Stress concentrations in anisotropic plates by the method of caustics

Abstract

The optical method of caustics has been extended to study, theoretically and experimentally, the stress fields developed around discontinuities or singularities in anisotropic plates. The equations of the caustic to be expected from illuminating the anisotropic plate by a coherent light beam were derived in terms of the two complex stress functions used in the complex formulation of the plane anisotropic stress problem, the coefficients of the optical anisotropy of the material and the characteristics of the optical arrangement. The particular case of the singular stress field developed at the tip of a crack in an orthotropic plate was studied in detail. A series of experiments was then undertaken with slotted plates taken from the neck region of a polycarbonate plate which had been necked in tension and therefore showed a significant amount of anisotropy. The experimental data corroborated the theoretical predictions. It was concluded that singular or discontinuous stress fields can be successfully studied by the method of caustics.