Asymptotic description of the logarithmic singular stress field and its application

Abstract

In a joint of two dissimilar materials under mechanical or thermal loading the stresses at the intersection of the edges and the interface are very high or singular for elastic materials behaviour. For most joint geometries and material combinations there is a type of r−ω singularity. However, for some joint geometries and material combinations there is a type of ln(r) singularity. In this paper, the type of ln(r) stress singularity for a two dissimilar materials joint under thermal loading is treated by the Mellin transform method. Emphasis is placed on the asymptotical description of the stress distribution near the singular point. The angular functions used to describe the stresses are given in a general form, which are different to those of the same joint under edge tractions. For a quarter-planes joint angular functions are given in an explicit form. Finally, examples are presented to show when the asymptotical solution for the type of ln(r) stress singularity can be used to describe stresses near the singular point in the practical relevant joints. For a finite joint the unknown factor, K used to describe the stress is given as well.