Elastic-plastic stress-strain analysis of notches under non-proportional loading paths
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An analytical method for calculating notch tip stresses and strains in elastic-plastic bodies subjected to non-proportional loading sequences is discussed in the paper. The method is based on the incremental formulation relating the hypothetical linear elastic and elastic-plastic strain energy densities at the notch tip, and the material stress-strain behavior simulated according to the Mróz-Garud cyclic plasticity model. Two formulations involving the strain energy density and the complementary strain density are discussed in the paper, and they appear to give the lower and the upper bound estimates for the elastic-plastic notch tip strains. Each formulation consists of a set of incremental algebraic equations that can easily be solved for elastic-plastic stress and strain increments, knowing the increments of the hypothetical elastic notch tip stress history and the material stress-strain curve. The validation of the proposed model against finite element data obtained for non-proportional loading is also presented. The method is particularly suitable for fatigue life analysis of notched bodies subjected to multiaxial cyclic loading paths.
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