Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals

The effect of aggregate size (number of crystals per aggregate) on texture development and mechanical response of hexagonal close-packed (HCP) polycrystals has been studied numerically. The single crystal deforms only by basal and prismatic slip, and, hence, has an inextensible hexagonal direction (c-axis). The polycrystal is modeled using the hybrid approach developed by Parks and Azhi, where a fourth-order projection tensor depending on the average of the c-axis orientation plays a key role in the formulation. In this model, the deformation applied to the crystals of the aggregate is determined by this projection tensor, which depends on aggregate size, and the imposed macroscopic deformation. The dependence of the average projection tensor on aggregate size is studied by simulating plane strain compression tests on aggregates of different size comprised of inextensible HCP crystals. Both material point and finite element simulations are used. Numerical results show that (i) the average projection tensor is very sensitive to aggregate size, resulting in predictions of sharper texture and stronger hardening for smaller aggregates, and (ii) the spatially non-uniform deformation among aggregates within a finite element discretization increases as the aggregate size is reduced, tending to diffuse texture. Based on this study, a minimum number of 250 crystals per aggregate is suggested to minimize the aggregate size effect in numerical simulations of large-scale HCP metal deformation processes using Parks and Azhi's hybrid model.