NASA Techn_ica! Memora_n_d_um 103153 ..............................................................

ICOMP-90.14 ...........................

-i " - Y--_-/-?-

_, _:_ _ Metal Matrix Composites Microfracture:

' Computational Simulation ...................................

........ Sub_o__d_h_K.Mi_!a_!...........................................................................................

Lewis Research Center .............................

Cleveland,, Ohio =

and

John J. Caruso _nd. Christos_ C. Chamis ...............................

Lewis Research Center ................. : .......

Cleveland, Ohio

Prepared for the

Symposium on Computational Technology forFlight Vehicles

cosponsored by NASA and George Washington University

_--_-_ ..... -_-'_Washington, D.C., November 5-7, 1990 __

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METAL MATRIX COMPOSITES MICROFRACTURE: COMPUTATIONAL SIMULATION

Subodh K. Mital*

Institute for Computational Mechanics in Propulsion

Lewis Research Center

Cleveland, Ohio 44135

and

John J. Caruso and Christos C. Chamis

National Ae:onautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135

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ABSTRACT

Fiber/matrix fracture and fiber-matrix interface debonding in a metal

matrix composite (_',_C) are computationally simulated. These simulations are

part of a research activity to develop computational methods for microfracture,

microfracture propagation and fracture toughness of the metal matrix composites. The three-dimensional finite element model used in the simulation consists of a group of nine unidirectional fibers in three by three unit cell

array of SiC/Til5 metal matrix composite with a fiber volume ratio of 0.35.

This computational procedure is used to predict the fracture process and establish the hierarchy of fracture modes based on strain energy release rate. It

is also used to predict stress redistribution to surrounding matrix/fibers due

to initial and progressive fracture of fiber/matrix and due to debonding of

fiber-matrix interface. Microfracture results for various loading cases such

as longitudinal, transverse, shear and bending are presented and discussed.

Step-by-step procedures are outlined to evaluate composite microfracture for a

given composite system.

INTRODUCTION

In a recent effort at NASA Lewis (ref. 1), three-dimensional finite element

simulation was used to evaluate the effects of partial debonding on unidirectional composite (ply) properties. It was shown that, in general, single fiber

fracture and/or debonding have little effect on most of the ply level properties. Among the material properties most effected are longitudinal modulus

E_I 1 and longitudinal thermal expansion coefficient _11 due to substantial

fiber matrix debonding, particularly _Ell making it a good indicator of the

level of debonding in the composite. The present research is an extension of

that work with emphasis on microfracture, fracture propagation and stress

redistribution in surrounding matrix/fibers due to brittle fracture of fiber/

matrix or debonding of the fiber-matrix interface. The objective of this study

is to develop a computational simulation procedure to predict the direction of

crack propagation, based on strain energy release rate and to predict stress

redistribution, Fiber/matrix fracture and fiber-matrix interface debonding has

been simulated in the present work to predict fracture toughness, fracture

propagation direction and extent of stress redistribution when the composite is

subjected to longitudinal, transverse, shear or bending loads.

*Work funded by Space Act Agreement C-99066-G.
NOMENCLATURE

d diameter

E Young's modulus

G strain energy release rate

L fiber length

u displacement in X direction

v displacement in Y direction

w displacement in Z direction

a coefficient of thermal expansion

Poisson's ratio

Subscripts:

f

m

II

22,33

fiber

ply

matrix

is the longitudinal (along the fiber) direction

are transverse directions

FINITE ELEMENT MODEL

The finite element model used in this computational simulation procedure

consists of a group of nine fibers, all unidirectional, in a three by three

unit cell array ("nine cell model") as shown in figure 1. The procedure is

illustrated by using a composite system consisting of 35 percent fiber by volume SiC/Til5 metal matrix composite with the properties as shown in table I.

The finite element mesh consists of 16 "bays" along the length as shown in figure 2, Finite element mesh in each cell consists of 40 six-sided solid element

with eight grid points (CHEXA) and 8 five-sided solid element with six grid

points (CPE_YFA) elements. The overall mesh statistics are shown in figure 2.

