Microstructure generation of severely deformed materials using Voronoi diagram in Laguerre geometry: Full algorithm

A new Voronoi diagram in Laguerre geometry based on closed-pack non-overlapping circles was proposed. This diagram was used to simulate microstructure of severely deformed materials at different applied strains. Grains size and their fractions were introduced by controlling the size and distribution of nuclei. Edge number distribution and neighboring cells edge number along with area distribution of the simulated Voronoi cells were determined. The edge number distribution was observed to fit gamma distribution more accurately. However, due to high inhomogeneity in the microstructure of the deformed samples at low strains, edge number distribution could not be matched by any distribution functions. The broad range of edge numbers in the simulated microstructure of sample deformed at low strains also confirmed this inhomogeneity. The mean number of edges for the neighboring grains showed development of a uniform structure with increasing strain. The area distribution of the simulated microstructures was found to be different from those in the Poisson–Voronoi tessellations. It was found that it is not possible to fit the area distributions with gamma distribution functions accurately. However, due to grain refinement phenomenon which takes place at high deformation strains, gamma distribution has been observed to be a good fit in the case of microstructures deformed with highest strains.