Generalized balanced power diagrams for 3D representations of polycrystals

Alpers, Andreas; Brieden, Andreas; Gritzmann, Peter; Lyckegaard, Allan; Poulsen, Henning Friis

doi:10.1080/14786435.2015.1015469

Cited by 40 publications

(78 citation statements)

References 41 publications

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“…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: 92%

“…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%

“…This local metric model is further extended in Alpers et al (2015) to obtain the generalized balanced power diagram (GBPD). This is a tessellation generated by the local distance measure…”

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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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Section: Introductionmentioning

confidence: 92%

“…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%

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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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“…The basic Voronoi tessellation [5] is often too simple to be used for fitting polycrystals [18], on the other hand the Laguerre tessellation [12] became quite popular for microstructures with approximately convex grains [13], [23]. More complex models exhibiting anisotropy or curved boundaries [1], [22] rely on higher-dimensional marks and are thus more difficult to handle.…”

Section: Introductionmentioning

confidence: 99%

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Seitl

Petrich²,

Staněk

et al. 2020

Methodol Comput Appl Probab

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Random tessellations are well suited for the probabilistic modeling of three-dimensional (3D) grain microstructure of polycrystalline metals. The present paper deals with so-called Gibbs-Laguerre tessellations where the generators of a Laguerre tessellation form a Gibbs point process. The goal is to construct an energy function of the Gibbs point process from a suitable set of potentials, such that the resulting Gibbs-Laguerre tessellation matches some desired geometrical properties. Since the model is analytically hardly tractable, our main tool of analysis are stochastic simulations based on Markov chain Monte Carlo. These enable us to investigate the properties of the models, and, in the next step, to apply the thus gained knowledge to do a statistical reconstruction of an aluminum alloy based on 3D tomographic image data.

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“…This approach has the advantage that techniques established for fitting tessellation models to foams (Redenbach, ; Liebscher & Redenbach, ) can be exploited for fitting the model to observed microstructures. Furthermore, the same model class and fitting techniques can also be used for modelling the grain structure of the aluminium matrix (Fritzen et al ., ; Alpers et al ., ; Šedivý et al ., ). Finally, also intermetallic precipitates can be incorporated in our microstructure model.…”

Section: Introductionmentioning

confidence: 99%

A stochastic microstructure model for particle reinforced aluminium matrix composites

Losch

Schuff

Balle

et al. 2018

Journal of Microscopy

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Summary Metal matrix composites are complex materials consisting of various phases which can display largely different mechanical properties. The deformation behaviour of these composites cannot be sufficiently modelled by averages or simple particle shapes due to the local stresses that occur on the particle edges. Therefore, a sophisticated model of the microstructure is needed. We introduce a method for stochastic modelling of a silicon carbide (SiC) particle reinforced aluminium matrix composite. The SiC particles are modelled by Laguerre polyhedra generated by densely packed spheres. The shape factors of the polyhedra have been fitted to the particle shapes observed in three‐dimensional images. Particle elongation in extrusion direction and the observed log‐normal volume distribution of the particles are included in the model by suitable scaling. An outlook is presented on how to model the grains of the polycrystalline aluminium matrix and intermetallic precipitates, which result from the strengthening mechanism of the matrix. Lay Description Metal matrix composites are complex materials consisting of different phases which can display largely different mechanical properties. The deformation behaviour of these composites cannot be sufficiently modelled by averages or simple particle shapes due to the local stresses that occur on the particle edges. Therefore, a sophisticated model of the microstructure is needed. We introduce a method of stochastic modelling of a silicon carbide (SiC) particle reinforced aluminium matrix composite. The SiC particles are modelled by Laguerre polyhedra generated by densely packed spheres. The shape factors of the polyhedra have been fitted to the SiC shapes observed in three‐dimensional images. Additionally, the polyhedra are scaled anisotropically to account for orientation anisotropy and to obtain a log‐normal volume distribution. An outlook is presented on how to model the aluminium phase's grains and intermetallic precipitates, which result from the strengthening mechanism of the aluminium matrix alloy.

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Generalized balanced power diagrams for 3D representations of polycrystals

Cited by 40 publications

References 41 publications

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

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

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

A stochastic microstructure model for particle reinforced aluminium matrix composites

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