Plastic deformation of bicrystals within continuum dislocation theory

Abstract

We analyze the evolution of the plastic distortion and the nucleation and accumulation of dislocations within a model bicrystal with one active slip system in each single crystal (symmetric with respect to the interface), which is subject to prescribed displacements of plane-strain shear and extension, and we present closed-form analytical solutions.

Continuum dislocation theory accounting for redundant dislocations and Taylor hardening

“…Due to the boundary conditions ( 21) β (x) should change its sign on the interval (0, a). One-dimensional theory of dislocation pile-ups [9,18,19,31,32,33] suggests to seek the solution in the form…”

“…The general structure 1 corresponding author: ++49 234 32-26033, email: chau.le@rub.de of continuum dislocation theory (CDT) must therefore reflect this physical reality: energy decrease by nucleation of GNDs and resistance to the motion of GNDs due to dissipation. Just in recent years various phenomenological models of crystals with continuously distributed dislocations which are able to predict the density of GNDs as well as the accompanying size effects have been proposed in [1,11,12,6,7,9,31,32,33,18,19,20,30,16,28,29] (see also the finite strain CDT proposed by Le and Stumpf [34,35,36], Ortiz and Repetto [38], Ortiz et al [39], Le and Günther [27], Koster et al [21]).…”

Dislocation impediment by the grain boundaries in polycrystals

“…During the load reversal, one sees hills instead of grooves. Note that depending on the types of dislocations and the slip systems activated, the distribution of plastic slip in two adjacent grains may have distinct highest magnitudes [18,19].…”

Polygonization: Theory and comparison with experiments

“…Read (1957) and Bilby, Gardner, and Smith (1958) have extended this result to the case when the stress due to dislocations does not vanish. However, the qualitative modelling of polygonization based on the continuum dislocation theory (Berdichevsky, 2006a(Berdichevsky, , 2006bBerdichevsky & Le, 2007;Le & Sembiring, 2008a, 2008b, 2009Kochmann & Le, 2008;Kochmann & Le, 2009a, 2009bKaluza & Le, 2011) was proposed only recently by Le and Nguyen (2011). In that paper the simplest case of polygonization of the single crystal beam with one active slip system parallel to the beam axis was considered.…”