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Continuum Dislocation Dynamics: Classical Theory and Contemporary Models

  • Anter El-AzabEmail author
  • Giacomo Po
Reference work entry
  • 26 Downloads

Abstract

The continuum theory of dislocation fields is discussed in this chapter with an emphasis on the formulations relevant to infinitesimal deformation of single crystals. Both the classical and contemporary developments are concisely outlined. The classical theory of dislocation fields is introduced first for static and dynamic dislocation configurations, followed by a brief discussion of the shortcomings of the classical theory in predicting plasticity of crystals. In this regard, the lack of connection between the evolution of the dislocation field and internal stress state of the crystal is particularly highlighted. The more recent phenomenological and statistically-based formalisms of continuum dislocation dynamics are then introduced. As discussed in the pertinent sections, these formalisms properly connect the evolution of the dislocation fields with the internal stress state in and thus offer frameworks for predicting the plastic behavior of crystals.

Notes

Acknowledgments

Anter El-Azab was supported by the US Department of Energy, Office of Science, Division of Materials Sciences and Engineering, through award number DE-SC0017718, and by the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation (CMMI), through award number 1663311 at Purdue University. Giacomo Po acknowledges the support of the US Department of Energy, Office of Fusion Energy, through the DOE award number DE-FG02-03ER54708; the Air Force Office of Scientific Research (AFOSR), through award number FA9550-11-1-0282; and the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation (CMMI), through award number 1563427 with UCLA.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.School of Materials EngineeringPurdue UniversityWest LafayetteUSA
  2. 2.Mechanical and Aerospace Engineering DepartmentUniversity of CaliforniaLos AngelesUSA

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