A simplified ratcheting limit method based on limit analysis using modified yield surface

Two effective approaches for obtaining ratchet boundaries of a structure undergoing cyclic loads are presented. The approaches use limit analysis of a structure whose yield surface is modified according to the cyclic load. In the first approach, Uniform Modified Yield (UMY) surface is used. UMY approach reduces the Mises-based cylindrical yield surface by Mises stress of the cyclic stress amplitude. UMY method was slightly conservative, and sometimes overly conservative, especially at high ratio of cyclic load to primary steady load. Conservatism, caused by the assumption that the modified yield surface remains isotropic, is eliminated by considering anisotropic Load Dependent Yield Modification approach, LDYM. This approach reduces yield strength based on relative orientation of steady primary and cyclic stress tensors. This work assumed elastic perfect plastic material behavior, with no strain hardening for both original and modified yield surfaces. Ratchet boundaries of several structures, published in literature, were obtained using UMY and LDYM approaches and verified against published data and results of conventional methods. Numerical procedures for UMY and LDYM approaches are extremely fast relative to conventional numerical schemes, and are not restricted by complex geometry or loading.