Approximate local elasto-plastic solution for notched plates undergoing cyclic tensile loading

This work presents a simple methodology to estimate the inelastic stress and strain histories at the root of the notch of a thin elasto-plastic plate undergoing any complex non-monotonic tensile loading. It is proposed an extension of the classical Neuber and Linear projection rules to the case of non-monotonic loading. Using such extended projection techniques, the stress–strain curve at the root of the notch is similar to the curve obtained in a non-monotonic tensile test with prescribed strain. In this test, the limit strain at each reversal depends on the loading history and on the adopted projection technique, what is very important mainly if cyclic hardening (or softening) occurs. The basic idea is to replace this experimental curve by a numerically generated one. A very easy to implement algorithm is proposed to automatically generate the stress–strain curve and to perform the projection. A constitutive theory that accounts for the hardening effects induced by cyclic plasticity is considered. A simple procedure to identify all the material constants that arise in this theory from only one cyclic tensile test with controlled deformation is also presented. Examples concerning cyclic loading in notched aluminium plates are presented to show the main features of the proposed methodology.