7
,- y ELSEVIER Theoretical and Applied Fracture Mechanics 25 (1996) 203-209 theoretkal and applied fracture mechanics Computational simulation of microfracture in high temperature composites S.K. Mital a,1, P.L.N. Murthy b, C.C. Chamis * a The University of Toledo, Toledo, OH, USA b National Aeronautics and Space Administration Lewis Research Center, Cleveland, OH 44135-3191, USA Abstract This paper presents a summary and typical results of the research activities pertaining to composite microfracture in high temperature metal matrix composites carried out by the authors. The various failure modes and their effect on macro behavior as well as the hierarchy of their occurrences are examined by computationally simulating these events using three-dimensional finite element analyses. The procedure is based on the macro strain energy release rate which predicts the direction of crack growth and establishes the hierarchy and sequence of respective failure modes. Step-by-step procedures are outlined for evaluating composite microfracture. Microfracture results for various loading cases for a unidirectional metal matrix composite are presented and discussed. A key result is that interfacial debonding is a consequence of either fiber or matrix fracture. 1. Introduction It is a fairly well known fact that fiber reinforced composites offer distinct advantages over conven- tional monolithic materials which is why they are potential candidate materials for engine applications. The high temperature metal matrix composites in particular, offer very high stiffness and strength to specific weight, high thermal stability, high fatigue and fracture resistance as well as tailorable anisotropic properties. These qualities make them very attractive candidate materials for aerospace propulsion structures. However, the inherent com- plexity introduced due to the heterogeneous structure * Corresponding author. Tel.: + 1-216-433-3252; e-mail: ccha- [email protected]. Resident Research Associate, NASA-Lewis Research Center, Cleveland, OH, USA. of fiber composites coupled with the demanding engine service environments pose formidable tasks to analysts in formally describing the structural be- havior. Over the past several years at NASA-Lewis Research Center, metal matrix composite behavior has been evaluated using computational simulation procedures based on simplified micromechanics equations as well as three-dimensional finite element analyses. The present report is a comprehensive sum- mary of the research activities pertaining specifically to computational simulation of composite microfrac- ture in high temperature metal matrix composites. Microfracture is defined as fiber/matrix fracture, fiber/matrix debonding or inter-play delamination. The objective of this evaluation was to predict the direction of crack propagation due to the crack initia- tion in a constituent and to predict/quantify the change in macro behavior due to some quantifiable micro damage in the composite. A global or a macro 0167-8442/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0167-8442(96)00022-5

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Page 1: Computational simulation of microfracture in high temperature composites

, - y

ELSEVIER Theoretical and Applied Fracture Mechanics 25 (1996) 203-209

theoretkal and applied fracture

mechanics

Computational simulation of microfracture in high temperature composites

S.K. Mital a,1, P.L.N. Murthy b, C.C. Chamis * a The University o f Toledo, Toledo, OH, USA

b National Aeronautics and Space Administration Lewis Research Center, Cleveland, OH 44135-3191, USA

Abstract

This paper presents a summary and typical results of the research activities pertaining to composite microfracture in high temperature metal matrix composites carried out by the authors. The various failure modes and their effect on macro behavior as well as the hierarchy of their occurrences are examined by computationally simulating these events using three-dimensional finite element analyses. The procedure is based on the macro strain energy release rate which predicts the direction of crack growth and establishes the hierarchy and sequence of respective failure modes. Step-by-step procedures are outlined for evaluating composite microfracture. Microfracture results for various loading cases for a unidirectional metal matrix composite are presented and discussed. A key result is that interfacial debonding is a consequence of either fiber or matrix fracture.

1. Introduction

It is a fairly well known fact that fiber reinforced composites offer distinct advantages over conven- tional monolithic materials which is why they are potential candidate materials for engine applications. The high temperature metal matrix composites in particular, offer very high stiffness and strength to specific weight, high thermal stability, high fatigue and fracture resistance as well as tailorable anisotropic properties. These qualities make them very attractive candidate materials for aerospace propulsion structures. However, the inherent com- plexity introduced due to the heterogeneous structure

* Corresponding author. Tel.: + 1-216-433-3252; e-mail: ccha- [email protected].

Resident Research Associate, NASA-Lewis Research Center, Cleveland, OH, USA.

of fiber composites coupled with the demanding engine service environments pose formidable tasks to analysts in formally describing the structural be- havior. Over the past several years at NASA-Lewis Research Center, metal matrix composite behavior has been evaluated using computational simulation procedures based on simplified micromechanics equations as well as three-dimensional finite element analyses. The present report is a comprehensive sum- mary of the research activities pertaining specifically to computational simulation of composite microfrac- ture in high temperature metal matrix composites.

