Mathematical modeling of creep and viscoplastic flow of a cylindrical layer material

Abstract

Within the framework of a mathematical model of large elastoplastic deformations, taking into account viscous properties of materials, a boundary value problem of creep and viscoplastic flow of a material in the gap between two rigid coaxial cylindrical surfaces under rectilinear motion of the inner surface is considered. Irreversible deformations accumulate from the beginning of the deformation process and are initially associated with the creep process of the material, which is described using the Norton creep power law. With a subsequent increase in the speed of movement of the inner cylinder at some time point, the stress state will reach the yield surface and a viscoplastic flow will begin in the material. As a plastic potential, we use the Tresca yield criterion, generalized in the case of taking into account the viscous properties of the material. The viscoelastic deformation, the emergence and development of the viscoplastic flow under uniformly accelerated motion of the inner surface, the flow under constant speed, and the flow inhibition under equal slow motion of the surface to a full stop are considered. Stresses, reversible and irreversible deformations, displacements are calculated, stress relaxation after the complete stop of the cylinder is investigated.