Micromechanical modeling of damage growth in titanium based metal-matrix composites

Compulers

00457949(95)00040-2

& S~rucrurrs Vol. 56, No. 213, pp 505-514, 1995 Elsevier Saence Ltd Pnnted I” Great Bntam 0045.7949/95 39.50 + 0.00

MICROMECHANICAL MODELING OF DAMAGE GROWTH IN TITANIUM BASED METAL-MATRIX COMPOSITES J. A. Sherwood and H. M. Quimhy Department

of Mechanical

Engineering,

University

of Massachusetts

at Lowell, One University

Avenue,

Lowell, MA 01854, U.S.A. Abstract-The thermomechanical behavior of continuous-fiber reinforced titanium based metal-matrix composites (MMC) is studied using the finite element method. Fiber and interface failures are modeled as discrete damage. The evolution of matrix failure is considered as continuum damage. A thermoviscoplastic unified state variable constitutive theory is employed to capture inelastic and strain-rate sensitive behavior in the TimetaPs matrix. The SCS-6 fibers are modeled as thermoplastic and can fail at some prescribed plastic strain to failure. The effects of residual stresses generated during the consolidation process on the tensile response of the composites are considered. Unidirectional and cross-ply geometries are studied. Differences between the tensile responses in composites with perfectly bonded, weakly bonded and completely debonded fiber/matrix interfaces are discussed.

sider the fiber-matrix interface bond and the immediate surrounding region. While discrete characterization of the interphase region may not be crucial to the overall macroscopic response of the composite, it is important to consider the state of the fiber-matrix interface bond. At a minimum, the finite _I_-__-. ---2-l _c AL_ -_-.-__ll_ _1__..12 L_ -L,_ L_ e,ieIIienL IIl”UCi “1 Lilt: c”rnp”siLe bn”Lu” De anie L” simulate perfect bonding of the fiber and matrix as well as complete debonding of the constituents. It is also desirable to simulate partial debonding and the evolution of the strength of the interface during composite loading. One goal of this study is to investigate the role of the interface-bond strength on the predicted thermomechanical macroscopic resnnnse PICCh “. -r--a-- of the commosite, Titnetal’~-21 yllvl In the past five years, many experimental and numerical research efforts have been directed toward titanium-based composites. Experimental research still represents the major portion of the effort. However, numerical techniques have been established as a viable means of composite analysis, and their use is becoming more common. Numerical studies typically employ a constitutive theory with the ability to capture the plastic and time-dependent behaviors inherent to the matrix in some composite materials. Several comprehensive constitutive theories have been developed in the past, and new theories continue to emerge [l-5]. Most of the theories share common ingredients in that they use some plastic-flow rule in cooperation with evolution equations for state variables. The new constitutive models are often implemented into finite element codes in the form of user-supplied material models and/or incorporated into stand-alone composite analysis packages.

1. INTRODUCTION

The aerospace, automotive and gas-turbine industries all share the never-ending quest for lighter and stronger materials suitable for use in increasingly demanding high-temperature environments. The de.._l_--__-l _r c”inp”siK __-_-__:r_ -_r_-Z-1.. I_-.._ -_>..__1 “e‘“p”ie”L “1 inalC1iaib rti_r L‘iiil iiave icouceu weight and increased strength relative to the previously used materials is critical to achieving the goal of higher operating temperatures, long-life and reduced weight. One such composite system is the titanium-based silicon-carbide fiber reinforced metal-matrix composite. To accurately predict the complex thermomechanical resnonse for this class of rQp_nnsite mat&&, ihe r----r----rate- and temperature-dependent properties of the constituents must be considered in the model. Adding to the complexity of the composite-material model is the lack of a complete understanding of the behavior at the fiber-matrix interface. The nature of the interface bond is a combination of mechanical and chemical bonding, and the contribution of each is not well understood. The use of a unit cell in the finite element method (FEM) is a common numerical tool for investigating the stress state on the microscale. This approach assumes that the respective thermomechanical properties of the matrix and fiber can be characterized individually. The individual constituents can then be used together in the finite element model such that the overall response of the composite can be simulated. In addition to the material properties of the constituents, the finite element model should also con505

