Quantitative kinetic rules for plastic strain-induced $\alpha$-$\omega$ phase transformation in Zr under high pressure

Plastic strain-induced phase transformations (PTs) and chemical reactions under high pressure are broadly spread in modern technologies, friction and wear, geophysics, and astrogeology. However, because of very heterogeneous fields of plastic strain ${\mathbf{E}}^p$ and stress $\mathbf{\sigma }$ tensors and volume fraction $c$ of phases in a sample compressed in a diamond anvil cell (DAC) and impossibility of measurements of $\mathbf{\sigma }$ and ${\mathbf{E}}^p$, there are no strict kinetic equations for them. Here, we develop combined experimental-computational approaches to determine all fields in strongly plastically predeformed Zr and kinetic equation for $\alpha$-$\omega$ PT consistent with experimental data for the entire sample. Kinetic equation depends on accumulated plastic strain (instead of time) and pressure and is independent of plastic strain and deviatoric stress tensors, i.e., it can be applied for various above processes. Our results initiate kinetic studies of strain-induced PTs and provide efforts toward more comprehensive understanding of material behavior in extreme conditions.