A multivariate grain size and orientation distribution function: derivation from electron backscatter diffraction data and applications

Lopez, Jesus Galan; Kestens, Léo

doi:10.1107/s1600576720014909

Cited by 8 publications

(8 citation statements)

References 25 publications

(20 reference statements)

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“…In this technique, consecutive steps of sample preparation and EBSD scanning are employed to obtain 2D EBSD slices. More details about the material and the technique can be found in [13].…”

Section: Analysis Of Materials Datamentioning

confidence: 99%

“…The left panel in Figure 9 (taken by J. G. López [13]) illustrates a sample of the steel data consisting of 20 EBSD scans with a spacing of 4µm. On average ≈ 2, 700 grains (sd ≈ 120) are observed in each 2D EBSD scan.…”

Section: Exploratory Analysismentioning

confidence: 99%

“…where the a i,j,k, 1 are suitable combinatorial coefficients such that these coefficients depend only on which of the indices i, j, k, are equal. In the following, up to a permutation of (i, j, k, ) we need to distinguish three cases in bounding the right-hand side of (13), where we set δ := 1/64:…”

Section: Lemma B4 (Moment Bound) It Holds Thatmentioning

confidence: 99%

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Topology-based goodness-of-fit tests for sliced spatial data

Cipriani¹,

Hirsch²,

Vittorietti³

2022

Preprint

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In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. In the present paper, we illustrate how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, we devise goodness-of-fit tests that become asymptotically exact in large sampling windows. We illustrate the testing methodology through a detailed simulation study and provide a prototypical example from materials science.

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“…In this technique, consecutive steps of sample preparation and EBSD scanning are employed to obtain 2D EBSD slices. More details about the material and the technique can be found in [13].…”

Section: Analysis Of Materials Datamentioning

confidence: 99%

Section: Exploratory Analysismentioning

confidence: 99%

See 1 more Smart Citation

Topology-based goodness-of-fit tests for sliced spatial data

Cipriani¹,

Hirsch²,

Vittorietti³

2022

Preprint

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“…As the stress-strain response of the RVE is dependent on the morphological properties, these quantities must be precisely represented in the RVE. Grain size and texture are considered two of the most important influencing factors [8].…”

Section: Introduction and State Of The Artmentioning

confidence: 99%

“…They used two different types of kernel functions in the density estimates, namely de la Valle e Poussin kernels and Dirichlet kernel for fitting the weights. Lopez et al [8] proposed an extended ODF, named grain size orientation distribution function (GSODF) which is a combination of grain size distribution and ODF. Firstly, grains (obtained from EBSD) are grouped according to their size, and an individual ODF for each group is calculated.…”

Section: Introduction and State Of The Artmentioning

confidence: 99%

On Sampling Discrete Orientations from XRD for Texture Representation in Aggregates with Varying Grain Size

2021

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The amount of orientation difference of crystallites, i.e., the texture in a metallic polycrystal governs, plastic anisotropy, electrical and magnetic properties of the material. For simulating the microstructure and texture evolution during forming processes, representative volume elements (RVEs) often generated based on experimental measurements are commonly used. While the grain size and morphology of polycrystals are often determined via light-optical microscopy, their texture is conventionally analyzed through diffraction experiments. Data from these different experiments must be correlated such that a representative set of sampled orientations is assigned to the grains in the RVE. Here, the concept Texture Sampling through Orientation Optimization (TSOO) is introduced, where based on the intensity the required number of orientations is first assigned to the grains of the RVE directly. Then the Bunge–Euler angles of all orientations are optimized in turn with respect to the experimental measurements. As orientations are assigned to grains of variable size during optimization, the compatibility between inhomogeneity in the microstructure and texture is inherently addressed. This method was tested for different microstructures of non-oriented electrical steels and showed good accuracy for homogenous and inhomogeneous grain size distributions.

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