A germ-grain model applied to the morphological study of dual phase steel

The mechanical properties of dual Phase steels (DP steels) are strictly related to the spatial distribution and the geometry of the two phases composing the steel, ferrite and martensite. Due to the high costs to obtain images of sections of steel samples, one important industrial problem is the reduction of the number of 2D sections needed to build and simulate a geometric model which may reproduce in a realistic way the 3D geometry of the material. In this context, the availability of suitable techniques of parameter estimation or identification is fundamental to solve the problem. In this work we present a germ-grain model which approximates the main geometric characteristics of the martensite, taking into account the inhomogeneities of the material. The parameters of the model are estimated on the basis of the morphological characteristics of the images of about 150 tomographic sections of a real sample, quantified by the Minkowski functionals. Here we replace the Mahalanobis distance, introduced in previous literature, with the N-distance, which provides computational advantages. In order to test if the estimated model is reproducing the distribution of the Minkowski functionals of the real material, both confidence bands from the simulated model are computed and compared with the real data and techniques for the detection of functional outliers are applied to quantify the accuracy of fit of the estimated model.