Microfracture is defined as fiber/matrix fracture, fiber/matrix debonding or inter-play delamination. The objective of this evaluation was to predict the direction of crack propagation due to the crack initia- tion in a constituent and to predict/quantify the change in macro behavior due to some quantifiable micro damage in the composite. A global or a macro

0167-8442/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0167-8442(96)00022-5

Page 2: Computational simulation of microfracture in high temperature composites

204 S.K. Mital et a l . / Theoretical and Applied Fracture Mechanic's 25 (1996) 203-209

strain energy release rate is also defined and is used to establish the hierarchy and sequence of fracture modes. This task is accomplished by running several three-dimensional finite element analyses for a com- posite system with some form of assumed damage and computing strain energy release rate form one damage state to another. This procedure is not in- tended to predict the load level at which a particular constituent will fail or a failure mode will occur. It is intended to predict the fracture propagation direction, macro fracture toughness and extent of stress redis- tribution given a particular failure mode in a com- posite subjected to thermal or mechanical loads. Step-by-step procedures are outlined to evaluate composite microfracture for thermal or mechanical loading. A unidirectional 35% fiber volume ratio SiC/Ti-15 metal matrix composite under various types of mechanical and thermal loading is evaluated for microfracture. A summary of the results is pre- sented herein.

z / ~ S a y ~, M,,,*...;~ r- Interphase

Leng'U't - 6.8 ~ ' ~ 'i , fiber diam j ~ = ~ - - . - - - _ . - I R b e r - - 3 ~ ,~k~ /

otal 6912 Elements 6953 Nodes

Fig. 1. Schematic of the unidirectional composite.

sis purposes. The dimensions of the model relative to the fiber diameter are shown in Fig. 1. The proper- ties of the constituent materials at reference (room) temperature are shown in Table 1. The interphase properties are assumed to be same as those of the matrix properties in this work. However, the capabil- ity exists in the finite element mesh to assign differ- ent properties for the interphase material.

2. Finite e l ement mode l

A group of nine fibers in a three-by-three unit cell array is considered for microfracture evaluation in this work. The unidirectional composite system con- sists of 35% fiber volume ratio (fvr) SiC/Ti-15 metal matrix composite (silicon carbide SCS-6 fibers in a titanium alloy matrix). A three-dimensional finite element model of such a fiber arrangement is created. There are 16 elements or 'bays ' along the length of the fiber, as shown in the Fig. 1. Each unit cell consists of 40 hexahedron (six-sided) and eight pentahedron (five-sided) solid elements for a total of 6912 elements and 6953 nodes. The model has suffi- cient degrees of freedom to provide a very detailed stress gradient. A general purpose finite element code M S C / N A S T R A N code [1] was used for analy-

3. Microfacture evaluat ion

Microfracture is evaluated due to a pre-existing defect and a given loading condition. The procedure outlined here is used to evaluate composite mi- crofracture behavior, i.e. to quantify the effects of microffacture on the macro behavior of composite laminates and to establish the hierarchy and se- quence of failure modes for a given geometry and loading conditions.

To simulate a fracture, duplicate nodal or grid points are placed on either side of an assumed defect. These nodal points have the same geometrical loca- tion, but no connectivity exists between them, thus in effect producing the defect of zero width. The load and boundary conditions are applied to the model through uniform boundary displacements. In a typi-

Table 1 Properties of constituent materials of SiCfTi- 15 at room-temperature

SiC fiber Ti- ! 5 matrix lnterphase

Modulus (GPa) 428 85 85 Poisson's ratio 0.3 0.32 0.32 Shear modulus (GPa) 164 32 32 Coefficient of thermal expansion, a ( 10 - 6 °C i ) 3.2 8.1 8.1

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S.K. Mital et al. / Theoretical and Applied Fracture Mechanics 25 (1996) 203-209 205

cal set of simulations, fracture is initiated in the center fiber in the middle of the center cell and is allowed to propagate either through the matrix or along the fiber matrix interface. Similarly, a crack could be initiated in the matrix or the fiber/matrix interface. Resulting nodal forces corresponding to the applied boundary displacements are computed by finite element analyses. As the defect is propagated, comparison in the resulting nodal forces is made to compute the reduction in global stiffness and to compute the global strain energy release rate (SERR) as described below. In the case of thermal loads, symmetric boundary conditions are applied in the middle plane, so that the composite is free to move on either side. As before, the strain energy release rate is computed for different damage states to quan- tify and establish different fracture modes.

