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Effect of Reinforcement-Particle-Orientation Anisotropy on the Tensile and Fatigue Behavior of Metal-Matrix Composites V.V. GANESH and N. CHAWLA The effect of extrusion-induced particle-orientation anisotropy on the mechanical behavior of metal-matrix composites (MMCs) was examined. In this study, we have shown that this anisotropy has a significant influence on the tensile and fatigue behavior SiC particle–reinforced Al alloy composites. The preferred orientation of SiC particles was observed parallel to the extrusion axis, with the extent of orientation being highest for the lowest-volume-fraction composites. The composites exhibited higher Young’s modulus and tensile strength along the longitudinal direction (parallel to the extrusion axis) than in the transverse direction. The extent of anisotropic behavior increased with increasing volume fraction, because of the increasing influence of the SiC reinforcement on the Young’s modulus and tensile properties. The preferred orientation also resulted in anisotropy in the fatigue behavior of the composite material. The trends mirrored those observed in tension, with higher overall fatigue strengths for both orientations and a higher anisotropy with increasing volume fraction of particles. The influence of particle-orientation anisotropy and the resulting tensile and fatigue damage mechanisms is discussed.

I.

INTRODUCTION

THE combination of ceramic particles and a light-metal matrix results in a composite material with improved stiffness, strength, fatigue resistance, and wear resistance, when compared to the unreinforced light alloy.[1–4] The microstructure and mechanical properties of particle-reinforced metal-matrix composites (MMCs) are inherently dependent on several factors such as matrix microstructure,[5,6,7] reinforcement volume fraction, size, morphology, and distribution.[8–14] Processing plays an important role in determining the inherent characteristics of the matrix, reinforcement, and composite.[1] Thus, processing-induced changes in the microstructure of the composite will have important implications on the mechanical behavior of the material. Several processing techniques have been used to fabricate particle-reinforced MMCs. These are generally classified as liquid-phase[15] or solidphase processes.[16] Liquid-phase processes, such as casting or infiltration, are typically more cost-effective than solidphase processes. The main drawback associated with these techniques is the difficulty in controlling particle distribution and obtaining a uniform matrix microstructure.[15] Furthermore, an interfacial reaction between the matrix and the reinforcement often takes place, which has an adverse effect on the mechanical properties of the composite.[17] The most common solid-phase processes are based on powdermetallurgy processing.[16] The ceramic and metal powders are mixed, isostatically cold compacted, and hot pressed to full density. The fully dense compact then typically undergoes a secondary operation such as extrusion or forging.[18] Novel low-cost approaches, such as sinter forging, have aimed at eliminating the hot-pressing step, with promising results.[19] One of the important attributes of extrusion processing of particle-reinforced MMCs is the alignment of particles along V.V. GANESH, Graduate Research Associate, and N. CHAWLA, Associate Professor, are with the Department of Chemical and Materials Engineering, Arizona State University, Tempe, AZ 85287-6006. Contact e-mail: [email protected] Manuscript submitted June 30, 2003. METALLURGICAL AND MATERIALS TRANSACTIONS A

the extrusion axis and refinement of the matrix grain size.[14,20] While several investigators have examined the tensile and fatigue behavior of these materials, the properties of the material are typically measured parallel to the extrusion axis.[5–14] Very few studies have attempted to examine the effect of extrusion-induced particle-orientation anisotropy on the microstructure and mechanical behavior of particle-reinforced MMCs.[21,22] Logsdon and Liaw[21] studied the tensile-strength anisotropy behavior in SiCparticle and whisker-reinforced aluminum alloys and noted that the strength was higher parallel to the extrusion axis than perpendicular to the extrusion axis. Jeong et al.[22] also noted a higher Young’s modulus of the composite along the extrusion axis. In this study, we have examined the microstructure and mechanical-behavior anisotropy of SiC particle–reinforced 2080 Al matrix composites parallel and perpendicular to the extrusion axis. A systematic investigation of the effect of SiC volume fraction, at a fixed particle size, on the microstructure and mechanical-behavior anisotropy was conducted. It will be shown that extrusioninduced microstructure changes are deeply affected by the volume fraction of SiC, and that the degree of microstructural anisotropy is directly related to the tensile and fatigue behavior of the composites. II.

