Tessellation growth models for polycrystalline microstructures

Teferra, Kirubel; Graham‐Brady, Lori

doi:10.1016/j.commatsci.2015.02.006

Cited by 28 publications

(17 citation statements)

References 49 publications

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“…Here, geometric properties such as grain size, centroid location, and aspect ratio are fitted by minimising a measure of the fitting error using deterministic and stochastic optimisation methods, e.g. [3,9,11,19,20]. While optimisation methods can give very accurate results, they can also be computationally expensive.…”

Section: State Of the Artmentioning

confidence: 99%

Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes

Bourne

Kok

Roper

et al. 2020

Philosophical Magazine

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We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD measurements of metals. Given a list of desired cell volumes, we solve a convex optimisation problem to find a Laguerre diagram with cells of these volumes, up to any prescribed tolerance. The algorithm is built on tools from computational geometry and optimal transport theory which, as far as we are aware, have not been applied to microstructure modelling before. We illustrate the speed and accuracy of the algorithm by generating RVEs with user-defined volume distributions with up to 20,000 grains in 3D. We can achieve volume percentage errors of less than 1% in the order of minutes on a standard desktop PC. We also give examples of polydisperse microstructures with bands, clusters and size gradients, and of fitting a Laguerre diagram to 3D EBSD measurements of an IF steel.

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Section: State Of the Artmentioning

confidence: 99%

Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes

Bourne

Kok

Roper

et al. 2020

Philosophical Magazine

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“…Such methods were presented, e.g., in Alpers et al (2015); Teferra and Graham-Brady (2015). However, they are difficult to apply to large data sets.…”

Section: Model Fittingmentioning

confidence: 99%

“…These models are based on isotropic or anisotropic grain growth, where the tessellations are constructed on the basis of an initial approximation of the grains by balls or ellipsoids. Optimized methods for fitting these models to real data were presented in Alpers et al (2015), Teferra and Graham-Brady (2015) anď Sedivý et al (2016). These results have shown that, in particular, the ellipsoid-based tessellation models are able to describe a great variety of grain microstructures with very high precision.…”

Section: Introductionmentioning

confidence: 99%

“…As for the Voronoi tessellation, this definition leads to planar cell facets. However, the additional parameter allows for the generation of tessellations with greater variation in terms of both cell size and shape than Voronoi tessellations (Jeulin, 2013;Teferra and Graham-Brady, 2015). Actually, any normal tessellation in 3D can be described by a Laguerre tessellation (Lautensack and Zuyev, 2008).…”

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confidence: 99%

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Description of the 3d Morphology of Grain Boundaries in Aluminum Alloys Using Tessellation Models Generated by Ellipsoids

Šedivý

Dake²,

Krill³

et al. 2017

Image Anal Stereol

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Parametric tessellation models are often used to approximate complex grain morphologies of polycrystalline microstructures. A big advantage of such models is the substantial reduction in disk space required to store large, three-dimensional data sets, especially when compared with voxel-based alternatives. By selection of an appropriate tessellation model, a reasonably small loss of information on the real grain shapes can usually be achieved. Special attention has recently been devoted to models based on ellipsoidal approximations fitted to each grain. Faces of these tessellations are portions of quadric surfaces whose parameters can be derived easily. In this paper, we deal with geometric features of the structure, notably curvatures and dihedral angles, which are closely related to the kinetics of grain growth. These characteristics are computed for ellipsoidbased tessellations fitted to two different aluminum alloys with nominal composition Al-3 wt% Mg-0.2 wt% Sc and Al-1 wt% Mg. The results are then compared with estimations based on meshed empirical data. We observe that the model offers more consistent estimations of grain shape characteristics than do the meshed empirical data. Precise description of grain boundaries by the model is also promising with respect to possible applications of these tessellations in stochastic space-time modeling of grain growth.

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“…Alternatively, iterative simulations with many realizations of varying microstructure can be used to investigate material's variability [35,36]. This approach eliminates assumptions on probabilistic distributions of materials behavior or plasticity processes.…”

Section: Introductionmentioning

confidence: 99%

Investigation of grain-scale microstructural variability in tantalum using crystal plasticity-finite element simulations

Lim

Dingreville

Deibler

et al. 2016

Computational Materials Science

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In this work, a crystal plasticity-finite element (CP-FE) model is used to investigate the effects of microstructural variability at a notch tip in tantalum single crystals and polycrystals. It is shown that at the macroscopic scale, the mechanical response of single crystals is sensitive to the crystallographic orientation while the response of polycrystals shows relatively small susceptibility to it. However, at the microscopic scale, the local stress and strain fields in the vicinity of the crack tip are completely determined by the local crystallographic orientation at the crack tip for both single and polycrystalline specimens with similar mechanical field distributions. Variability in the local metrics used (maximum von Mises stress and equivalent plastic strain at 3 % deformation) for 100 different realizations of polycrystals fluctuates by up to a factor of 2-7 depending on the local crystallographic texture. Comparison with experimental data shows that the CP model captures variability in stress-strain response of polycrystals that can be attributed to the grain-scale microstructural variability. This work provides a convenient approach to investigate fluctuations in the mechanical behavior of polycrystalline materials induced by grain morphology and crystallographic orientations.

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Tessellation growth models for polycrystalline microstructures

Cited by 28 publications

References 49 publications

Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes

Laguerre tessellations and polycrystalline microstructures: a fast algorithm for generating grains of given volumes

Description of the 3d Morphology of Grain Boundaries in Aluminum Alloys Using Tessellation Models Generated by Ellipsoids

Investigation of grain-scale microstructural variability in tantalum using crystal plasticity-finite element simulations

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