Modelling of Grain Structure in Polycrystalline Materials Using Voronoi Diagrams for Welding Applications

Voronoi diagram models were applied to calculate grain structure using randomly distributed nuclei in 2 dimensions. The taxicab distance which is a non-Euclidean distance was used because its circle (diamond shape in 2D) resembles the envelope of dendritic growth for materials with BCC and FCC crystal systems. The grain geometry calculated based on the taxicab distance showed, however, an unrealistic, somewhat regular structure. The taxicab Voronoi diagram had to be modified, and different crystallographic orientations of grains were additionally considered. Each grain assumed to have a random crystallographic orientation, and the taxicab distance was calculated in the rotated axis system. A rotated taxicab Voronoi diagram showed a more realistic grain geometry for the materials, and it seems to be applicable for welding applications.