Crack Tip Enrichment Functions for the XFEM Applied to the Elastic-Plastic Fracture Mechanics Taking Account for the Constraint Effect

Abstract

In this paper we propose a family of crack tip enrichment function for the XFEM implementation of elastic-plastic crack based on the J - Q theory Such a family of crack tip enrichment function consists of 9 enrichment functions in total namely 6 ones previously proposed based on the HRR singular field as well as 3 ones taking account for the crack tip constraint effect 3 additional enrichment functions are the bases for the higher terms in the asymptotic expansion of elastic-plastic crack tip displacement field The introduction of these functions into the XFEM enrichment functions enables to improve the approximation of crack tip displacement field significantly In numerical analysis for the validation of proposed enrichment functions crack faces are coincident with element boundaries and a crack tip is taken as a node in order to eliminate other possible errors besides error concerned with the crack tip enrichment functions By using the general purpose finite element software ANSYS 2-dimensional elastic-plastic XFEM is implemented for the MBL model as well as various fracture specimens Numerical result shows that the enrichment functions suggested by ours could improve the accuracy of fracture parameters significantly as compared with ones based on HRR field