MATERIALS AND EXPERIMENTAL PROCEDURE

The composite examined in this study was a 2080 aluminum alloy (3.6 pct Cu, 1.9 pct Mg and 0.25 pct Zr) reinforced with 10, 20, and 30 vol pct SiC particles (with an average particle size of 8 ␮m). The SiC and Al powders were blended, cold isostatically compacted, vacuum degassed, hot pressed, and extruded (Alcoa Technical Center, Alcoa, PA). A cylindrical billet (23 cm in diameter) was extruded several times to obtain final billets of elliptical cross section (3.8 cm by 8.9 cm). Details of the powder-metallurgy process for the fabrication of these materials can be found elsewhere.[5,7,14] The billets were sectioned into rectangular VOLUME 35A, JANUARY 2004—53

bars by electrodischarge machining (EDM) and heat treated using the following conditions: solution treatment at 493 °C for 2 hours, water quenching, and peak aging at 175 °C for 24 hours. Scanning electron microscopy (SEM) and optical microscopy were used to analyze the reinforcement-particle orientation. The planes parallel and perpendicular to the extrusion direction were designated as longitudinal and transverse, respectively. The axis perpendicular to the longitudinaltransverse plane was defined as the short-transverse axis. Thus, the composite microstructure was examined along all three planes to examine the distribution of reinforcement particles. The micrographs obtained from the three planes were segmented using conventional image-analysis software, and the particles were fitted to an ellipse in order to characterize the aspect ratio, size, and degree of orientation of the particles (with respect to the longitudinal or transverse axis). Polished surfaces were also etched using Keller’s reagent to reveal the matrix grain structure. The grain size of the matrix and aspect ratio were also calculated using the image-analysis techniques described previously. Transmission electron microscopy (TEM) was used to characterize the precipitate structure in the matrix of the composite. Foils were prepared by slicing a thin sample and polishing to an 80 ␮m thickness. A dimple was created at the center of the foil by grinding and polishing to a thickness of about 10 ␮m. Final thinning was carried out by ion milling in liquid nitrogen to avoid microstructural changes due to heat generation. Specimens for tensile and fatigue testing were machined, parallel (longitudinal) and perpendicular (transverse) to the extrusion axis, by low-stress grinding. Uniaxial tensile tests were carried out on cylindrical smooth-bar tensile specimens

of 15 mm gage length and 4 mm gage diameter.[14] All testing was carried out on a precision-aligned servohydraulic load frame. Tensile tests were performed in strain control at a strain rate of 10⫺3/s, while fatigue tests were conducted in stress control, at a frequency of 40 Hz and stress ratio (R ⫽ ␴min/␴max) of ⫺1. Tensile and fatigue fracture surfaces of the composites were analyzed by SEM. III.

RESULTS AND DISCUSSION

A. Microstructure characterization Microstructure characterization of the composites showed a preferred orientation of reinforcement particles along the extrusion direction (Figure 1). Quantitative analysis of the degree of orientation of the particles, given by the angle of a given particle to the longitudinal or transverse axis, is shown in Figure 2. As expected, the degree of alignment of particles in the longitudinal plane, at a given volume fraction of particles, was much higher than that in the transverse plane. However, the degree of orientation in the longitudinal plane decreased with an increase in volume fraction of particles. This can be explained by noting that the larger the fraction of particles, the lower the mean free path available for particle rotation and alignment along the extrusion axis. In the transverse plane, the particle orientation was about the same for all volume fractions. The microstructure of the matrix was affected by the large degree of plastic flow associated with the rigid SiC particles in the composite. Figure 3 shows that the matrix grain size was much smaller than the SiC particle size, and that the grains were severely refined during extrusion. “Bands”

Fig. 1—Scanning electron micrographs showing particle distribution on all three planes of the composite materials. 54—VOLUME 35A, JANUARY 2004

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(a) Fig. 3—Microstructure of 2080/SiC/10p parallel to the extrusion axis, showing very fine and banded matrix grain structure. The grain structure is also smallest at the particle/matrix interface, due to dynamic recrystallization at the particle surface during hot extrusion.

