10
Advanced Methods in Materials Processing Defects M. Predeleanu and P. Gilormini (Editors) 1997 Elsevier Science B.V. All rights reserved. 185 Microplasticity and Tensile Damage in Ti-15V-3Cr-3AI-3Sn Alloy and Ti- 15V-3Cr-3AI-3Sn/SiC Composite W.O. Soboyejo+, B. Rabeeh +, Y. Li+, A.B.O. Soboyejo x and S. Rokhlin* + Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, OH 43210-1179 x Department of Aeronautical Engineering, Applied Mechanics and Aviation, The Ohio State University, 155 West Woodruff Avenue, Columbus, OH 43210 * Department of Industrial, Welding and Systems Engineering, The Ohio State University, 190 W. 19th Ave. Columbus OH 43210 ABSTRACT Microscopic evidence of plastic flow at stresses below the bulk yield stress is presented for a met~tstable 13 titanium alloy (Ti-15V-3Cr-3A1-3Sn) and model Ti-15V-3Cr- 3A1-3Sn/SiC composite deformed to failure under monotonic loading at room-temperature. Microplasticity is shown to initiate in Ti-15V-3Cr-3A1-3Sn (Ti-15-3) alloy at stress levels between 5 and 10% of the bulk yield stress. Evidence of microplasticity is obtained via scanning electron microscopy examination of the deformed surfaces of smooth specimens that are loaded in incremental stages to failure. In the case of the monolithic Ti-15-3 alloy, deformation is shown to occur by a wide range of mechanisms at room temperature. These include: grain boundary sliding, grain boundary flow and bulk flow mechanisms. A wider range of matrix damage is observed in the model Ti-15-3/SiC composite deformed to failure under monotonic loading. These include all the damage components observed in the matrix and additional damage shear localization/slip band formation which is presumed to occur as a result of constraint effects in the composite. Plasticity in the Ti-15-3/SiC composite is also shown to involve early interfacial debonding, fiber fracture and multiple crack coalescence stages prior to the onset of catastrophic failure. The potential implications of the above results are also discussed. 1. INTRODUCTION It is generally accepted that the elastic deformation of metallic materials occurs by bond stretching at low stress levels. It is also commonly accepted that the onset of bulk plastic deformation occurs at stresses beyond the bulk yield stress due to the onset of dislocation motion. However, recent work [ 1] has shown that localized plasticity may initiate at stress levels that are significantly below the bulk yield stress. Such localized plasticity, which henceforth will be described as microplasticity, may occur in favorably oriented grains by a range of deformation mechanisms. Similarly, composites may exhibit a range of microplastic deformation phenomena in the so-called "elastic" regime. There is, therefore, a need for careful studies of microplasticity in metallic alloys and their composites. The current paper presents recent evidence of microplasticity in a metastable 13 titanium alloy (Ti-15V-3Cr-3A1-3Sn). Evidence of microplasticity and tensile damage mechanisms are also presented for a symmetric eight ply [0/9012s Ti-15V-3Cr-3A1-3Sn composite reinforced with silicon carbide fibers. Microplasticity in the monolithic alloy is shown to occur at room-temperature by a wide range of mechanisms that include: grain boundary sliding, grain boundary flow and bulk flow. A wider range of mechanisms are

[Studies in Applied Mechanics] Advanced Methods in Materials Processing Defects Volume 45 || Microplasticity and tensile damage in Ti-15V-3Cr-3Al-3Sn alloy and Ti-15V-3Cr-3Al-3Sn/SiC

  • Upload
    wo

  • View
    212

  • Download
    0

Embed Size (px)

Citation preview

Advanced Methods in Materials Processing Defects M. Predeleanu and P. Gilormini (Editors) �9 1997 Elsevier Science B.V. All rights reserved. 185

Microplasticity and Tensile Damage in Ti-15V-3Cr-3AI-3Sn Alloy and Ti- 15V-3Cr-3AI-3Sn/SiC Composite

W.O. Soboyejo +, B. Rabeeh +, Y. Li +, A.B.O. Soboyejo x and S. Rokhlin* + Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, OH 43210-1179 x Department of Aeronautical Engineering, Applied Mechanics and Aviation, The Ohio State University, 155 West Woodruff Avenue, Columbus, OH 43210 * Department of Industrial, Welding and Systems Engineering, The Ohio State University, 190 W. 19th Ave. Columbus OH 43210

