Three-dimensional virtual grain structure generation with grain size control

Abstract

A three-dimensional (3D) controlled Poisson Voronoi tessellation (CPVT) model has been developed for generating 3D polycrystalline grain structures for micromechanics simulations. A virtual grain structure generated using the CPVT model has the property that its grain size distribution is statistically equivalent to the actual grain structure in term of the specified physical parameters: the mean grain size, a small grain size, a large grain size, and the percentage of grains within that range. Development of the CPVT model requires three steps: (1) Defining the regularity that specifies the uniformity of a tessellation, and deriving the control parameter based on the regularity, (2) establishing the mapping from the regularity to the distribution parameter of a one-parameter gamma distribution, (3) defining the mapping from the set of physical parameters to the distribution parameter. Relations between the regularity and distribution parameter, for a range of regularity values, are determined by a comprehensive set of statistical experiments, in which data fitting for the grain size distribution model is in each case obtained by an evolutionary optimisation algorithm. A software system (VGRAIN) has been developed for implementing the proposed three-dimensional CPVT model to generate the grain structure for crystal plasticity finite element (CPFE) analysis. To demonstrate the proposed scheme and the VGRAIN system, CPFE analyses of compression of micro-pillars are performed, and the effects of both regularity and grain size on the deformation are studied.