On generalized crystal‐plasticity based on defect‐densities in a second‐order continuum

Abstract

Single crystals display various defects that may potentially act as obstacles to further evolution of inelastic deformations, i.e. to further plastic flow. These are translational defects in terms of dislocations, rotational defects in terms of disclinations, and (dilatational) pointdefects in terms of lattice vacancies or interstitial atoms. A formulation of generalized crystalplasticity is proposed that incorporates the densities of these defects in order to capture the hardening of the material. In particular the inclusion of the defect densities other than the dislocation density requires to root the formulation in a second-order continuum description.

Single crystal plasticity with bend–twist modes

“…This extended micromechanics perspective thus facilitates a construction of models for material performance that relate directly to microstructural mechanisms which material scientists can recognize and aim to control in their material development cycles. Recent examples of such an extended micromechanics approach include micro-polar single crystal plasticity (Aslan et al, 2011;Forest, 2012;Forest et al, 2014;Mayeur and McDowell, 2014;Mayeur et al, 2011), and second gradient crystal plasticity theory (Gurtin, 2002;Gurtin and Daya Reddy, 2014;Kuroda and Tvergaard, 2010;Steinmann, 1996Steinmann, , 2013, often through an introduction of the burgers or Nye tensors.…”

Geometrical Foundations of Continuum Mechanics

“…It is the aim of the subsequent exposition to extend previous modeling approaches to the hardening in generalized crystal plasticity (such as [181,128]), that solely incorporate the dislocation density tensor, to more complex continuum models that additionally take into account more general defects such as disclination and point-defect densities, see also [187].…”