ABSTRACT

Microscopic evidence of plastic flow at stresses below the bulk yield stress is

presented for a met~tstable 13 titanium alloy (Ti-15V-3Cr-3A1-3Sn) and model Ti-15V-3Cr- 3A1-3Sn/SiC composite deformed to failure under monotonic loading at room-temperature. Microplasticity is shown to initiate in Ti-15V-3Cr-3A1-3Sn (Ti-15-3) alloy at stress levels between 5 and 10% of the bulk yield stress. Evidence of microplasticity is obtained via scanning electron microscopy examination of the deformed surfaces of smooth specimens that are loaded in incremental stages to failure. In the case of the monolithic Ti-15-3 alloy, deformation is shown to occur by a wide range of mechanisms at room temperature. These include: grain boundary sliding, grain boundary flow and bulk flow mechanisms. A wider range of matrix damage is observed in the model Ti-15-3/SiC composite deformed to failure under monotonic loading. These include all the damage components observed in the matrix and additional damage shear localization/slip band formation which is presumed to occur as a result of constraint effects in the composite. Plasticity in the Ti-15-3/SiC composite is also shown to involve early interfacial debonding, fiber fracture and multiple crack coalescence stages prior to the onset of catastrophic failure. The potential implications of the above results are also discussed.

1. INTRODUCTION

It is generally accepted that the elastic deformation of metallic materials occurs by bond stretching at low stress levels. It is also commonly accepted that the onset of bulk plastic deformation occurs at stresses beyond the bulk yield stress due to the onset of dislocation motion. However, recent work [ 1] has shown that localized plasticity may initiate at stress levels that are significantly below the bulk yield stress. Such localized plasticity, which henceforth will be described as microplasticity, may occur in favorably oriented grains by a range of deformation mechanisms. Similarly, composites may exhibit a range of microplastic deformation phenomena in the so-called "elastic" regime. There is, therefore, a need for careful studies of microplasticity in metallic alloys and their composites.

The current paper presents recent evidence of microplasticity in a metastable 13 titanium alloy (Ti-15V-3Cr-3A1-3Sn). Evidence of microplasticity and tensile damage mechanisms are also presented for a symmetric eight ply [0/9012s Ti-15V-3Cr-3A1-3Sn composite reinforced with silicon carbide fibers. Microplasticity in the monolithic alloy is shown to occur at room-temperature by a wide range of mechanisms that include: grain boundary sliding, grain boundary flow and bulk flow. A wider range of mechanisms are

186

observed in the composite presumably as a result of local constraint effects due to the composite architecture. These include: all the mechanisms identified previously in the monolithic alloy, slip band and subgrain formation, interfacial debonding and composite cracking phenomena. The potential implications of the results are. discussed for the modeling of elasticity and plasticity phenomena.

2. MATERIALS

The monolithic titanium alloy (Ti-15V-3Cr-3A1-3Sn) was supplied by the NASA Lewis Research Center. It was produced by the rolling of foil at Textron Specialty Materials,

Lowell, MA. The as-rolled material had a metastable 13 microstructure with an average grain size of 180 ktm. Two types of heat treatment were used to control the monolithic alloy microstructure. The first type of heat treatment involved annealing at 540~ for different durations (10, 50, and 100 hours) followed by air cooling. This heat treatment resulted in the

transformation of the metastable 13 (as-received) structure to a Widmanst~itten colony structure

(ct+13 phase field). The second type of heat treatment involved annealing at 815oc for the same durations (10, 50 and 100 hours) followed by air cooling. Recreystallization of the as- received structure occurred in the 13 phase field at 815 oC.

The symmetric eight ply [0/9012s Ti-15V-3Cr-3AI-3Sn/SiC (SCS-6)composite material that was used in this study was supplied by Textron Specialty Metals, Lowell, MA. It was produced by the foil/fiber/foil technique via hot pressing at 982~ for 2h. A slightly non-uniform distribution of SiC fibers was produced in the [0/9012s composite due to the effects of fiber "swimming" during composite processing. Large (--500 l.tm average diameter) 13 grains are also observed in the as-received composite. The layered interface has a highly complex microstructure [2, 3] that consists predominantly of titanium carbides (TiC and Ti2C).

