Analysis of the mesoscopic high cycle fatigue strength of FCC metals with polycrystalline plasticity and extreme value probability methods

Abstract

This study analyzes the influence of microstructure properties on the extreme value distributions of the fatigue indicator parameter (FIP) corresponding to the multiaxial HCF Dang Van criterion. The following loading cases are considered: uniaxial loading, proportional and non-proportional multiaxial loadings. The mesoscopic FIP determined from FE calculations on 2D polycrystalline synthetic aggregates using the ZeBuLoN code. The approach adopted in this work is to replace the RVE by random microstructure elements that can be considered as “statistical volume element” (SVE). A set of extreme values is constructed by determining the maximum value of the FIP for each SVE. The type of extreme value distribution is analyzed with a generalized extreme value function and is shown to follow a Gumbel type distribution. The shape factors of this distribution are compared for the different loading conditions. This comparison shows the limitations of the used criterion, especially in the case of multiaxial loadings. The effect of anisotropy on these distributions is finally investigated by comparing the results of two types of texture (isotropic and rolling). The introduction of a preferential texture reduces the shape factor and the criterion applied with the classic stress field becomes conservative, and also decreases the scatter parameter of the extreme value distributions of the FIP.