NASA Technical Memorandum 102295 

Optimum Interface Properties for 

Metal Matrix Composites 

Louis J. Ghosn 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

Cleveland, Ohio 

and 

Bradley A. Lerch 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 

August 1989 

. 

(NASA -TU- 10 229 5 1 

PBOPEBTIES FOR l!lETAL HIBTBIX COMPOSITES 

(NASA.. Levis Research Center) 

OPT IaUH I WT ERFACE N 89-27223 

21 pCpCL 20A 

Unclas 

G3/39 0225958 
OPTIMUM INTERFACE PROPERTIES FOR METAL MATRIX COMPOSITES 

Louis J. Ghosn 

Sverdrup Technology, Inc. 

NASA Lewis Research Center Group 

Cleveland, Ohio 44135 

and 

Bradley A. Lerch 

National Aeronautics and Space Administration 

Lewi s Research Center 

Cleveland, Ohio 44135 

SUMMARY 

Due to the thermal expansion coefficient mismatch (CTE) between the fiber 

and the matrix, high residual stresses exist in metal matrix composite systems 

upon cool down from processing temperature to room temperature. An interface 

material can be placed between the fiber and the matrix to reduce the high 

tensile residual stresses in the matrix. A computer program was written to 

minimize the residual stress in the matrix subject to the interface material 

properties. The decision variables are the interface modulus, thickness and 

thermal expansion coefficient. The properties of the interface material are 

optimized such that the average distortion energy in the matrix and the interface is minimized. As a result, the only active variable is the thermal expansion coefficient. The optimum modulus of the interface is always the minimum 

kt3 allowable value and the interface thickness is always the maximum allowable 

e- value, independent of the fiber/matrix system. The optimum interface thermal 

W expansion coefficient is always between the values of the fiber and the matrix. 

Using this analysis, a survey of materials was conducted for use as fiber coatof coating possibilities 

imited. In order to 

ements with less than 

stress state in the matrix 

ecn 

I 

ings-in some specific composite systems. The number 

E fit the optimized values were 

of possible coating materials, e 

CTE were examined. The residual 

culated for these materials. 

whose modulus and C 

increase the number 

optimum modulus and 

and coating were ca 

INTRODUCTION 

Metal matrix composites are presently being considered for aerospace appl ications due to their attractive high strength to low density ratio (ref. 1). 

The fiber system is usually a ceramic material with a high elastic modulus and 

low thermal expansion coefficient. The matrix system is an intermetallic with 

a low elastic modulus and high thermal expansion coefficient. During the manufacturing process of the composite, high complex residual stresses are introduced in each of the constituents (refs. 2 and 4) due to the thermal expansion 

mismatch. This has been found to cause cracking in some composites, especially 

those with brittle matrices (ref. 2). Using a simple two cylinder model to 

approximate the micromechanical behavior of a fiberlmatrix system, Harris 

(ref. 3) has determined that the fiber is under a compressive state of stress, 

while the longitudinal and hoop stresses of the matrix are tensile and the 

radial stress is compressive. The tensile residual stresses are the cause of 

I 
the observed matrix cracking. 

around the fiber is more complex making the radial stresses around the fiber 

oscillate between tension and compression depending on the fiber packing 

sequence (ref. 3). Although acknowledged, the effect of the neighboring fibers will not be considered in the present analysis. 

Others have shown that the state of stress 

The approach taken for the stress analysis in the present study is based 

on a three cylinder model (ref. 51, isolating one fiber with a layer of interface material and another layer of matrix material (fig. 1). The analysis considers only the residual stresses due to one cool down cycle. The analysis is 

limited to an elastic solution as a first approximation and it is assumed that 

each of the constituents are isotropic. For simplicity, the variation of material properties with temperature is not considered in the present study. In 

terms of the stress analysis, the longitudinal stresses are decoupled from the 

transverse stresses. 

The objective of this paper is to define the properties of an interfacial 

layer necessary to minimize the local tensile residual stresses in the matrix 

thereby reducing the tendency towards cracking. 

ducing an interfacial layer between the fiber and the matrix. The objective 

function of the minimization process is chosen to be the average distortion 

energy In the matrix and the interface. The decision variables are the elastic modulus, thermal expansion coefficient, and thickness of the interface 

layer. The distortional energy of the fiber is not included In the minimization function for the following two reasons: first, the fibers considered in 

this analysis are brittle ceramics, thus the distortional energy is not the 

corresponding failure criteria, and second the determined stresses in the 

fiber are compressive and the compressive strength of ceramics is very high. 

