Study of the plastic flow, strain-induced phase transformations (PTs), and nanostructure evolution under high pressure is important for producing new nanostructured phases and understanding physical 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 produces a steady nanostructure 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. Kinetics of strain-induced PT, in addition to plastic strain, unexpectedly depends on time. The obtained results significantly enrich the fundamental understanding of plasticity, PTs, and nanostructure, and create new opportunities in material design, synthesis, and processing of nanostructured materials by coupling severe plastic deformations and PT at low pressure.