Effects of a compliant interphase layer on internal thermal stresses within an elliptic inhomogeneity in an elastic medium

This paper studies the effect of a compliant interphase ayer on internal thermal stresses induced inside an elliptic inhomogeneity embedded within an infinite matrix in plane elasticity. The compliant interphase layer between the inhomogeneity and the surrounding matrix is modeled as a spring layer with vanishing thickness. The behavior of this interphase layer is based on the assumption that tractions are continuous but displacements are discontinuous across the layer. Complex variable techniques are used to obtain infinite series representations of the internal thermal stresses (specifically, the mean stress and the von Mises equivalent stress) which, when evaluated numerically, demonstrate how the internal thermal stresses vary with the aspect ratio of the inhomogeneity and the parameter h describing the interphase layer. These results are used to evaluate the effects of the interphase layer and the aspect ratio of the inhomogeneity on internal failure caused by void formation and plastic yielding within the inhomogeneity. Remarkably, the mean stress and von Mises equivalent stress are both found to be non-monotonic functions of the parameter h. Consequently, we identify a specific value (h*) of h which corresponds to the maximum peak (mean or von Mises) stress inside the inhomogeneity. We also obtain another value (hR) of h below which the peak (mean or von Mises) stress within the inhomogeneity is smaller than that corresponding to the case of a perfect interface (that is, in the absence of the compliant interphase layer). These special values h* and hR of the parameter h depend on the aspect ratio of the elliptic inhomogeneity. In particular, when the interphase layer is designed so that the value of h is close to unity, the internal peak thermal stress is reduced to a fraction of its original value obtained in the absence of the interphase layer.