This is accomplished by introSTRESS ANALYSIS 

The stress analysis is based on the self consistent method where a single 

fiber is assumed to be embedded in concentric cylinders of interface and 

matrix materials (fig. 1). The radii of the cylinders correspond to the volume frac ions of each constituent in the original composite. In this analysis 

the long tudinal stresses are decoupled from the transverse stresses. The longitudina stresses in each constituent, after a temperature drop of AT and 

assuming an isostrain in the z-direction, are given by: 

oJ=E (a -a)AT jQ j 

where Ej and aj are the modulus and the thermal expansion coefficient 

respectively of constituent j (i.e., fiber (f), interface (I), and matrix 

(m)), AT is the change in temperature from processing to room temperature, 

a& is the effective longitudinal thermal expansion coefficient of the composite and can be approximated by: 

(2) 

where the vj's are the volume fraction of the constituents. 

2 
The transverse radial and hoop stresses are derived from the superposition of the thermal stresses and the confining pressures applied to each cylinder. 

given by the free expansion, the poisson's effect of the longitudinal stresses 

and the confining pressure between two materials 

(ref. 6): 

for the fiber 

The radial displacement (Ur) relations for each of the constituents are 

for the interface 

a,2 1 - VI 1 - v, 

for the matrix 

+[al - v (a - ai)lAl iQ 

(4) 

(5) 

where r is the radial distance measured from the center of the fiber, and 

a, b and c are the radii of the fiber, the outer interface and the outer 

matrix, respectively, and pi is the confining pressure between the fiber and 

the interface, and po is the conflning pressure between the interface and 

the matrix, and vj is the poisson's ratio of constituent j. 

ties and the dimensions of the Constituents, by satlsfylng the continuity of 

the radial displacement at material boundaries, which are given by: 

The confining pressures can be determined in terms of the material proper- 

(6) f i 

= UrIa 

where r = a is the fiberlinterface boundary and r = b is interfacelmatrix 

boundary. 

Solving for the unknown pressures, a system of two simultaneous equations 

are derived and given by: 

3 
where : 

+ a2 1 - Vf 

- 2 

a12 - 

Ei(1 - $) 

bl =/(ai - af) - v (a - a 1 + v fQ (a - af) 

b2 =I (am - a 1 - v (a - a 1 + v iQ (a - 

iQ 1 

1 mQ m 

The residual radial and hoop stresses can now be solved for by uslng the 

elastic solutlon of thick cylinders under confining pressures (ref. 6). 

stresses are given here for completeness in terms of the solution of 

equation 8: 

The 

for the fiber 

f f 

pi arr = am = - 

~ 

for the interface 

I for the matrix 

m 

0 rr =-Po 

(9) 

(12) 

I 4 
C 

m 

"&zJ = + Po (13) 

where arr is the radial stress and is the tangential stress in a given 

constituent cylinder. 

After cool down to room temperature, AT is defined as the difference 

between room and processing temperature and it will be negative. 

pi is positive, the radial and hoop stresses of the fiber are compressive and 

the longitudinal stresses are also compressive from equation 1 given that AT 

is negative and UQ is greater than q. For the matrix, given that po is 

positive, the radial stress is compressive while the hoop stress is tensile. 

The longitudinal stress in the matrix is also tensile since UQ is less than 

am. These tensile hoop and longitudinal stresses are the cause of radial and 

transverse matrix cracking observed in some composite systems. 

Given that 

MINIMIZATION FUNCTION 

To minimize the local tensile stresses in the matrix, an interface layer 

is placed between the fiber and the matrix. 

interface material are the modulus of elasticity El, the thermal expansion 

coefficient ai, and the interface layer thickness t. The Poisson's ratio of 

the interface is assumed to be a constant value equal to 0.3. The objective 

function Is assumed first to be the distortion energy in the matrix as governed 

by all the stress components of the matrix. 

energy as the minimization function is justified because of the matrix ductility 

and the restriction of the optimization to a single objective function. Therefore, the objective function can be written in terms of the stresses in the 

matrix as (ref. 6): 

The decision variables of the 

The choice of the distortion 

Initial analysis has shown that by considering only the minimization of 

The resulting high compressive stresses in the fiber could be 

the matrix distortion energy, high relative stresses in the fiber and interface 

are observed. 

tolerated if the fiber system is a brittle ceramic with very high compressive 

strength. On the other hand, the high tensile hoop stress in the interface 

cannot be tolerated. Therefore, the objective function was modified to include 

the distortion energy of the interface. The final objective function used to 

minimize the residual stresses in the matrix was taken to be the distortion 

energy in the matrix plus the distortion energy in the interface divided by the 

total volume of the matrix and interface: 

