The breakdown of the columnar grains and lamellar α + β colony microstructure in two-phase Ti alloys during conversion of ingot to billet is critical to the development of desired combination of mechanical properties. Colony breakdown occurs during a series of thermomechanical processing steps in the α + β phase field. However, fundamental knowledge of the microstructural dependence of this transformation is limited, particularly its dependence on the initial orientation of the α + β colony relative to the imposed strain-path. In this study, the viscoplastic self-consistent polycrystal plasticity model is used to examine deformation behavior as a function of crystal loading direction. Criteria were developed to predict relative globularization rates; it was found that both slip system activities in the α phase and relative crystal rotations of each phase must be considered. Predictions are demonstrated to be consistent with literature and suggest that further experimental investigation of relative globularization rates is necessary.