MELTING OF A CYLINDRICAL POLYMERIC MEDIUM SUBJECTED TO CYCLIC TORSIONAL SHEAR-STRESS

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