Study of the plastic flow and strain-induced phase transformations (PTs) under high pressure with diamond anvils is important for material and geophysics. We introduce rough diamond anvils and apply them to Zr, which drastically change the plastic flow, microstructure, and PTs. Multiple steady microstructures independent of pressure, plastic strain, and strain path are reached. Maximum friction equal to the yield strength in shear is achieved. This allows determination of the pressure-dependence of the yield strength and proves that omega-Zr behaves like perfectly plastic, isotropic, and strain path-independent immediately after PT. Record minimum pressure for alpha-omega PT was identified. Kinetics of strain-induced PT depends on plastic strain and time. Crystallite size and dislocation density in omega-Zr during PT depend solely on the volume fraction of omega-Zr.