5 
Objective function 

1 Ud(matrix) dV + 1 Ud(interface) dV 

JV JV 

volume matrix + volume interface f(Ei, ai, t) = (15) 

mi ni mi ze 

subject to: 

ELb 5 L Eub 

where superscripts ub and Lb stand for the upper and lower bound, respectively. The constraints on the decision variables are required to guarantee a 

realistic solution which must fall into the range of typical material properties. The range of the interface modulus is assumed to be between 69 and 

517 GPa. The lower and upper bound of the interface thermal expansion coefficient is 4x10-6 11°C and 20x104 1/"C, respectively. 

zero as a lower bound and an arbitrary upper bound as will be seen next in the 

application section. 

The thickness, t has 

APPLICATIONS AND RESULTS 

A computer program was written to minimize the average distortion energy 

in the matrix and the interface. The minimization routine (from the IMSL 

library) (ref. 7) uses the Quasi-Newton iteration method from given starting 

points. Twenty different initial sets of points are used to guarantee convergence to a global minimum. The first run consisted of a single fiber system 

and a variance of matrix properties with a temperature drop of -800 "C. The 

upper and lower bound of the interface modulus is taken to be 69 and 517 GPa, 

respectively, corresponding to the modulus of materials ranging from aluminum 

to carbon. The minimization shows that the optimum elastic modulus is controlled by the lower bound, taken to be 69 GPa (10 Msi). 

thickness always reaches the upper bound at the global minimum. Therefore, 

two different upper bound thicknesses are considered. In case 1 the 

ratio (t/d) of the upper bound thickness to the fiber diameter is 0.12 and for 

case 2, t/d = 0.20. For a fiber diameter of 145 pm (typical of the majority 

of fibers used in today's MMC's), this translates to interface thicknesses of 

17.4 and 29 pm, typical of standard coating thicknesses. Figures 2 and 3 show 

the variation of the optimum interface thermal expansion coefficient as a function of the matrix material properties for t/d = 0.12 and t/d = 0.20, respectively. The selected fiber is SIC, the most common reinforcement fiber for 

today's MMC's, having an elastic modulus Ef = 427.5 GPa and a thermal expansion coefficient af = 4.9~10-6 1/"C. The initial fiber volume fraction is 

0.4. For this analysis, the matrix volume fraction is kept constant at 0.6. 

The optimum interface thermal expansion coefficient increases with increasing 

matrix modulus and matrix thermal expansion coefficient. A greater interface 

thickness also results in an increase of the optimum interface thermal expanI 

l 

The optimum interface 

I sion coefficient. The effect of the interface layer on the distortion energy 

I (i.e., the objective function) is considered by comparing figures 4 to 6 

I 6 
for different matrix thermal expansion coefficients. The reduction in the distortion energy relative to a composite without an interface is in the range of 

30 to 40 percent with t/d = 0.12, and for t/d = 0.20 this reduction range 

is 44 to 72 percent. 

depends on the matrix material properties. 

on the actual stress components is limited to only a set of candidate composite 

systems as seen next. 

The specific value of the reduction for a given t/d 

The effect of the interface layer 

The remainder of this study dealt with finding the optimum interface layer 

properties for some candidate matrix (Ti-15-3, Ti3A1, NiAl) and fiber (SIC, 

TiB2) systems. Table I summarizes the assumed material properties of the two 

fiber systems .(Sic and TiB2) and the three metal matrix systems(Ti-15-3, Ti3A1 

and NiA1) used. In table I, E is the room temperature elastic modulus. The 

thermal expansion coefficient was approximated by taking the slope of the 

experimental strain versus temgerature curve using the end points. The temperature change assumed was -800 C which is the difference between room temperature and half the melting temperature of the various matrix materials. The 

selection of half the melting temperature as the upper limit is prompted from 

the assumption that above one half the melting temperature the residual stresses 

will be relieved due to creep or annealing (ref. 8). The optimum thermal 

expansion coefficients of the interface layer for the above composite systems 

are shown in table I1 for two interface thicknesses. When the modulus of elasticity of the matrix is close to the optimum interface modulus (69 GPa) (e.g., 

Ti-15-3 or Ti3A11, the interface thermal expansion coefficient can be approximated as the average of the thermal coefficients of the matrix and the fiber. 

When the modulus of elasticity of the matrix is higher than the interface 

(e.g., for NiAl), the optimum thermal expansion coefficient of the interface 

tends toward the matrix value. 