Various finite element analyses are made using MSC/NASTRAN version 65

(ref. 2). The load and boundary conditions are applied to the model through

enforced displacements. The fiber diameter used is 223 _m (8.8 mil). The

length to diameter ratio of the fiber (L/df) is 6.8 and width of the interface

is 6.8 percent of fiber diameter. In a typical set of simulations, fracture

is initiated in the fiber at the middle of the center cell and is allowed to

grow either in the matrix or along the fiber-matrix interface. Similarly, the

crack could be initiated in the matrix or the fiber-matrix interface. Fracture

is simulated by placing duplicate node points on either side of the crack.
These duplicate nodal or grid points have the samegeometrical location, but no

connectivity exists between them, thus, in effect producing a crack of zero

width. Cracks are introduced symmetrically around the center fiber. For a

given fracture configuration, fixed boundary displacements are applied to the

model in a given direction. Resulting nodal forces corresponding to those

applied displacements are found by the finite element analysis. Comparison of

resulting nodal forces is made for reduction in global stiffness as the fracture propagates. The corresponding strain energy release rates are computed

for perturbed fracture configurations by using the respective elementary definitions as described below.

STRAIN ENERGY RELEASE RATE

Strain energy release rate (SERR) is a very commonly used indicator of the

fracture toughness of a material. Strain energy release rate gives a measure

of the amount of energy required to propagate a defect in the laminate. Hence,

one can make a direct comparison of damage tolerances between different microfracture configurations, materials and geometries. It provides the capability

to identify particular fracture damage influences, such as geometry effects,

material property dependence etc. This approach has been very effective in a

previous investigation by Wilt et al. (ref. 3), where the strain energy release

rates have been used to predict general delaminations in a composite laminate.

One of the methods used to calculate strain energy release rate is the

crack closure method. In this method, nodal displacements and the corresponding nodal forces at the crack tip location, are used to determine the amount of

work required to close the crack, which has been extended by an incremental

amount. This is continued until the strain energy release rate increases very

rapidly for equal increments of crack growth. The damage extent at which such

a rapid increase in strain energy release rate would occur is critical damage,

beyond which the damage becomes unstable and laminate fracture is imminent.

The above approach is a local level or a microfracture approach since the

amount of energy produced by the local displacements and forces at the crack

tip location are used to calculate the corresponding strain energy release

rate. However, in the present research, a global approach has been used to

calculate the strain energy release rate. In this approach, applied nodal

displacements and the corresponding nodal forces obtained from finite element

analysis at the loaded end of the composite are used to calculate the work

done. Strain energy release rate is then, calculated as:

dW 1 F2 u - F 1

where

I1 applied displacement at the loaded end of the model

AA area of the new surfaces generated

F1,F 2 forces at the end nodes before and after 5A
This equation is simply incremental change in work divided by the incremental change in new surface area that opens up. The applied displacements, u,

remain constant but the resulting force required to maintain that displacement

changes because of the reduction in stiffness of the composite as the fracture

propagates.

CASES STUDIED AND RESULTS

The cases studied and the results obtained therefrom are described for the

different loading cases below.

Longitudinal Loading

For the case of longitudinal loading, the model is fixed in X-direction on

the back face (u = 0.0) (fig. 1) and on the front face, a fixed displacement is

applied in the X-direction (u = 0.0012 in. or 0.03 mm). For this loading case,

the center cell fiber is assumed to fracture first and then the crack is allowed

to grow either into the matrix or along the fiber-matrix interface as shown

schematically in figure 3. Due to the initiation and propagation of fracture,

stresses are redistributed in the surrounding matrix and the neighboring fibers. The longitudinal stress variation along the length of the specimen in

matrix and also in neighboring fiber due to center fiber fracture is shown in

figure 4. Shear stress in the interface also increases as a result of fiber

fracture. For example, in the case of fiber fracture only, the longitudinal

stresses in surrounding matrix become twice of those in the reference (no fracture) case. Similarly, longitudinal stresses in neighboring fibers increase by

15 percent as compared to the reference case (fig. 4). It should be noted that

constituent stresses are normalized by average ply level stresses, which are

obtained by summing up all the forces on the loaded face and dividing that by

the surface area of that face. It is also observed that stresses redistribute

around a microfracture within a short distance away from it and the stress concentration factors are lower than what would be expected in an isotropic case.

