Further investigation of Neuber’s rule and the equivalent strain energy density (ESED) method

On the basis of the analysis of energy of elastic-plastic body subjected to monotonic and cyclic loading, a physical relationship between Neuber’ s rule and the equivalent strain energy density (ESED) method is found. It is shown that Neuber’s rule is actually a particular case of ESED method, namely when the dissipation of the plastic strain energy at the notch root is neglected in ESED method. The reason for the overestimation of the local strains using Neuber’s rule is thus explained essentially and the physical meaning of ESED method in both monotonic and cyclic form is further defined. In terms of the real physical behavior occurring at the notch root during cyclic plastic deformation, a modified version of ESED method, in which only the heat energy is considered as a dissipation and the stored energy is regarded as a contribution to local stress and strain ranges, has been developed in this paper. It is shown that, for the case of cyclic loading, the modified ESED method further improves the accuracy of the original ESED method in prediction of the nonlinear stress/strain behavior of notches. It is also shown that the relation developed in this paper can easily be used for a simulation of the local strain-stress history near a notch root.