Generalized thermoelastic analysis of the stress-focusing effect in a solid cylinder under rotationally asymmetrical instantaneous thermal loading

Abstract

This paper investigates the stress-focusing effect in an infinitely long cylinder under rotationally asymmetrical instantaneous thermal loading on the basis of the generalized thermoelastic Lord-Shulman (L-S) and Green-Lindsay (G-L) theories. Combined forms of the governing equations of both theories are given in a cylindrical coordinate system. The twodimensional generalized thermoelastic problems are solved by numerical inversion of Laplace transform. Calculations have been performed to find distributions of thermal stresses on the basis of the L-S theory. Stress-focusing phenomena under different heating conditions are presented. The effects of thermomechanical coupling and relaxation time on the stress-focusing phenomena as well as the singularity of stresses are discussed. IntroductionIn recent years, the use of rapid-heating techniques, such as laser and microwave with extremely short duration or very high frequency, has found numerous applications such as surface melting of metals and sintering of ceramics. This has introduced situations where an instantaneous heating or temperature rise can be established at the boundaries. Then, some effects, which may be ignored for slow-heating process, become important.When a cylindrical or a spherical body is subjected to a sudden rise in temperature, the stress wave induced at the surface propagates radially inward to the center. Because of the accumulation of the waves, the magnitude of the stress may rise to a very large value at the center, even though the initial thermal stress is relatively small. Such a phenomenon is called the stress-focusing effect. This was studied in [1], where a dynamical thermoelastic problem in a cylindrical rod was considered. Since then, a series of papers have been concerned with the analysis of the effect in cylindrical and spherical bodies, [2][3][4][5][6][7]. The relevant progress can be found in the review paper [8]; all these studies were based on the classical dynamical theory of thermoelasticity.The classical thermoelasticity, which leads to an infinite propagation speed of the thermal signal, should be no longer valid to model the thermoelastic problem of high-speed heating processes. Nonclassical thermoelasticity theories admitting finite speeds for thermal signals have been formulated either by incorporating a flux-rate term into the Fourier law (L-S model, [9]) or by including temperature-rate among the constitutive variables (G-L theory, [10]), which are referred to as generalized thermoelasticity theories. Reviews on thermal wave and generalized thermoelasticity were given in [11,12] and [13,14]. Various initial boundary-value problems concerning these theories have been studied for different kinds of mediums in [15][16][17][18]. A paper, which would be concerned with the applications of the two theories to the phenomenon of the stress-focusing, is seldom, however, in literature. Our recent work, [19], on the analysis of a one-dimensional problem in a cylinder showed for the first time the stressfocusing effect on the ba...