Self-organization and spatio-temporal dissipative structures in fatigued metals

Many strongly nonequilibrium systems of different physico-chemical nature may exhibit a tendency to self-organization either in the form of emerging temporal rhythms or spatial scales, or both [1], and we demonstrate that fatigued metallic alloys fall into this behavior as well. In the first paragraph we discuss the "cyclic analog" of the classical Portevin-Le-Chatelier (PLC) effect as an example of a temporal dissipative structure in fatigued metals. We use the modified Ananthakrishna nonlinear dynamical model [2], which is most adequate for describing the temporal instabilities in fatigued metals "the Yan-Hong-Laird bursts" (cyclic deformation) and "the Neumann bursts" (occurring under the conditions of ramp loading). In the second and third sections of the work we show that the introduction of spatial coupling into the systems of ordinary differential equations modeling temporal instabilities in fatigued metals allows one to describe different types of dislocation patterns. In order to choose the most adequate form of spatial coupling, we perform a quantitative analysis of different dislocation patterns by means of Fast Hartley Transform, enabling us to establish the fundamental length scales involved in the formation of a given pattern. Using the so-called "reaction+diffusion approach" [3,4], we demonstrate that dislocation patterning in fatigued metals can be understood as a result of competition between the grain size and the characteristic length scales of the model [5,6]. Finally, we draw some conclusions and briefly discuss the prospects of future work.