Abstract
Deformation of metals has attracted great interest for a long time. However, the constitutive models for viscoplastic deformation at high strain rates are still under intensive development, and more physical mechanisms are expected to be involved. In this work, we employ the newly-proposed methodology of mesoscience to identify the mechanisms governing the mesoscale complexity of collective dislocations, and then apply them to improving constitutive models. Through analyzing the competing effects of various processes on the mesoscale behavior, we have recognized two competing mechanisms governing the mesoscale complex behavior of dislocations, i.e., maximization of the rate of plastic work, and minimization of the elastic energy. Relevant understandings have also been discussed. Extremal expressions have been proposed for these two mesoscale mechanisms, respectively, and a stability condition for mesoscale structures has been established through a recently-proposed mathematical technique, considering the compromise between the two competing mechanisms. Such a stability condition, as an additional constraint, has been employed subsequently to close a two-phase model mimicking the practical dislocation cells, and thus to take into account the heterogeneous distributions of dislocations. This scheme has been exemplified in three increasingly complicated constitutive models, and improves the agreements of their results with experimental ones.
Highlights
Published: 19 August 2021Understanding the viscoplastic behavior of metals at high strain rates is of critical importance in many significant fields [1,2], and developing effective Crystal Plasticity (CP)constitutive models has been a continuous effort for decades [2,3]
It is apparent that the realization of both the two dominant mechanisms is based on dislocation behaviors, and the compromise in competition between these two dominant mechanisms is reflected in their effects on the dislocation density, distribution, and speed
We have elucidated the mesoscale complexity in the viscoplastic deformation of metals, under the framework of mesoscience
Summary
Understanding the viscoplastic behavior of metals at high strain rates is of critical importance in many significant fields [1,2], and developing effective Crystal Plasticity (CP). Heterogeneous structures have not been well accounted for, and size effects have hardly been addressed [15] This means that more physical mechanisms are still needed to provide more bases or constraints for the models. Based on decades of efforts in modeling several important complex systems in chemical engineering, mesoscience was proposed and gradually enriched recently [16,17,18,19,20] In this methodology, for a system with massive elements, the length scale of an element is called the element scale, the length scale of the system is called the system scale, both of which are called boundary scales, and the length scale between the element scale and the system scale (i.e., two adjacent boundary scales) is called the mesoscale scale.
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