Related papers: A crystal symmetry-invariant Kobayashi--Warren--Ca…
The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present…
In this paper, we consider a coupled system, known as Kobayashi--Warren--Carter system, abbreviated as the KWC system. KWC system consists of an Allen--Cahn type equation and a singular diffusion equation, and it was proposed by [Kobayashi…
In this paper we study the Dirichlet problem for the Kobayashi--Warren--Carter system. This system of parabolic PDE's models the grain boundary motion in a polycrystal with a prescribed orientation at the boundary of the domain. We obtain…
Grain growth in polycrystals is often simulated using orientation-field models, which employ a field to represent the local orientation of the crystal lattice. These models can be challenging to represent a realistic misorientation…
A continuum grain boundary model is developed that uses experimentally measured grain boundary energy data as a function of misorientation to simulate idealized grain boundary evolution in a 1-D grain array. The model uses a continuum…
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of the study is the existence of solutions to this system which…
When a metal is loaded mechanically at high temperatures, i.e. above 300 $^o$C, its grain microstructure evolves due to multiple physical mechanisms. Two of which are the curvature-driven migration of the grain boundaries due to increased…
Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth…
This paper is devoted to the study of a class of optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems, which are based on a phase-field model of grain boundary motion, proposed by [Kobayashi et al, Physica D, 140,…
The original KWC-system is widely used in materials science. It was proposed in [Kobayashi et al, Physica D, 140, 141--150 (2000)] and is based on the phase field model of planar grain boundary motion. This model suffers from two key…
Grain boundaries dramatically affect the properties of polycrystalline materials because of differences in atomic configuration. To fully understand the relationship between grain boundaries and materials properties, systematic studies of…
The dynamical mechanisms underlying the grain evolution and growth are of fundamental importance in controlling the structural properties of large-scale polycrystalline materials, but the effects of lattice ordering and distinct atomic…
A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradient plasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and…
Recent experiments, atomistic simulations, and theoretical predictions have identified various new types of grain boundary motions that are controlled by the dynamics of underlying microstructure of line defects (dislocations or…
Plastic deformation in polycrystals is governed by the interplay between intra-granular slip and grain boundary-mediated plasticity. However, while the role played by bulk dislocations is relatively well-understood, the contribution of…
In this paper we propose a quaternion formulation for the orientation variable in the three dimensional Kobayashi--Warren model for the dynamics of polycrystals. We obtain existence of solutions to the $L^2$-gradient descent flow of the…
We propose a two dimensional frame-invariant phase field model of grain impingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are computed. We are…
The KWC system is a well-known generic framework for phase-field models of grain boundary motion, whose original formulation is given as a parabolic gradient flow of a free energy. In the original KWC system, the results of uniqueness have…
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…
This paper investigates the statistical behavior of two-dimensional grain microstructures during grain growth under anisotropic grain boundary characters. We employ the threshold-dynamics method, which allows for unparalleled computational…