Effect of Finite Velocity of Thermal Wave on Stress Focusing Phenomena

Abstract

The analysis of a long cylindrical rod subjected to a sudden rise in temperature uniformly over its cross section has been studied by Ho [1]. Due to the instantaneous heating, the stress waves reflected from the cylindrical surface of the rod may accumulate at the center and give rise to very high stresses, even though the initial thermal stress is relatively small. This phenomenon is called the stress focusing effect. Hata has studied this effect for several cases of cylindrical rod [2-4]. The stress focusing effect for spheres has been studied by Mann-Nachbar [5] and Hata [6, 7]. However, these series of papers have been studied in the context of classical uncoupled theory of dynamic thermoelasticity. The theory of dynamic thermoelasticity which takes into account the coupling effects between temperature and strain fields involves the infinite thermal wave speed. The theory of generalized thermoelasticity has been developed in an attempt to eliminate the physical paradox of the infinite velocity of thermal propagation. At present, there are two theories of the generalized thermoelasticity: the first is proposed by Lord and Shulman [8], the second is proposed by Green and Lindsay [9]. Recently, other theories have presented (see Ignaczak and Hetnarski [10]). Furukawa et al. used the fundamental equations of generalized thermoelasticity introduced by Noda et al. [11], which include the Lord-Shulman theory and Green-Lindsay theory, and analyzed the one- and two-dimensional problems for plate, for example. In this paper, we treat an isotropic and homogeneous solid sphere. We use the fundamental equations of generalized thermoelasticity which include two theories. The effects of the thermo-mechanical coupling and the relaxation times on the stress focusing phenomena are examined.