(b) Fig. 2—Orientation of the reinforcement particles with increase in volume fraction of SiC particles: (a) longitudinal plane and (b) transverse plane. Notice a decrease in the degree of orientation in the longitudinal plane with increase in volume fraction of SiC, while the transverse plane shows a relatively random orientation.

of grains were also observed due to the highly localized flow of the matrix (Figure 3). The grain size in the composite was also inhomogeneous, increasing in size with increasing distance from the particle/matrix interface. Similar observations have also been reported by Humphries et al.[23] The finer grain structure at the particle/matrix interface can be attributed to dynamic recrystallization of new grains at the particle surface during hot extrusion.[24] It is interesting to note that the size and morphology of matrix bands and individual grains appear to be dictated by the rigid SiC particles that act as obstacles for matrix flow. The presence of the ceramic particles in the matrix thus results in an increased macroscopic flow stress for extrusion of the composite, when compared to that of the unreinforced alloy.[20] The large degree of shearing between the particles and matrix is conMETALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 4—Transmission electron micrograph showing precipitate structure in the matrix of the as-processed composite (⬍100⬎ zone axis). Needle-like Al2CuMg, spherical clusters Al2Cu, and Al-Zr spherical dispersoids are shown in the micrograph.

ducive to a very strong mechanical bond between the particle and matrix. A strong mechanical bond between the particle and matrix is highly desirable in strengthening of MMCs, because it maximizes the degree of load transfer from the matrix to the particle and, thus, increases the chance that a given particle will be loaded to its fracture stress.[25] The microstructure of precipitates within the grains was revealed by TEM. Thermal-expansion mismatch in these materials induces thermal-misfit dislocations at the particle/ matrix interface. As a result, a larger precipitate density was found near the particle/matrix interface. Figure 4 shows the precipitate structure produced by the T6 heat treatment. The S’ precipitates (Al2CuMg), typical of Al-Cu-Mg alloys, which have a needlelike morphology and are semicoherent with the matrix, were observed.[26] The S’ precipitates can nucleate VOLUME 35A, JANUARY 2004—55

Fig. 5—Effect of particle orientation, with increasing volume fraction, on Young’s modulus of the composite. Note the highest anisotropy at the highest volume fraction, since the influence of the particles on the modulus increases with increasing reinforcement volume fraction.

heterogeneously, particularly at dislocations and grain boundaries.[27,28] Some spherical Al2CuMg precipitates, a small fraction of Al2Cu precipitates, and some Al3Zr dispersoids were also observed.

B. Tensile and Fatigue Behavior As expected, the tensile strength of the composites, independent of orientation, increased with increasing fraction of reinforcement, while the strain to failure decreased with increasing volume fraction. A comparison of properties in the longitudinal and transverse orientations indicated a pronounced anisotropy in the tensile behavior of the composites. Both the Young’s modulus (Figure 5) and tensile strength, (Figure 6) were higher in the longitudinal orientation than in the transverse orientation. This is consistent with the findings of Liaw and co-workers.[21,22] It is interesting to note that the anisotropy in modulus and strength increased with increasing volume fraction of SiC particles. We first discuss the Young’s-modulus and tensile-strength trends as a function of reinforcement volume fraction, but independent of orientation. The increase in Young’s modulus of the composite with an increase in volume fraction of SiC particles can be attributed to an increase in load transfer to the high-modulus SiC particles.[1,9,14,29,30] The increase in tensile strength and decrease in strain to failure with increasing volume fraction can also be explained in terms of increased load transfer,[31,32] but there is also a contribution from the enhanced density of precipitates in the matrix with increasing volume fraction of particles.[7,33,34] The enhanced precipitate density with increasing reinforcement volume fraction is a result of the larger amount of particle/ matrix interfacial area, which results in a higher amount of processing-induced dislocation punching during thermal cooldown. The dislocations act as heterogeneous sites for precipitate nucleation and growth during heat treatment.[35,36] Thus, with an increase in volume fraction of particles, the matrix is “indirectly strengthened” due to the enhanced dislocation density and subsequent precipitate formation. 56—VOLUME 35A, JANUARY 2004

Fig. 6—Effect of particle orientation, with increasing volume fraction, on tensile strength of the composite. The increased anisotropy of tensile strength with increasing reinforcement volume fraction can be attributed to an increase in the degree of load transfer and the increase in matrix precipitate density (from thermally induced dislocation punching, during processing, at that particle/matrix interface).

