Hill,

Auckland, 1970.

[7] Boyer, H.E. and Gall, T.L., "Metals Handbood, Desk Edition," ASM, Metals Park,

1985.

[8] Lemaitre, J. and Chaboche, J.L., "Mechanics of Solid Materials," Cambridge

University Press, 1990.

19

_ Layer

Matrix

Fig. 1 Concentric 3 cylinder model.

2O

O-cm I

O'Om I

I

AIIowoblePressure

-2__1.0 -0.5 0.0 0.5

p/E A AT

1.0

Fig. 2 Stresses at the inner surface of the matrix cylinder as a function of normalized

pressure.

21

1.0

0.5

W

t2)..

O tl)

-1 0 1 2

AG,t/AGmR,

Fig. 3 Normalized pressure as a function of the layer _ and thickness.

22

2.5

<3E

Lt.!

b

J

m

m

m

D

m

m

D

m

2.0 -m

m

J

m

D

m

1.5 -J

1.0

I

0.5-1

\

\

\

\

\

\

\

\

\

\

\

\

/

/

/

/

/

/

/

/

/

/

I

I

/

/

I

I

i J I I I I I i I J ! I I I I J I I J I | I I a I i i i i

0 1

Ao ,t/A mR,Fig. 4. Maximum principal stress and Mises equivalent stress at the inner surface of the

matrix cylinder as a function of the layer CTE and thickness.

2

23

10

8

F--<3

"<3E

Ld

m

N

b

2

0

E,/E,. = 0.5

n

Illillll

N n l

1 2 3 4 5 6 7 8 9 10

Fig. 5 Longitudinal and hoop tensile stress in interface layer.

24

("-

x

._ E g

_ _.×c'---_ (I) .4.._

_.2 (D(D c-

IIIIIIIIIIIIIIIIIIII| ll]llllllJlllllllllllllllll II]IIIIIII|I

0c_

0 0 0 0 00 O0 _ _ C_•- o d d d

sseJJ,s ooueJeloJ/ss_J_,s sOS!lAI "XDIAI

0(D

i

0

(DI:L "_..o

v- _

-- ,_

Ea2

:d -o_ ;-0 C-

(23

OOO

dki.

25

j i i i I I I I I I ] I I I I I I I I I | I I I I I I I 1 I ] I I I I I I I I I i I I I I I I I I I

0 0 0 0 00 0 0 0 0

£N _-" _--

•xolA 1

26

1.00

_n0.80 -

IDL)CIDI,,__0.60 ':

_._ ",

_30.40 -

..4,.a

0.028

Stress inthe motrix

0.16

0.28

- E_=6 9 coPa ,,.-- _-tress ]n•-- 0.20 -. . _ _. _c_c_X. MISe_ _ , -:_ : ref. stress -- ""_,, -- -.--io,,er

- _he matrix when there is _u y

:_ o.oo - _.u_ • • -_, "

0.00 CTE of the Ioyer k/u /

Fig. 7 Influence of the layer CTE on the stresses in the mamX.

27

•._ 0O0 C

0 0 0 0 0 0

,_ o d d d dsseJ_,s e0ueJe_e_/sseJ_,s ses!_ "x0_

n

-o

-u3

-("4. _

o_-_

- ._2__ _- _ _

- , 03 _

= c" P)

-o__ _

- _- _,

-0

FT'_mT_T I I I i I I I I I I I I I I I l'i I I I I I I I I I I I I I I "I I I I I I I I I i

28

\

\

\\

\

\

\

0 CD 0 0 00 _) 0 _) 0

d ,- "- o d

0

2g

m

U

20--

v

15-

0lO-

B6-

I

Oo

Contours of max. mlsos Mrus in tlm mitrlx/rot, stress

Fef. stres_mi_x, mlxs stress in tho matrix wlwn no hlyw"

ll,l lii,llllilll i,llslill.06 .I .16 .2 25

l,ymr l.hicknm/Mms" rli_us

Fig. 10 Contours of constant reduction factor of the Mises equivalent stress in the

matrix.

3O

ORIGiI_IAL PAGE ISOF POOR QUALITY

U

I

o

m

D

w

20--

16--

10--

6--

I0 o

I I

Contours d maz. DtmJqlestressIn the mtrlz/rd. 8,trees

reg. stress-maz. Demale 8ire88in the matrix when no layer

,l ,,,,l,, t,i i,,, ,ill t,iil.06 .I .16 .2 ._5

layer thickneu/flber radius

I

Fig. 11 Contours of constant reduction factor of the damage equivalent stress in the

matrix.

31

30

0

Contours of max. OO strmm in the matrlx/rd, stress

ref. stress-max. O 0 strum In the matrix when no layer

n

_l J i Ji J _,_.1 I _ I J I J j j i I i i t..i ! i i.0 .06 .l .18 2 25

layer thicknus/flber radius

Fig. 12 Contours of constant reduction factor of the hoop stress in the matrix.

32

ORiGf_tAL PAGE ISOF POOR QUALITY

U

QDI

r_

v

0

0

20

15

10

6

0

i

0

Contoun d max. ZZ d, ro_ ks the mtrix/rd, d, re_

rat. dxmm-mex. ZZ d, rmm la the mtrix _ ao layer

illll lii,llIItlllllilllllll.06 .1 .16 2 .28

layer thlclml.m/nl_r rldlul

Fig. 13 Contours of constant reduction factor of the axial stress in the matrix.

-OfftQl_lA l" PAuF Pooo ,.,.. _ I,_

-'" w41.j_

33

N/L.q Report Documentation Page

Si)ace Adrninisttal_o=_

3. Reciplenl's Catalog No.1 Report No. 2, Government Accession No.

NASA CR- 185307Tm

4. Title and Subtitle

Optlmizaiidrl of Interface Layers in the Design of Ceramic Fiber

Reinforced Metal Matrix Composites

7. Author(s)

9.

12.

I. Doghri, S. Jansson, F.A. Leckie, and J. Lemaitre

5. ReportDate

November 1990

6. PerformingOrganization Code

8, PerformingOrganization ReportNo,

None

10. WorkUnit No.

510-01-01PerformingOrganizationName andAddress

University of California

Department of Mechanical and Environmental Engineering

Santa Barbara, California 93106 13.

SponsoringAgencyNameand Address

National Aeronautics and Space AdministrationLewis Research Center

Cleveland. Ohio 44135-3191

11. Contractor GrantNo.

NAG3-894

Typeof ReportandPeriodCovered

Contractor ReportFinal

14. Sponsoring Agency Code

'15. Supplementary Notes

Project Manager, Steven M. Arnold, Structures Division, NASA Lewis Research Center.

f 6. Abstract//

t The potential of using interface layer to reduce thermal stresses in the matrix of composites with a mismatch incoefficients of thermal expansion (CTE) of fiber and matrix has been investigated. It was found that the

performance of the layer can be defined by the product of the CTE and the thickness, and that a compensatinglayer with a sufficiently high CTE can reduce the thermal stresses in the matrix significantly. A practical

procedure offering a window of candidate layer materials is proposed.

7 Key Words (Suggestedby Author(s))

Composites; Metallic; Thermal mismatch;

Compliant layer; Metal matrix composites

18. Distribution Statement

Unclassified - Unlimited

Subject Category 24

tg. SecurityClassif.(of thisreport) 20. SecurityClassif. (of this page) 21. "No. of pages

Unclassified Unclassified 36

NASAFORMlS2Soct 86 *For sale by the National Technical Information Service, Springfield, Virginia 22161

22. Price"

A03