Two sets of heat treatments were used to control the matrix and interfacial microstructure. The first set of heat treatments involved annealing for different durations (10h, 50h and 100h) at 540~ (below the 13 solvus of approx. 800~ for Ti-15-3). The heat treatment at 540~ resulted in a Widmanst~itten colony microstructure with small circular t~ grains in a matrix of 13 �9 The changes in the matrix microstructure occurred without significant coarsening of the interfacial structure. Some slip bands were also observed in the Widmanst~tten matrix microstructure. It is presumed that these were induced as a result of matrix yielding due to residual stresses in the composite.

The second set of heat treatments were carried out at 815oc. Annealing durations of 10, 50 and 100h were employed. These heat treatments were designed to promote significant coarsening of the interfacial microstructure without inducing significant alteration of the matrix microstructure. However, unlike the four-ply unidirectional Ti-15-3/SiC (SCS-9) composite that was examined in previous studies [ 14], the degree of coarsening of interfacial microstructure was observed to be limited in the [0/90] 2s Ti-15-3/SiC (SCS-6)composite that was examined in this study. Further details on the complex structure of the layered interfacial

region are provided in Ref. 3. The coarse grained (500 ktm average grain size) as-received

microstructure is retained after annealing in the 13 phase field.

3. EXPERIMENTAL

Tensile tests were performed at room temperature on two sets of specimens. The first set of tensile specimens were 125 mm long with rectangular cross sections (1.7 mm x 10

187

mm). The second set were smooth 125 mm long tensile specimens with rectangular cross sections (2 mm x 12 mm). A servohydraulic test machine was employed in the mechanical testing. The first set of tensile specimens were loaded continuously to failure at a strain rate of 5x10 -4 sec-1. Strain was measured with contact extensometer with a gauge length of 25.4 mm.

A second set of tensile tests were conducted on smooth specimens to study the deformation and cracking phenomena associated with damage under monotonic loading. The

specimens were loaded in incremental steps of 0.1 CYtrrs, to various fractions of the ultimate

tensile stress, Ctrrs, determined from the first set of tests. Damage phenomena associated with the different incremental monotonic loading steps were then identified by ex-situ scanning electron microscopy examination of the sides (of the gauge sections) of the deformed tensile specimens. In this way, the sequence of damage was identified for the two microstructural conditions that were employed.

4. RESULTS AND DISCUSSION

4.1. Stress-Strain Behavior

Monolithic Ti- 15-3 Alloy

Tensile properties of monolithic Ti-15-3 alloy at room temperature under the as- received and the heat treated conditions are summarized in Table 1. Characteristic stress- strain plots of the as-received material and materials annealed at 540oc for 50 hours are presented in Fig. 1. The stress-strain plots of 540oc materials was almost identical after annealing for 10, 50 or 100 hours. This is consistent with the similar microstructures of the materials annealed at 540~ The material strength of 540~ was also higher than as-received material strength, presumably as a result of phase transformation from metaste.ble

13 phase (as-received) to o~+13 phase (Widmanst~itten) microstructures. Annealing at 540oc was also associated with smaller plastic strains to fracture as shown in Table 1. The stress- strain plots of materials annealed at 815~ for 50 hours is also presented in Fig. 1. The strength of 815~ Ti-15-3 alloy was also similar to that of the as-received material, and the strengths of materials heat treated at 815~ decreased with increasing annealing duration (Table 1).

The stress-strain response of monolithic Ti-15-3 alloy at different heat treatments was identical conventional stress-strain with distinguishable elastic and plastic rejoins. The higher

strengths obtained after the 540oc heat treatments are attributed to the cx+13 phase Widmanst~itten structure. Similarly, the improved ductility of the material annealed at 815~ is consistent with the results obtained from previous studies of titanium alloys. Furthermore, both 540oc and 815~ heat treated materials have different yield stresses, although the yield strains were almost identical in the heat treatment conditions that were examined (Table 1).

Ti- 15-3/SIC Composite

Tensile properties of the as-received and heat treated Ti-15-3/SIC composite materials are summarized in Table 2. Characteristic stress-strain plots are also presented in Fig. 2 for 540oc/50h/AC and 815oc/50h/AC materials compared to the as-received material. The stress-strain characteristics of the as-received and 815~ materials were almost identical, consistent with the similar composite microstructures in these two conditions. The composite strength were also higher after annealing at 540oc for 50h which resulted in the

188

Table 1 Summary of Tensile Properties of Ti- 15-3 Allo~ Modulus (E) Yield Stress/Strain

Condition Heat Treatment

AR 540 ~ C/10h/AC 540~ C/50h/AC 540~ C/100h/AC 815~ 815~ C/50h/AC 815~

[GPa]

