Stress-Focusing Effect in a Uniformly Heated Cylindrical Rod

Abstract

A long cylindrical rod is considered brought suddenly to a uniform temperature rise over its cross section. Stress-focusing effects occur when stress waves reflect from the outer surface of the rod and proceed radially inward to the axis. The focusing effect can cause a very high peak dynamic stress in both tension and compression in the rod. The magnitude of the peak stress depends upon the magnitude of the temperature rise and the effective heating duration. For instantaneous heating, the infinite peak of stress propagates outward from the center while these peaks are finite for nonzero heating duration. The solutions are carried out by using Laplace transform on time and presented as infinite series summations after the end of heating.