Interfacial thermal stress analysis of an elliptic inclusion with a compliant interphase layer in plane elasticity

Stresses induced by thermal mismatch are known to be a major cause of failu re in a wide variety of composite materials and devices ranging from metal- ceramic, composites to passivated interconnect lines in integrated circuits . One of the most effective procedures used to reduce these thermal stresse s is the addition of a compliant intermediate or interphase layer between t he different material components. This paper is concerned with the interfacial thermal stress analysis of an elliptic inclusion embedded within an infinite matrix with uniform change i n temperature. A compliant interphase layer is assumed to occupy the region between the inclusion and the matrix. This interphase layer is modeled as a spring layer with vanishing thickness (henceforth referred to as the inte rface between the inclusion and the matrix). Its behavior is based on the a ssumption that tractions are continuous but displacements are discontinuous across the interface. Complex variable techniques are used to obtain infinite series representati ons of the thermal stresses which, when evaluated numerically, demonstrate how the peak interfacial thermal stresses vary with the aspect ratio of the inclusion and the parameter h describing the interface. In addition, and p erhaps most significantly, for different aspect ratios of the elliptic incl usion, we identify a specific value (h*) of the interface parameter h which corresponds to the maximum peak thermal stress along the inclusion-matrix interface. Similarly, for different aspect ratios, we identify a specific v alue of h (also referred to as h* in the paper) which corresponds to the pe ak maximum thermal strain energy density along the interface (J. Appl. Mcch . 57 (1990) 956-963). In each case, we plot the relationship between the ne w parameter h* and the aspect ratio of the ellipse. This gives significant and valuable information regarding the failure of the interface using two e stablished failure criteria. (C) 2001 Elsevier Science Ltd. All rights rese rved.