An analysis of elasto-plastic strains and stresses in notched bodies subjected to cyclic non-proportional loading paths

Abstract Fatigue and durability analyses of machine components and structures require calculation of elastic-plastic stresses and strains in notched bodies subjected to non-proportional loading sequences. Analytical methods are seldom feasible even in the case relatively simple geometrical configurations and therefore numerical methods are often employed. The numerical-analytical method discussed below is based on the incremental relationships relating the fictitious elastic and elastic-plastic Neuber type strain energy densities near the notch tip, and the material stress-strain behavior simulated according to the Mroz-Garud cyclic plasticity model. The method consists of a set of algebraic incremental equations that can be easily solved for elastic-plastic stress and strain increments near a notch knowing the increments of the hypothetical elastic notch tip stress history and the material stress-strain curve. The validation of the proposed model against numerical data includes two non-proportional loading histories. In particular the basic equations involving the equivalence of the strain energy density are carefully examined. Finally, the numerical procedure for solving the basic set of equations is briefly described. The method is particularly suitable for fatigue life analyses of notched bodies subjected to cyclic multiaxial loading paths.