506

J. A. Sherwood and H. M. Quimby

Several researchers have completed numerical and experimental investigations of the microscopic and macroscopic thcrmomcchanical behaviors of titanium-based fiber-reinforced composites. The numerical investigations all required some a priori assumptions about the interfaciai bond strength. Many computational works have considered the fiber-matrix interface as completely bonded, e.g. Kroupa et al. [6], Aboudi [7], Santhosh and Ahmad [8], Gosz et al. [9], and Arnold et al. [lo]. While others have considered the interface as completely debonded or strong, e.g. Grady and Lerch [I 11, Nimmer et al. [12], and Mital and Chamis [13], still other studies have considered it to be between perfectly bonded and debonded, i.e. weak, e.g. Lissenden et al. [14], Eggleston and Krempl 1151, Mital et al. [16], Majumdar et al. [17]. In addition, other analyses of Ti-based composites have been completed and are worthy of attention [ 188261. The evolution and effect of fiber-matrix debonding is a major concern in composites which are loaded transversely to the fiber direction [27]. Previous numerical studies by the authors considered how the state of the fiber-matrix interface influences the composite material behavior. The effect of perfectly bonded vs completely debonded was investigated using an FEM unit cell model and discussed [28]. As was expected, the experimentally observed response of the [O/90],, composite for a tensile test fell between the two extreme conditions of fiber-matrix bonding. It was concluded that the numerical simulations using the perfectly debonded assumption more closely matched experimental observations than did those using a perfectly bonded interface. While these previous numerical studies :__-11-1 rl-_r r,._ l.-l_..r__- L--A c-.. .I._ _--.-__:r_ nnpneu unit me interlace uonu ior me compobitc under consideration was relatively weak, they did not quantify the strength of the bond. The goal of this paper is to try and characterize the strength of the interface bond. The numerical investigations will use the unit cell in the finite element method to investigate the macroscopic response of the composite due to tensile loadings at 23 and 650°C. The influence of the residua! stresses deve!oped during the consolidation process is addressed. Unidirectional [0], and cross-ply [O/90],, lay-ups are considered. The effects of perfect and imperfect fiber-matrix interfaces and rate-dependent matrix behavior on the response are investigated.

2.

CONSTITUTIVE

THEORIES FOR THE FIBER AND MATRIX

A unified constitutive theory was used in this study to model the matrix thermomechanical behavior. The theory was chosen for its ability to model the nonlinear time-dependent behavior. The model was proposed by Ramaswamy and Stouffer [29] and is based on the theoretical development of Bodner and Partom [30]. Sherwood and Boyle [31] implemented the

theory into the ADINA finite element program [32] in the form of a user-supplied material model for twoand three-dimensional analyses. Ramaswamy, et al. demonstrated that the model had the ability to accurately predict the tensile, creep and cyclic behavior of Rene 80 over a wide range of temperatures. In addition, Sherwood and Stouffer [33] used the model in analyses of Rene 95 and added a continuumdamage state variable to the formulation. Boyle [34] used the model to investigate the thermomechanical response of a titanium-matrix composite. Sherwood and Fay [35] demonstrated its ability to accurately capture material response to nonproportional loadings. Material constants are derived from experimental testing of monolithic matrix materials. The work of Sherwood and Doore [36] has streamlined the process of finding the necessary temperatureand rate-dependent material constants. The state variables Z and R,, represent changes in the microstructure and describe the isotropic and kinematic hardening contributions, respectively. An extensive review of the RamaswamyStouffer constitutive theory is presented in [33] and is readily available in other references [37]. Thus, a detailed review of the theory will not be reproduced here. Rather, the following equations summarize the constitutive theory. The flow rule is represented by

where K2 is analogous

to J2 and is given by

(2) with the back-stress-evolution

equation

ir,=iz;+ti; expressed

(3)

in terms of the elastic component n; = f; s,,

and the inelastic

(4)

component

(51 The back-stress-recovery

equation

is

(6) The drag-stress

evolution

is described

i=m(Z,-z)ri/‘-A,(Z-Zzr. The value of D, is typically

by (71

assumed

to be lo4 and

Micromechanical

modeling of damage growth in metal-matrix

composites

507

Table 1. Timetal@-21 s material constants as a function of temperature Temperature

CTE 10-6/T

“C

23 260 482 560 584 600 610 620 627 634 639 643 641 650 760 815

9.49 10.45 !:.24 11.50 11.57 11.62 11.66 11.69 11.71 11.73 11.75 11.76 11.78 11.79 12.11 12.27

