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 layer on internal t hermal stresses induced inside an elliptic inhomogeneity embedded within al l infinite matrix in plane elasticity. The compliant interphase layer betwe en the inhomogeneity and the surrounding matrix is modeled as a spring laye r with vanishing thickness. The behavior of this interphase layer is based on the assumption that tractions are continuous but displacements are disco ntinuous across the layer, Complex variable techniques are used to obtain i nfinite series representations of the internal thermal stresses (specifical ly, the mean stress and the von Mises equivalent stress) which, when evalua ted numerically, demonstrate how the internal thermal stresses vary with th e aspect ratio of the inhomogeneity and tile parameter h describing the int erphase layer. These results are used to evaluate the effects of tile inter phase layer and the aspect ratio of the inhomogeneity on internal failure c aused by void formation and plastic yielding within the inhomogeneity. Rema rkably. the mean stress and von Mises equivalent stress are both found to b e non-monotonic functions of the parameter h, Consequently. we identify a s pecific value (h*) of h which corresponds to the maximum peak (mean or von Mises) stress inside the inhomogeneity. We also obtain another value (h(R)) of h below which the peak (mean or von R lisps) stress within the inhomoge neity is smaller than that, corresponding to the case of a perfect interfac e (that is, in the absence of the compliant interphase layer). These specia l values h* and hR of the parameter h depend on the aspect ratio of the ell iptic inhomogeneity. Iii 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 t he interphase layer.