Dislocation microstructures and strain-gradient plasticity with one active slip plane. (August 2016)

• Record Type: Journal Article
• Authors: Conti, Sergio; Garroni, Adriana; Müller, Stefan
• Is Part Of: Journal of the mechanics and physics of solids. Volume 93(2016:Aug.)
• Page Start: 240
• Page End: 251
• Publication Date: 2016-08
• Subjects: Dislocations -- Strain-gradient plasticity -- Cell structures -- Relaxation; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2015.12.008
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: We study dislocation networks in the plane using the vectorial phase-field model introduced by Ortiz and coworkers, in the limit of small lattice spacing. We show that, in a scaling regime where the total length of the dislocations is large, the phase field model reduces to a simpler model of the strain-gradient type. The limiting model contains a term describing the three-dimensional elastic energy and a strain-gradient term describing the energy of the geometrically necessary dislocations, characterized by the tangential gradient of the slip. The energy density appearing in the strain-gradient term is determined by the solution of a cell problem, which depends on the line tension energy of dislocations. In the case of cubic crystals with isotropic elasticity our model shows that complex microstructures may form in which dislocations with different Burgers vector and orientation react with each other to reduce the total self-energy.