Influence of anisotropic grain boundary properties on the evolution of grain boundary character distribution during grain growth—a 2D level set study
30 Oct 2014-Modelling and Simulation in Materials Science and Engineering (IOP Publishing)-Vol. 22, Iss: 8, pp 085005
TL;DR: In this paper, the influence of anisotropic grain boundary energy and mobility on microstructure evolution was investigated using a 2D level set model of polycrystal microstructures, and it was shown that grain growth alone does not seem to promote any significantly increased overall presence of CSL boundaries.
Abstract: The present study elaborates on a 2D level set model of polycrystal microstructures that was recently established by adding the influence of anisotropic grain boundary energy and mobility on microstructure evolution. The new model is used to trace the evolution of grain boundary character distribution during grain growth. The employed level set formulation conveniently allows the grain boundary characteristics to be quantified in terms of coincidence site lattice (CSL) type per unit of grain boundary length, providing a measure of the distribution of such boundaries. In the model, both the mobility and energy of the grain boundaries are allowed to vary with misorientation. In addition, the influence of initial polycrystal texture is studied by comparing results obtained from a polycrystal with random initial texture against results from a polycrystal that initially has a cube texture. It is shown that the proposed level set formulation can readily incorporate anisotropic grain boundary properties and the simulation results further show that anisotropic grain boundary properties only have a minor influence on the evolution of CSL boundary distribution during grain growth. As anisotropic boundary properties are considered, the most prominent changes in the CSL distributions are an increase of general low-angle Σ1 boundaries as well as a more stable presence of Σ3 boundaries. The observations also hold for the case of an initially cube-textured polycrystal. The presence of this kind of texture has little influence over the evolution of the CSL distribution. Taking into consideration the anisotropy of grain boundary properties, grain growth alone does not seem to be sufficient to promote any significantly increased overall presence of CSL boundaries.
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TL;DR: A new efficient implementation of the static recrystallization (SRX) model which aims to overcome this limitation by taking full advantage of recent numerical developments (Shakoor et al., 2015; Scholtes et al, 2015).
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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.
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TL;DR: In this paper, two full field methods (level set (LS) and multi-phase field (MPF) methods) are implemented into finite element (FE) formulations for simulation of anisotropic grain growth in polycrystalline structures.
33 citations
TL;DR: In this paper, a mesoscale model of microstructure evolution is formulated by combining a crystal plasticity model with a graph-based vertex algorithm, which provides a versatile formulation capable of capturing finite-strain deformations, development of texture and microstructures evolution through recrystallization.
Abstract: A mesoscale model of microstructure evolution is formulated in the present work by combining a crystal plasticity model with a graph-based vertex algorithm. This provides a versatile formulation capable of capturing finite-strain deformations, development of texture and microstructure evolution through recrystallization. The crystal plasticity model is employed in a finite element setting and allows tracing of stored energy build-up in the polycrystal microstructure and concurrent reorientation of the crystal lattices in the grains. This influences the progression of recrystallization as nucleation occurs at sites with sufficient stored energy and since the grain boundary mobility and energy is allowed to vary with crystallographic misorientation across the boundaries. The proposed graph-based vertex model describes the topological changes to the grain microstructure and keeps track of the grain inter-connectivity. Through homogenization, the macroscopic material response is also obtained. By the proposed modeling approach, grain structure evolution at large deformations as well as texture development are captured. This is in contrast to most other models of recrystallization which are usually limited by assumptions of one or the other of these factors. In simulation examples, the model is in the present study shown to capture the salient features of dynamic recrystallization, including the effects of varying initial grain size and strain rate on the transitions between single-peak and multiple-peak oscillating flow stress behavior. Also the development of recrystallization texture and the influence of different assumptions on orientation of recrystallization nuclei are investigated. Further, recrystallization kinetics are discussed and compared to classical JMAK theory. To promote computational efficiency, the polycrystal plasticity algorithm is parallelized through a GPU implementation that was recently proposed by the authors.
