Evaluation of the strain energy density method of notch stress concentration calculations in the plastic range

Abstract

Accurate stress and strain calculations at a notch usually require a non-linear finite element analysis when local yielding has occurred. The strain energy density hypothesis is a method to predict these stress and strain values. This method proposes that the plastic strain energy density is equivalent to the strain energy density found assuming the material to be entirely elastic. This hypothesis was evaluated using the finite element method, which was tested by comparing to exact solutions of elastic and elasto-plastic problems, to calculate the stress and strain field for two notched plates of varying widths under elasto-plastic loading. For both geometries, a plane stress and plane strain analysis was performed. The elasto-plastic strain energy density from the finite element method was found to be greater than that predicted by this proposal, which in turn resulted in under-predicting the local stresses and strains. This difference was greater for the plane stress condition than for the plane strain condition. Comparisons were also made with notch stresses based the Neuber method. The two methods appear to give an upper and lower bound to the actual stresses and strains. By combining the results of the strain energy density method and the Neuber method, reasonably accurate estimates of stress and strain values can be obtained.