Controlled Poisson Voronoi tessellation for virtual grain structure generation: a statistical evaluation

Abstract

A controlled Poisson Voronoi tessellation (CPVT) model has been developed for producing two-dimensional virtual grain structures that are statistically equivalent to metallographic observations of polycrystalline materials in terms of the tessellation's regularity and grain size distribution. The descriptive fitting model, which is critical to link the grain size distribution parameter to the regularity parameter, has been improved in this work; previously, the descriptive model was poor for large values of the distribution parameter c. A set of four physical parameters is involved in uniquely determining the grain size distribution properties and configuring the CPVT system. Emphasis is devoted to examining the effectiveness and robustness of the CPVT system in generating virtual grain structures with specified properties. Two series of statistical tests are performed to validate the agreement between the prescribed regularity and that of the resultant tessellations, and to investigate the details of the overall grain size distribution. In order to explore sample size effects, three statistical tests were conducted for a range of regularity values. In addition, a materials modelling system for crystal plasticity finite element analysis is demonstrated, which implements the CPVT model for grain structure generation. Two real microscopic images with different grain size distribution features are employed to examine the capability of the system to generate virtual grain structures that match physical measurements.

Keywords:

• micromechanics
• numerical method
• computational mechanics
• microstructure
• crystal plasticity
• Voronoi tessellation