An integrated scheme for crystal plasticity analysis: Virtual grain structure generation

Abstract

An integrated scheme is developed based on the controlled Poisson Voronoi tessellation (CPVT) model to generate the polycrystalline grain structure for micromechanics simulations. The proposed model of CPVT involves a single control parameter that is used to produce the grain structure with regularity control, by which the yielded tessellation varies from the purely random Voronoi tessellation to the regular hexagonal tessellation. The system extends the standard CPVT model by the addition of two features: a one-parameter gamma distribution and a mapping from a set of quantitative metallographic measurements to the distribution parameter. Based on this scheme, a grain structure can be constructed such that the virtual tessellation is statistically equivalent to the expected grain size distribution. To validate the modules that utilise the physical parameters that dictate the regularity, a series of theoretical investigations is performed. Efforts are devoted to proving the uniqueness of the mapping from the physical parameters to the distribution parameter and the regularity parameter. An efficient numerical algorithm is provided to facilitate the mapping solution process. A software system (VGRAIN) is developed implementing the proposed CPVT model to generate the grain structure for crystal plasticity finite element (CPFE) analysis. To demonstrate the proposed scheme and the VGRAIN system, a plane strain CPFE analysis is conducted. Two microstructures are generated with different regularities, and the deformation under uniaxial tension is simulated.