13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- randomly positioned and oriented germs so as to have a distance greater than or equal to 0.02 between two germs. The CAD model was discretized by around to 5.105 linear tetrahedral finite elements (figure 1-(b)). Computed microstructure contains 200 equiaxed grains (figure 1-(a)) with an average of 2500 finite elements per grain. In addition to loading, periodicity conditions were applied on the planes corresponding to X1min, X1max, X2min and X2max. To take into account the free surface effect, the symmetry conditions were applied on the face corresponding to X3min. The grain number on the free surface (corresponding to X3max) is about 50. Finally, the random selection of 200 crystal orientations was carried out in the Euler space defined by the three angles ( 2 1, , φ ϕ φ ) assuming cubic crystal symmetry and triclinic sample symmetry. Figure 1-(c) shows the {100} and {110} pole figures of these 200 orientations. Given the low number of orientations, this crystallographic aggregate can be considered as having no preferential orientations. Figure 1. (a) Grain morphology, (b) Mesh and (c) {100} and {110} pole figures showing the selected crystallographic orientations 2.3. Fatigue loading conditions Different loading conditions are investigated in this section: uniaxial loading, and tension /torsion loadings with different biaxiality ratios a a k τ σ= and different phase shifts. The selected loading ratio is 1 ,max ,min =− =∑ a a R σ σ . The combined loading levels equivalent to the median fatigue limit at 107 cycles are determined using the Crossland criterion [9]. These load levels are given in Table1.
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