EDGE STRESS INTENSITY FUNCTIONS FOR CIRCULAR CRACKS IN A 3-D ELASTIC DOMAIN

摘要

Solutions to the elasticity system in the vicinity of a circular singular edge in a three-dimensional domain are provided in an explicit form. These asymptotic solutions are represented by a family of eigen-functions with their shadows, and the associated edge stress intensity functions (ESIFs), which are functions along the circular edge. We provide explicit formulas for a penny-shaped crack for an axisymmetric case as well as cases in which the loading or geometry is non-axisymmetric. The precise representation of the asymptotic series allows the development of a new extraction technique based on the quasi-dual function method, for the edge stress intensity functions which are of practical engineering importance in predicting crack propagation as well as failure initiation. Numerical examples are provided, demonstrating the extraction of ESIFs from high-order finite element models.