The reduction in global longitudinal stiffness as more fibers are fractured in a plane is shown in figure 5. The reduction in global stiffness when

all the fibers are fractured in a plane is only about 9 percent for this composite system. Hence, when all the fibers are fractured in one plane, there is

a reduction in strength in that plane, but the reduction in global stiffness is

small. It is well within the experimental scatter and perhaps difficult to

detect experimentally (unless the strain gage bridges the fracture plane).

The strain energy release rate as fibers are fractured in a plane is shown in

figure 6. It shows that once, one out of nine (11 percent) fiber is fractured

in the middle, it is the onset of instability. The crack, in this particular

fracture mode, propagates without requiring any additional energy. This level

of energy can also be thought of as the equivalent of fracture toughness of the

material, which is, by definition, the level of energy at which crack propagates without requiring any additional energy. It also indicates that once

one out of nine fibers is fractured, all other fibers can fracture at the same

energy level, which will lead to a brittle failure. But, for such brittle

fracture to happen, the interface has to be very strong, as will be discussed

later.

4
If only the center fiber is fractured at middle and the crack is allowed

to grow along the fiber-matrix interface, then there is about 10 percent reduction in longitudinal stiffness for fully debonded center fiber, same as was

reported in a previous study (ref. 4). There is a reduction in stiffness as

the center fiber debonds following the fiber fracture as shown in figure 7.

The corresponding strain energy release rate versus the fiber length debonded

is shown in figure 8(a). If the fracture initiates in the matrix and the crack

is allowed to grow along the fiber-matrix interface without a fiber fracture,

the reduction in stiffness is very small and thus, the strain energy release

rates are also very small as shown in figure 8(b). If the fracture initiates

and progresses along the fiber-matrix interface, there is no reduction in the

global longitudinal stiffness and hence the corresponding strain energy release

rates are also zero. Thus, even though, it takes less energy to drive the

crack in this fracture mode (debonding along fiber-matrix interface), one could

not reach this state prior to fiber or matrix fracture (fig. 8(a)). In other

words, the debonding will not take place by itself, it follows the fiber fracture. Figure 8(a) and (b) show similar type of behavior. If the matrix were

to fracture first, interface debonding will follow instantaneously. Although,

the energy required to propagate the crack in interface debonding mode following the matrix fracture is much less than the energy required when the debonding follows the fiber fracture. Also, from figures 8(a) and (b), it can be

concluded that if the matrix strength is more than 1/20 of the fiber strength,

the fracture will not initiate in the matrix. Fracture will, then, initiate in

the fiber and interface debonding will follow instantaneously. On the other

hand, in the case of ceramic composites, for example, where the fiber and

matrix stiffnesses are almost the same, but the matrix strength is much less

than the fiber strength, then the fracture will initiate in matrix, followed by

instantaneous interface debonding.

Hence, for the case of longitudinal loading, due to fracture in one fiber,

the increase in longitudinal stress, a_l 1, in neighboring fibers is small,

implying that the random fracture in a fiber is unlikely to initiate fracture

in neighboring fibers. Following a fiber fracture, depending upon the local

matrix tensile strength and the local interface shear strength, the crack grows

either in the matrix or along the fiber-matrix interface. It is also concluded

that for a unidirectional composite subjected to longitudinal loading, interface debonding does not initiate by itself. It propagates along the fibermatrix interface as a followup of fiber or matrix fracture.

Transverse Loading

For the case of transverse loading, the bottom XY-plane (fig. 1) is fixed

in Z-direction (w = 0.0) and the top XY-plane is given a fixed displacement in

Z-direction (w = 0.0008 in. or 0.02 mm). For this loading case, if the fracture initiates in the fiber or in the matrix, there is no reduction in the

transverse stiffness, unlike the case of longitudinal loading when fiber fracture did cause a reduction in longitudinal stiffness. However, if the crack

initiates at the fiber-matrix interface and as the fiber surface debonds from

the matrix, there is a considerable reduction in transverse stiffness as the

debonded fiber surface area increases. The reduction in transverse stiffness

versus the percentage of fiber surface area debonded is shown in figure 9.

