Studies on thermal stresses in elastic solids

Abstract

Some results, following Gibbs and Murnaghan, on the general thermodynamical properties of a continuous and isotropic medium are reviewed in Part I. These discussions lead to the formulation of various thermodynamic functions for a thermo-elastic solid in small strain. The expression for the free energy is useful, in particular, for approximate solutions of thermal stress problems involving either steady or transient heating. Also in Part I, a rather general condition is established under which the inertia effect due to transient thermal expansions may be neglected. Conditions under which temperature distributions may be calculated independently of stresses and strains are also given. Attention is given to the order of approximations involved in such simplifications. The general results in Part I are applied to two problems in Part II and Part III. The problem of thermal shock, a type of failure due to sudden heating or cooling, is studied in Part II. The analytic results obtained there are compared with the experimental results on thermal shock carried out by N.A.C.A. investigators on circular ceramic and ceramal dics. The correlation between theory and experiment is considered satisfactory. Thermal stresses in thin cylindrical shells and plates are formulated and discussed in Part III. It is assumed that the temperature varies only across the thickness, and the Young's modulus may be an arbitrary function of temperature. A convention regarding the choice of the reference surface is introduced, by means of which the present theory becomes comparable to the ordinary theory of plates and shells. Methods based on similarity considerations are devised such that the resulting stresses and strains in a shell or plate caused by temperature gradient and external loads can be predicted by experimenting with a similar specimen at a uniform temperature. These considerations are motivated by the necessity to overcome the difficulties both in analytic calculations and experimental measurements of stresses and strains at elevated temperatures, especially when transient heating and complicated loads are involved. Such a situation arises, for example, in the combustion chamber of a rocket engine, where stresses produced by supporting seats are often too complicated to compute by purely analytical methods.