THE HYSTERESIS LOOP 1. A STATISTICAL THEORY

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Abstract
Abstract— Starting from a knowledge of inhomogeneous dislocation structures observed in cyclically strained metals, a model for cyclic straining is developed. A distribution of volumes with different internal critical flow stresses is assumed characterized by a probability density function. A generalization which includes a thermally activated component of the flow stress is derived assuming that the saturated microscopic effective stress, μes, is equal in all volumes. The relations to obtain the probability density function from experimental data are derived. The theory yields the macroscopic internal stress, σe and the macroscopic effective stress, σe, along the hysteresis loop. Experimental observations on cyclically strained metals can be explained using this statistical theory.