Strain-induced multivariant martensitic transformations: A scale-independent simulation of interaction between localized shear bands and microstructure

Abstract A scale-independent model for the interaction between multivariant phase transformations (PTs) and discrete shear bands is advanced and utilized to simulate plastic strain-induced PTs at high pressure. The model includes a scale-free phase-field theory for martensitic PTs. The localized shear bands are introduced via a contact problem formulation. That is, the continuous distribution of sliding displacements along the prescribed slip surfaces is modeled to reproduce the plastic-strain-induced stress concentrators necessary for nucleation of a high-pressure phase (HPP). The strain-induced PTs in the bi/polycrystalline samples subjected to compression and shear are studied. The simulations show a severe reduction in the PT pressure by the plastic shear in comparison to a hydrostatic condition, even below the phase equilibrium pressure, like in known experiments. Transformation kinetics versus shear strain for each martensitic variant and the volume fraction of the HPP in individual grains and the entire aggregate are determined. The stationary volume fraction of the HPP is the same for polycrystals consisting of 13 and 38 grains, and a further shearing does not cause PT. The local phase equilibrium condition based on the transformation-work criterion is satisfied at almost all stationary phase interfaces. A similar phase equilibrium condition in terms of stresses averaged over the entire polycrystal or HPP is fulfilled. These results are important for the development of the microscale kinetic equations and modeling the sample behavior in traditional and rotational diamond anvils during the high-pressure torsion, ball milling, friction, and other deformation-transformation processes.