There is approximately 20 to 25 percent reduction in transverse stiffness when

50 percent of total fiber surface area is debonded. The corresponding strain
energy release rate curve versus the percentage of fiber surface area debonded

is shown in figure 10. The crack growth in this mode is stable. Once, 10 percent of total fiber surface area is debonded, it takes much less energy to

drive the crack further, indicating crack propagation instability and high sensitivity of debonding extension due to transverse loading. Hence, it can be

concluded that the transverse tensile test is much more indicative of interfacial conditions than it is of either fiber or matrix conditions.

Shear Loading

Shear loading is applied to the specimen both in XY-plane and YZ-plane.

For the shear loading in the XY-plane, entire model is fixed in Y and Z direction (fig. 1). The left XZ-plane is fixed in X-direction (u = 0.0) (fig. 1)

and right XZ-plane is given a prescribed displacement in the X-direction

(u = 0.0008 in. or 0.02 mm). For the shear loading in the YZ-plane, entire

model is fixed in the X and ¥ directions. The left ×Z-plane is fixed in

Z-direction and right XZ-plane is given a prescribed displacement in the

Z-direction (w = 0.0008 in. or 0.02 mm). Results for both of these shear loadings are similar. If only a fiber or the matrix is fractured, it does not

reduce the global shear stiffness of the composite, and hence, the strain energy release rates are negligibly small. However, there is a gradual decrease

in shear stiffness as the center fiber starts to debond (fig. 11). There is

approximately 6 percent reduction in stiffness as the center fiber is fully

debonded. The corresponding strain energy release rate as the center fiber

debonds is shown in figure 12. The fracture propagation in this loading case

is stable. Additional energy needed to drive the crack reduces as the fracture

propagates along the fiber-matrix interface. Thus, the shear loading shows the

same type of behavior as was observed under transverse loading i.e., shear

loading is much more indicative of the interfacial conditions than it is of

either fiber or matrix conditions.

Bending Load

Load was applied on the model so as to bend it in the XZ-plane (refer to

fig. 1). The model was fixed in the z-direction (w = 0.0) on the back face

(X/L = O, fig. 1). On the front face (X/L = 1), a total vertical toad of 445 N

(100 lb) was applied in the - z direction equally distributed over the nine

fiber surfaces (fig. 13). Resulting displacements corresponding to the applied

nodal forces are found by finite element analyses for different fracture configurations. In one set of simulations, one fiber in top layer was fractured

at the middle and then all three fibers were fractured. Similarly, the crack

was initiated in the matrix and in all cases it was allowed to propagate along

the fiber-matrix interface following the fiber/matrix fracture. It was found

that there is no reduction in global bending stiffness when fiber/matrix frac'

ture or fiber-matrix interface debonds. _

Even though, the fiber or matrix fracture has no effect on the global

bending stiffness, it provides a site for the initiation of delamination.

Hence, the effect of delamination on the global bending stiffness was also

investigated. The delamination was initiated between the top and middle plies

symmetrically about the middle plane (X/L = 0.5). The delamination is then

propagated outward towards the free edges of the laminate and also along the
length. It is found that the internal (interior) delaminations (fig. 14) do

not reduce the global stiffness in bending. Only, when the delamination

extends over the full width of the laminate, there is approximately 10 percent

reduction in global bending stiffness as compared to the case with no delamination. The reduction in global bending stiffness is independent of the extent

of delamination longitudinally even when it extends over the full width. The

strain energy release rate versus percentage of area delaminated curve is shown

in figure 15. It shows that once interior delamination, extending up to full

width initiates, it is the onset of instability. The delamination can extend

longitudinally at the same fracture energy level. The reason being that the

shear which is driving the delamination is constant along the length.

PROCEDURES FOR EVALUATING COMPOSITE MICROFRACTURE

The collective results from the computational simulations previously

described can be used to provide step-by-step procedures for evaluating composite microfracture. It can be used to predict fracture toughness, fracture

process, hierarchy of fracture modes and extent of stress redistribution in a

given composite system for various loading cases. The following steps outline

the procedure for evaluating composite microfracture:

(1) Obtain the room temperature properties of the fiber and matrix (constituent) materials.

