The effect of the curvature of a grain boundary network in the three-dimensional polycrystal on the response to a cyclic thermal loading: an FEM study

Department of Materials Science EngineeringIn this work, the effect of curvature of the grain boundary network in a polycrystalline material under external loading on the mechanical field distribution is examined. First, a three-dimensional digital voxellated polycrystal is generated using the Monte Carlo Potts model in the context of normal grain growth. Then, three-dimensional conformal, smoothed surface mesh elements on the grain boundary network of the such a digital microstructure are created using a set of both in-house codes. From surface mesh, the three-dimensional conformal volume elements are created using a commercial package. Finally, a finite element method (ABAQUS) is used on the resultant mesh elements to simulate the mechanical response inside the polycrystal under cyclic thermal loading. Specifically, we compared mechanical fields distribution inside the polycrystal as the grain boundary curvature changes.ope

A Virtual Grain Structure Representation System for Micromechanics Simulations

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

Crystal Plasticity Finite Element Simulation of Deformation and Fracture in Polycrystalline Microstructures

The mechanical response of metals and their alloys are governed by the deformation mechanisms in the underlying microstructure. High-fidelity modeling of deformation in metals requires development of proper constitutive laws at single crystal scale. Image-based crystal plasticity FE framework is regarded as one of the most powerful tools for deformation simulations, allowing the modelers to explicitly represent the elastic and plastic anisotropy of the material using physics-based laws in a computational domain which statistically represents the morphological and crystallographic properties of the microstructure. In this work, a thermodynamically-consistent coupled crystal plasticity-crack phase field framework is derived to model fracture prcoess in polycrystalline microstructures. The governing differential equations for the displacement and crack phase field are coupled via the Helmholtz free energy density (HFED). Using the volumetric-deviatoric decomposition of the elastic deformation gradient, a new HFED formulation is proposed which respects the unilateral damage conditions (tension-compression asymmetry of material response in the presence of cracks) and can be used for modeling fracture in anisotropic media under finite deformation conditions. Numerical modeling of fracture is computationally daunting, partly due to the frequent convergence issues and occurrence of instabilities. Recognizing that the instabilities take place due to an excess energy, three viscous stabilization methods are proposed in this work to dissipate this excess energy and effectively overcome the instabilities. Unlike arc-length methods, the viscous stabilization is applicable for rate-dependent constitutive models and its implementation into any existing FE code is straightforward. Crystal plasticity simulations of polycrystalline are generally carried out with linear tetrahedral elements due to their capability in conforming to complex geometries. These elements are known to suffer from volumetric locking in modeling (nearly-) incompressible materials, leading to numerical artifacts such as underestimation of displacements and overestimation of pressure levels. A modified F-bar-patch technique is developed in this work to alleviate volumetric locking in phase field modeling of ductile fracture. In the course of plastic deformation, the local strain rate experienced by different material points in the microstructure could be orders of magnitude different from the applied macroscopic strain rate. It is of paramount significance to develop a unified crystal plasticity law which could be applied for a wide range of strain rates. Using the dislocation glide mechanisms in \textit{hcp} metals, a unified flow rule is developed by combining the thermally-activated and drag-dominated processes. This unified law can be employed to model deformation over a wide range of strain rates and its explicit dependence of temperature makes it suitable for modeling high rate deformation of metals where adiabatic heating is significant

Etude numérique statistique des champs locaux de contraintes en surface de polycristaux cubiques et hexagonaux en élasticité

The first stages of fatigue damage in metallic polycrystalline materials are governed by local mechanical field at the grain scale. Fatigue crack initiation is often related to the emergence of persistent slip band at surface.Localization of cyclic plasticity occurs within grains of polycristals in which elastic stress field can be highly heterogeneous due to the granular microstructure and crystalline anisotropic elasticity. The main goal of this study is to evaluate and analyse statistically the stress fields in surface grains of polycristals. In this work, the elasticregime only is considered in order to study the subsequent activation of plastic slip and its variability. The possibleconsequences regarding crack formation are also addressed but in a lesser extent. The methodology is based on fullfield finite element numerical simulation of the elastic response of a set of polycrystalline aggregates in which grains orientation is chosen randomly.The two materials chosen for this study exhibit different characteristics regarding crystal elasticity and slip systems.The first one is an austenitic stainless steels 316L (face centered cubic) and the second one a titanium alloy TA6V(hexagonal close packed). The distribution of resolved shear stress within several sets of surface grains, for different classes of crystal orientation, are analysed in relation to local crystallographic configurations in order to identify those which promote - or prevent from - plastic slip activation. For TA6V, the results suggest in particular that basal slip is activated earlier than prismatic slip. In addition, the simulation strategy has been modified tomodel the presence of some sharp band-like crystallographic textures named “macrozones” whose influence has been qualitatively predicted. Plastic slip activation in TA6V is also studied experimentally. In situ tensile test using SEM has shown the earlier activation of basal slip. Experimental data has been combined with simulated distribution of resolved shear stress in order to estimate the critical resolved shear stress of basal and prismatic slip systems.Les premiers stades d'endommagement par fatigue au sein des matériaux métalliques polycristallins sont pilotés par les champs mécaniques locaux se développant à l'échelle des grains en surface. La formation de bandes de glissement persistantes est souvent à l'origine des fissures de fatigue. Cette localisation de la plasticité cyclique apparaît au sein de grains d'un polycristal dans lequel les champs de contraintes élastiques peuvent être fortement hétérogènes en fonction de la microstructure granulaire et de l'anisotropie élastique cristalline. La majeure partie de ce travail est consacrée à évaluer puis à analyser statistiquement les champs de contraintes au sein des grains de surface de polycristaux. Ce travail s'est concentré sur la réponse élastique des matériaux considérés afin d'étudier l'activation du glissement plastique et sa variabilité, puis, de façon un peu moins directe, ses conséquences vis-à-vis de la formation des fissures de fatigue. La méthodologie retenue est basée sur la simulation numérique en champs complets par éléments-finis de la réponse élastique d'un ensemble d'agrégats polycristallins dont les orientations cristallographiques sont tirées aléatoirement.Deux matériaux très différents du point de vue de l'élasticité cristalline et des systèmes de glissement ont été choisis comme support de l'étude. Le premier est l'acier inoxydable austénitique 316L à structure cubique à faces centrées et le second l'alliage de titane TA6V à structure hexagonale compacte. Les distributions de la cission résolue au sein d'ensembles de grains de surface, par classe d'orientation, sont analysées en relation avec les configurations cristallographiques locales afin d'identifier celles qui favorisent - ou au contraire inhibent - l'activation du glissement plastique. Les résultats obtenus, dans le cas du TA6V, suggèrent notamment une activation plus précoce et importante du glissement basal devant le glissement prismatique. De plus, la stratégie de simulation a été adaptée pour rendre compte de la présence de zones texturées appelées « macrozones » dont l'influence sur l'activation de plasticité peut être qualitativement prédite. L'activation du glissement dans le TA6V est également étudiée expérimentalement par la réalisation d'un essai in situ sous MEB où la précocité du glissement basal est constatée.Cet essai a également permis de caractériser la cinétique d'activation des différents types de glissements. Ces données, couplées aux statistiques des cissions simulées, permettent une estimation de la cission résolue critique sur les 2 types de glissement