AGGREGATE SIZE EFFECT ON THE PREDICTED PLASTIC RESPONSE OF HEXAGONAL CLOSE-PACKED POLYCRYSTALS

The effect of aggregate size (number of crystals per aggregate) on tex ture development and mechanical response of hexagonal close-packed (HC P) polycrystals has been studied numerically. The single crystal defor ms only by basal and prismatic slip, and, hence, has an inextensible h exagonal direction (c-axis). The polycrystal is modeled using the hybr id approach developed by Parks and Azhi, where a fourth-order projecti on tensor depending on the average of the c-axis orientation plays a k ey 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 deformat ion. 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 materi al point and finite element simulations are used. Numerical results sh ow that (i) the average projection tensor is very sensitive to aggrega te size, resulting in predictions of sharper texture and stronger hard ening for smaller aggregates, and (ii) the spatially non-uniform defor mation among aggregates within a finite element discretization increas es as the aggregate size is reduced, tending to diffuse texture. Based on this study, a minimum number of 250 crystals per aggregate is sugg ested to minimize the aggregate size effect in numerical simulations o f large-scale HCP metal deformation processes using Parks and Azhi's h ybrid model.