Regular Article

Geometrical and morphometrical tools for the inclusion analysis of metallic alloys

École Nationale Supérieure des Mines de Saint-Étienne, SPIN/LGF UMR CNRS 5307, 158 cours Fauriel, 42023 Saint-Étienne, France

^* e-mail: debayle@emse.fr

Received: 14 November 2018
Accepted: 12 March 2019

Abstract

The mechanical and use properties of metal alloys depend on several factors, including the amount and the geometry of impurities (inclusions). In this context, image analysis enables these inclusions to be studied from digital images acquired by various systems such as optical/electron microscopy or X-ray tomography. This paper therefore aims to present some geometrical and morphometrical tools of image analysis, in order to characterize inclusions in metal alloys. To achieve this quantification, many geometrical and morphometrical features are traditionally used to quantitatively describe a population of objects (inclusions). Integral geometry, via Minkowski’s functionals (in 2D: area, perimeter, Euler-Poincaré number), has been particularly investigated in image analysis. Nevertheless, they are sometimes insufficient for the characterization of complex microstructures (such as aggregates/agglomerates of objects). Other quantitative parameters are then necessary in order to discriminate or group different families of objects. In particular, shape diagrams are mathematical representations in the Euclidean plane for studying the morphology (shape) of objects, regardless of their size. In addition, this representation also makes it possible to analyze the evolution from one shape to another. In conclusion, image analysis using integral geometry and shape diagrams provide efficient tools with known mathematical properties to quantitatively describe inclusions (providing separate information on size and shape). The geometrical characteristics of these inclusions could thereafter be related to the mechanical properties of the metal alloys.