Weight Functions of Radial Cracks Emanating from a Circular Hole in a Plate

Abstract

Explicit nodal weight functions for a pair of symmetric radial cracks emanating from a hole in a plate are presented with special emphasis on the load-independent characteristics of the explicit weight functions that can obviate repeated calculations of the Mode I stress intensity factors (KI) under different loading conditions. An analytical expression, which relates the explicit crack-face weight function component for Mode I deformation to the radial distance from the crack tip along the crack face, is also provided to facilitate KI evaluation by combining the uncracked stress field and the explicit crack-face weight functions through the use of the linear superposition principle. The utilization of the explicit weight functions, which are obtained from a simple loading, for calculating KI under complex loading conditions such as biaxial loading and pin-joint loading with and without interference pressure, is uniquely demonstrated by combining the superposition principle and the weight function concept.