Determination of Two-Dimensional Plastic Zone Shape and SIF at Crack-Tip Using RKPM

Abstract

Reproducing kernel particle Method (RKPM) is a meshless technology which has proven very useful for solving problems of elastic-plastic fracture mechanics. The mode I plastic zone shape at the crack-tip in a work-hardening material is obtained using RKPM. Ramberg-Osgood stress-strain relation is assumed and the crack-tip stress intensity factor (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. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. The effects of different dilation parameters on SIF under plane-stress and plane-strain conditions are studied. Results including plastic zone shape are compared with finite element method (FEM) to show the accuracy of RKPM. The main objective is to study the effects of different dilation parameters on SIF under plane stress and plane strain conditions and to obtain the mode I plastic zone shape at the crack-tip in a work-hardening material using RKPM.