The decrease in strain to failure with increasing fraction of particles (once again, independent of orientation) can be explained by the higher work-hardening rate that takes place with increasing particle fractions.[1] The higher observed work-hardening rate is a function of the lower matrix volume (by incorporation of the particles) and is not necessarily due to a change in work-hardening mechanisms. Rather, the higher work-hardening rate is due to geometric constraints imposed by the presence of the reinforcement. When the matrix is significantly work hardened, the matrix is placed under great constraint, with an inability for strain relaxation to take place.[25,37] This causes the onset of void nucleation and propagation, which takes place at a lower far-field applied strain than that observed in the unreinforced material, resulting in a lower macroscopic ductility. We now discuss the orientation dependence of the Young’s modulus and tensile strength. For a given reinforcement volume fraction, particle size, and aspect ratio, the Young’s modulus of the composite can be controlled by the degree of particle alignment. Since the contribution of the particles to the overall modulus of the composite increases with increasing volume fraction (particularly when the particle has a much higher Young’s modulus than the matrix, as in the case of SiC and Al), the contribution of particle alignment will also be more significant at a higher volume fraction. Examination of the particle-orientation analysis in Figure 2 shows that the 2080/SiC/10p composite exhibited the highest degree of microstructural anisotropy, but that the Young’s modulus in the longitudinal and transverse orientations was quite similar. The 2080/SiC/30p composite, on the other hand, exhibited a slightly lower degree of microstructural anisotropy but a higher anisotropy in Young’s modulus. Thus, the higher volume fraction of 2080/SiC/30p and, thus, the larger contribution of particle alignment, resulted in a greater anisotropy in the Young’s modulus than at 2080/SiC/10p, despite the slightly lower microstructural anisotropy. METALLURGICAL AND MATERIALS TRANSACTIONS A

The tensile anisotropy in the composites can also be rationalized by the mechanisms described previously. The observed anisotropy is also influenced by the nature of particle fracture. The tensile-fracture surface of the composites showed quite a contrast between the dimpled nature of fracture in the metal matrix and the brittle fracture of the SiC ceramic particles (Figure 7). This fracture morphology has also been observed by other investigators.[1,8,10,25] Notice that the particle/matrix interface remained intact, indicating that the shear

strength at the interface was higher than the particle fracture strength. The high shear strength can be attributed to the strong mechanical bond formed during extrusion. Quantitative analysis of particle fracture (Figure 8) showed a higher degree of particle fracture in the longitudinal orientation, indicating that a larger fraction of the particles, aligned along the extrusion axis, were loaded to their ultimate tensile strength, leading to the higher observed tensile strength in the longitudinal orientation. A higher fraction of fractured particles was observed

Fig. 7—Tensile fracture surfaces for longitudinal and transverse orientations, for all reinforcement volume fractions. A significant amount of particle fracture is observed in both orientations. METALLURGICAL AND MATERIALS TRANSACTIONS A

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Fig. 8—Quantitative particle fracture analysis during tensile fracture. The degree of particle fracture is highest at lowest volume fraction and in the longitudinal orientation, due to the highest degree of particle alignment.

at a lower volume fraction, independent of orientation, which correlates well with the particle-orientation analysis. Nevertheless, as discussed previously, a significant anisotropy at a low volume fraction, such as 10 pct SiC, is not sufficient to induce a significant anisotropy in the macroscopic tensile strength or the Young’s modulus of the composite. The trends observed in tension were mirrored in fatigue (Figure 9). An increase in reinforcement volume fraction resulted in enhanced fatigue resistance of the composite, independent of orientation. Longitudinal samples, however, exhibited higher fatigue strength than transverse samples, particularly in the high-cycle regime. As in the tensile behavior, the degree of fatigue-strength anisotropy increased with increasing volume fraction of reinforcement. The fatigue fracture morphology, shown in Figure 10, was quite different from the tensile fracture shown in Figure 7. The fracture surface showed three distinct regions typical of fatigue failure in these materials: initiation, propagation, and fast fracture.[14] Crack initiation took place primarily at Fe-rich inclusions and particle clusters located at the surface of the specimen. This is consistent with the observation of Chawla et al.,[38] who showed that the stress concentration at an inclusion is greater when it is located at or near the surface than in the interior of the composite. The inclusions are believed to be a result of slight contamination of the Al powder during processing and likely contributed to scatter in fatigue life, due to the variation in strength-limiting inclusion size from sample to sample. While the crack-initiation region had very few fractured or decohered particles, the fast-fracture region exhibited a high degree of particle fracture, presumably due to the high crack velocity associated with this stage of the fatigue fracture. It should be noted that particle clusters have also been shown to be potential fatiguecrack initiation sites,[14] but that crack initation at particle clusters was not evident in the materials studied here. It is quite possible that particle clusters, while certainly present, may not have been severe enough to cause crack initiation. Work to establish a link between a critical particle cluster size and fatigue-crack initiation is currently underway.[39] 58—VOLUME 35A, JANUARY 2004