(2) Generate a three-dimensional finite element model as described in the

Finite Element Model section.

(3) Perform the simulation for the reference case (no fracture) under

desired loading condition (longitudinal, transverse etc.).

(4) Initiate the fracture in the fiber and perform the simulation under

same loading condition as in step 3. Then, propagate the fracture in the

matrix and/or along the interface and perform various computational simulations

for different extent of damage.

(5) Repeat step 4, except that initiate the fracture in the matrix or in

the fiber-matrix interface.

(6) For a given loading condition, compare the different fracture configurations for reduction in global stiffness and corresponding strain energy

release rates.

(7) Determine the most likely direction for crack propagation for a given

loading condition based on the strain energy release rates. It may happen that

a particular fracture configuration requires a very small amount of fracture

energy to drive the crack, but a certain other fracture configuration requiring

high fracture energy must be reached prior to reaching a fracture configuration

requiring a low fracture energy (fig. 8(a)).

(8) Knowing the fiber, matrix and interface in-situ strengths and strain

energy release rates for various loading conditions and fracture configurations, estimate the most likely direction of fracture propagation as well as

fracture modes and fracture sequence.
SUMMARY

A three-dimensional finite element computational simulation procedure was

developed for microfracture propagation and to evaluate fracture toughness in

metal matrix composites based on strain energy release rates. The procedure

was applied to simulate microfracture for fiber, matrix and fiber-matrix interface. Step-by-step procedures were outlined to predict the fracture process

and establish hierarchy of fracture modes. The significant results from this

work are as follows:

1. Fracture in one fiber is unlikely to initiate fracture in neighboring

fibers when the composite is subjected to longitudinal loading. Also, the

interface debonding will not initiate by itself under such loading. It will

progress along the interface as a follow up of fiber or matrix fracture.

2. Even if a substantial percentage of fibers are fractured in a plane,

there is a reduction in the strength in that plane, but the reduction in global

longitudinal stiffness is small and perhaps difficult to detect by experiments,

at least for the composite system and fiber volume ratio investigated.

3. Debonding along the fiber-matrix interface is the only likely event for

the fracture propagation for composites subjected to transverse or shear type

loading. Although, under shear loading, the composite is not as sensitive to

debonding extension as it is under transverse loading.

4. Composites subjected to bending loads show that the fiber/matrix frac

ture or fiber-matrix interface debonding is not sensitive to bending loads.

Delamination is the only likely mode of fracture propagation under such

loading.

5. The stresses redistribute around a microfracture within a short distance for the composite system investigated. Also, the stress concentrations

around a microfracture are lower than what would be expected for an isotropic

case due to the composite being subjected to far field stresses.

REFERENCES

I. Caruso, J.J.; Trowbridge, D.; and Chamis, C.C.: Finite Element Applications to Explore the Effects of Partial Bonding on Metal Matrix Composite

Properties. AIAA Paper 89-1175, Apr. 1989.

2. MSC/NASTRAN, Version 64, Vol. [ and II, Users Manual, The MacNealSchwendler Corporation, Los Angeles, 1982.

3. ffilt, T.E.; Murthy, P.L.N.; and Chamis, C.C." Fracture Toughness Computational Simulation of General Delamination in Fiber Composites. J. Reinf.

Plast. and Compos., vol. 8, no. 1, Jan. 1989, pp. 2-17.

4. Caruso, J.J.; and Chamis, C.C.: Superelement Methods Applications to

Micromechanics of High Temperature Metal Matrix Composites. Structures,

Structural Dynamics and Materials Conference, 29th, Williamsburg, VA, Apr.

1988, Technical Papers, Pt. 3, AIAA, Washington, DC, 1988, pp. 1388-1400.

(Also AIAA Paper 88-2390, 1988.)
TABLEI. - PROPERTIES OF CONSTITUENT MATERIALS OF SiC/Ti15

Modulus, E, mpsi

Poisson's ratio, v

Shear mosulus, G, mpsi

Coefficient of thermal

expansion a, ppm/°F

SiC fiber Til5 matrix Interface

62.0

.3

23.8

1.8

12.3

.32

4.6

4.5

12.3

.32

4.6

4.5

X/L = 0

BACK FACE -'_ Z

FIBER "_

-ei-_ J:e2...".j z.

