Crystal plasticity based homogenized model for lamellar colonies of near-alpha and alpha plus beta titanium alloys

The microstructure of near a and alpha + beta Ti-alloys consists of globular a grains, and transformed beta colonies, which have a lamellar structure with alternating a hexagonal close packed and beta body centered cubic laths. Due to the disparate length scales between the laths of the colonies and the globular alpha grains, a homogenized representation of the lath microstructure is necessary for computationally feasible and efficient crystal plasticity (CP) based fullfield simulations of polycrystalline aggregates of these alloys. Thus, equivalent models of the lath microstructure based on iso-strain and virtual crystal (consisting of both alpha and beta slip systems) assumptions were developed. However, these models fail to capture the response of the lath aggregate (colony), the individual phases (alpha and beta laths), and slip systems, accurately. The deficiencies in the earlier models have been overcome in the equivalent model developed in this work in which the individual laths are allowed independent iso-stress and iso-strain conditions, while strain compatibility and stress equilibrium of the lath aggregate is ensured by enforcing periodic motion of the laths and traction balance at the interface. Additionally, an anisotropic size dependent CP constitutive model, due to the semi-coherent nature of the lath interfaces, is also developed for the alpha and beta laths in the colony. The improvements of the present model are elucidated by comparing its response with the existing equivalent models and periodic CP finite element method simulations of a alpha + beta lath representative volume element for two different sets of Euler angles and four different deformation histories. The comparisons clearly show that the present model is significantly more accurate than the existing models in predicting the stress-strain response of the lath aggregate and the individual phases, as well as the slip activities on the various systems. The formulation of the developed model is generic and can also be applied to other materials with lamellar microstructure.