Analysis of bimaterial singular regions for orthotropic and isotropic materials under thermal loading

Abstract

A method to formulate an asymptotic elasticity solution for bimaterial singular regions in orthotropic materials is presented for the thermal case. In the vicinity of material and geometric singularities, approximate methods such as finite elements fail to converge and procedures to improve these solutions become necessary. The results presented herein can be used in conjunction with approximate numerical techniques for the determination of stresses and stress intensity factors in composite bonded joints, cracked bimaterial interfaces, or a junction of dissimilar materials under thermal loading. The thermal displacement and stress fields at the tip of a bimaterial wedge are developed by means of eigenfunction expansions including both singular and nonsingular terms. The thermal elasticity solution for isotropic materials as the limiting case of the orthotropic solution is also obtained. The formulations obtained are applicable to bonded joints with interfacial or interlaminar cracks, geometric and material discontinuities, and uniform thermal loading. The detailed formulation presented provides an essential component in the application of finite elements for the determination of generalized intensity factors and stresses in composites, bonded joints, or other dissimilar materials under thermal loading. Formulation results for orthotropic materials, including the limiting case of isotropic materials, are compared with published and closed form results that use different formulations, and excellent agreement is observed. Furthermore, the existence of logarithmic stress singularities of the form (k⋅ΔT⋅lnr) is investigated and discussed.