1.950 1.850 :.:K? 0.850 0.650 0.517 0.433 0.350 0.292 0.233 0.192 0.158 0.125 0.100 0.120 0.116

MPa

339 382 498 1565 3173 6684 13256 35973 100730 468069 2471755 17518370 351869405 12400000000 247000000 245000000

is temperature

independent. The remaining material constants n, fi, f,, B, r, m, Z,, Z,, A, and p are temperature dependent. 3. CONSTITUENT MATERIALS

TimetalB-21 s, the matrix material, was developed by TIMET to be roughly equivalent to the Ti-15V-3Cr-3Sn-3Al (atomic percent) material with much improved oxidation resistance. Previously designated Ti-/?21 s, Timetales is characterized by a high melting point, low density and improved oxidation resistance due to the removal of the vanadium (V). The exact chemical composition is proprietary information. The temperature-dependent material constants used in the present study were developed in Ref. [36], and are given in Table 1. These material constants were derived from neat materiai test data supplied by the University of Dayton Research Institute (LJDRI) and the NASA Lewis Research Center (NASA LeRC). The Textron Specialty Materials SCS-6 silicon carbide fiber is the reinforcement constituent used in the composites under investigation. The fiber behavior is such that a thermoelastic material model can be ..“^A ^^_+.._^ &I.:.. +L, “,--.-.“:*,._“I..^^” “>GU &^ I,” cayru,r; L‘IGCL..... ll”Gl 1‘1 L‘IGL”‘llp”alrG a,,a,yX&

Table 2. Material properties of KS-6 fibers in TimetalEmatrix composites

“C 21.1 93.3 204.4 315.6 426.7 537.8 648.9 760.0 871.1 1093.3

modulus MPa 393000 390000 386000 382000 378000 374000 370000 365000 36 1000 354000

Poisson’s ratio

Fiber CTE lo-6/“C

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25

3.93 3.97 4.04 4.12 4.20 4.29 4.38 4.45 4.53 4.56

114290 108038 ClnZPln l”J”J” 83022 80760 79252 78309 77367 76707 76047 75576 75199 74822 74539 60278 53224

f, 44988 37002 ZGCP0 J,JVI 28583 26428 24991 24093 23194 22566 21937 21488 21129 20769 20500 990 760

MPa

h 0.8795 0.8152 n“.,/_‘-r ,cl
744 573 5l2 300 235 191 164 136 118 99 85 74 63 55 3 1

Table 2 summarizes the material constants for the fiber. In Tables 1 and 2, the secant coefficients of thermal expansion (CTE) were adjusted to correspond to a reference temperature equal to that for the consolidation of composite. The consolidation temperature is proprietary information and can not be presented here. The CTE reference temperature is the temperature at which the thermal strains are equal to zero. 4. FINITE ELEMENT MODELING

The fully three-dimensional finite element model of the SCS-6/Timetal%-21 s [0], system is the first in a series of models used to numerically investigate the macroscopic behavior of the composite. The TimetalEs composites considered in this work ^ _^^, have a fiber-voiume fraction of 3.5%. The three-dimensional model is used to capture changes in the stress state that occur during consolidation and the subsequent external load application. A square unit cell of a unidirectional composite is shown in Fig. 1. The unit cell is representative of a typical internal nominal section of the composite that is not influenced by edge effects. Figure 1 also shows +L, -I,...-_ “1 ,.E >YllllllFllY “..--.%*“.. rk”* ,...,. &lIG>FIIL -_..^“,...t 111 :.. +l.* LI,G+...LW” plallG> LllaL air; CIIC:

s

Elastic Temperature

n SAT

E

20 MPa

n

Fig.

v

1. Unidirectional

composite symmetry.

