Simultaneous grain boundary motion, grain rotation, and sliding in a tricrystal

Abstract

a b s t r a c tGrain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by capillary and external stress, is significantly affected by the presence of junctions. Our aim is to develop and apply a novel continuum theory of incoherent interfaces with junctions to derive the kinetic relations for the coupled motion in a tricrystalline arrangement. The considered tricrystal consists of a columnar grain embedded at the center of a non-planar GB of a much larger bicrystal made of two rectangular grains. We examine the shape evolution of the embedded grain numerically using a finite difference scheme while emphasizing the role of coupled motion as well as junction mobility and external stress. The shape accommodation at the GB, necessary to maintain coherency, is achieved by allowing for GB diffusion along the boundary.

Plasticity in multi-phase solids with incoherent interfaces and junctions

“…The exact form of c i , however, depends on the constitutive nature of the interfacial free energy; this will be made clear in the ensuing discussion. Similar considerations as those outlined above have been made recently by the present authors [3][4][5] in the context of grain boundaries. Our treatment should be contrasted with the earlier works based on the concept of configurational forces [9,15,32], which require postulation of additional (configurational) balance laws besides the standard balance laws of continuum mechanics.…”

“…We note from (5) and (8) 3 that v int A = (v) A . The interfacial stretch vector, defined as f = ∂ x(X(s), t)/∂s, is related to the bulk deformation gradient as…”

“…On the other hand, junctions and edges have been incorporated in a theory of deforming solids but only for coherent interfaces and without any plasticity [8,31,32]. The present thermodynamic formalism, which follows our recent work on grain boundaries [3][4][5], should be seen as an alternative to the configurational mechanics formalism proposed by Gurtin and his coauthors [9,15]. (iii) Flow rules coupled with kinetic relations: Assuming rate-independent plasticity and isotropic material response, we use maximum dissipation postulate to derive associative flow rules within the bulk and at the surfaces.…”

“…This is followed by a derivation of various local dissipation inequalities associated with the bulk, boundaries, and junctions in Sect. 3. The dissipation inequalities are taken as the starting point in Sect.…”

A three-dimensional study of coupled grain boundary motion with junctions

“…The proposed kinetic relations also emphasize the coupling of junction dynamics with both grain and GB motion. Depending on the junction mobility, grain dynamics can experience a substantial drag compared with the case with no junctions [2].…”