733 1044 957 1320 774 732 847

AR = As-Received f = Failure UTS= Ultimate Tensile Stress

OYield Strain [MPa] %

801 0.1 1125 0.1 1205 0.1 1008 0.1 809 0.1 806 0.1 755 0.1

Ultimate Tensile Stress/Strain

Ours Strain [MPa] % 812 0.2 1234 0.4 1223 0.2 1208 0.3 826 0.2 798 0.3 783 0.2

Failure Stress/Strain of

[MPa] 723 1224 1223 1197 744 718 704

Strain %

1.40 0.50 0.16 0.38 0.90 2.34 1.30

Table 2 Summary of Tensile Properties of Ti-15-3/SiC Composi tes Condition Heat Modulus of Elasticity Deformation Stress Treatment [GPa] [MPa]

E1 E2 E 3 E4 Ol o2 o3 (Failure)

As-Received 106 88 80 54 211 472 616.6 540o C/50h/AC 133 116 97 87 124 345 800 815oc/50h/AC 151 104 85 58 57 377 611

OUTS

[MVa] OUTS

856 1028 891

Strain to Failure

%

0.11 0.10 0.11

t_...a

r~

ra~

1500

1000

500:

~-- A s - R e c e i v e d

~, 5 4 0 C / 5 0 h

" 8 1 5 C / 5 0 h

0 ~

0.00 0.01 0.02 0.03

S t r a i n

Fig.1. Stress-Strain Behavior of Ti- 15-3 Alloys.

t......a

r~

ra~

1200

900

600

300

A s - r e c e i v e d 5 4 0 C / 5 0 h

8 1 5 C / 5 0 h

0 ~

0.000 0.003 0.006 0.009 0.012

S t r a i n

Fig.2. Stress-Strain Behavior of Ti- 15-3/SIC Composites .

189

transformed c~+13 Widmanst~itten microstructure. Such annealing was associated with lower ductility than that of the as-received and 815~ materials (Table 2 and Fig. 2).

However, unlike monolithic Ti-15-3 alloy, the composite does not have a distinguishable elastic or plastic range of deformation. The stress-strain plots (Fig. 2) revealed similar stress-strain characteristics in the composites annealed at 540oc and 815oc prior to tensile loading. The stress-strain response was approximately linear at room

temperature until a critical stress was reached. Average values of this critical stress, Crl, with the slope (modulus) are presented in Table 2. Non-linear behavior ensued beyond this critical stress. In all cases, the curves exhibit almost four distinct critical stresses with different slopes (modulus). The ultimate tensile stresses of 540~ annealed material are higher than that of as-received and 815 ~ annealed material, and the plastic strain remained almost the same (unlike monolithic Ti-15-3 alloy). The non-linear stress-strain response of titanium metal matrix composite was due to the underlying damage mechanisms which will be discussed later.

4.2. Damage Mechanisms

Monolithic Ti- 15-3 Alloy

Local evidence of damage initiation was observed early in the deformation sequence, i.e., prior to bulk yielding across the gauge of the Ti-15-3 alloy specimens annealed at 540oc/50h/AC. Damage initiation in the specimens occurred by microcracking along grain boundaries (GB) at very low stresses. Local evidence of microplasticity was also observed early in deformation sequence at 0.3 crtrrs (Fig. 3a). The microplasticity manifested itself in the form of localized flow of material. This is illustrated in Fig. 3b in which surface damage features are observed to flow with increasing load. Note also that the flow results in the widening of the region between the boundaries. However, flow in this microplasticity regime is associated with linear stress-strain characteristics.

Beyond the initial regime of microplasticity, fracture initiated rapidly from grain boundaries. Catastrophic failure occurred by ductile dimpled fracture mechanisms along prior

13 grain boundaries (Fig. 3c). Defects observed in the Widmanst~itten structure were observed to flow across the grains during deformation in the microplastic regime. Such large scale (micrometer levels) evidence of flow is clearly inconsistent with current elasticity and plasticity theories. However, the mechanisms of such flow processes are not fully understood at present. The stress and strain levels associated with the observed deformation and cracking phenomena are summarized schematically in Fig. 4 for Ti-15-3 alloy annealed at 540oc for 50 hours.