1 , Fiber

unit

Matrix

cell and

lines

of

508

J. A. Sherwood AD*u OnloW moQol

and H. M. Quimby

WUN -.olaoa XWAY 07787 Es ‘S

Fiber-Matrix Interface L

Fig. 2. Finite element

mesh of 3-D [O], model.

unit cell. Symmetry boundary conditions can therefore be used in a finite element model to capture the behavior of an entire unit cell with a mesh which is only one-quarter of the total cell geometry. The finite element models in this paper take advantage of these symmetries. The finite element mesh of the unidirectional [0], composite in Fig. 2 represents one-quarter of a square unit cell. The fiber is modeled using 48 elements, and the matrix is modeled with 32 elements. This mesh density was determined in a previous study [33] to be

suitable for use in three-dimensional composite analyses. All elements employ the 20-noded THREEDSOLID element formulation in ADINA. The thickness of the model was chosen to yield the optimum aspect ratio for the matrix elements and represents an average of the matrix element side lengths. A step change in material properties occurs at the fibermatrix interface. The fiber-matrix interface bond for this unidirectional composite was characterized as either perfectly bonded, weakly bonded or completely

Fiber-Matrix Interface Fiber-Matrix Interface L

Fig. 3. Finite element

mesh of 3-D [O/90],, model.

Micromechanical

modeling

of damage

debonded. The perfect bond was modelled by the fiber and the matrix elements sharing the nodes on the interface. A complete debond or weak bond at the fiber-matrix interface was modeled using the contactsurface option in ADINA. This approach required pairs of coincident nodes at the interface. One node is used in the element connectivity of the matrix and the other for the fiber. The contact surface permits compressive loads normal to the surface to be transmitted across the interface without violating compatibility between the fiber and matrix. To properly define the contact in ADINA, the midside nodes were deleted from the element faces on which contact surfaces were applied. Finite element contact algorithms are typically not equipped to handle midside element nodes. The ADINA contact algorithms require that midside nodes be removed if compatibility between contacting surfaces is to be strictly enforced. The coefficient of friction between the two surfaces was assumed to be zero. This assumption is consistent with that of other composite modeling efforts [8, 17, 331. Symmetry boundary conditions were imposed on the three negative faces of the model. The orientation of the fiber coincides with the x-axis. The displacements of nodes on the negative x-face are confined to the y-z plane. The displacements of nodes on the negative y-face are confined to the x-z plane. Similarly, the displacements of nodes on the negative z-face are confined to the x-y plane. All nodes belonging to the positive x-face are constrained to have the same axial displacements. This boundary condition is used to obtain the behavior in a nominal layer of the composite and satisfy compatibility. The nodes belonging to the positive y-face are constramed to have the same y-dispiacements. Similarly, the nodes belonging to the positive z-face are constrained to have the same z-displacements. The latter two boundary conditions serve to satisfy compatibility requirements. The modeling of the perfectly debonded fiber-matrix interface introduces some difficulty in the definition of the boundary condition for the x-displacement of plane sections to rpmain Y.U”W’ nlrrnc.= Th;q ic y’ya nsrtin,l~r I-1I.U.11 _l.l” .rliffir>,ltv . ..““..‘C. .Y LIW..IUI tn L” 1AnINA .YII 1‘ I and is addressed in the Appendix. It is important to note that use of the above boundary conditions in the modeling of imperfect fiber-matrix interfaces can introduce physically unrealistic behaviors. The above boundary conditions used to capture the response of a nominal layer of the composite will artificially hold the fiber in place when complete interface separation occurs. This behavior is physically unreasonable as complete interface separation would allow the fiber to move independently of the matrix. Thus, these boundary conditions carry the inherent assumption that due to variation in the gripping along the length of the fiber, the fiber is never free to move independently from the matrix. The finite element mesh of the [O/90],, composite in Fig. 3 represents l/16 of a unit cell and takes advan-

growth

in metal-matrix

composites

509

tage of the symmetry found in a complete [O/90],, unit cell. The fiber is modeled using 96 elements and the matrix is modeled with 54 elcmcnts. The mesh density is based upon that used in the three-dimensional [0], modeling. However, the computational resources required to compiete the [Oj, modeiing were significant. This fact had to be considered when developing the [O/90]zs models. The depths of the finite elements used in the cross-ply model were extended to lengths equal to the length of a side of one-quarter of a unidirectional unit cell. Finite elements used in the transition between the [0] and [90] fiber orientations were degenerated to allow mating of [0] and [90] unit cells which make up the complete cross-ply model. The mating of the [0] and [90] unit cells is accomplished using 20-noded THREEDSOLID elements located at the midpoint of the two fiber orientations. Most elements employ the 20-noded THREEDSOLID element formulation. The exception occurs with the use of 12 degenerated THREEDSOLID elements to be 16-noded which were used to complete the [O]-[90] transition. The correlation of the numerical and experimental results presented later justify the appropriateness of the cross-ply model presented here. The displacement boundary conditions are analogous to those used for the unidirectional model. The model also considered the weak and strong interface conditions as described previously for the unidirectional model. 5. ANALYSIS

