Cyclic J-integral using the Linear Matching Method

The extended version of the latest Linear Matching Method (LMM) has the capability to evaluate the stable cyclic response, which produces cyclic stresses, residual stresses and plastic strain ranges for the low cycle fatigue assessment with cyclic load history. The objective of this study is to calculate ΔJ through the LMM and suggest future development directions. The derivation of the ΔJ based on the potential energy expression for a single edge cracked plate subjected to cyclic uniaxial loading condition using LMM is presented. To extend the analysis so that it can be incorporated to other plasticity models, material Ramberg–Osgood hardening constants are also adopted. The results of the proposed model have been compared to the ones obtained from Reference Stress Method (RSM) for a single edge cracked plate and they indicate that the estimates provide a relatively easy method for estimating ΔJ for describing the crack growth rate behaviour by considering the complete accumulated cycle effects.