Stress and displacement singularities near corners

Abstract

The optical method of caustics, as it has been developed by the author, was used for the study of the stress singularity at the singular corner of a bimaterial composite consisting of two materially dissimilar wedges bonded together along either one or two of their interfaces and submitted to any type of loading. The equations of the caustics were derived by putting the complex stress functions of the Muskhelishvili formulation of the plane stress problem in their asymptotic forms, which are valid at the close vicinity of the corner. By comparing the theoretically defined caustics to those obtained by the experiments the order of the elastic stress singularity in the particular cases studied was calculated. The following special cases were considered: (i) a homogeneous wedge with various values of its angle; (ii) Two dissimilar wedges bonded together along one interface to form any part of a plane; (iii) Two dissimilar wedges bonded together along both their interfaces to form a full plane; and (iv) Two dissimilar half-planes bonded together along their interface while an oblique crack is traversing either of the half-planes and terminating at the interface. The values of the elastic stress singularities, as they have been defined experimentally, corroborate the theoretical results.