13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Castelluccio and McDowell [3] proposed to quantify the driving force for transgranular failure with a crystallographic version of the Fatemi-Socie FIP defined for each octahedral slip system, i.e., FIP 1 2 p n y k (4) where p is the cyclic plastic shear strain range on slip system , n is the peak stress normal to this slip system, y is the cyclic uniaxial yield strength of the polycrystal, and 1 k , as proposed by Fatemi and Socie [10]. The algorithm computes the FIP on each slip system and for each element using the range of plastic strain over the third loading cycle [3]. This methodology allows for an approximate stress redistribution to almost represent ―steady state‖ cyclic conditions in terms of stress and plastic strain redistribution within the polycrystal in the HCF regime, since the microstructure exerts a dominant influence on the transient cyclic plastic deformation fields. 2.3.1 Mesoscale averaging volumes for FIPs To numerically regularize the FEM discretization and also to represent the finite physical scale of the fatigue damage process zone, the FIPs calculated at each integration point in the mesh are averaged over a selected mesoscale volume. In the present approach we consider three volumes (Figure 2): (i) individual elements, (ii) bands parallel to slip planes, and (iii) entire grain volume. Figure 2 presents a cluster of finite elements that form one grain. Each grain is subdivided in bands of one element of width that are parallel to slip planes as described in Refs. [3][4][8]. The nonlocal FIP is averaged separately over each of these volumes—elements, bands and grains. Figure 1. Example of a mesh with the explicit microstructure for axial loading of smooth specimens. Quasistatic mean relative displacement of the upper and lower boundary planes is depicted by the red arrows.
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