13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- 3 Assessment of non-local FIP averaging volumes A total of 50 equivalent realizations with random grain distributions for nominally the same microstructure with mean grain size of about 18 µm were utilized to compare the FIP averaged over grains (FIPgrains), bands (FIPband), or the local FIP on every element (FIPelement). In each case, the average is computed for each octahedral slip system over the corresponding domain. Figure 3 presents the distributions of the FIP for each element (FIPelement) and the averages over bands (FIPband) and grains (FIPgrains) compiled from 50 equivalent realizations considering all the octahedral slip systems. Since fatigue life is dominated by the extreme distributions, these results consider only values larger than FIPthresh =MAX(FIPgrains)/1000. The three cases present similar distributions and the extreme value of the three distributions lie between 2x10-3 and 3x10-3. Since elements are smaller than the grain scale, the FIPs averaged over elements have somewhat higher extreme values than either grain- or band-averaged FIPs. Figure 4 presents the distributions of band-averaged FIPs that result from dividing the grain into seven regions, each aligned along slip planes which are oriented perpendicular to the slip plane normal. Note that the number of bands per grain is not constant, so each region may include more than one band from a single grain and slip system. The FIPband presents similar distributions from all sections of the grains, which suggests that there is no dependence of the FIPs on the section from which it belongs (e.g., closer to the center of the grain). Figure 2: Schematic representation of elements, bands and grains in which FIPs are averaged to estimate transgranular fatigue crack growth. The implementation in a FEM model with unstructured, voxellated meshing is shown, with bands color coded and numbered for a single spherical grain.
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