Melting of a cylindrical polymeric medium subjected to cyclic torsional shear stress

Abstract

The problem of phase change in a cylindrical polymeric material subjected to a constant amplitude cyclic torsional shear stress is analyzed. The steady state as well as the transient behavior of a long solid cylinder and a cylindrical shell are examined when the hysteresis heat generation G, in the medium is spacially variable and exponentially dependent on the local temperature in the form G = y/(r)exp(A/T). f(r) accounts for the stress distribution within the solid, y and Ar are related in part to the amplitude and frequency of the cyclic torque, and T is the sample local temperature. The analysis is carried through for heat generation parameters high enough to induce melting within the medium. The onset of melting and the propagation of the solid-liquid interface (two interfaces can arise), are examined for various heat generation parameters, external and internal boundary conditions for the case of a cylindrical shell. Analytical solutions for the steady-state temperature profiles are developed, and an explicit finite difference approach is used for the study of the full transient problem.