Modeling of grain growth under fully anisotropic grain boundary energy
02 Apr 2019-Modelling and Simulation in Materials Science and Engineering (IOP Publishing)-Vol. 27, Iss: 4, pp 045002
TL;DR: In this paper, a level set formulation is proposed that can accurately trace the evolution of grain boundary networks in polycrystalline aggregate while respecting grain boundary energy anisotropy.
Abstract: A level set formulation is proposed that can accurately trace the evolution of grain boundary networks in a polycrystalline aggregate while respecting grain boundary energy anisotropy. Commonly adopted simplifying assumptions related to the grain boundary energy variation with local microstructure conditions are avoided and the grain boundary energy dependence on both crystallographic misorientation and boundary plane inclination is respected. Key components in the formulation are discussed, such as an efficient and simple scheme for unequivocal identification of crystal neighbors at grain boundary junctions where an arbitrary number of crystals intersect. The method works without modifications in both two and three dimensions and is shown to provide grain boundary junction configurations that comply with classical equilibrium conditions as well as topological transforms of the grain boundary network that agree with theoretical predictions. Full grain boundary energy anisotropy is considered by adopting a parametrization of the five-parameter grain boundary energy space, as previously proposed by Bulatov et al 2014 Acta Mater. 65:161–75. Examples are provided to illustrate the relevance of the level set framework for simulations of microstructure evolution in polycrystalline solids. For example, it is clearly shown that the proposed modeling framework provides a grain boundary inclination dependence of the grain boundary energy that cannot be neglected in mesoscale simulations of grain growth. (Less)
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TL;DR: The question of the formation mechanism of annealing twins in face-centered cubic metals and alloys, which is still not resolved in spite of the fact that the existence of these defects is known for long, is addressed in this article.
Abstract: The question of the formation mechanism of annealing twins in face-centered cubic metals and alloys, which is still not resolved in spite of the fact that the existence of these defects is known for long, is addressed in this paper. The different mechanisms proposed through the years are reviewed. Most of them focus on coherent twin boundaries. However, incoherent twin boundaries are very frequent as well, notably in recrystallized microstructures and would definitely deserve more specific attention. Twin topologies are so much different after recrystallization and after grain growth that distinct names would be better suited than the general term of annealing twins. Because twins are at the core of most grain boundary engineering approaches, the mechanisms by which an interconnected network of twin and related boundaries can be formed are discussed, in the light of the current knowledge on annealing twin formation mechanisms. Finally, the state of the art of mesoscopic models and simulations able to account for twin boundaries is presented. Accounting for twins is a requirement since they not only play a role in microstructure evolution upon thermomechanical processing but also affect the in-service material behavior, positively or negatively depending on the involved properties.
46 citations
TL;DR: In this paper, a level-set finite element formulation for pure grain growth with heterogeneous grain boundary energies (i.e., one energy per grain interface) was developed and validated for simple configurations.
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TL;DR: In this article, oriented and nanotwinned copper (nt-Cu) was electroplated on a Si wafer substrate for thermal stress measurement from room temperature to 400 °C by bending beam method.
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TL;DR: A different adaptation strategy is used that maintains the benefits of the classical Eulerian LS framework, while enforcing at all times the conformity of the FE mesh to implicit interfaces by means of local remeshing operations.
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TL;DR: The presented method maintains the discretization of the interior of the domains using an evolving triangular mesh and treats the topological events such as the disappearance of domains or the creation of interfaces by means of selective local remeshing operations.
15 citations
References
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TL;DR: In this article, the authors investigated the energies and motions of grain boundaries between two crystallites using the dislocation model of grain boundary and provided a quantitative expression for energy per unit area for small angles.
Abstract: The energies and motions of grain boundaries between two crystallites are investigated theoretically using the dislocation model of grain boundaries. Quantitative predictions made for simple boundaries for cases in which the plane of the boundary contains the axis of relative rotation of the grains appear to agree with available experimental data. The quantitative expression for energy per unit area for small angles is approximately $[\frac{\mathrm{Ga}}{4\ensuremath{\pi}(1\ensuremath{-}\ensuremath{\sigma})}]\ensuremath{\theta}[A\ensuremath{-}\mathrm{ln}\ensuremath{\theta}]$ where $G$ is the rigidity modulus, $a$ the lattice constant, $\ensuremath{\sigma}$ Poisson's ratio, $\ensuremath{\theta}$ the relative rotation and $A$ approximately 0.23. Grain boundaries of the form considered may permit intercrystalline slip and may act as stress raisers for the generation of dislocations.
1,767 citations
TL;DR: In this paper, a coupled level set method for the motion of multiple junctions (of, e.g., solid, liquid, and grain boundaries), which follows the gradient flow for an energy functional consisting of surface tension and bulk energies, is developed.
1,158 citations
TL;DR: Monotonicity and stability properties of the fast sweeping algorithm are proven and it is shown that 2 n Gauss-Seidel iterations is enough for the distance function in n dimensions.
Abstract: In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses Gauss-Seidel iterations with alternating sweeping ordering to solve the discretized system. The crucial idea is that each sweeping ordering follows a family of characteristics of the corresponding Eikonal equation in a certain direction simultaneously. The method has an optimal complexity of O(N) for N grid points and is extremely simple to implement in any number of dimensions. Monotonicity and stability properties of the fast sweeping algorithm are proven. Convergence and error estimates of the algorithm for computing the distance function is studied in detail. It is shown that 2 n Gauss-Seidel iterations is enough for the distance function in n dimensions. An estimation of the number of iterations for general Eikonal equations is also studied. Numerical examples are used to verify the analysis.
998 citations
TL;DR: The new method is a modification of the algorithm which makes use of the PDE equation for the distance function introduced by M. Sussman, P. Smereka, and S. Osher and provides first-order accuracy for the signed distance function in the whole computational domain, and second- order accuracy in the location of the interface.
393 citations
TL;DR: In this article, the kinetics and topology of grain growth in 3D are simulated using a phase-field model of an ideal polycrystal with uniform grain-boundary mobilities and energies.
376 citations