An estimation method for the determination of the second elastic–plastic fracture mechanics parameters

Abstract

An engineering method is developed for estimating the A-term, which is the second parameter in three-term elastic–plastic asymptotic expansion. The method is based on the interpolation of small-scale yielding and large-scale yielding solutions of A. It is demonstrated that under small-scale yielding, the A can be obtained through the elastic T-stress. The existence of a one-to-one relationship between constraint parameter A and elastic T-stress is established, and detailed expressions of the A– T relationship for various hardening exponent n are obtained from finite element analyses. For power law materials, through the analysis of crack tip stress fields, it is demonstrated that A-solution scales with load according to an exponent which is a particular function of n. This relation enables the estimation of the A-variation under fully plastic conditions. A method of combining these two solutions together is proposed for materials following the Ramberg–Osgood stress strain relationship. The proposed method is used to develop A solutions for 2D test specimens under remote tension loading in handbook format. It is shown this method can provide accurate A solutions for 2D test specimens for a wide range of crack depths and material hardening exponents, from small-scale yielding to large-scale yielding loading conditions. The present developed method can be further used in developing A solutions in handbook format for other engineering structural components.