The effect of the optimum interface on the maximum stresses in the matrix 

are shown in table I11 for r = b. The percent drop of the stress in the 

matrix is generally largest for the NiAl matrix system and smallest for Ti3A1. 

To combine all the stress components, the maximum effective stress in the 

matrix based on the Von-Mises (distortion energy) criterion is shown in 

table 4 with and without the interface. The effective stress in the matrix 

decreases as the interface thickness (t/d> increases. For the NiAl matrix system, the effective stress is decreased well below the yield stress of the material when an interface layer with thickness t/d = 0.2 is introduced, thus 

indicating the benefit of this coating. Also, it should be emphasized that 

TiB2 offers a large reduction in residual stresses compared to Sic (tables I11 

and IV) for all of the matrix materials investigated. For the Ti3A1 matrix, 

this reduction is sufficient to reduce the effective stress of the matrix 

below the yield point. The effective stresses in the interface are also shown 

in table V for comparison at two locations: at r = a and r = b. Contrary 

to what is suggested in reference 9, the state of stress in the interface is 

not under hydrostatic compression since the effective stress based on the VonMises criterion is not zero. Although the optimized interface decreases the 

effective stresses in the matrix, the compressive stresses in the fiber are 

increased with increasing interface thickness. However, the maximum compresalculated after optimization was still below the fiber compressive 

a1 1 the composite systems analyzed. 

sive stress 

strength for 

The var 

composite is 

ation of the effective longitudinal and transverse moduli of the 

shown in table VI. The effective moduli of the composite are 

7 
determined from a one-dimensional theory of elasticity with constant displacement and constant force for the longitudinal and transverse modulus respectively. The effect of the low modulus interface layer is to decrease the 

effective modulus of the composite as seen in table VI. Therefore, an optimally designed interface layer can reduce the deleterious tensile residual 

stresses in the matrix of a metal matrix composite system. The main motivation for reducing the residual stresses in the matrix is to avoid matrix cracking upon cool-down from processing temperature to room temperature therefore 

reducing the number of initial flaws which In turn should increase the fatigue 

life of the metal matrix composites. In practice, the choice of an appropriate coating material is difficult due to the limited number of possibilities 

as is described below. 

A variety of elements and compounds were surveyed for use as possible 

coating materials. These materials are listed in table VII, together with 

their CTE, and modulus. Since exposure to high temperatures and weight reduction are important factors in choosing high temperature materials, the melting 

temperatures and density have also been included in table VI1 for completeness. 

The desired coating properties for any of the composite systems required a low 

modulus (-69 GPa) and a CTE as listed In table 11. Only the thicker coating 

(i.e., t/d = 0.20) is considered in the remaining discussion. For use with the 

three matrix materials and the two fibers, only six possible materials from 

table VI1 had elastic moduli -69 GPa (i.e., actual range of 57 to 80 GPa) and 

these are given in table VIII. Since the number is small, the first group of 

coating materials in table VI11 also includes those materials with moduli up 

to 103 GPa, which doubles the possible number of coating materials. Based on 

their CTE, the possible coating systems were chosen from this table for each 

composite system. Those materials indicated with a "x" are the best choices 

for use as a coating, those marked with a dash are less than optimum possibilities, but may still be usable. The criteria for determining best choices or 

less than optimum choices are as follows: 

~ 

(1) Only materials having moduli 5103 GPa can qualify as best choices. 

(2) Best choices had CTE values within 22x104 11°C of the optimized 

Materials having larger moduli were classified as less than optimum. 

values. 

(3) Less than optimum choices had CTE values at the optimized CTE va 

23x10-6 l/"C. 

Based on these selection criteria, the following two points were observed 

i nte 

hlgh 

mod u 

ue 

(1) The best candidates for coatings are generally metals. Ceramics/ 

metallics are not appropriate as coating materials due to their extremely 

moduli. Silicon Nitride and Ti3Al are exceptions. 

(2) There are a limited number of coating possibilities which satisfy the 

us and CTE requirements. 

To increase the number of possible coating candidates, materials having 

moduli between 103 and 207 GPa are also given in table VIII. These materials 

were again selected based on the proximity of their CTE to the optimum value 

given in table 11. Note that these are less than optimum choices since their 

a 
5 

moduli are higher. Analysis has shown (table 1x1 that the optimum CTE for 

coating materials with moduli of 138 and 207 GPa does not vary much from that 

of materials with a modulus of 69 GPa (compare table IX with table 11). However, there is an increase in the matrix stress, as observed in table X, when 

using coatings with a higher than optimum modulus. 

minimal for the Ti-15-3 and Ti3Al matrix systems, but is significant for the 

NiAl system: 

The increase appears to be 

a manifestation of the higher modulus and CTE of NiAl. 