Fig. 9—Stress vs cycle curves for longitudinal and transverse samples, at varying volume fraction. The degree of fatigue anisotropy increases with volume fraction of particles, because of the enhanced contribution of the reinforcement to the Young’s modulus of the composite.

As in the discussion of the tensile behavior, we first discuss the fatigue behavior of the composites, independent of orientation. Several studies have demonstrated that increasing the volume fraction and decreasing the particle size both result in enhanced fatigue resistance.[14,40] In the composite, most of the load is carried by the high-modulus, high-strength reinforcement, so, for a given stress, the composite undergoes a lower strain than the unreinforced alloy. Thus, the fatigue lives of particle-reinforced MMCs are generally longer than those of unreinforced metals. These improvements are most pronounced at lower stresses, in the high-cycle fatigue regime, while at high stress, the differences between reinforced and unreinforced materials are reduced. This has been attributed to “ductility exhaustion” of the composites in the low-cycle fatigue regime, since the higher ductility of the unreinforced alloy in this regime contributes to higher fatigue life than that of the composite.[1] The observed anisotropy in fatigue behavior can be attributed to the anisotropy in particle orientation, as in tensile deformation. Since an increase in the Young’s modulus is directly related to in an increase in fatigue strength, we can equate the fatigue resistance of the composites, for a given orientation, with the Young’s modulus. Since the 2080/SiC/10p exhibited a negligible difference in Young’s modulus, this composite did not show any noticeable anisotropy in the fatigue behavior either. At higher volume fractions, however, the difference in modulus was more significant, so a greater difference in fatigue strength of the two orientations was observed. It should be noted that due to the difference in the Young’s modulus, the anisotropy in the fatigue behavior in the longitudinal and transverse orientation was more evident in the high-cycle regime. The evolution of fatigue deformation was not controlled by anisotropy of SiC particles alone. Rather, the size and precipitate particles in the matrix, as well as the coherency relationship between the matrix and precipitate particle, is also very important.[7,41,42] Chawla et al.[7] compared the tensile and fatigue resistance of 2080/SiCp composites heat treated to a T6 condition vs a T8 condition (solution treating, followed by rolling and subsequent aging). Because of finer METALLURGICAL AND MATERIALS TRANSACTIONS A

Fig. 10—Fatigue fracture surface of a 2080/SiC/30p composite showing three distinct regions: initiation, propagation, and fast fracture.

and more closely spaced precipitates, the composite that underwent a T8 treatment exhibited higher yield strengths than the T6 materials. Despite its lower yield strength, however, the T6-matrix composites exhibited higher fatigue resistance than the T8-matrix composites. This contrasting behavior between monotonic and cyclic behavior was attributed to the fact that the S’ precipitates formed by the T6 heat treatment were coarser and less prone to shearing and, thus, were less susceptible to persistent slip band formation during fatigue. The TEM micrographs of the dislocation structures in the matrix of the composite, shown in Figure 11, support the original hypothesis of Chawla et al.[7] The micrographs clearly show a homogeneous dislocation structure consisting of dislocation bowing/loops around the METALLURGICAL AND MATERIALS TRANSACTIONS A

S’ precipitates. The dislocation structures shown here are similar to those reported by Vyletel et al.,[43] who studied the dislocation structures in a 2124-matrix composite with TiC particles. It should be mentioned that precipitate size alone should not be taken as the determining factor for fatigue resistance of the matrix. Rather, the precipitates should be of sufficient size to not be susceptible to precipitate shearing, but semi- or completely coherent with the matrix to impose repulsive stress fields that resist dislocation motion. Fatigue damage processes may also be affected by additional microstructural factors such as pileup of dislocations and refinement of cyclic slip due to reinforcement particles. Microscopic investigations into these mechanisms are currently being pursued. VOLUME 35A, JANUARY 2004—59

