Summary
This paper examines the thermal behavior of a plane elastic compliant interphase layer surrounding an elliptic inhomogeneity which is embedded within an infinite matrix. To allow continuity of traction but discontinuity of displacements, the compliant interphase is modeled as a spring layer with a vanishing thickness. Furthermore, to obtain the resulting thermal stresses, the complex variable method was used, together with a series solution. A commerical finite element package was used to validate the theoretical predictions. The results reveal that thermal stresses vary with the aspect ratio of the inhomogeneity and the parameterh describing the spring constant of the interphase layer for four different types of inhomogeneous materials: aluminum, copper, gold and silver. In all these cases, the matrix was assumed to be made of silicon and the thermal stresses were assumed to result from a uniform change in temperature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wikstrom, A., Gudmundson, P., Suresh, S.: Thermoelastic analysis of periodic thin lines deposited on a substrate. J. Mech. Phys. Solids47, 1113–1130 (1999).
Gouldstone, A., Shen, Y.-L., Suresh, S., Thompson, C. V.: Evolution of stress in passivated and unpassivated metal interconnects. J. Mater. Res.13, 1956–1966 (1998).
Wu, C. C., Kahn, M., Moy, W.: Piezoelectric ceramics with functional gradients: a new application in material design. J. Am. Ceram. Soc.79, 809–812 (1996).
Niwa, H., Yagi, H., Tsuchikawa, H.: Stress distribution in an aluminum interconnect of very large scale integration. J. Appl. Phys.68, 328–333 (1990).
Korhonen, M. A., Paszkiet, C. A., Li, C. Y.: Mechanisms of thermal stress relaxation and stress-induced voiding in narrow aluminum-based metallization. J. Appl. Phys.69, 8083–8091 (1991).
Ashby, M. F., Blunt, F. J., Bannister, M.: Flow characteristics of highly constrained metal wires. Acta Metall. Mater.37, 1857–1965 (1989).
Huang, Y., Hutchinson, J. W., Tvergaard, V.: Cavitation instabilities in elastic plastic solid. J. Mech. Phys. Solids39, 223 (1991).
Lee, Y. D., Erdogan, F.: Residual thermal stresses in FGM and laminated thermal barrier coatings. Int. J. Fract.69, 145–165 (1995).
Hashin, Z.: The spherical inhomogeneity with imperfect interface. J. Appl. Mech.58, 444–449 (1991).
Achenbach, J. D., Zhu, H.: Effect of interfacial zone on mechanical behavior and failure of hexagonal-array fibre composites. J. Mech. Phys. Solids37, 381–393 (1989).
Achenbach, J. D., Zhu, H.: Effect of interphase on micro and macromechanical behavior and failure of fibre-reinforced composites. J. Appl. Mech.57, 956–963 (1990).
Hashin, Z.: Thermoelastic properties of fiber composites with imperfect interface. Mech. Mater.8, 333–348 (1990).
Hashin, Z.: Thermoelastic properties of particulate composites with imperfect interface. J. Mech. Phys. Solids39, 745–762 (1991).
Ru, C. Q., Schiavone, P.: A circular inclusion with circumferentially inhomogeneous interface in anti-plane shear. Proc. R. Soc. London A453, 2551–2572 (1997).
Shen, H., Schiavone, P., Ru, C. Q., Mioduchowski, A.: An elliptic inhomogeneity with imperfect interface in anti-plane shear. Int. J. Solids Struct37, 4557–4575 (2000).
Shen, H., Schiavone, P., Ru, C. Q., Mioduchowski, A.: Analysis of internal stress in an elliptic inclusion with imperfect interface in plane elasticity. Math. Mech. Solids5, 501–521 (2000).
Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity. Groningen: Noodhoff 1963.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shen, H., Fawaz, Z. Thermal behavior of an elliptic inhomogeneity surrounded by a compliant interphase layer. Acta Mechanica 159, 29–38 (2002). https://doi.org/10.1007/BF01171445
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01171445