Modeling of Stress–Strain Fields Below U-Notch Root Using Plasticity Approximation Rules Under Variable-Amplitude Loading

Abstract

This paper evaluates the applicability of Neuber's and equivalent strain energy density (ESED) rules to predict the material response below the root of a sharp U-notch under variable-amplitude (VA) loading for crack propagation simulations. The Voce–Chaboche (V-C) combined hardening constitutive model, coupled with the above-mentioned approximation rules, is used to resolve the elasto-plastic response over a range of depths below the notch root. The response at each load reversal is extracted, and the maximum and minimum stress and strain quantities are used to evaluate fatigue damage using the Smith–Watson–Topper parameter. Results from approximation rules are compared to finite element method (FEM) at and below the notch root. Prediction accuracy varied at different points below the root depending on the size of the plastic zone, with predictions made using the original Neuber's and ESED rules being less accurate below the root. Applying stress redistribution correction to the stress field improves its accuracy below the root; however, strain values are significantly amplified as a result. A modified Neuber's rule with stress redistribution and constraint corrections predicts the distribution of the material response and fatigue damage with consistent accuracy.