CONDITIONS

A series of strain-rate control simulations was performed for each of the interface bond conditions. The composites were subjected to the manufacturing process foiiowed by a strain-rate controi tensiie test at either 23 or 650°C. The manufacturing process assumed a one-hour linear cooldown from the consolidation temperature to room temperature. For tensile tests performed at 23°C the pull was done immediately following the manufacturing process. For the 650°C tensile tests, a reheat from room temperature to 650°C was performed before pulling. Fnr mmnn.ite the VP_ I “1 the= C.LW nnirlir,wtinnol UILI..IIW~LI”IIL&I ~““~y”U‘L’, LL1U m~tm-i-1 lllUL”llUL Iusponse was investigated for displacement loads in and normal-to the fiber direction. The cross-ply pull was such that it was in line with the O”-fibers and normal to the 90”-fibers. To explore the influence of the residual stresses resulting from the manufacturing process on the overall response, some tensile tests were run without first simulating the manufacturing process. 6. UNIDIRECTIONAL

COMPOSITE

RESULTS

The numerical investigations of the unidirectional composite system were conducted as outlined above. The effect of the residual stresses (RS) on the overall response was minimal. Figure 4 shows the unidirectional composite response to the axial loading at

510

J. A. Sherwood

and H. M. Quimby

4000

C

oeeeE,PB @%EBEIPB bb&+bFMCS

)pG 0 000

0 005

0010

w/o

RS RS w,’ RS

w/

0015

0 020

0 000

0010

0 005

Strain

stran

Fig. 4. 0” lamina

response

at 23°C.

Fig. 5. 90” lamina

23°C. The inclusion of the fiber-matrix contact surface with the residual stresses (FMCS w/RS) yields the same result as that without fiber-matrix contact. This result is expected as a direct result of the boundary condition that constrains the fiber and matrix to move together in the axial direction such that the axial face remains plane. The unidirectional composite response for a displacement load normal to the fiber is shown in Fig. 5. The response of the completely debonded composite (FMCS w/RS) to the transverse load is far less than the bonded specimens due to the inability of the debonded matrix to transfer loads to the fiber. The resulting response is essentially controlled by the mechanical behavior of the matrix material. Figure 6 shows the fiber/matrix debonding observed in uni-

Fig. 6. Interface

debonding

response

a

015

0 020

at 23°C.

directional systems transversely loaded in the y-direction. The results of the unidirectional tests conducted at 650°C closely parallel the behavior observed at room temperature in the same system. 7. CROSS-PLY

COMPOSITE

RESULTS

The [O/90],, cross-ply composite system was investigated at 23 and 650°C as discussed previously. Figure 7 shows the results of the evaluations completed at 23°C. The perfectly debonded model with residual stresses (FMCS w/RS) shows the lowest stress level of the three simulations. A comparison of the analytical results with experimental data provided by the NASA Lewis Research Center (NASA LeRC) indicates that the completely debonded analysis is the most realistic.

in [0], system

under

transverse

load.

Micromechanical

modeling of damage growth in metal-matrix

composites

511

Z

L

1500

Rigid Beam Element

-

Y

0 g1000 w 6 L ;i; -PB W/O RS EEDPB w/ RS &Y%+FMCS w/ RS W&X NASA LeRC 1 x.?H+&NASA LeRC 2 -NASA LeRC 3

5oc

Fig. 9. Schematic of discrete interface damage model J

( 3

0.

0.002

0.004

0.006

0.008

0010

Strain

Fig. 7. [O/90], laminate response at 23°C.

