  The first in situ quantitative synchrotron X-ray diffraction (XRD) study of
plastic strain-induced phase transformation (PT) has been performed on
$\alpha-\omega$ PT in ultra-pure, strongly plastically predeformed Zr as an
example, under different compression-shear pathways in rotational diamond anvil
cell (RDAC). Radial distributions of pressure in each phase and in the mixture,
and concentration of $\omega$-Zr, all averaged over the sample thickness, as
well as thickness profile were measured. The minimum pressure for the
strain-induced $\alpha-\omega$ PT, $p^d_{\varepsilon}$=1.2 GPa, is smaller than
under hydrostatic loading by a factor of 4.5 and smaller than the phase
equilibrium pressure by a factor of 3; it is independent of the
compression-shear straining path. The theoretically predicted plastic
strain-controlled kinetic equation was verified and quantified; it is
independent of the pressure-plastic strain loading path and plastic deformation
at pressures below $p^d_{\varepsilon}$. Thus, strain-induced PTs under
compression in DAC and torsion in RDAC do not fundamentally differ. The yield
strength of both phases is estimated using hardness and x-ray peak broadening;
the yield strength in shear is not reached by the contact friction stress and
cannot be evaluated using the pressure gradient. Obtained results open a new
opportunity for quantitative study of strain-induced PTs and reactions with
applications to material synthesis and processing, mechanochemistry, and
geophysics.