Unlike the specimens annealed at 540oc/50h/AC, the specimens annealed at 815~ doesn't exhibit early damage initiation. However, some grain boundary

sliding were observed under monotonic loading at 0.40trrs , follow by initiation of small voids along grain boundaries.. Subsequent damage is associated with slip band formation

along small o~ precipitates, nucleation of voids along the ~ precipitates on these slip bands and surface roughening due to the intersection of slip bands. Microvoid linkage/coalescence then occurs predominantly along slip bands. Localized plastic flow and further surface roughening are observed just before the onset of catastrophic failure, which occurred by intergranular/ transgranular ductile dimpled fracture and secondary cracking between the slip bands.

190

Fig. 3. Damage Mechanisms of Ti-15-3 Alloy Specimens Annealed at 540oc/50h/AC and Deformed under Monotonic Loading at Room Temperature.

(a). Crack Nucleation from Grain Boundary and Localized Plastic Flow at 0.3 Gtrrs;

(b). Localized Plastic Flow and Bulk from Grain Boundary at 0.5 ~UTS;

(c). Ductile Dimpled Fracture at 1.0 GUTS.

191

Fig. 4. Summary of Stress-Strain Behavior with Underlying Damage Mechanisms of Ti- 15-3 Alloy Annealed at 540~ and Deformed to Failure under Monotonic Loading.

Ti- 15-3/SIC Composite

The damage phenomena associated with the different regions of the stress-strain curves at room temperature are presented in Fig. 5 for 540oc/50h/AC. Note that damage initiation is described arbitrary to include all the damage events (interfacial cracking, slip band formation and sub-grains) prior to matrix cracking, while damage propagation/evolution is considered here to involve all the subsequent stages of damage (multiple crack growth, fiber fracture and crack coalescence) after the onset of matrix cracking.

Local evidence of plasticity (damage initiation) was observed early in the deformation sequence, i.e., prior to bulk yielding across the gauge of the specimens annealed at 540oc. This form of local plasticity, which is referred to subsequently as microplasticity, occurred at

the very low stress (approx. 0.1 ~trrs), and is illustrated in Fig. 5a. The microplasticity manifested itself in the form of slip bands, which were observed to nucleate from the fiber/matrix interface. Similar slip band initiation mechanisms have been observed in previous studies by Majumdar et al. [4, 5] on 0 and 90 degree Ti-15-3/SCS-6 composites. Note that the stress-strain behavior of the composite is still approximately linear in the microplasticity regime, as is typically observed in conventional monolithic materials.

Beyond the initial regime of microplasticity, crack initiation occurred in the outer 900 plies (Fig. 5b), followed by slip band intersection in the regions between the 0 and 900 plies. These slip bands appeared to have been initiated by the localization of strain in the vicinity of interfacial/reaction zone cracks, as reported by Majumdar et al. in Refs. [4, 5] for 0 and 900 composites. Debonding was observed to occur at the region between the titanium carbide interface and the Ti-15-3 matrix. Subsequent matrix crack initiation occurred by the

192

extension of interfacial crack into the matrix at higher stresses of 0.6 C trrs (Fig. 5c). Transgranular matrix cracks were nucleated by the extension of interfacial cracks into the matrix. This occurred initially in the inner plies, while slip band activity was still dominated in the inner plies. Intergranular matrix crack growth/coalescence was observed at the boundaries between the large [3 grains in outer plies. The initiation of matrix crack growth preceded final fracture via the coalescence of matrix and fiber cracks in the mode I direction. Catastrophic failure occurred by ductile dimpled fracture and cleavage/quasi-cleavage fracture of SCS-6 fibers in 540~ microstructure (Fig. 5d). The stress and strain levels associated with the observed deformation and cracking phenomena are summarized schematically in Fig. 6.

The damage phenomena associated with the different regions of the stress-strain curves at room temperature for the specimens annealed at 815 oC/50h/AC are similar to those observed in the specimens annealed at 540oc/50h/AC. However, unlike the specimens annealed below beta transus, slip bands were not observed in these specimens. Instead, matrix microplasticity occurred by formation of sub-grain structure. Fiber fracture was also found to precede catastrophic failure, which occurred in the mode I direction during monotonic loading at room temperature. Catastrophic failure occurred by ductile dimpled fracture in the matrix, and cleavage/quasi-cleavage fracture of SCS-6 fibers in composites annealed at 815~ as those observed in the specimens annealed at 540oc/50h/AC.