The ultimate selection of the fiber coating will also depend on its chemical compatibility with both the fiber and the matrix. The small choice of 

coating materials listed in table VI1 will be reduced to an even smaller number 

when chemical compatibility is taken into account. Therefore, to increase the 

possible number of coatings, nonoptimized materials were also examined for use 

in the SIC/NiAl composite, since this composite shows the largest benefit from 

the use of a compliant coating. A variety of coating elements are given in 

table XI along with the effective stress in the matrix and the interface. The 

optimum coating for the SiC/NiAl system is Au, yielding the lowest effective 

stresses in both the matrix and the coating. Other coatings (e.g., Cu, Co) 

will reduce the matrix effective stress to a lower value than the stress which 

is obtained when an optimized modulus and CTE for the interface are used, but 

have the disadvantage that the coating stress will greatly increase. The high 

effective stress in the coating could lead to fiber/matrix debonding, although 

the actual effects of such a high stress in the coating are unknown. 

Experimental work is needed to determine in which constituents the stresses 

should be kept minimal. 

rials are not intuitively obvious based solely on having a CTE between that of 

the fiber and the matrix. For example, Pt has a CTE halfway between that of 

the fiber and the matrix, yet yields very high effective stresses in the matrix. 

This indicates the important relationship between the modulus and the CTE. 

Table XI also indicates that the optimum coating mateCONCLUSIONS 

An analysis was performed to determine the optimum interface material 

properties required to reduce the tensile residual stresses in a given metal 

matrix composite system. The objective was to study the concept of a compliant layer to minimize the tensile residual stresses in the matrix upon cool 

down from processing to room temperature. Based on the elastic isotropic 

analysis of a three cylinder model with constituent properties assumed to be 

temperature independent and the longitudinal stresses decoupled from the transverse stresses, the fol lowing polnts were concluded: 

1. A well designed interface layer can reduce the tensile residual 

stresses in a metal matrix composite system. 

2. To reduce the residual stresses in the matrix, the average distortion 

energy in the matrix and the interface was minimized. 

3. The optimum interface thlckness was always at the given upper bound 

for thi s part i cu 1 ar objective funct 1 on. 

4. The optimum interface modulus was always at the lower bound for this 

particular objective function. 

9 
5. For a given fiber system, the optimum interface thermal expansion 

coefficient increases with increasing matrix modulus and thermal expansion 

coefficient. 

6. For low matrix elastic modulus the optimum thermal expansion coefficient can be approximated by the average thermal expansion coefficient of the 

matrix and fiber. 

7. For high matrix modulus, the optimum thermal expansion coefficient of 

the interface approaches the matrix value. 

8. The effect of the low modulus optimum interface is to decrease the 

effective modulus of the composite. 

9. From a variety of materials, coating selections were made to reduce 

the residual stresses in the matrix and coating for composites containing the 

fiber constituents Ti62 and Sic and matrix constituents Ti-15-3, Ti3Al and 

N1 A1 . 

10. Selection of Ti62 fibers over SIC fibers results in significantly 

lower effective stresses in the matrix for all the matrix materials studied 

herein. 

10 
REFERENCES 

. 

1. Stephens, J.R.; and Nathal, M.V.: Status and Prognosis for Alternative 

Engine Materials. Superalloys 1988, D.N. Duhl, et al., eds., Metallurgical 

Society of AIME, 1988, pp. 183-192. 

2. Chou, T.W.; Kelly, A.; and Okura, A.: Fibre-Reinforced Metal-Matrix 

Composites. Composites, vol. 16, no. 3, July 1985, pp. 187-206. 

3. Harris, B.: Shrinkage Stresses in GlasslResin Composites. J. Mater. 

4. Haener, J., et al.: 

Sci., vol. 13, no. l., Jan. 1978, pp. 173-177. 

Reinforced Plastics. USAAV LABS-TR-67-66, (Avail. NTIS, 1968 AD-667901). 

Investigat'ion of Micromechanical Behavior of Fiber 

5. Vedula, M.; Pangborn, R.N.; and Queeney, R.A.: Modification of Residual 

Thermal Stress in a Metal-Matrix Composite with the use of a Tailored 

Interfacial Region, Composites, vol. 19, no. 2, Mar. 1988, pp. 133-137. 

