Numerical determination of coefficients of multi-parameter asymptotic expansion of the crack-tip stress field using FEM

Abstract

In this study coefficients of the multi-parameter Williams series expansion for the stress field in the vicinity of the central crack in the rectangular plate and are obtained by the use of finite element analysis. The higher-order terms in the Williams asymptotic expansion are retained. It allows us to give more accurate estimation of stress, strain and displacement fields and to extend the domain of validity for the Williams series expansion. The higher-order coefficients are extracted from finite element method calculations implemented in multi-purpose software package Simulia Abaqus. The plate with a small central crack has been considered either. This kind of the cracked specimen has been utilized for comparison of coefficients of the Williams series expansion obtained from finite element analysis with the coefficients known from the theoretical solution based on the complex variable theory in plane elasticity. It is shown that the coefficients of the Williams series expansion match with good accuracy.