A Novel Homogenized Crystal Plasticity Model for Near α and α + β Titanium Alloys

Abstract

The deformation behavior of two-phase α + β titanium alloys is dictated by its microstructure which typically consists of primary α grains and transformed β colonies having alternating α (HCP) and β (BCC) laths. As the length scales between the primary α grains and the laths differ by nearly two orders of magnitude, it pose a problem for effective meshing and an efficient Crystal Plasticity Finite Element Method (CPFEM) polycrystalline simulation of the alloy. To address this issue several authors have represented the colonies by equivalent homogenized models. Two types of homogenization models can be found in the literature. In the first type of model, the transformed β colony is homogenized by creating a virtual crystal consisting of the slip systems of α and β phases, while in the second type, the equivalent stress from the homogenized transformed β colony is derived by using the mixture rule. There are certain drawbacks to both of these homogenization schemes. In our work, we have proposed a CPFEM homogenization model of the transformed β colony that maintains the existence of both the phases, traction balance at the interface, and strain compatibility which is lacking in the earlier models. A comparative study is done between the material response from Taylor’s iso-strain model, volume averaged results from Representative Volume Element (RVE) and our new proposed model for homogenizing Ti-6242 titanium alloy under complex macroscopic deformation histories. The results show a significant improvement in the stress–strain response from the new model over the other schemes. This new formulation is generic and can also be applied to any other material having a lamellar microstructure.