Correction: Crystal plasticity-based homogenized models of transformed β colonies in titanium alloys

The microstructure of near α and α + β Ti alloys consists of equiaxed α (HCP) grains, and lamellar colonies having alternating α and β (BCC) laths. The orientation and size distribution of α grains, colonies and the laths, as well as their volume fractions have strong influence on the mechanical properties of these alloys and is widely studied using crystal plasticity finite element method (CPFEM) analysis of polycrystalline representative volume elements (RVEs). Additionally, the burgers orientation relation (BOR) between the laths results in anisotropic size dependent behavior of the colonies, which are incorporated as Hall–Petch factor in the CPFEM models. A key challenge of CPFEM analysis of RVE of these alloys is the disparate sizes of the equiaxed grains and laths, which necessitates a homogenized representation of the colonies for computational tractability. Homogenized models of the transformed β colony based on iso-strain and virtual single-phase assumptions can be found in the literature. However, the simplifications in these models can lead to inaccurate estimates of deformation behavior of the colony for multiaxial strain histories and have not yet been studied in detail. Asymptotic expansion-based homogenization accurately estimates the average response of representative periodic micro-domain and has been used in this work to evaluate the accuracy of the two homogenized models. The comparisons show that the inaccuracy in response of the homogenized models increase with β lath thickness and depends on the activation of certain soft and hard slip systems.