Grain size and orientation distributions: Application to yielding of α-titanium

A method to incorporate grain size effects into crystal plasticity is presented. The classical Hall–Petch equation inaccurately predicts the macroscopic yield strength for materials with non-equiaxed grains or variable grain size distributions. These deficiencies can be negated by incorporating both grain size and orientation characteristics into crystal plasticity theory. Augmented homogenization relationships based on a viscoplastic Taylor-like approach are introduced along with a new function, the grain size and orientation distribution function (GSODF). Estimates of the GSODF for rolled high-purity α-titanium are recovered through multi-section orientation imaging microscopy using chord length measurements to quantify grain size. It is illustrated that considerable variation in the grain size distribution occurs with lattice orientation in this material. Yield surface predictions calculated from the augmented and traditional models indicate that grain size distribution as a function of lattice orientation may play a significant role in explaining the large yield strength anisotropy of rolled α-titanium.