The good correlation at 23°C between the experimental data and the analytical model of [0/9Ob system with completely debonded interfaces and with the inclusion of residual stresses may be indicative that the actual material interfaces are very weak following consolidation, i.e. the bond is essentially only a mechanical one. Figure 8 shows the results of the cross-ply analyses conducted at 650°C and a strain rate of 1 x 10e4 s-i. At this elevated temperature, the response is rate-dependent. The results exhibit the same behavior observed during the room temperature analyses. However, the more distinct separation between the perfectly bonded models with and without residual stresses is once again indicative of the weakened matrix at elevated temperature and the increased role of the fiber. As before, the completely debonded model with residual stresses shows the lowest stress level. The agreement between the analytical and experimental results is essentially as good as was observed at 23°C. The shape of the experimental 1000

[:

stress-strain curve indicates an evolution of damage. This damage evolution may be due to the development of microcracks and microvoids in the matrix material. It may also be a consequence of fiber-matrix debonding.

8. ADDITION

OF A VARIABLE

STRENGTH

INTERFACE

A unidirectional composite subject to a tensile pull normal to the fiber direction is the critical test for the interfacial bond strength. To investigate this interfacial bond strength numerically, a method of combining rigid beams and TWODSOLIDS was devised for this study. The intention of this modelling approach was to have a thermoplastic interface between the fiber and the matrix in conjunction with using the contact surface option between the fiber and the matrix. The thermoplastic interface permits the strength of the interface to degrade with increasing tensile deformation and ultimately fail upon reaching a critical plastic strain. The contact option prohibits the matrix and fiber materials from passing through one another.

I

800

I

0

I O.COZ

1

I

I

I O.w6

O.W‘l

I

I 0.008

I

0010

STRAIN

O~,,,,,,,l”,‘,,,,‘l,,,,,,,~,l,,‘,,,,,”’,,,,,’,,’ 0.000 0.002 0.004

0.006

0 008

Strain

Fig. 8. [0.90], laminate response at 650°C.

0.010

Fig. 10. Observed vs calculated response as a function of interfacial strength in a undirectional composite to a pull normal to fiber at 650°C.

512

J. A. Sherwood Table Temperature “C

Elastic

21 316 482 566 621 650

3. Material

modulus MPa

117000 101000 95400 78100 73200 68065

properties

and H. M. Quimby

for weak interface

Poisson’s ratio

Yield stress MPa

0.34 0.34 0.34 0.34 0.34 0.34

1050 775 690 470 289 varied

The configuration of the interface model is presented in Fig. 9. One end of each of the essentially rigid beams is connected to a fiber node which is on the contact surface. The other end of the beam is connected to a TWODSOLID element. These TWODSOLID elements are in turn connected to the matrix nodes which are on the contact surface. The result of the BEAM-TWODSOLID model is an interface element which is effectively of “zero” length but does not present the difficulty of having a zero Jacobian in the finite element formulation. The beam material is elastic with an elastic modulus of 400 x lo3 GPa. The TWODSOLZD material is thermoplastic. The properties for the thermoplastic material are summarized in Table 3. Comparisons of experimental and calculated results for tensile pulls of unidirectional layups at 23 and 650°C are given in Figs 10 and 11, respectively. The test data are shown in the open symbols. All of the experiments and numerical simulations were completed at a strain rate of 1 x 10m4 ss’. For the 650°C calculated results, the interface yield strength was varied from 50 to 100 MPa. An interface yield strength of 70 MPa closely matched the saturated stress level observed in the experiments. For the 23°C calculated results, a zero-strength interface, i.e. no interface elements, proved to be the best approximation to the experimental data. The conclusion of the computational studies is that the interfacial bond

500

23C [90]

TWODSOLID Plastic

modulus MPa

elements Plastic strain to failure

CTE

0.01 0.01 0.01 0.01 0.01 0.01

0.0 0.0 0.0 0.0 0.0 0.0

3840 5400 6380 16960 14720 0

Fig. 12. [O/90],, laminate response at 650°C as a function discrete fiber and continuum matrix damages.

of

is purely mechanical at room temperature, while it is a combination of chemical and mechanical forces at the elevated temperature. Figure 12 depicts how the crossply response varies as a function of strain rate and damage evolution. The circles denote the experimental data at 1 x 10e4 s-l. The diamonds and stars denote simulations at 8.33 x 10m4 SKI where some continuum damage has been considered. This continuum damage still does not show the curvature in the stressstrain response observed in the experiment. The triangles and the squares denote simulations which include matrix damage and fiber damage at two

400

x 4m

300

l-

r

A

zl z Li

Y

200

0 \ / L

Rigid Beam A 1

i

100

0

iL,

0 000

/

1-,.--J 0031

0 002

0003

ow4

L

Fiber 0005

STRAIN

Fig. 11. Observed vs calculated response in a unidirectional composite to a pull normal to fiber at 23°C.