Young’s modulus of the composite in the longitudinal orientation than in the transverse orientation. 4. Microscopic fatigue damage in the matrix of the composite, in both orientations, was predominantly in the form of Orowan bowing of dislocations around S’ precipitate particles. ACKNOWLEDGMENT The authors are grateful for financial support from the Office of Naval Research (Dr. A.K. Vasudevan, Program Manager, Contract No. N000140110694). REFERENCES

Fig. 11—Dislocation structure in the matrix of the 2080/SiC/10p composite after fatigue (⬍100⬎ zone axis). The micrographs clearly show evidence of dislocation bowing/loops around the S’ precipitates, as well as the formation of dislocation cells.

IV.

CONCLUSIONS

Extrusion-induced particle-orientation anisotropy of MMCs was shown to have a significant influence on tensile and fatigue behavior. The following conclusions can be made, based on our study of the effect of particle-orientation anisotropy on the mechanical behavior of 2080/SiCp composites. 1. A preferred orientation of SiC particles was observed parallel to the extrusion axis. The extent of orientation was highest for the lowest-volume-fraction composites, since with increasing volume fraction, the mean free path for rotation and alignment of a given particle decreased. As expected, the Young’s modulus and tensile strength of the composites, independent of orientation, increased with increasing volume fraction of reinforcement. The increase in Young’s modulus was attributed to an increase in load transfer to the particles, while the increases in strength were due to load transfer, as well as the increased precipitate density in the matrix (from higher thermally induced dislocation density from processing) with increasing reinforcement volume fraction. 2. The composites exhibited a higher Young’s modulus and tensile strength along the longitudinal direction (parallel to the extrusion axis) than in the transverse direction. The extent of anisotropic behavior increased with increasing volume fraction, because of the increasing influence of the SiC reinforcement on the Young’s modulus and tensile properties. Thus, although the degree of microstructural anisotropy was greatest for 2080/SiC/10p, the greatest anisotropy in mechanical behavior was observed at 2080/SiC/30p. 3. The preferred orientation also resulted in anisotropy in the fatigue behavior of the composite material. The trends mirrored those observed in tension, with higher overall fatigue strengths and a higher anisotropy with increasing volume fraction of particles for both orientations. The anisotropy in fatigue behavior was attributed to the higher 60—VOLUME 35A, JANUARY 2004

