A Crack Originating from an Angular Corner of a Semi-infinite Plate With a Step

Abstract

A semi-infinite plate with a step and a crack originating from its angular corner is analyzed as a plane elastic problem. Uniform tension is considered as the boundary condition. Stress distributions are analytically calculated for the state before and after the occurrence of a crack. Stress intensity factors which are important in linear fracture mechanics are analytically calculated and are investigated for some angles of the angular corner and various crack lengths. The influence of the step on the stress intensity factors is also investigated. A rational mapping function which maps the semiinfinite region with a step and a crack into a unit circle is formed as a sum of fractional expressions. The rational mapping function and Muskhelishvili's method are used for the analysis. A closed solution which is exact for the shape represented by the rational mapping function is obtained.