Multiaxial Stress-Strain Notch Analysis

Fatigue and durability analyses require the use of analytical and/or numerical methods for calculating elastic-plastic notch tip stresses and strains in bodies subjected to nonproportional loading sequences. The method discussed in the paper is based on the incremental relationships, which relate the elastic and elastic-plastic strain energy densities at the notch tip and the material stress-strain behavior, simulated according to the Mroz-Garud cyclic plasticity model. The formulation described below is based on the equivalence of the total distortional strain energy density, which appears to give the upper-bound estimations for the elastic-plastic notch tip strains and stresses. The formulation consists of a set of algebraic incremental equations that can easily be solved for elastic plastic stress and strain increments, based on the increments of the hypothetical elastic notch tip stress history and the material stress-strain curve. The validation of the proposed model against the experimental and numerical data includes several nonproportional loading histories. The basic equations involving the equivalence of the strain energy density are carefully examined and discussed. Finally, the numerical procedure for solving the two sets of equations is briefly described. The method is particularly suitable for fatigue life analyses of notched bodies subjected to cyclic multiaxial loading paths.