A new simple method for calculating notch root stress and strain of plane problems subjected to monotonic loading up to general yielding

Abstract

In the present study, a new method for calculation of notch-root stress and strain is proposed. This novel method couples Neuber’s rule and incremental ESED method. A numerical procedure for solving the equation is presented. Also, the advantages and disadvantages of the numerical procedure are discussed. The coupling method is simple, and its accompanying numerical solution is easy to handle and straightforward. The proposed method is based on the total strain energy density, and strain energy density increment of the actual and elastic problem. Three cases of monotonic uniaxial loading in isotropic homogeneous plates with different material properties, namely nonlinear hardening obeying Ramberg–Osgood behavior, bilinear behavior, and elastic-perfectly plastic behavior, are investigated. The results show that, up to general yielding, the present method offers better accuracy compared to the previous methods. It is also observed that for the particular case of linear hardening, the difference of calculated stress and strain at the notch-root, compared to FEM, is less than 1%.