A Virtual Grain Structure Representation System for Micromechanics Simulations
Creators: name: Zhang, Pan
Publisher: name: Imperial College London
Year: 2011

description: Representing a grain structure within a combined finite element computer aided engineering environment is essential for micromechanics simulations. Methods are required to effectively generate high-fidelity virtual grain structures for accurate studies. A high-fidelity virtual grain structure means a statistically equivalent structure in conjunction with desired grain size distribution features, and must be represented with realistic grain morphology. A family of controlled Poisson Voronoi tessellation (CPVT) models have been developed in this work for systematically generating virtual grain structures with the aforementioned properties. Three tasks have been accomplished in the development of the CPVT models: (i) defining the grain structure’s regularity that specifies the uniformity of a tessellation as well as deriving a control parameter based on the regularity; (ii) modelling the mapping from a grain structure’s regularity to its grain size distribution; and (iii) establishing the relation between a set of physical parameters and a distribution function. A one-gamma distribution function is used to describe a grain size distribution characteristic and a group of four physical parameters are employed to represent the metallographic measurements of a grain size distribution property. Mathematical proofs of the uniqueness of the determination of the distribution parameter from the proposed set of physical parameters have been studied, and an efficient numerical procedure is provided for computing the distribution parameter. Based on the general scheme, two- and three-dimensional CPVT models have been formulated, which respectively define the quantities of regularity and control parameters, and model the mapping between regularity and grain size distribution. For the 2D-CPVT model, statistical tests have been carried out to validate the accuracy and robustness of regularity and grain size distribution control. In addition, micrographs with different grain size distribution features are employed to examine the capability of the 2D-CPVT model to generate virtual grain structures that meet physical measurements. A crystal plasticity finite element (CPFE) simulation of plane strain uniaxial tension has been performed to show the effect of grain size distribution on local strain distribution. For the 3D-CPVT model, a set of CPFE analyses of micro-pillar compression have been run and the effects of both regularity and grain size on deformation responses investigated. Further to this, a multi-zone scheme is proposed for the CPVT models to generate virtual gradient grain structures. In conjunction with the CPVT model that controls the seed generating process within individual zones, the multi-zone CPVT model has been developed by incorporating a novel mechanism of controlling the seed generation for grains spanning different zones. This model has the flexibility of generating various gradient grain structures and the natural morphology for interfacial grains between adjacent zones. Both of the 2D- and 3D-CPVT models are capable of generating a virtual grain structure with a mean grain size gradient for the grain structure domain and grain size distribution control for individual zones. A true gradient grain structure, two simulated gradient grain structure, and a true gradient grain structure with an elongated zone have been used to examine the capability of the multi-zone CPVT model. To facilitate the CPFE analyses of inter-granular crack initiation and evolution using the cohesive zone models, a Voronoi tessellation model with non-zero thickness cohesive zone representation was developed. A grain boundary offsetting algorithm is proposed to efficiently produce the cohesive boundaries for a Voronoi tessellation. The most challenging issue of automatically meshing multiple junctions with quadrilateral elements has been resolved and a rule-based method is presented to perform the automatically partitioning of cohesive zone junctions, including data representation, edge event processing and cut-trim operations. In order to demonstrate the novelty of the proposed cohesive zone modelling and junction partitioning schemes, the CPFE simulations of plane strain uniaxial tension and three point bending have been studied. A software system, VGRAIN, was developed to implement the proposed virtual grain structure modelling methods. Via user-friendly interfaces and the well-organised functional modules a virtual grain structure can be automatically generated to a very large-scale with the desired grain morphology and grain size properties. As a pre-processing grain structure representation system, VGRAIN is also capable of defining crystallographic orientations and mechanical constants for a generated grain structure. A set of additional functions has also been developed for users to study a generated grain structure and verify the feasibility of the generated case for their simulation requirements. A well-built grain structure model in VGRAIN can be easily exported into the commercial FE/CAE platform, e.g. ABAQUS and DEFORM, via script input, whereby the VGRAIN system is seamlessly integrated into CPFE modelling and simulation processing.