Plastic flows and strain-induced alpha to omega phase transformation in zirconium during compression in a diamond anvil cell: Finite element simulations

Coupled plastic flows and the strain-induced α→ω phase transformation (PT) in a zirconium sample under compression in a diamond anvil cell are investigated using finite element method (FEM). The PT is treated as strain-induced rather than pressure-induced and the previously developed model for strain-induced PTs is utilized. Very heterogeneous fields of stress tensor, accumulated plastic strain, and concentration of the ω phase are obtained for different applied loads. The PT starts at the center of a sample when pressure exceeds the minimum pressurepεd=1.7GPa, below which a direct strain-induced PT to a high pressure phase cannot occur, and it propagates from the center to the periphery with an increasing load. Even at the maximum pressure of 7 GPa, the PT is not completed everywhere. With an increasing load, the pressure and pressure gradient along the radial direction significantly increase in the two-phase region due to the much larger yield strength of the ω phase. This in turn promotes transformation and produces a positive mechanochemical feedback. Obtained results are utilized for the interpretation of published experimental data on pressure-, stress-, and strain-induced α→ω PTs in Zr and Titanium (Ti) and α→β and ω→β PTs in Zr under compression and high pressure torsion. This includes correcting the reported minimum pressures for these transformations by a factor of 3-6 due to the stress heterogeneity, the effect of transmitting media, the pressure hysteresis, and the reversibility of the transformation.