13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- attribute [1] (for example inclusion size). This is only valid when the considered element of microstructure is a representative volume element (RVE) with regards to fatigue. Although the definition of the RVE is possible for some deterministic behaviour aspects (such as elastoplastic behaviour), it is difficult to evaluate a RVE for the HCF strength which is macroscopically highly dispersed. Therefore the use of a single microstructure element (with a smaller volume than the RVE with regards to the fatigue behaviour but equal to the RVE size with regards to the elastoplastic behaviour) does not make it possible to take into account the contribution of the microstructure heterogeneities in the HCF response. To solve this issue, Liao [2] used the Monte Carlo method to build statistical volume element (SVE) of a microstructure with a random distribution of grain sizes and crystallographic orientations. Despite considering elastic behaviour of crystal only, Liao showed a good correlation between the results obtained by modeling the extreme value probability with a Fréchet distribution and experimental results. Recently, Przybyla et al. [3, 4] introduced a new framework taking into account the effects of neighborhood through the extreme values of the marked correlation functions to quantify the influence of microstructure on the fatigue limit and the contribution of interactions in the microstructure in the case of uniaxial loading. Przybyla used Gumbel distribution function to describe the extreme value probability of the studied parameters. The purpose of this work is, first, to analyze the microstructure sensitivity (morphology and orientation) of the fatigue indicator parameter (FIP) corresponding to the adaptation of multiaxial fatigue strength criteria at the mesoscopic length scale. Then a statistical study is used to define new mesoscopic thresholds for the FIPs, different from the original thresholds of the macroscopic criteria. Finally, the capability of the macroscopic criteria to take into account the microstructure sensitivity will be discussed through a comparison between the thresholds determined by the statistical response of the microstructure at the grain scale (called mesoscopic) and the original macroscopic thresholds. Free surface effects are also discussed with the comparison between FIPs determined from different FE models: 2D, 3D and 3D taking into account the grain surface only. 2. Numerical model 2.1. Constitutive relations The material parameters considered in this work are those of pure copper. This material has a face-centered cubic crystal structure with 12 slip systems (<111> {110}). The behaviour is modeled by cubic elasticity and crystal plasticity constitutive law. The crystal plasticity model used in this work is the one introduced by Meric and Cailletaud [5]. The cubic elasticity constants, the material parameters and the coefficients of the interaction matrix have been identified on a high purity copper by Gérard et al. [6]. 2.2. Grain morphology and crystallographic texture The simulations performed in this study were done using 3D semi-periodic microstructures (periodicity along X1 and X2 directions). The Voronoï polyhedra method was used to model the morphology of the grains. The initial domain (with dimensions x1=1, x2=1 and x3=0.5) is filled by
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