Related papers: Phase field dislocation dynamics formulation coupl…
Large twist-angle grain boundaries in layered structures are often described by Scherk's first surface whereas small twist-angle grain boundaries are usually described in terms of an array of screw dislocations. We show that there is no…
Grain 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…
A numerical investigation of grain-boundary grooving by means of a Level Set method is carried out. An idealized polygranular interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average…
We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low angle grain boundaries interacting with a disordered stress landscape provided by solute…
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…
Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters…
We present a unified framework for the calculation of defect energies for those defects that can be represented as a superposition of isolated dislocations, and obtain both self and interaction energies of combinations of grain boundaries…
We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. {\bf 19}1-24 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multi-well potential energy…
Grain Boundaries (GB) whose energy is larger than twice the energy of the solid/liquid interface exhibit the premelting phenomenon, for which an atomically thin liquid layer develops at temperatures slightly below the bulk melting…
Grain boundary (GB) migration is a pivotal process that significantly impacts the development of microstructures, thereby influencing the practical performance of polycrystalline materials. Recent advances in 3D experimental techniques have…
Disconnections, long recognized as the key mediators of grain boundary (GB) kinetics in polycrystalline materials, have traditionally been understood to nucleate through thermal or mechanical activation. In this work, using atomistic…
This study undertakes the mathematical modelling and numerical analysis of dislocations within the framework of differential geometry. The fundamental configurations, i.e. reference, intermediate and current configurations, are expressed as…
The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…
We investigate the ability of a multi-order parameter phase field model with obstacle potentials to describe grain boundary premelting in equilibrium situations. In agreement with an energetic picture we find that the transition between dry…
A novel continuum theory of incoherent interfaces with triple junctions is applied to study three-dimensional coupled grain boundary (GB) motion in polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…
Although continuum theory has been widely used to describe the long-range elastic behavior of dislocations, it is limited in its ability to describe mechanical behaviors that occur near dislocation cores. This limit of the continuum theory…
A phase field model of a crystalline material at the mesoscale is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase field free energy…
The control of solute segregation at grain boundaries (GBs) is essential in engineering alloy properties, however the structure-activity relationship of the key parameter-the segregation energies-still remains elusive. Here we propose the…
A generalized disclination (g.disclination) theory [AF15] has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of…