Stochastic and deterministic aspects of strain localization during cyclic plastic deformation

A phenomenological model of slip patterning in fatigued metals is developed. The localization of slip in persistent slip bands (PSBs) is related to the existence of a region of negative slope in the saturation-stress vs local strain-amplitude graph and an internal length scale associated with dynamical dislocation interactions that governs the width of the bands. Statistical characteristics of the slip patterns are derived from a stochastic dislocation dynamics approach. This not only allows the determination of the value of the plateau stress in the cyclic stress-strain curves, but also demonstrates certain limitations of the analogy between matrix-PSB patterns and two-phase systems in thermodynamics. The internal length scale considered yields a second-order gradient of the logarithm of the strain amplitude that allows the determination of the shape and width of the persistent slip bands. The results of the stochastic and gradient approaches are found to be mutually consistent and in good agreement with experimental findings. © 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved