A Renewal Theory of Inelastic Thermo-Mechanical Behavior of Metal Alloys

The mathematics of probability theory have been applied to the construction of a framework which describes the main features of primary and secondary creep in metal alloys, and this theory has been extended to accommodate time dependent stresses and varying temperatures. The underlying assumption is that dislocation slip and annihilation are probabilistic events. The resulting mathematical framework takes the form of renewal theory, a subset of probability theory. The one-dimensional renewal thermo-mechanical theory provides a mathematical framework for primary creep which accommodates previously developed empirical descriptions, predicts the existence of secondary creep as an asymptotically constant strain rate phenomenon and accommodates stress and temperature variations with respect to time through the concept of accumulating intrinsic or internal time. The generalization is made possible through the concept of an intrinsic time which arises from the mathematical theory of probability applied to dislocation slip and annihilation, and is presented as an incremental rate theory. The incremental rate theory is applied to predicting the thermo-mechanical behavior of a steel alloy, based on parameters identified from creep test data under a wide range of stresses and temperatures. The results show that the theory is both descriptive and predictive, and hold promise for further development and practical application.