Thermal Shock Following Rapid Uniform Heating of Spheres and Long Cylindrical Rods

摘要

Stress waves, that develop following rapid uniform internal heating of linear-elastic spheres and long cylindrical rods, display a focussing effect as they proceed radially towards the center in these geometries. This effect can cause peak interior dynamic stresses in both tension and compression that are much larger in magnitude than the magnitude of the uniform compressive stress which is initially induced by constrained thermal expansion. Two fundamental problems are treated by the Heaviside wave method, one for the heating of a long cylindrical core in an infinite medium, and the other for heating of a complete sphere with zero surface traction. A simple closed-form formula for the stress at the center of the cylinder in the first problem allows determination of the effect of a finite heating time (a ramp function) on reducing the amplitude of the peak tensile stress at the center. The peak tensile stress at the center becomes infinite for the cylinder problem in the limit as heating time goes to zero. For the sphere problem, however, the stress at the center is calculated for a duration of several wave-reflection times, and the center stress is found to be finite even for the limit of zero heating time. (Author)