1. N. Chawla and Y.L. Shen: Adv. Eng. Mater., 2001, vol. 3, p. 357. 2. N. Chawla and J.E. Allison: in Encyclopedia of Materials: Science and Technology, B. Ilschner and P. Lukas, eds., Elsevier Science, New York, NY, 2001, vol. 3, pp. 2969-74. 3. D.J. Lloyd: Int. Mater. Rev., 1994, vol. 39, p. 1. 4. J. Llorca: Progr. Mater. Sci., 2002, vol. 47, p. 283. 5. P.E. Krajewski, J.E. Allison, and J.W. Jones: Metall. Mater. Trans. A, 1993, vol. 24, p. 2731. 6. J.J. Lewandowski, C. Liu, and W.H. Hunt: Mater. Sci. Eng., 1989, vol. 107, pp. 241-55. 7. N. Chawla, U. Habel, Y.-L. Shen, C. Andres, J.W. Jones, and J.E. Allison: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 531-40. 8. P.M. Mummery, B. Derby, D.J. Buttle, and C.B. Scruby: Proc. Euromat 91, T.W. Clyne and P.J. Withers, eds., Cambridge, United Kingdom, 1993, vol. 2, pp. 441-47. 9. L.C. Davis, C. Andres, and J.E. Allison: Mater. Sci. Eng., 1998, vol. 249, pp. 40-45. 10. M. Manoharan and J.J. Lewandowski: Mater. Sci. Eng., 1992, vol. A150, pp. 179-86. 11. J. Hall, J.W. Jones, and A. Sachdev: Mater. Sci. Eng., 1994, vol. A183, p. 69. 12. N.L. Han, Z.G. Wang, and L. Sun: Scripta Metall. Mater., 1995, vol. 33, p. 781. 13. A.R. Vaidya and J.J. Lewandowski: Mater. Sci. Eng., 1996, vol. A220, p. 85. 14. N. Chawla, C. Andres, J.W. Jones, and J.E. Allison: Metall. Mater. Trans. A, 1998, vol. 29A, pp. 2843-54. 15. V.J. Michaud: Fundamentals of Metal Matrix Composites, ButterworthHinemann, Stoneham, MA, 1993, pp. 3-22. 16. A.K. Ghosh: Fundamentals of Metal Matrix Composites, ButterworthHinemann, Stoneham, MA, 1993, pp. 3-22. 17. P. Sahoo and M.J. Koczak: Mater. Sci. Eng., 1991, vol. A144, pp. 37-44. 18. D.J. Lloyd: in Composites Engineering Handbook, P.K. Mallick, ed., Marcel Dekker, New York, NY, 1997, pp. 631-70. 19. N. Chawla, J.J. Williams, and R. Saha: J. Light Met., 2003, vol. 2, pp. 215-27. 20. L.M. Tham, M. Gupta, and L. Cheng: Mater. Sci. Eng., 2002, vol. 326, pp. 355-63. 21. W.A. Logsdon and P.K. Liaw: Eng. Fract. Mech., 1986, vol. 24, pp. 737-51. 22. H. Jeong, D.K. Hsu, R.E. Shannon, and P.K. Liaw: Metall. Mater. Trans. A, 1994, vol. 25A, pp. 799-809. 23. F.J. Humphreys, W.S. Miller, and M.R. Djazeb: Mater. Sci. Technol., 1990, vol. 6, pp. 1157-66. 24. A. Borbely, H. Biermann, and O. Hartmann: Mater. Sci. Eng., 2001, vol. 313, p. 34. 25. J.J. Williams, G. Piotrowski, R. Saha, and N. Chawla: Metall. Mater. Trans. A, 2002, vol. 33A, pp. 3861-69. 26. G.C. Weatherly and R.B. Nicholson: Phil. Mag., 1968, vol. 17, p. 801. 27. R.N. Wilson and P.G. Partridge: Acta Metall., 1965, vol. 13, pp. 1321-27. 28. E.A. Starke, Jr., T.H. Sanders, and I.G. Palmer: J. Met., 1981, vol. 8, p. 24. 29. T. Chrisman, A. Needleman, and S. Suresh: Acta Metall., 1989, vol. 37, p. 3029. METALLURGICAL AND MATERIALS TRANSACTIONS A

30. S.V. Kamat, J.P. Hirth, and R. Mehrabian: Acta Metall., 1989, vol. 37, p. 2395. 31. V.C. Nardone and K.M. Prewo: Scripta Metall., 1986, vol. 20, p. 43. 32. V.C. Nardone: Scripta Metall., 1987, vol. 21, p. 1313. 33. M. Vogelsang, R.J. Arsenault, and R.M. Fisher: Metall. Trans. A, 1986, vol. 17A, pp. 379-89. 34. R.J. Arsenault and N. Shi: Mater. Sci. Eng., 1986, vol. 81, p. 175. 35. S. Suresh and K.K. Chawla: in Fundamentals of Metal Matrix Composites, S. Suresh, A. Mortensen, and A. Needleman, eds., Butterworth-Heinemann, London, 1993, pp. 119-36. 36. K.K. Chawla, A.H. Esmaeili, A.K. Datye, and A.K. Vasudevan: Scripta Metall. Mater., 1991, vol. 25, pp. 1315-19.

METALLURGICAL AND MATERIALS TRANSACTIONS A

37. P.M. Singh and J.J. Lewandowski: Metall. Trans. A, 1993, vol. 24A, pp. 2531-43. 38. N. Chawla, L.C. Davis, C. Andres, J.E. Allison, and J.W. Jones: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 951-57. 39. J.J. Williams, N. Chawla, and R.J. Fields: unpublished work, Arizona State University, Tempe, AZ, 2003. 40. J. Hall, J.W. Jones, and A. Sachdev: Mater. Sci. Eng. A, 1994, vol. A183, p. 69. 41. C. Calabrese and C. Laird: Mater. Sci. Eng., 1974, pp. 141-57. 42. C. Calabrese and C. Laird: Mater. Sci. Eng., 1974, pp. 159-74. 43. G.M. Vyletel, J.E. Allison, and D.C. Van Aken: Metall. Mater. Trans. A, 1995, vol. 26A, p. 3143.

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