Determination of the stress intensity factor at the single edge crack tip using RKPM

Abstract

Reproducing Kernel Particle Method (RKPM) is a mesh-free technology which has proven very useful for solving problems of elastic-plastic fracture mechanics. In this study, the stress intensity factor (SIF) at the crack-tip in a work-hardening material is obtain using RKPM. Ramberg-Osgood stress-strain relation is assumed and the crack-tip SIF before and after formation of the plastic zone are examined. To impose the essential boundary conditions, penalty method is used. To construct the shape functions in the vicinity of the crack and crack-tip, both the diffraction and visibility criteria are employed and the crack tip region is also refined using more particles in two various model particle arrangements. The effects of different dilation parameters on SIF under plane-stress and plane-strain conditions are studied for plane-stress and plane-strain conditions. Results show that dilation parameter has a great impact on the performance of the RKPM and especially on the SIF value for the edge crack problems. The main objective is to study the effects of different dilation parameters on SIF value under plane-stress and plane-strain conditions at the crack-tip using diffraction and visibility criteria.