PPubMed1 Feb 2021Cited 9×

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

Jesús Galán López, Leo A. I. Kestens

Abstract

Grain size distribution and orientation distribution functions are combined in a single multivariate continuous grain size orientation distribution function (GSODF). Several examples of practical applications to low carbon steels are presented, in which it is shown how the GSODF can be used in the analysis of 2D and 3D electron backscatter diffraction data, and as input in full-field and mean-field crystal plasticity simulations.

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The paper introduces a continuous multivariate grain size‑orientation distribution function (GSODF) derived from EBSD data, enabling combined analysis and simulation of texture and grain size.

What’s new

i.Derivation of a continuous multivariate grain size‑orientation distribution function (GSODF).
ii.Method to fit the GSODF from 2D and 3D EBSD data using size‑dependent ODFs and MTM‑FHM software.
iii.Demonstration on low‑carbon steels showing GSODF reproduces textures and predicts grain‑size‑dependent misorientations.
iv.Integration of GSODF into crystal plasticity simulations without extra computational cost.
v.Insight into microstructural mechanisms such as grain fragmentation and gamma‑fibre texture‑size relationships.

How they did it

EBSD data were binned by grain size, and an ODF was calculated for each bin using MTM‑FHM software. The C‑coefficients of the ODF were expressed as functions of grain size (linear interpolation or linear fit) and combined with the grain‑size frequency function to obtain the continuous GSODF. The resulting GSODF was fitted to the data (R² > 0.99) and used for texture prediction and simulation inputs.

What they found

Processed >28,000 valid grains for the ELC steel (28,605 total, 28,605 valid).
2D EBSD scan contained 2,679 grains (≈530 grains per bin) and still achieved fitting R² > 0.99.
GSODF accurately reproduced experimental textures for 3D and 2D data, including gamma‑fibre intensity trends with grain size.
Observed that high gamma‑fibre intensity corresponds to smaller grain sizes, linking texture to deep‑drawability and strength.
Boundary analysis revealed most grain boundaries occur between grains of different size, suggesting fragmentation mechanisms.

Caveats

✕Fitting quality decreases for datasets with few grains (e.g., warm‑rolled material).
✕Linear relationship between C‑coefficients and grain size may not hold for all microstructures.
✕Application to multiphase materials remains unresolved and requires further work.
✕Deriving continuous C‑functions can be difficult for complex microstructures.

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