Institute of Metals Division - The Thermoelastic Effect in Iron and Nickel as a Function of Temperature

THE adiabatic elastic deformation of a body is accompanied by a change in temperature. This phenomenon is known as the thermoelastic effect. Under adiabatic conditions the temperature of a metal bar is decreased by an elastic elongation and is increased by an elastic compression. All materials which elongate on heating behave in this manner. The sign of the thermoelastic temperature change is reversed for the few materials which have a negative coefficient of thermal expansion. The following equation for the thermoelastic effect can be derived from fundamental thermody-namic theorems, as shown in the Appendix: dT8 =-a1/cs T dss [1] Cs In this equation, T is the absolute temperature, S is the entropy, a, is the coefficient of linear thermal expansion, cs' is the heat capacity per unit volume at constant stress and s is the stress (positive in tension). Eq 1 can be applied to small, but finite changes in stress in the following form: ?Ts =- a1/cs T?ss [2] The sign of the temperature change AT is opposite to that of the change in stress s for materials which have a positive coefficient of thermal expansion. Eq 2 has been verified for many different materials and stresses at room temperature. No previous publication appears to have been devoted to an in- vestigation of the thermoelastic effect over a range of temperatures. Review of Literature Lord Kelvin (W. Thomson) presented a general theory of the thermoelastic effect in 1851' and later applied it to a solid, subject to an arbitrary system of stresses'. His analysis was based on a cycle of isothermal and constant-strain transformations and led to Eq 2 above. Even today, one of the clearest expositions of the thermoelastic effect is found in Lord Kelvin's article on elasticity in the Ninth Edition of the Encyclopedia Britannica (1878). R. ROCCA, Junior Member, and M. B. BEVER, Member AIME, are Research Assistant in Metallurgy and Associate Professor of Metallurgy, respectiuely, Massachusetts Institute of Technology, Cambridge, Mass. AIME New York Meeting, Feb. 1950. TP 2760 E. Discussion (2 copies) may be sent to Transactions AIME before APT. 1, 1950, and is scheduled for publication Nov. 1950. Manuscript received Oct. 15, 1949.