Abstract
Finite element analyses of the effective coefficient of thermal expansion (CTE) of metal-matrix composites are presented, with a focus on composites with potential for use in electronic packaging applications. The analyses are based on two-dimensional plane strain and axisymmetric unit-cell models. The brittle phase is characterized as an isotropic elastic solid with isotropic thermal expansion. The possibility of plastic deformation, described by an isotropic-hardening flow rule, is allowed for in the ductile phase. A wide range of reinforcement volume fractions is considered. The effects of phase geometry, phase contiguity, ductile phase material properties, processing-induced residual stresses, and brittle particle fracture are considered. The CTE is found to be much less sensitive to phase distribution effects than is the tensile stiffness. The results show that there is a significant dependence of the overall CTE on the phase contiguity (i.e., on whether the brittle or the ductile phase is continuous).
Similar content being viewed by others
References
C. Zweben:J. Met., 1992, vol. 44 (7), pp. 15–23.
A. Levy and J.M. Papazian:J. Eng. Mater. Technol., 1993, vol. 115, pp. 129–33.
B.W. Rosen and Z. Hashin:Int. J. Eng. Sci., 1970, vol. 8, pp. 157–73.
V.M. Levin:Mekhanika Tverdogo Tela, 1967, vol. 2, pp. 88–94; Mech. Solids, 1967, vol. vn2, pp. 58-61 English translation.
R.A. Schapery:J. Comp. Mater., 1968, vol. 2, pp. 380–404.
M. Finot: Master’s Thesis, Brown University, Providence, RI, 1993.
K. Janghorban:J. Mater. Process. Technol., 1993, vol. 38, pp. 361–68.
T. Christman, A. Needleman, and S. Suresh:Acta Metall., 1989, vol. 37, pp. 3029–50.
J. Llorca, A. Needleman, and S. Suresh:Acta Metall. Mater., 1991, vol. 39, pp. 2317–35.
J. Llorca, S. Suresh, and A. Needleman:Metall. Trans. A, 1992, vol. 23A, pp. 919–34.
V. Tvergaard:Int. J. Fract., 1982, vol. 18, pp. 237–52.
M.B. Bush:Mater. Sci. Eng., 1992, vol. A154, pp. 139–48.
V. Tvergaard:Acta Metall. Mater., 1990, vol. 38, pp. 185–94.
A. Levy and J.M. Papazian:Metall. Trans. A, 1990, vol. 21A, pp. 411–20.
N. S0rensen, A. Needleman, and V. Tvergaard:Mater. Sci. Eng., 1992, vol. A158, pp. 129–37.
C.L. Horn:J. Mech. Phys. Solids, 1992, vol. 40, pp. 991–1008.
G.L. Povirk, M.G. Stout, M. Bourke, J.A. Goldstone, A.C. Lawson, M. Lovato, S.R. MacEwen, S.R. Nutt, and A. Needleman:Acta Metall. Mater., 1992, vol. 40, pp. 2391–412.
M.A.M. Bourke, J.A. Goldstone, M.G. Stout, and A. Needleman: inMetal-Matrix Composites, S. Suresh, A. Mortensen, and A. Needleman, eds., Butterworth-Heinemann, Stoneham, MA, 1993, pp. 61–80.
V. Tvergaard:J. Mech. Phys. Solids, 1976, vol. 24, pp. 291–304.
D. Peirce, C.F. Shih, and A. Needleman:Compos. Struct., 1984, vol. 18, pp. 857–87.
S. Suresh, T. Christman, and Y. Sugimura:Scripta Metall., 1989, vol. 23, pp. 1599–1602.
ASM Handbook, 10th ed., ASM INTERNATIONAL, Metals Park, OH, 1990, vol. 2.
H.J. Böhm: Doctoral Thesis, Technical University of Vienna, Vienna, Austria, 1991.
Y.-L. Shen, M. Finot, A. Needleman, and S. Suresh:Acta Metall. Mater., 1994, vol. 42, pp. 77–97.
J.R. Brockenbrough, S. Suresh, and H.A. Wienecke:Acta Metall. Mater., 1991, vol. 39, pp. 735–52.
T. Nakamura and S. Suresh:Acta Metall. Mater., 1993, vol. 41, pp. 1665–81.
M.K. Premkumar, W.H. Hunt, Jr., and R.R. Sawtell:J. Met., 1992, vol. 44 7, pp. 24–28.
M.H. Poech and H.F. Fischmeister:Acta Metall. Mater., 1992, vol. 40, pp. 487–94.
M.H. Poech, H.F. Fischmeister, and R. Spiegler:J. Hard Mater., 1991, vol. 2, pp. 197–205.
G.L. Povirk, A. Needleman, and S.R. Nutt:Mater. Sci. Eng., 1991, vol. A132, pp. 31–38.
J. Bonnen, J. Allison, and J.W. Jones:Metall. Trans. A, 1991, vol. 22A, pp. 1007–19.
T. Mochida, M. Taya, and D.J. Lloyd:Mater. Trans., JIM, 1991, vol. 32, pp. 931–42.
Y. Sugimura and S. Suresh:Metall. Trans. A, 1992, vol. 23A, pp. 2231–42.
Y. Brechet, J.D. Embury, S. Tao, and L. Luo:Acta Metall. Mater., 1991, vol. 39, pp. 1781–86.
P.M. Mummery, B. Derby, and C.B. Scruby:Acta Metall. Mater., 1993, vol. 41, pp. 1431–45.
D.J. Lloyd:Acta Metall. Mater., 1991, vol. 39, pp. 59–71.
W.H. Hunt, Jr., J.R. Brockenbrough, and P.E. Magnusen:Scripta Metall. Mater., 1991, vol. 25, pp. 15–20.
J. Yang, C. Cady, M.S. Hu, F. Zok, R. Mehrabian, and A.G. Evans:Acta Metall. Mater., 1990, vol. 38, pp. 2613–19.
M.S. Hu:Scripta Metall. Mater., 1991, vol. 25, pp. 695–700.
S. Kumai, J.E. King, and J.F. Knott:Fatigue Fract. Eng. Mater. Struct., 1992, vol. 15, pp. 1–11.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shen, Y.L., Needleman, A. & Suresh, S. Coefficients of thermal expansion of metal-matrix composites for electronic packaging. Metall Mater Trans A 25, 839–850 (1994). https://doi.org/10.1007/BF02665460
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02665460