Strain energy release rate is an indicator of the fracture toughness of a material. It gives a measure of the amount of energy required to propagate a defect in a material. That allows one to make a direct comparison of damage tolerances between different microfracture configurations, materials and geome- tries. One of the common methods used to compute strain energy release rate is the crack closure method. In this method, nodal displacements and the corre- sponding 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 during the propagation. This approach is a local approach. An alternate approach is a macro approach and has been used to compute SERR herein. In this approach, applied nodal displacements and corresponding nodal forces are used to calculate the work done to propagate the crack. Strain energy release rate, G, is then calculated as [4]

dW 1 ( F 2 - F l ) ' u

G = dA = 2 " AA (1)

in which dW stands for the change in the work done, A A is the area of new surfaces generated, u is the applied displacement at the loaded end of the model, and F 1 and F 2 are the forces at the loaded nodes before and after A A, respectively.

The above equation simply represents the incre- mental change in work divided by the new surface area that opens up from one fracture state to another.

In the case of thermal loads, SERR is calculated

by comparing the internal strain energies before and after the crack propagation. Strain energy release rate, G, is then calculated as

dW 1 ( S E ) 2 - ( S E ) I

G = OA = 2 " AA (2)

Internal strain energies prior to and after A A are given by (SE) l and (SE) 2, respectively.

The SERR computation was done using both the crack closure method and the total strain energy in the case of thermal loads. Both methods give the same answer, although using total strain energy re- lease rate is computationally more efficient. The crack closure method helps identify the contribution of each mode of failure, while the total strain energy formulation would not be able to provide this infor- mation. The following assumptions are also used in evaluating microfracture by the procedure outlined above:

- Damage grows when the local microstress state exceeds the corresponding material strength in that mode.

- Damage propagates when the stress exceeds the material strength near the damage periphery.

- The strain energy release rate shows whether the damage growth is stable and which way the damage will grow (as illustrated in the sample cases in Section 4).

It should be mentioned that the advantage of using a macro (total) SERR formulation is that it bypasses local stress details, like stress gradients, that may cause convergence inconsistencies.

4 . D i s c u s s i o n s

The cases evaluated and the typical results ob- tained for a 35% fiber volume ratio unidirectional SiC/Ti-15 composite are presented to illustrate the methodology. Additional discussions and results are presented in [2-4].

4.1. Longitudinal load

The fracture initiation and propagation is associ- ated with stress redistribution in the surrounding fibers and matrix regions. For example, when the center cell fiber is fractured at the middle at X = L / 2

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206 S.K. Mital et al. / Theoretical and Applied Fracture Mechanics 25 (1996) 203-209

due to an applied longitudinal load, the longitudinal stress in the surrounding matrix increases twofold, while the neighboring fibers see only a 15% increase in the longitudinal stress as compared to the refer- ence (no fracture) case, as shown in Fig. 2. Hence a premature fiber fracture (fiber stress less than 85% of the typical fiber fracture stress) is unlikely to initiate fracture in the neighboring fibers in this composite.

If the crack propagates along the f iber /matr ix interphase, there is about 10% reduction in global stiffness for a fully debonded center fiber as shown in Fig. 3. The corresponding SERR curve is shown in Fig. 4. If the fracture initiates in the matrix and propagates along the f iber /matr ix interface without a fiber fracture, the reduction in macro stiffness is rather small and so is the SERR as shown in Fig. 4(b). The following observations can be made based on the SERR curves:

Fracture initiates in the fiber: o'f~/Sfi~T > 0.85 leads to fracture in neighboring fibers and thus causes a 'brit t le ' failure, < 0.85 is premature fiber fracture; then G i / G f < 0.5 (or Sis < Sf~ IT ) leads to interphase

X/L=O back face --~ Plane of frac.

f iberX/L.O.5~ ~

v ~ ~ /7 , - " . - " / _ . ' l " . , " J

- ~ - ~

/XA,.= I X.u f'r'o~ face

100

90

re

85

10% Reduction in sliffne~ for fully debonded center fiber - /

I I .J J .25 .50 .75 1.00

Ratio of debond length to total length of fiber

Fig. 3. Reduction in stiffness versus debond length of the center fiber (longitudinal load; unidirectional composite).

