Phase-field study on the formation of α variant clusters induced by elastoplastic stress field around the void in titanium alloys

Abstract

The formation of α variant clusters during β to α transformation under the elastoplastic stress field around a void was investigated using J2 plasticity theory and phase field simulation. Compared with elastic materials, taking an elastic–plastic phase field model in the present work, the stress fields around the void can be partially relaxed by plastic deformation, and the maximum amplitude of the stress reduces. With the increase of the void size, the selection effect on α variant clusters in titanium alloys is gradually enhanced. The variant selection is asymmetric under the conditions of applied tensile and compressive stresses, and the influence of the stress fields around the void under external shear stress is stronger. These could be predicted and confirmed by the interaction energy calculations between the stress fields around the void and α variants. Some interesting variant clusters appear, such as “windmill”, “butterfly”, and “wing” types under external tensile, compressive and shear stresses respectively. The “equilateral triangle”, “nearly parallel” and “quasi equilateral triangle” type variant clusters can form through sympathetic nucleation, given the particular α/α orientation relationship corresponding to lower energy. The ultimate microstructures of α variant clusters around a void are determined by both inter-variant and variant-external stress field interactions. The high-throughput calculations under different applied stress states would provide support for the generation and optimization of the microstructures of titanium alloys in follow-up work.