5. Implications

It is apparent from the above results and discussion that the observed "linear elastic" behavior (Figs. 1 and 2) is clearly associated with plasticity phenomena at stress levels well below the bulk yield stress levels. The local scale of some of the observed plastic flow processes (e.g. grain boundary sliding and bulk flow in Ti-15-3 alloy, or formation of slip bands and crack initiation in T-15-3/SiC composite) is also considerable greater than the submicroscopic ~ levels of flow that are typically associated with conventional dislocation glide/climb. Such non-linearities have been measured in previous studies on other material systems [6-8] using strain gauges that can detect strains that are low as 10-8. Such small strain changes and associated non-linear stress-strain behavior may be importance in the design of high tolerance components such as the lenses in the Hubble telescope. It also gives a insight light on damage initiation mechanisms of fatigue, especially at stresses well below the bulk yield stresses of materials. However, more work is needed to understand the mechanisms of plastic flow at such low stresses. Nevertheless, it is apparent from the observed microplasticity phenomena that the so-called linear elastic response of materials may correspond to linear elastic behavior. This is in spite of micro-scale of the observed plasticity phenomena.

6. Summary

The stress-strain response of Ti-15-3 alloy and Ti-15-3/SiC composite has been studied under monotonic loading. The damage mechanisms in these two materials under monotonic loading were investigated via incremental techniques. Strong evidence of microplasticity is observed at stresses well below the bulk yield stress levels (at -30% of the bulk yield stress for Ti-15-3 alloy and at -10% of the bulk yield stress for Ti-15-3/SiC

composite). Microplasticity in Ti-15-3 alloy with 13 structure occurs initially via grain boundary sliding and slip band formation/intersection, while microplasticity in Ti-15-3 alloy

with a model Widmanst~itten ct+~ microstructure occurs by bulk or grain boundary flow

mechanisms that are not well understood at present. Final fracture in the model 13 and

193

Fig. 5. Damage Mechanisms of Ti-15-3/SIC Composite Specimens Annealed at 540oc/50h/AC and Deformed under Monotonic Loading at Room Temperature.

(a). Slip Bands Initiation in Outer 900 Ply with Debonding at 0.2 CUTS;

(b). Matrix Crack Nucleation from Interface in Outer Ply at 0.3 CUTS;

(C). Matrix Crack Nucleation from Interface with Debonding in Inner Ply at 0.6 ~UTS;

(d). Ductile Dimpled Matrix Fracture at 1.0 ~UTS.

194

r~ r~

r~

Matrix Crack Coalescence

ire Debonding And PS 7ormation in Inner Ply

Vlatrix Crack Nucle in Inner Plies at 0.6

Inner Ply

Band Formation in~ .j~"~,,"/" Matrix Cracking in

Strain

Fig. 6. Summary of Stress-Strain Behavior with Underlying Damage Mechanisms of Ti-15- 3/SIC Composite Annealed at 540~ and Deformed under Monotenic Loading.

Widmanst~itten ~+13 structures occurs by classical ductile fracture mechanisms. In Ti-15- 3/SIC composites, a wider range of microplasticity mechanisms are observed. These mechanisms include: all the mechanisms identified previously in the monolithic alloy, slip band and subgrain formation, interfacial debonding and composite cracking phenomena.

ACKNOWLEDGMENTS

The research was supported by the Division of Mechanics and Materials of the National Science Foundation. The authors are grateful to the Program Monitors, Dr. William A. Spitzig and Dr. Oscar Dillon, for their encouragement and support.

REFERENCES 1. B.M. Rabeeh, S.I. Rokhlin and W.O. Soboyejo, Scripta Materialia, 35 (1996) 1429. 2. B.A. Lerch, T.P. Gabb, and R.A. Mckay, A Heat Treatment Study of SiC/Ti-15-3

Composite System, NASA Technical Report No. 2970 (1990). 3. J. Shyue, W.O. Soboyejo and H.L. Fraser, Scripta Materialia, 33 (1995) 1695. 4. B.S. Majumdar, G.M. Newaz and J.R. Ellis, Metall. Trans. A24 (1993) 1597. 5. B.S. Majumdar, G. Newaz, Phil. Mag., A66 (1992) 187. 6. A. Pusk~ir, Microplasticity and Failure of Metallic Materials, Elsevier Publishing, First

Edition, 1989. 7. J.F. Bell, The Physics of Large Deformation of Crystalline Solids, Springer-Verlag, 1968. 8. C.W. Marchal and R.E. Maringer, Dimensional Instability, Pergamon, 1977.