Characterization of the Flow Localization History in Dynamic Viscoplasticity

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Abstract
The evolution of narrow regions of intense plastic flow during the dynamic deformation of rate–sensitive materials is an outstanding problem in mechanics. A unified framework for the analysis of the pre–localization regime was recently presented by Shawki (1991a, b). In the former work, the onset of flow localization was tied to the increased importance of inertial effects. An energy criterion was developed for the characterization of localization initiation. On the other hand, the aforementioned criterion does not provide the critical strain associated with severe localization. The current work examines the extension of the energy criterion towards the determination of the critical strain for the onset of the so–called “stage III” of the localization evolution history. The onset of severe localization appears to be tied to the attainment of an inflection point in the total system kinetic energy evolution profile. Fully nonlinear numerical solutions of the governing system of coupled, dynamic and thermo–mechanical equations are carried out to the late–time, post–localization regime. The foregoing numerical solutions establish the role of the total kinetic energy as a possible single parameter for the characterization of the full localization history.

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