6. Saada, A.S. : Elastic! ty Theory and Applications. Robert Krieger 

Publisher, 1983. 

7. IMSL MathlLibrary User's Manual Version l., International Mathematical and 

Statistical Libraries Inc. Apr. 1987. 

8. Dieter, G.E.: Mechanical Metallurgy, 2nd ed., McGraw-Hill, 1976, 

pp. 451-489. 

9. Nimmer, R.P.; and Banket, R.J.: Micromechanical Modeling of FiberlMatrix 

Interface Effects in SiC/Ti MMC. Presented at 13th Annual Conference on 

Composites Materials and Structures, Cocoa Beach, FL, Jan. 1989 (to be 

published in Ceram. Eng. Sci. Proc.). 

10. Metal 1 ic Materials and Elements for Aerospace Vehicle Structures. 

MIL-HDBK-SE, June 1987, pp. 5-121 to 5-125. 

11. Lerch, B.A.: Ongoing Research. NASA Lewis Research Center, Cleveland, OH. 

12. Textron Specialty Materials Data Sheet, Silicon Carbide Composite 

Materi a1 s. 

13. Brindley, P.K.: Ongoing Research NASA Lewis Research Center, Cleveland, 

OH. 

14. Desai, P.D.; and Chaney, J.F.: Thermal Linear Expansion of TiB2. High 

Temperature Materials - Mechanical, Electronic and Thermophysical 

Properties Information Analysis Center, Purdue University, 1988. 

15. McDanels, D.L., and Stephens, J.R.: High Temperature Engine Materials 

Technology - Intermetallic and Metal Matrix Composites. NASA TM-100844, 

1988. 

11 
16. Harmouche, M.R.; and Wolfenden, A: 

Fiber 

E, GPa 

a, 1/OC 

Temperature and Compos 

Ti 62 

427.5 365.4( 5, 

4.9~10-~ 8.0~10-~(~~) 

tion Dependence 

of Young's Modulus in Polycrystal1,ne 62 Ni-AI. J. Test Eval., vol. 15, 

1987, pp. 101-104. 

17. Clark, R.W.; and Whittenberger, J.D.: Thermal Expansion of Binary CoAl, 

FeAl, and NiAl Alloys. Thermal Expansion 8, T.A. Hahn, ed., Plenum Press, 

1984, pp. 189-196. 

18. Shaffer, P.T.B.: Materials Index, (Handbooks of High - Temperature 

Materials, No. 1) Plenum Press, 1964. 

19. Metals Handbook, Vol. 1, Properties and Selection of Metals, 8th ed., ASM, 

Metals Park, OH, 1961. 

20. Barrett, C.R; Nix, W.D.; and Tetelman, A.S: The Principles of Engineering 

Material. Prentice-Hall Inc., 1973. 

(3, 1/OC 

379.2 1765.1 

12 
0.12 0.20 I I 

Matrix I Fiber I ai, 1/OC 

Ti-15-3 

Ti 3Al 

Ni A1 

Sic 6.8~10-~ 7.1~10-~ 

Ti62 ~ 8.3 8.3 

Si C 7.9~10-~ 8.4~10-~ 

Si C 14.1~10-~ 14.6~10'~ 

Ti62 14.7 15.0 

Ti82 9.7 10.0 

TABLE 111. - MAXIMUM MATRIX STRESSES AT THE INNER RADIUS (r = b) in HPa 

[Numbers in parentheses indicate percent drop as compared to no interface.] 

13 
TABLE IV. - MAXIMUM EFFECTIVE STRESS (at r = b) IN THE 

MATRIX (IN MPa) BASED ON THE VON-MISES CRITERION 

[Numbers in parenthesis indicate percent drop 

as compared to no interface.] 

Matrix 

I Composite I system 

Fiber 0.0 0.12 0.20 

t/d 

0.12 

I Oyields 

MPa 

0.20 

Matrix 

Ti-15-3 

Ti3A1 Sic 602 490(19) 434(28) 379 I I Ti62 I 315 I 260(17) I 229(27) I 379 

Fiber r = a r = b r = a r = b 

Sic 199 139 215 123 

Ti B2 28 19 30 17 

1 NiAl 1 sic I 2595 1 1655(36) I 1304(50) 1 1766 

Ti82 1754 1135(35) 888(49) 1766 

TABLE VI. - EFFECTIVE ELASTIC LONGITUDINAL AND TRANSVERSE MODULI 

IN GPa IN THE COMPOSITE WITH AND WITHOUT INTERFACE 

[Numbers in parenthesi s indicate percent drop 

as compared to no interface.] 

