An efficient procedure for modelling limited plastic flow

Abstract

A degree of plasticity is often tolerated at stress raising features in severely loaded, nominally elastic, components. Conventionally, the methods available for analysis are the finite element method (FEM) or an approximate notch root plastic strain method. The method introduced here is based on the idea of distributing dislocations to form a perturbation on an elasticity solution to solve the problem for an elastic—perfectly plastic material in transverse plane strain. Specialized kernels are used to satisfy exactly the far field boundary conditions and those at the stress raiser, so that only the small plastic enclave of material need be discretized. The method is seen to follow the incremental nature of the problem and to take into account the stress redistribution in plasticity. The problem of a circular hole under remote tension is solved and good agreement with an FEM analysis of a similar problem is observed.