32 citations
Cites background from "Influence of anisotropic grain boun..."
...where Os is one of the 24 operators in the cubic symmetry group Gc [50]....
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01 Oct 1986
TL;DR: A review of geometric criteria for low interfacial energy which have been proposed in the literature is given in this article, which includes: (i) low reciprocal volume density of coincidence sites; (ii) high planar density of similarity sites, GAMMA; (iii) high GAMMA at constant interplanar spacing, d; (iv) large d; and (v) high density of locked-in rows of atoms.
Abstract: A review of geometric criteria for low interfacial energy which have been proposed in the literature is given. These include: (i) low reciprocal volume density of coincidence sites; (ii) high planar density of coincidence sites, GAMMA; (iii) high GAMMA at constant interplanar spacing, d; (iv) large d; and (v) high density of locked-in rows of atoms. These criteria are then tested against available experimental results which include measurements of: (a) interfacial energy; (b) rotations of crystallites on flat crystal substrates; (c) boundary faceting; (d) boundary dissociation; and (e) observations of grain boundary dislocations. No support for the general usefulness of criteria (i), (ii), (iv) and (v) is found. In all cases, significant numbers of results violating these criteria are found or else it is demonstrated that their range of validity is undefined, and hence, their predictive power is highly limited. Criterion (iii) is found to apply for a limited number of cases involving metal/metal or ionic/ionic interfaces but fails for metal/ionic interfaces. Further testing and consideration of this criterion seems called for. It is concluded that no general and useful criterion for low energy can be enshrined in a simple geometric framework. Any understanding of the variations of interfacial energy more » must take account of the atomic structure and the details of the bonding at the interface. « less
31 citations
References
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TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
13,020 citations
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07 Nov 1996
TL;DR: In this paper, the authors discuss the extent to which we are able to formulate quantitative, physically-based models which can be applied to metal-forming processes, and the subjects treated in this book are all active research areas and form a major part of at least four regular international conference series.
Abstract: Paperback. The annealing of deformed materials is of both technological importance and scientific interest. The phenomena have been most widely studied in metals, although they occur in all crystalline materials such as the natural deformation of rocks and the processing of technical ceramics. Research is mainly driven by the requirements of industry, and where appropriate, the book discusses the extent to which we are able to formulate quantitative, physically-based models which can be applied to metal-forming processes.The subjects treated in this book are all active research areas, and form a major part of at least four regular international conference series. However, there have only been two monographs published in recent times on the subject of recrystallization, the latest nearly 20 years ago. Since that time, considerable advances have been made, both in our understanding of the subject and in the techniques available to the researcher.The
7,149 citations
"Influence of anisotropic grain boun..." refers background in this paper
...wherem is the boundary mobility, γ the grain boundary energy and κ the boundary curvature [15, 11]....
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...When it comes to grain boundary mobility, experiments and simulations suggest that the mobility increases with increasing misorientation [14, 15, 11]....
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01 Jan 1988
TL;DR: New numerical algorithms, called PSC algorithms, are devised for following fronts propagating with curvature-dependent speed, which approximate Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws.
Abstract: We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be also used for more general Hamilton-Jacobitype problems. We demonstrate our algorithms by computing the solution to a variety of surface motion problems.
2,501 citations
"Influence of anisotropic grain boun..." refers background or methods in this paper
...The level set method was introduced by Osher and Sethian in [41] to trace the evolution of interfaces....
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...[41], and is gaining increasing interest in the representation of polycrystal microstructures and for tracing the evolution of grain boundaries....
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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
"Influence of anisotropic grain boun..." refers methods in this paper
...For low-angle grain boundaries, the classical Read-Shockley relation is usually employed in models to describe the dependence of grain boundary energy on misorientation [13]....
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TL;DR: In this paper, a superimposed dislocation network is proposed for the cubic system, which is a natural extension of previous dislocation models and models based on coincidence relationships, and explains many of the observed properties of grain boundaries.
1,665 citations