Analysis of Residual Stress Distribution in Anisotropic Thermo-Elastic Bimorph Systems

Abstract

We present an analysis of residual stresses in longitudinal and transversal direction of a bimorph element induced by a change in external temperature field due to mismatch in thermal and elastic characteristics in dissimilar two-phase composite material with laminated structure. Representative Volume Element of the system is defined as a heterogeneous two-phase layered element bonded at an interface in a sense of coherent bi-layer, where each phase possesses distinct anisotropic material characteristics. We use a homogenization procedure with particular form of strain field, which satisfies compatibility equations in the bulk and at an interface. Special rule of mixtures derived from a spatial averaging principle yields explicit dependence of through-thickness residual stress on a compositional parameter defined as a volumetric fraction of one phase of the system.