Effect of interphase layers on thermal stresses within an elliptical inclusion

Abstract

Thermal mismatch induced stresses are identified as the major cause of failure in a wide variety of materials and devices, ranging from metal–ceramic composites to passivated interconnect lines in integrated circuits. To reduce thermal stresses, an effective method is to add an intermediate layer, with appropriate thermal expansion coefficient, between the components of dissimilar materials. This paper gives a general analysis of the effects of the intermediate layers on thermal stresses within an elliptical inclusion, with particular emphasis on the role of thermal mismatch. The exact closed-form solution is obtained for stress field. One of the unique features of the present model is that the thermal stresses within the elliptical inclusion are uniform, making simple formulas available for quantitative analysis of the effects of the interphase on thermal stresses within the inclusion. It is found that the interphase layers have a strong effect on the deviatoric stress and a moderate effect on the mean stress within the inclusion. In particular, the effect of the interphase on the mean stress is sensitive to both the aspect ratio of the elliptical inclusion and the elastic mismatch between the inclusion and the surrounding materials, but not for the deviatoric stress within the inclusion. To reduce the thermal stresses within the inclusion, the optimum thermal expansion coefficient of the interphase is not necessarily between those of the inclusion and the matrix. However, if the design goal is to reduce the thermal stresses within both the inclusion and the interphase layer, the optimum interphase should have an intermediate thermal expansion coefficient between those of the matrix and the inclusion.