Matrix

Fiber-Matfix InterfaCe Fig.

13. Schematic

of rigid beam element axial compatibility.

used to satisfy

Micromechanical

modeling

of damage

different strain rates. These fiber breakage models depict the shape of the curve which is seen in the experiment. Thus, it is concluded from the simulations that the fiber and its breakage dominate the crossply composite tensile response. Furthermore, the macroscopic response of the crossply when numerically investigated using the interface model proposed in this study did not differ from the completely debonded simulation-giving additional evidence to the dominant role of the fiber. 9. CONCLUSIONS

Three-dimensional finite element models were used to investigate the influence of residual stresses and interfacial bond condition on the macroscopic response of two composite layups. The thermomechanical behavior in [0], and [O/901zS layups of the composite system is a function of residual stresses and the level of fiber-matrix interface bonding. Depending on the direction of the applied tensile load, the residual stresses developed during cooldown from the consolidation temperature will either slightly increase or decrease the macroscopic stress-strain response as compared to the same response in the absence of these residuals. The influence of a debonded interface as given by the loss of any chemical bonding is significant when the applied strain is normal to a fiber. For the titanium-based metal matrix considered in this study, the use of a completely debonded fiber-matrix interface matched experimental data at 23°C very well. This correlation suggests that the interface is significantly weak following the consolidation process for the composite system investigated in this study at room temperature. The composite response at 650°C was shown to be strain-rate dependent. The simulations also indicated that a combination of chemical and mechanical bonding. Thus, the use of a rate-dependent constitutive theory and an interfacial bond model are critical for numerically investigating the thermomechanical response of the composite at elevated temperature. authors wish to thank Drs Theodore Nicholas and Lt Cal. James Hansen of Wright Laboratory Materials Directorate for their support. This

Acknowledgements-The

work was completed under NASA grant NCC3-218 through funds from the NIC/NASP. WL/MLLN was the program manager. The authors wish to express their gratitude to WLLN and Dr Michael Castelli of NASA Lewis Research Center for supplying the experimental date. The University Licensing Program and useful discussions with Dr Jan Walczak of ADINA R&D, Inc. are also appreciated.

REFERENCES 1. D.

N. Robinson, S. F. Duffy and J. R. Ellis, A viscoplastic constitutive theory for metal-matrix composites at high temperature. In Thermal Stress, Material Deformation, and Thermo-Mechanical Fatigue (Edited by H. Sehitoglu and S. Y. Zamrik), pp. 49-56. ASME (1987).

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in metal-matrix

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APPENDIX The use of a contact surface in ADINA requires the definition of a target surface and a contactor surface. In this case, the face of the matrix at the interface is defined as the target and the face of the fiber at the interface is defined as the contactor. However, ADlNA does not allow displacements to be prescribed for nodes belonging to a contactor surface. Thus, fiber-element nodes located at the fiber-matrix interface and on the positive x-face of the model could not be constrained to have the same axial displacements as other nodes on the face. The failure to constrain these nodes would have resulted in an analysis that did not represent the behavior of a nominal layer of the composite. The appropriate constraint of the contactor nodes was achieved through the use of short and rigid beam elements. The two-noded beam element in ADINA is a 12 degree-offreedom (DOF) element allowing displacements and rotations at each node. All rotational DOFs were inactive when used in coniunction with the THREEDSOLID element type. The short and rigid beam elements were defined as outward normals to the positive x-face of the model using the contactor nodes of the fiber and partner nodes located slightly above the positive x-face. The rigid beam element modulus was set to 40 x lo6 MPa and is roughly two orders of magnitude stiffer than the SCS-6 fiber at room temperature. This value of the modulus was chosen because it is sufficiently large to truly represent a stiff member without impacting the stability of the overall finite element solution. The partner nodes to the contactor nodes used to define the beam elements were all constrained to have the same axial displacements as the other nodes on the positive x-face as shown by Fig. 12. This figure provides a close-up view of the fiber-matrix interface region. Thus, by use of the rigid beam elements, the contactor nodes had axial displacements consistent with the modeling of a nominal layer of the composite.