Kinetics of Stress Relaxation in Metals

Abstract

The phenomenon of stress relaxation, the time decrease of internal stress due to localized flow in a solid under constant uniaxial strain, is viewed in terms of present kinetic theories and available data for metals. Rate equations for shear flow, derived from molecular models of liquids and gases, are reviewed briefly. Combined with the theory of elasticity, these equations are shown to be identical to the classical Maxwell model and to the empirical logarithmic form in limiting cases for stress relaxation in solids. Without reference to the specific details of the localized flow, the general equations are found to correlate uniaxial data for many types of steels, copper, aluminum, magnesium, and lead for various temperatures and stress levels. In all of the data, one characteristic controlling reaction is found, and in some cases a secondary reaction dependent upon the level of the uniaxial prestress is also found. For nonaging metals, the data fit equations in which the relaxation stress approaches zero asymptotically in time. A simple modification of the rate equations is made so that an age-hardening metal can approach a nonzero stress during relaxation. Prestress is used as a controlling variable in correlating data for uniaxial stress relaxation. Apparent heats and entropies of activation are calculated for Inconel and copper at elevated temperatures. For nearly all metals, the apparent free energy of activation for the controlling reaction in the relaxation process decreases slightly as the prestress is increased.