2

b 1

X/L=O Plane of file, back face --~ f iberX/L=0.5~ ~

Fi~r ~,,~, .." . . ' ~ ..'I" . - " J

, ' l e ; ~ l l ) . k ~ ¢ 1' - - *"v . V z..- X/L = 1

front face t_ Location of b'~ ~kl po~t

s ~ ere plott~

jr, / / i f t

15% Increase in stress / in nelgbbodng tibet --"

of11 . . . . °ml I

100% Increase in matrix stress at fiber frac. ~

x

I

I I I I I 0 .10 .20 .30 .40 .50

XA_

Fig. 2. Longitudinal stress variation along the length in a neigh-

boring fiber and matrix for longitudinal loading (center cell fiber fractured at the middle).

6O

40

Fiber -7 r- Interface

/,--- Fiber fractu, re; I / L ~ I I Debond

1 I I I

/-- Matrix fracture; / no debonding

'T

,

w

0 .25

Fiber ~ r- Interphase

I I .50 .75

I 1.00

Ratio of debond length to totat kmglJh of tibet

Fig. 4. Strain energy release rate for center fiber debonding under longitudinal loading (1 lb in . / in . 2 = 175 N / m ) .

Page 5: Computational simulation of microfracture in high temperature composites

S.K. Mital et al. / Theoretical and Applied Fracture Mechanics 25 (1996) 203-209 207

debonding, > 0.5 leads to fracture in neighboring fibers.

Fracture initiates in the matrix (O'ml I =Smllx): Gi/G m <0.25 (or Sis <SmltX) will lead to inter- phase debonding, > 0.25: fracture will propagate in the matrix up to adjacent fibers.

In the observations above, longitudinal stress in fiber and matrix are given by Gfl I and Gml l, respec- tively while longitudinal fiber and matrix tensile strength are given by SfllT and SmlIT, respectively. The interphase shear strength is Sis and the initial fracture toughness of fiber, matrix and interphase are Gf, G m and G i, respectively.

If the fracture initiates and propagates in the fiber/matrix interface debonding without any fiber or matrix fracture, there is no reduction in the macro stiffness and the corresponding SERR is zero. It can thus be concluded that if a unidirectional composite is subjected to longitudinal (along the fiber) loading, interphase debonding does not initiate by itself. It will only occur as a consequence of fiber or matrix fracture.

It was also noticed that even when a substantial percentage of fibers are broken in a plane, there is a reduction in strength in that plane, the reduction in macro stiffness is small and perhaps difficult to detect by conventional experiments.

4.2. Transverse load

If the fracture initiates in the fiber or matrix, there is negligible reduction in the macro transverse stiff- ness. However, if the fracture initiates in the matrix and propagates along the fiber/matrix interface and as the fiber surface starts to debond from the matrix, there is a considerable reduction in that stiffness as shown in Fig. 5(a). There is approximately 20% reduction in stiffness when 40% of the total fiber surface area is debonded. The corresponding SERR curve is also shown in Fig. 5(b). Once 10% of the 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 cracking.

4.3. Bending load

Load was applied so as to bend the composite in the XZ plane as shown in Fig. 6. It was observed

|

¢

i

100

90

80

Fiber -~

20

I I I I I 10 2O 3O 4O SO

Fiber sorface area debondsd,

Fig. 5. Reduction in stiffness and strain energy release rate versus fiber surface debonded under in-plane transverse loading (un- idirectional composite).

that there is no reduction in macro bending stiffness when the crack initiates in the fiber or matrix. It was also observed that there is no reduction in global bending stiffness for internal delaminations - - when the delamination does not extend across the full width of the specimen. Once the delamination ex- tends over the full width, then there is reduction in the global bending stiffness and the corresponding SERR curve is shown in Fig. 6. Once the delamina- tion extends across the full width, it is the onset of instability, i.e. delamination can extend at the same energy level. This type of fracture mode may be classified as shearing fracture mode (II) and is driven by the presence of interlaminar shear at that plane.

10o

i[ I I t x~ I 0 25 50 75 100

Ar~ del~llnntotl, p4tc*nt

Fig. 6. Swain energy release rate versus delaminated area.

Page 6: Computational simulation of microfracture in high temperature composites

208 S.K. Mital et al. / Theoretical and Applied Fracture Mechanics 25 (1996) 203-209

5. Thermally driven microfracture

Various thermal loading cases were evaluated for microfracture evaluation. Only selected and typical results are presented here; more detailed information can be found in [4].

