Transverse Flexure of a Semi-infinite Plate with a Step and a Crack at an Angular Corner

Abstract

A semi-infinite plate with a step and a crack originating from its angular corner is analyzed as a thin plate bending problem. Taking uniform bending moment as the load condition, stress distributions are investigated. Stress intensity factors which are important in linear fracture mechanics are analytically calculated for various crack lengths. The influence of the step and the angle of the corner is investigated. The relation between stress intensity factor and Poisson's ratio is also investigated. A rational mapping function which is formed as a sum of fractional expressions and the complex variable method are used for the analysis. By using this mapping function, a closed solution is obtained which is exact for the shape represented by the rational mapping function. By using a rational mapping function of a sum of fractional expressions, the stress analysis for a comparatively arbitrary shape can be carried out.