, L_ MATRIX X.u

z-X/L= 1

FRONT FACE

Figure 1. - Schematic diagram of nine cell model.

FIBER -n

_/

/

-.-_y

UNIT CELL

TOTAL

FIBER

4.3 FIBER

diarn

REPRESENTATION OF NINE

CELL MODEL

6912 ELEMENTS

6953 NODES

Figure 2. - Representation of nine cell model finite element mesh.

Figure 3. - Representation of fiber fracture

and interface debonding.

9
_L=0

BACK FACE

%

I

PLANE OFFRAC. FIBER/ ,-" ,-" j/]

- _! ! - -

IO'!OiOl.. i I -" ," "/

, l P Yv .;1.,

// pt X,u

z_ X/L = 1 " LOCATION OF THE GRID POINT

FRONT FACE IN FIBER ALONG WHICH

STRESSES ARE PLOTTED

CGftt

Gm 11

-- J

r ,/,

15% INCREASE IN STRESS ."

IN NEIGHBORING FIBER J

100% INCREASE IN MATRIX STRESS

AT FIBER FRAC. LOCATION

r .....

I

I

•m--m "L --I _. ......... j

i 1 1 1

• 10 .20 .30 .40

X/L

Figure 4. - Slmss variation along the length in fiber and

matrix for longitudinal loading.

I

_.50

X/L = 0

BACK FACE

\

PLANE OF FRAC. FIBER/ _" ," J/I

"'L ./" .." / ."1

if /I j"

FIBER--_ .," ," / ,- ,." j

.;.wL',I _ I _ I - " /

IliUigi.-" .-" /z,w

"-J,=t_=--_;_-_" .'" f L,,w

._____(B_k_l__l :"" j_1 / f

, ALIAILIJlh / P _--m,-fv

,' _i_illr_ _ '

ZX/L= t

FRONT FACE

10

_z

=,,u_5

aN

-- g% REDUCTION IN GLOBAL STIFFNESS

I I I I J I

20 40 60 80 100

% FIBERS FRACTURED

Figure 5. - Reduction in stiffness vs. percent fibers

fractured for longitudinal loading.

3O

04.

C

"2O

nLU

U3

10

40 --

/

¢ ¢ ¢ ¢ ¢ ¢ ¢ -

SERR = _1 (F2-F1)u

2 t_.

1 I I 1 1 1 ! 1 I I

10 20 30 40 50 60 70 80 90 100

% FIBERS FRACTURED

Figure 6. - Strain energy release rate vs. percent fibers

fractured for longitudinal load.

LU

Z

EL

EL

F- 10

</)

z

z

o

I0 5

FIBER ] r INTERFACE

1 / (MATRIX)

DEBOND

LENGTH

NO DEBONDING _ /

_ / / 10% REDUCTION IN

/ • ./- STIFF. FOR FULLY

/ 7 DEBONDED CENTER

FIBER

I I I I

.25 .50 .75 1.00

DEBOND LENGTH/TOTAL LENGTH OF FIBER

Figure 7. - Reduction in stiffness vs. debond length of

center fiber for longitudinal loading.

10
6O

O4

c40

c

c_

_. 2

tlr"

LLI OF)

0

I/ f-- FIBER FACTURE FIBER7

NO DEBONDING

r-INTERFACE

i l I' (MATRIX)

LENGTH

i

(a) I I I I

.25 .50 .75 1.00

DEBOND LENGTH/TOTAL LENGTH OF FIBER

MATRIX FACTURE

NO DEBONDING

(b) I

FIBER1

Ii i

- [------

I I

rlNTERFACE

(MATRI_

DEBOND

LENGTH

l

.25 .50 .75

I

1.00

DEBOND LENGTH/TOTAL LENGTH OF FIBER

Figure 8. - Strain energy release rate for center fiber

debonding for longitudinal loading.

