Elastic, plastic and creep deformations in long, thick-walled cylinders of workhardening material subjected to transient thermal and mechanical loading

Abstract

The author has attempted to apply the relatively old concepts of aggregate mechanics (Bishop and Hill 1, Bohnenblust and Duwez 2, Whitman 3, and others) to obtain a more realistic solution to the cylinder problem. The assumption that a solid is composed of a number of domains obeying simple stress-strain laws has been used frequently to explain certain aspects of inelastic deformation. This is mainly a result of the inability to formulate the problem from the elements of plasticity theory. Besseling 4 and White 5 have extended the concepts of aggregate mechanics to multiaxial analysis, but relatively little has been done to apply these techniques toward the solution of practical problems. In this paper, equations are developed for the stress rates in thick-walled cylinders subjected to transient thermal and mechanical loading. The aggregate equations are based on the generalized response of two parallel coupled domains—one elastic and the other elastic, viscous, perfectly plastic (Ref. 6). A numerical procedure for integrating the equations is given and then applied to a problem of interest.