title: Size-dependent energy in crystal plasticity and continuum dislocation models.
abstract: In the light of recent progress in coarsening the discrete dislocation mechanics, we consider two questions relevant for the development of a mesoscale, size-dependent plasticity: (i) can the phenomenological expression for size-dependent energy, as quadratic form of Nye's dislocation density tensor, be justified from the point of view of dislocation mechanics and under what conditions? (ii) how can physical or phenomenological expressions for size-dependent energy be computed from dislocation mechanics in the general case of elastically anisotropic crystal? The analysis based on material and slip system symmetries implies the negative answer to the first question. However, the coarsening method developed in response to the second question, and based on the physical interpretation of the size-dependent energy as the coarsening error in dislocation interaction energy, introduces additional symmetries. The result is that the equivalence between the phenomenological and the physical expressions is possible, but only if the multiplicity of characteristic lengths associated with different slip systems, is sacrificed. Finally, we discuss the consequences of the assumption that a single length scale governs the plasticity of a crystal, and note that the plastic dissipation at interfaces has a strong dependence on the length scale embedded in the energy expression.
authors: School of Mechanical and Materials Engineering , Washington State University , Pullman, WA 99164, USA.
authors: Sinisa Dj
authors: 0000-0002-0117-426X
authors: SD
authors: Mesarovic
authors: Centre des Matériaux , Mines ParisTech/CNRS UMR 7633, BP 87, 91003 Evry Cedex, France.
authors: Samuel
authors: 0000-0002-8869-3942
authors: S
authors: Forest
authors: Faculty of Mathematics , University of Belgrade , Jagiceva 5, 11000 Belgrade, Serbia.
authors: Jovo P
authors: JP
authors: Jaric
keywords: coarsening; crystal symmetries; geometrically necessary dislocations; material length scales; mesoscale models