Effective and internal stresses in cyclically strained materials

The plastic response during cyclic loading of crystalline materials and the methods for determining individual components of the cyclic stress are reviewed. Two basic approaches, the representative volume element and statistical description of the deformation of microvolumes with different critical internal stresses, are compared. Using the theory of thermally activated deformation, the behavior of a single microvolume during loading and unloading is analyzed. Basic features of the statistical theory of the hysteresis loop are described, and thermally activated processes are incorporated. The statistical approach leads to the rapid decrease of the effective stress during unloading and a slow buildup of the macroscopic stress in reverse straining. The analysis leads to a new interpretation of the unloading experiment and the evaluation of the effective stress component as approximately double the value obtained by the classical method. Using the statistical approach in modeling the plastic stress- strain response is emphasized.