Study on Equivalent Distributed Stress Determination Technique based on Generalized Matrix Inversion (Part 1) －Analysis of Two-dimensional Edge Cracks based on the Center Cracked Plate’s Weight Function－

Abstract

The authors (Toyosada and Niwa, 2001) proposed to evaluate the Elastic-Plastic Fracture Mechanics (EPFM) parameters of edge and surface cracks by applying a crack face traction to a center-cracked infinite plate so that the relation between the crack length and SIF (α-K relation) is reproduced. This crack face traction is called Equivalent Distributed Stress (EDS). An EDS determination technique based on spline interpolation and generalized matrix inversion has been developed. Three numerical procedures for cohesive force's EDS determination, Fictitious crack face Loading Method (FLM), Yield stress Loading Method (YLM) and Whole crack face Loading Method (WLM) are proposed. A computation system which carries out EDS determination and fracture mechanics analysis, EDSGI, is developed. Crack Cohesive Force (CCF) model analyses based on FLM, YLM and WLM are performed by EDSGI. The validity of EDSGI is examined by comparing the edge crack's EPFM parameters calculated by FLM, YLM and WLM with the reference solutions evaluated by a direct CCF model analysis. It is found that the EPFM parameters evaluated by FLM agree well with the reference solutions, while YLM overestimates the plastic zone size for large applied stress, and WLM underestimates both plastic zone size and CTOD under the conditions chosen.