Study of the plastic flow, strain-induced phase transformations (PTs), and microstructure evolution under high pressure is important for producing new nanostructured phases1–10 and understanding physical1,2,7−10 and geophysical11–13 processes. However, these processes depend on an unlimited combination of five plastic strain components and an entire strain path with no hope of fully comprehending. Here, we introduce the rough diamond anvils (rough-DA) to reach maximum friction equal to the yield strength in shear, which allows determination of pressure-dependent yield strength. We apply rough-DA to compression of severely pre-deformed Zr. We found in situ that after severe straining, crystallite size and dislocation density of α and ω-Zr are getting pressure-, strain- and strain-path-independent, reach steady values before and after PT, and depend solely on the volume fraction of ω-Zr during PT. Immediately after completing PT, ω-Zr behaves like perfectly plastic, isotropic, and strain-path-independent. Rough-DA produce a steady state in α-Zr with lower crystallite size and larger dislocation density than smooth diamonds. This leads to a record minimum pressure (0.67 GPa) for α-ω PT with rough-DA, much smaller than 1.36 GPa with smooth diamonds, 6.0 GPa under hydrostatic condition, and phase equilibrium pressure, 3.4 GPa14. Kinetics of strain-induced PT, in addition to plastic strain, unexpectedly depends on time. This opens an unexplored field of the simultaneous strain- and stress-induced PTs under pressure. The obtained results create new opportunities in material design, synthesis, and processing of nanostructured materials by severe plastic deformations at low pressure. Rough-DA can be utilized for finding similar laws for various material systems. The above plethora of results was obtained in a single experiment, thus transforming the main challenge—strongly heterogeneous fields in a sample—into a great opportunity.