2O

_z

W _

FIBER"I FINTERFACE

/ /i (MATRIX)

I I I I

10 20 30 40

% FIBER SURFACE AREA DEBONDED

Figure 9. - Reduction in stiffness vs. percent fiber

surface area debonded for _ansverse loading.

I

50

L F'BEi I_'NTERFACE

/ (MATRIX)

20 _

_ 10

0 10 20 30 40

% FIBER SURFACE AREA DEBONDED

Figure 10.- Strain energy release rate vs. percent fiber

surface area debondedfor transverse loading.

I

5O

Zm

pw

LlZ

LUI'--

n-CO

FIBER7 I"INTEPEACE

/ I / I (MATRIX)

.25 .50 .75 1.00

DEBOND LENGTH/TOTAL LENGTH

Figure 11. - Reduction in stiffness vs. center fiber

debonding for XY shear loading.

11
3

FIBER1 r INTERFACE

i I (MATRIX)

_-c 2 _-_-- " l

"? t I

_O DEBOND

E" LENGTH

I11

I I I I

0 25 .50 .75 1.00

DEBOND LENGTH/TOTAL LENGTH

Figure 12. - Strain energy release rate for center fiber

de[_onding for XY shear loading.

FIXED AT

BACK FACE

(X/L = O) --_ Z

Y

FIBER --_

Z,w

ii II1"

/ L_ MATRIX X,u

z- YJL = 1

FRONT FACE

Figure 13. - Application of bending loads.

FIBER

J

i/

t t

//

L_ X/L =0.5

MIDDLE PLANE

I

I

I

.i

,,'O', Y,v

X,u

Figure 14. - Internal delaminatJon between top and middle plies.

O4,

3OO

c200

¢-

t_

uJ 100 G)

X,U

I I l I

25 50 75 100

% AREA DELAMINATED

Figure 15. - Strain energy release rate for interior

delamination.

12
Report Documentation Page

4

National Aeronautics arid

Space Adminislration

1. Report No. NASA TM-103153 2. Government Accession No.

ICOMP-90-14

4. Title and Subtitle

Metal Matrix Composites Microfracture: Computational Simulation

7. Author(s)

Subodh K. Mita], John J. Caruso, and Christos C. Chamis

9.

12.

Performing Organization Name and Address

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

3. Recipient's Catalog No.

5. Report Date

6. Performing Organization Code

8. Performing Organization Report No.

E-5514

10. Work Unit No.

510-01-0A

1t. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

15. SupplementaryNotes

Prepared for the Symposium on Computational Technology for Flight Vehicles cosponsored by NASA and George Washington

University, Washington, D.C., November 5-7, 1990. Invited Paper. Subodh K Mital, Institute for Computational Mechanics

in Propulsion, Lewis Research Center, Cleveland, Ohio (work funded by NASA Space Act Agreement C-99066-G; Louis A.

Povinelli, Space Act Monitor). John J. Caruso and Christos C. Chamis, NASA Lewis Research Center.

16. Abstract

Fiber/matrix fracture and fiber-matrix interface debonding in a metal matrix composite (MMC) are computationally

simulated. These simulations are part of a research activity to develop computational methods for microfracture,

microfracture propagation and fracture toughness of the metal matrix composites. The three-dimensional finite

element model used in the simulation consists of a group of nine unidirectional fibers in three by three unit cell

array of SiC/Ti15 metal matrix composite with a fiber volume ratio of 0.35. This computational procedure is

used to predict the fracture process and establish the hierarchy of fracture modes based on strain energy release

rate. It is also used to predict stress redistribution to surrounding matrix/fibers due to initial and progressive

fracture of fiber/matrix and due to debonding of fiber-matrix interface. Microfracture results for various loading

cases such as longitudinal, transverse, shear and bending are presented and discussed. Step-by-step procedures are

outlined to evaluate composite microfracture for a given composite system.

17. Key Words (Suggested by Author(s))

Composites; Metal-matrix; Fiber fracture; Debonding;

Stress redistribution; Strain energy release rate;

Interface; Fracture; Microfracture

18. Distribution Statement

Unclassified- Unlimited

Subject Category 24

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

Unclassified Unclassified 14

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