Williams expansion terms and their importance for accurate stress field description in specimens with a crack

Abstract

The paper deals with an analysis of the stress and displacement fields in various cracked speci-mens (loaded in mode I as well as in mode II). The main goal is to determine an accurate appro-ximation of the near-crack-tip fields which can be subsequently used e.g. in the case of quasi-brittle materials for estimation of the extent of a nonlinear zone at the crack tip in general, the fracture pro-cess zone in particular. Values of coefficients of the so-called higher-order terms of the power expan-sion by which the fields can be expressed are determined via regression from results of numerical si-mulations. The analysis is conducted using 2D numerical models and ANSYS FE computational system is employed. Various aspects regarding the description of the stress/displacement fields by means of the Williams expansion are discussed; especially the convergence of the coefficients of the first several terms of the series expansion, their absolute values and importance for an accurate stress approximation.