3D reconstruction of grains in polycrystalline materials using a tessellation model with curved grain boundaries

Šedivý, Ondřej; Brereton, Tim; Westhoff, Daniel; Polívka, Leoš; Beneš, Viktor; Schmidt, Volker; Jäger, Aleš

doi:10.1080/14786435.2016.1183829

Cited by 30 publications

(28 citation statements)

References 37 publications

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“…Their method entirely avoids solving an optimisation problem; it includes explicit formulas for the generators (x i , w i , A i ) in terms of the data. It is reported in [13] that the method is comparable in accuracy with the optimisation methods of [1,11,21] but takes a small fraction of the computation time. No run times or volume errors are reported in [13] precluding a more precise comparison with our method.…”

Section: Discussionmentioning

confidence: 99%

“…Recently, several authors have generated RVEs with curved boundaries and non-convex cells grains using generalisations of Laguerre diagrams such as generalised balanced power diagrams [1,12,13,21] and multilevel Voronoi diagrams [5,17]. Complex geometries can also be created using the open-source software DREAM.3D [22] and Neper [23].…”

Section: State Of the Artmentioning

confidence: 99%

“…The main goal of our method is to fit grain volumes quickly and accurately. Unlike other methods [1,9,[11][12][13]21,24], it is not specifically designed for fitting grain morphology. We now discuss to what extent we can control the geometry of Laguerre diagrams.…”

Section: Controlling Grain Geometrymentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

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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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“…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: 91%

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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“…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: 97%

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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3D reconstruction of grains in polycrystalline materials using a tessellation model with curved grain boundaries

Cited by 30 publications

References 37 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

A stochastic microstructure model for particle reinforced aluminium matrix composites

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