Biphase filtrational model of flow materials at superplastic deformation

Considering plastically deformed material as a two-phase heterogeneous medium, the filtration model of plastic deformation has been proposed. The laws of momentum and mass conservation for each component, the equations of state, and boundary conditions are used for the model. The first component of the medium is treated as an elastic one, which is responsible for the structural transformations, and the second component is a plastic one, which is not associated with structural transformations. The filtration ratio between the phases has been found. The search for solutions in the form of a traveling wave has been performed. As a result of calculations, the solution in the form of "shock transition" and the speed limit of its propagation have been found. For traveling waves, the dispersion equation and the critical wavelength, at which instability takes place, have been determined.