  Various phenomena (phase transformations, chemical reactions, and friction)
under high pressures in diamond anvil cell are strongly affected by fields of
all components of stress and plastic strain tensors. However, they could not be
measured. Even measured pressure distribution contains significant error. Here,
we suggest coupled experimental-analytical-computational approaches utilizing
synchrotron X-ray diffraction, to solve an inverse problem and find all these
fields and friction rules before, during, and after $\alpha$-$\omega$ phase
transformation in strongly plastically predeformed Zr. Due to advanced
characterization, the minimum pressure for the strain-induced $\alpha$-$\omega$
phase transformation is changed from 1.36 to 2.7 GPa. It is independent of the
compression-shear path. The theoretically predicted plastic strain-controlled
kinetic equation is verified and quantified. Obtained results open
opportunities for developing quantitative high-pressure/stress science,
including mechanochemistry, material synthesis, and tribology.
