High and low cycle fatigue failure effects of metals predicted automatically from innovative elastoplastic equations with high-efficiency algorithms

Abstract

New finite strain elastoplastic $$J_2$$ -flow equations with no reference to the yield condition are proposed for the purpose of simultaneously simulating low-to-ultrahigh cycle failure effects of metals. As inherent response features of such new equations, the entire responses up to eventual failure under cyclic and non-cyclic loadings of constant and variable amplitudes are automatically predicted, in a direct sense without involving any additional damage-like variables and any ad hoc failure criteria. The thermodynamic consistency is ensured by demonstrating that the intrinsic dissipation is identically non-negative. Furthermore, a high-efficiency algorithm for integrating the elastoplastic rate equations is established toward bypassing very time-consuming numerical procedures in treating cyclic responses with high and even ultrahigh cycle number. With numerical examples, model predictions are shown to be in good agreement with fatigue failure data for low, high and very high cycle numbers, and the new algorithm is shown to be much faster and far more efficient than usual integration procedures.