As the SiC/Ti-15 composite is cooled down from processing temperature to room temperature, the lon- gitudinal stress in the fiber is compressive, while the matrix longitudinal stress is tensile (am > c~f). Hence during the cooldown process, the fracture is likely to initiate in the matrix. In one case, composites were uniformly heated form room temperature to 300°C (570°F), a temperature difference of about 280°C (500°F). Fracture was initiated in the matrix and various microfracture configurations were consid- ered. It was observed that for all possible fracture paths, SERR was very small. Hence, it was con- cluded that microfracture propagation is quite insen- sitive to temperature increase up to 280°C (500°F). A typical SERR curve is shown in Fig. 7 for a unidirec- tional composite under thermal loads. Fiber/matrix debonding is the only likely mode of fracture propa- gation in this case. Several other temperature profiles were also considered for microfracture evaluation. In summary, it was observed that in the case of a unidirectional composite subjected to a uniform tem- perature increase, the microfracture initiates in the matrix and propagates through the fiber/matrix in- terface. Pre-existing cracks in the interface or inter- ply regions would not propagate. In general, mi-

1.00

% .c

.so ¢" rr

n

/ I I I i I

20 40 60 80 1 O0 Fiber surface debonde<l, percent

Fig. 7. Strain energy release rate for a unidirectional composite under thermal load (AT = 500°F).

crofracture propagation is much less sensitive to thermal loads than it is to mechanical loads.

6. Procedures for evaluating composite microfrac- ture

The results from the computational simulation described above can be used to describe a step-by- step procedure to evaluate composite microfracture. This can then be used to predict a macro fracture toughness, direction of fracture propagation and ex- tent of stress redistribution in a given composite system for a variety of loading cases. The following steps describe this procedure: 1. Obtain the room-temperature properties of con-

stituent (fiber/matrix/interphase) materials. 2. Generate a three-dimensional finite element model

such as shown above. 3. Perform the simulation for a reference (no frac-

ture) case under the desired loading condition (mechanical/thermal).

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 or along the interphase and perform various anal- yses for different extent of damage.

5. Repeat step 4 but initiate the fracture in the matrix or interphase (for a given loading condi- tion and laminate geometry, one can get an esti- mate from stress analysis where a fracture is most likely to initiate).

6. For a given loading condition, compare the differ- ent fracture configurations for reduction in global stiffness and corresponding strain energy release rates.

7. Determine the most likely direction for crack propagation based on SERR under a given load- ing condition. It may happen that a particular fracture mode requires a very small amount of fracture energy to propagate the crack, but a certain other fracture mode must be reached prior to reaching a fracture configuration requiring a low fracture energy (see Fig. 4).

8. Knowing the fiber/matrix/interphase in-situ strengths and SERR for loading conditions and fracture configurations, determine the most likely direction of fracture propagation as well as frac- ture modes and fracture sequence.

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S.K. Mital et al. / Theoretical and Applied Fracture Mechanics 25 (1996) 203-209 209

7. Conclusions References

A computational simulation procedure was de- scribed to evaluate composite microfracture in high temperature metal matrix composites. The procedure is based on three-dimensional finite element analyses and macro strain energy release rates. It can predict the sequence and hierarchy of fracture modes in a composite subjected to thermal and mechanical loads. Results show that interfacial debonding does not initiate prior to fiber and matrix fracture. In general, microfracture propagation in metal matrix compos- ites is not as sensitive to thermal loads alone as it is under mechanical loads.

[1] The MacNeal-Schwendler Corporation, User's Manual, MSC/NASTRAN, Version 64, Vol. 1 and II (The MacNeal- Schwendler Corporation, Los Angeles, 1982).

[2] S.K. Mital, J.J. Caruso and C.C. Chamis, Metal Matrix Com- posites Microfracture: Computational Simulation, Comput. Struct. 37(2), 141-150 (1990) (also NASA TM-103153 (1990)).

[3] S.K. Mital and C.C. Chamis, Microfracture in High Tempera- ture Metal Matrix Crossply Laminates, NASA TM-104381 (1991).

[4] S.K. Mital and C.C. Chamis, Thermally-driven Microfracture in High Temperature Metal Matrix Composites, Proc. Syrup. on the Mechanics of Composites at Elevated and Cryogenic Temperatures, ASME Applied Mechanics Division Meeting, Columbus, Ohio, 16-19 June (1991).