14 
Densi iy, 

g/cm 

A1 

Ag 

Au 

Be 

Graphite 

co 

Cr 

cu 

DY 

Fe 

Gd 

Hf 

Ir 

Mn 

Mo 

Nb 

Nd 

Ni 

os 

Pd 

Pt 

Re 

Rh 

Si 

Ta 

Ti 

V 

W 

Zr 

CTE, Me1 ti ng E, 

1 /"C temperature, GPa 

"C 

Hf 

NbC 

Si C 

Ti C 

wc 

3.0 

2.5 

6.7 

1 

--------- 2800 ----- 

5.5~ 1 0-6 >3500 448 

10.0 1850 ----- 

2.7 

10.5 

19.3 

1.8 

1.9 

8.9 

7.1 

8.9 

8.5 

7.9 

7.9 

12.1 

22.4 

7.2 

10.2 

8.6 

6.9 

9.2 

22.4 

12.0 

21.4 

21 .o 

12.5 

2.3 

16.8 

4.5 

6.0 

19.3 

6.4 

4.9 

15.7 

23.9~ 1 0-6 

25.9 

17.0 

18.0 

5.0 

18.5 

11.0 

21.5 

12.3 

12.0 

10.0 

6.0 

7.9 

50.7 

5.8 

8.0 

9.0 

17.1 

5.6 

14.0 

10.5 

6.9 

10.8 

4.0 

7.1 

10.6 

10.7 

4.8 

5.3 

8.8 3160 439 

4.9 2870 668 

660 

96 1 

1063 

1300 

1490 

1890 

1083 

1407 

1535 

1312 

2200 

2400 

1260 

2620 

2410 

840 

1455 

2700 

1555 

1780 

3130 

1965 

1430 

3000 

1750 

1735 

3400 

1830 

---- 

A1 N 

BN* 

;; dN4 

62 

71 

80 

276 

7 

207 

248 

117 

63 

200 

57 

138 

524 

159 

317 

103 

38 

22 1 

558 

112 

147 

460 

24 1 

110 

186 

107 

124 

40 7 

94 

3.3 5.6~ 1 0-6 2230 345 

2.3 0.8/7.5 2730 86/34 

3.5 2.9 1900 90 

5.2 9.4 2945 250 

li A1 

-eAl 

r i 3Al 

5.9 15.6~1 0-6 1638 237 

6.1 21.8 1340 246 

5.1 11.7 1500 75 

15 
TABLE VIII. - SELECTED INTERFACE COATINGS 

[x indicates best coating materials; - indicates possible 

coating material s.1 

E. CTE. 

Gbi l/'C' Ti -1 5-3 Ti 3Al NiAl 

Sic Ti62 Sic Ti62 Sic Ti62 

I- Ei 1 103 GPa 

1 

7 5~10-~ X - - - X 

C 

Gd 57 10 X X 

A1 62 24 

63 12 - - 

71 26 

DY 

Ag 

Ti3A1 75 12 

Au 80 17 X X 

SigN4 90 3 

Zr 94 5 - 

Nb 103 8 X X X 

X 

- - 

X 

X 

- 

Ti 107 11~10-~ 

Si 110 4 

112 14 

cu Pd117 22 

V 124 11 

Hf 138 6 

- - 

- 

- - 

- - - 7 I I T 

TABLE IX. - OPTIMUM INTERFACE CTE FOR 

INTERFACE MATERIALS HAVING 

MODULI > 103 GPa 

I Matrix I Fiber I t/d t-L" CTEi, 1/OC 

Ti-15-3 tTi 3Al 

NiAl 

E; = 138 GPa 

7.2 

Si C 12.5 13.1 

Ti62 13.0 13.5 

Ei = 207 GPa 

Ni A1 11.9 12.5 

13.0 

16 
TABLE X. - MAXIMUM MATRIX STRESSES (IN MPa) AT THE INNER RADIUS (r = b) AS A 

FUNCTION OF INTERFACE MODULUS; t/d = 0.20 

[Numbers in parentheses indicate percent drop as compared to no interface.] 

