Modelling and characterization of ductile fracture surface in Al-Si alloys by means of Voronoi tessellation

In this study, a new approach to model the system of dimples on the fracture surface of Al-Si alloys using the weighted Voronoi tessellation is proposed. The tessellation model is applied to metallographic images of the eutectic phase to simulate a fracture surface appearance (as projected on a fractograph) that would potentially exhibit this structure if it had been fractured under uniaxial tensile loading. It enables the determination of geometrical features of virtual fracture surface projections, such as the dimple density, the area and equivalent diameter distributions, and topographic features, such as the dimple depth, the surface area and the roughness, by means of geometrical approximations, empirical and analytical relations. A brief review of the fractographic observations on different Al-Si alloys is made to demonstrate preconditions and motivation for using mosaic methods and in particular their weighted version. The simulation results are confirmed by experimental measurements indicating the credibility and usefulness of the model. The routine for generating the weighted Voronoi diagram is implemented as a Java plugin for the Fiji interface and is easy to execute.