Approximation of mean stress relaxation by numerical simulation using the Jiang model and extrapolation of results

Local mean stresses have a significant influence on the fatigue strength of many components. Often only the initial values of the mean stresses are known. Typically the quasi-stable values are lower because residual stresses as well as the absolute value of mean stresses in notch roots tend to be reduced during cyclic loading. Some simple, but coarse empirical estimations of the amount of mean stress relaxation have been proposed in literature. More complex material models like the Jiang model are able to give a better description of that process, but calculating a sufficient number of loading cycles for a real component using such a model is very time-consuming. In this paper an approach combining both methods is presented: The first loading cycles are simulated through FE analyses using Jiang's material model. The result of this simulation is extrapolated using equations according to the empirical estimation methods proposed by Landgraf, Kodama and Maxwell. Various extrapolation approaches are discussed and the results for sheet steel ZStE 500 and steel 1070 are shown.