Two methods for calculating notch tip stress and strain histories in elastic-plastic components subjected to non-proportional cyclic loads are presented. The key elements of the proposed methods are incremental relationships between elastic and elastic-plastic strain energy densities and material constitutive relations. The material is assumed to strain harden and a kinematic hardening model based on a multi-surface field of work hardening surfaces is employed.

Each method results in a set of seven independent algebraic equations. The equation sets can easily be solved for the notch tip elastic-plastic stress-strain histories with the knowledge of the materials uniaxial properties, the applied load, and the component geometry. Results of each method are compared with finite element and experimental data for monotonic and cyclic nonproportional loading sequences. The notch tip elastic-plastic strains found using each method predict the general trend in, and quantitatively agree well with the experimental and finite element data.