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

Abstract

A novel continuum theory of incoherent interfaces with triple junctions is applied to study coupled grain boundary (GB) motion in three-dimensional polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and migration of the boundary and junction evolution are developed. In doing so, a vectorial form of the geometrical coupling factor, which relates the tangential motion at the GB to the migration, is also obtained. Diffusion along the GBs and the junctions is allowed so as to prevent nucleation of voids and overlapping of material near the GBs. The coupled dynamics has been studied in detail for two bicrystalline and one tricrystalline arrangements. The first bicrystal consists of two cubic grains separated by a planar GB, whereas the second is composed of a spherical grain embedded inside a larger grain. The tricrystal has an arbitrary-shaped grain embedded inside a much larger bicrystal made of two cubic grains. In all these cases, analytical solutions are obtained wherever possible while emphasizing the role of various kinetic coefficients during the coupled motion.

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.…”

“…The time derivative of an interfacial fields g, continuously differentiable over S and continuous up to J , following S is given by the normal time derivative [17] g =ġ + V ∇g · N. (4) It represents the rate of change of g noted by an observer sitting on the moving S; see e.g. [15,17].…”

“…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.…”

A three-dimensional misorientation axis- and inclination-dependent Kobayashi–Warren–Carter grain boundary model

“…For example, sharp-interface models provide a far more natural framework to describe interfaces. In particular, the works of Gupta and co-workers ( Basak and Gupta, 2015a;2015b;2016;Gupta and Steigmann, 2012 ) (and references therein) serve as an excellent introduction to such models. On the other hand, sharp interface models are traditionally believed to be computationally more demanding.…”

Biological growth in bodies with incoherent interfaces

“…Let f ∈ R be a piecewise continuous field in B 0 and let g ∈ R be a continuously differentiable field over I 0 . The following transport relations hold [26]:…”