Ti -1 5-3 Ti 3Al NiAl I I 1 4 

sic I Ti 82 Si C Ti B2 Sic I Ti B2 

urr (radial) 

69 -89(36) -12(60) -138(30) -73(29) -423(52) -292(51) 

207 -101(28) -14(53) -153(23) -81(21) -549(38) -375(37) 

138 -98(30) -13(57) -149(25) -79(23) -514(42) -353(41) 

Gd 

DY 

Au 

Nb 

Pd 

cu 

Pt 

Ta 

Fe 

co 

Element 

57 

63 

80 

103 

112 

117 

147 

186 

200 

207 

E. CTE. ffg uef * Gbi l/Ot’ matrix i nterface 

(r = b) (r = a) 

10 * 0x1 0-6 

12.3 

17.0 

8.0 

14.0 

21.5 

10.5 

7.1 

12.0 

18.0 

1554 

1438 

1163 

1904 ~ 1435 

850 

1776 

2138 

1678 

1052 

662 

81 1 

1245 

664 

1294 

21 39 

1067 

662 

1545 

2854 

17 
INTERF 

MATRIX 

FIBER 

DIAMETER, 

d (2a) -.. 

i I r INTERFACE THICKNESS, t 

Figure 1. - Three cylinder model. 

LX 

300 

4 

50 100 150 200 250 

MATRIX MODULUS. GPa 

Flgure 2. - Optimum Interface thermal expansion meffident as a 

functbn of matrlx properties, for ffd = 0.12, and for a SIC fiber 

cy-. 

50 100 150 200 250 300 4 

MATRIX MODULUS. GPa 

Flgure 3. - Optimum interface thermal expevlslon coefficient as a function of matrix properties. for ffd = 0.20, and for a SIC fiber 

Sptem. 

18 
50 100 150 200 250 300 

MATRIX MODULUS, GPa 

Figure 4. - Average distortion energy as a function of matrix 

modulus and Interface thickness, for a m = 8x1W6 1/C, and a 

SIC Rber system. 

- 

w 

c 

-r Vd 

1400 L 

I , 

200 

50 loo 150 200 250 300 

MATRIX MODULUS, GPa 

Figure 5. - Average distortion energy as a tunctlon of maMx 

modu~us and In- UII~AMSS. f~ am = 12x10-6 IC, and a 

SK: nkr apm. 

P 

50 100 150 200 250 300 

MATRIX MODULUS, GPa 

modulus and interface thickness, for a,,, = 16~10~ 1/C. snd 

a SIC (Ibrr aysm. 

Figure 6. - Average dlstwlbn energy as a function of matrix 

19 
National Aeronautics and Space Administration 

1. Report No. 

NASA TM- 102295 

Report Documentation Page 

2. Government Accession No. 

17. Key Words (Suggested by Author@)) 

Composites; Metal matrix; Thermal residual stresses; 

Cylindrical model; Interface properties 

7. Author@) 

Louis J. Ghosn and Bradley A. Lerch 

18. Distribution Statement 

Unclassified - Unlimited 

Subject Category 39 

9: Performing Organization Name and Address 

National Aeronautics and Space Administration 

Lewis Research Center 

Cleveland, Ohio 44135-3191 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, D.C. 20546-0001 

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No of pages 

Unclassified Unclassified 20 

3. Recipient's Catalog No. 

22. Price' 

A03 

5. Report Date 

August 1989 

6. Performing Organization Code 

8. Performing Organization Report No. 

E-4964 

10. Work Unit No. 

5 10-0 1-OA 

11. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Memorandum 

14. Sponsoring Agency Code 

15. Supplementary Notes 

Louis J. Ghosn, Sverdrup Technology, Inc., NASA Lewis Research Center Group, Cleveland, Ohio 44135; 

Bradley A. Lerch, NASA Lewis Research Center. 

16. Abstract 

Due to the thermal expansion coefficient mismatch (CTE) between the fiber and the matrix, high residual stresses 

exist in metal matrix composite systems upon cool down from processing temperature to room temperature. An 

interface material can be placed between the fiber and the matrix to reduce the high tensile residual stresses in 

the matrix. A computer program was written to minimize the residual stress in the matrix subject to the interface 

material properties. The decision variables are the interface modulus, thickness and thermal expansion coefficient. 

The properties of the interface material are optimized such that the average distortion energy in the matrix and 

the interface is minimized. As a result, the only active variable is the thermal expansion coefficient. The optimum 

modulus of the interface is always the minimum allowable value and the interface thickness is always the maximum allowable value, independent of the fibedmatrix system. The optimum interface thermal expansion coefficient 

is always between the values of the fiber and the matrix. Using this analysis, a survey of materials was conducted 

for use as fiber coatings in some specific composite systems. The number of coating possibilities whose modulus 

and CTE fit the optimized values were limited. In order to increase the number of possible coating materials, 

elements with less than optimum modulus and CTE were examined. The residual stress state in the matrix and 

coating were calculated for these materials. 

~~ 

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