PSEUDO-ELASTIC ANALYSIS OF ELASTIC–PLASTIC CRACK TIP FIELDS USING ELEMENT-FREE GALERKIN METHOD

Abstract

A methodology for the characterization of asymptotic elastoplastic crack tip stress fields is presented by coupling the pseudo-elastic analysis with the element-free Galerkin method (EFGM). An iterative linear elastic analysis using EFGM is carried out for the determination of elastic–plastic crack tip stress fields by treating material parameters as spatial field variables. Effective material parameters are used to describe the constitutive behavior of the continuum and are defined by using the Hencky's total deformation theory of plasticity. The effective material parameters are updated in an iterative manner based on strain controlled projection method using experimental uniaxial tension test curve. The effectiveness of the method is illustrated by predicting the stress fields near the crack tip region of a square plate subjected to asymptotic linear elastic displacement field on the outer boundary of the plate. Different geometries subjected to mode-I and mode-II loadings are considered for the present study. The material model considered in these problems is Ramberg–Osgood model with different hardening exponent values. The predictions of the asymptotic elastic–plastic stress fields near the crack tip are compared with the results of nonlinear finite element analysis and also with the HRR singular stress fields and found to be in good agreement. J-integral values which characterize the amplitude of HRR stress field are also evaluated for the considered geometries and are found to close matching with the EPRI estimation scheme.