Quantitative characterization of the three-dimensional microstructure of polycrystalline Al-Sn using X-ray microtomography

Computer Methods in Applied Mechanics and Engineering

Aliabadi

2013

116

In this study, a novel three-dimensional micro-mechanical crystal-level model for the analysis of intergranular degradation and failure in polycrystalline materials is presented. The polycrystalline microstructures are generated as Voronoi tessellations, that are able to retain the main statistical features of polycrystalline aggregates. The formulation is based on a grain-boundary integral representation of the elastic problem for the aggregate crystals, that are modeled as threedimensional anisotropic elastic domains with random orientation in the three-dimensional space. The boundary integral representation involves only intergranular variables, namely interface displacement discontinuities and interface tractions, that play an important role in the micromechanics of polycrystals. The integrity of the aggregate is restored by enforcing suitable interface conditions, at the interface between adjacent grains. The onset and evolution of damage at the grain boundaries is modeled using an extrinsic non-potential irreversible cohesive linear law, able to address mixed-mode failure conditions. The derivation of the traction-separation law and its relation with potential-based laws is discussed. Upon interface failure, a non-linear frictional contact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. To avoid a sudden transition between cohesive and contact laws, when interface failure happens under compressive loading conditions, the concept of cohesive-frictional law is introduced, to model the smooth onset of friction during the mode II decohesion process. The incrementaliterative algorithm for tracking the degradation and micro-cracking evolution is presented and discussed. Several numerical tests on pseudo-and fully three-dimensional polycrystalline microstructures have been performed. The influence of several intergranular parameters, such as cohesive strength, fracture toughness and friction, on the microcracking patterns and on the aggregate response of the polycrystals has been analyzed. The tests have demonstrated the capability of the formulation to track the nucleation, evolution and coalescence of multiple damage and cracks, under either tensile or compressive loads.

Section: Artificial Microstructure Generationmentioning

confidence: 99%

Section: Artificial Microstructure Generationmentioning

confidence: 99%

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

Computer Methods in Applied Mechanics and Engineering

Aliabadi

2013

116

“…An alternative strategy, based on the use of level set functions for the generation of meshes with anisotropic refinement, was proposed by Resk et al 142 , who also extended their technique to remeshing procedures in case of problems involving large deformations. The meshing of experimentally reconstructed microstructures has been accomplished in several studies 7,118,112,120,121,17 Bhandari and Ghosh et al 119,143 developed a sophisticated methodology for meshing 3D polycrystalline microstructures, generated with a DB FIB-SEM system. The grains are segmented as a collection of voxels using crystallographic orientation data and the surface topology is smoothed using polynomial and NURBS functions.…”

Section: Microstructure Meshing and Remeshingmentioning

confidence: 99%

“…Their microstructure, at the grain scale, is characterized by the grain morphology, size distribution, anisotropy and crystallographic orientation, by the presence of flaws and porosity and by physical and chemical properties of the intergranular interfaces 6 , which also have a direct effect on the initiation and evolution of damage. The behavior of polycrystalline materials at the microscale can be studied using experimental 7,8,9,10,11,12,13,14,15 and computational techniques 4,16,17 . Much research has been carried out for developing numerical models for the analysis of polycrystalline microstructures and their failure processes.…”

Section: Introductionmentioning

confidence: 99%

Modelling Polycrystalline Materials: An Overview of Three-Dimensional Grain-Scale Mechanical Models

J. Multiscale Modelling

Barbe

2013

A survey of recent contributions on three-dimensional grain-scale mechanical modelling of polycrystalline materials is given in this work. The analysis of material microstructures requires the generation of reliable micro-morphologies and affordable computational meshes as well as the description of the mechanical behavior of the elementary constituents and their interactions. The polycrystalline microstructure is characterized by the topology, morphology and crystallographic orientations of the individual grains and by the grain interfaces and microstructural defects, within the bulk grains and at the inter-granular interfaces. Their analysis has been until recently restricted to twodimensional cases, due to high computational requirements. In the last decade, however, the wider affordability of increased computational capability has promoted the development of fully three-dimensional models. In this work, different aspects involved in the grain-scale analysis of polycrystalline materials are considered. Different techniques for generating artificial micro-structures, ranging from highly idealized to experimentally based high-fidelity representations, are briefly reviewed. Structured and unstructured meshes are discussed. The main strategies for constitutive modelling of individual bulk grains and inter-granular interfaces are introduced. Some attention has also been devoted to three-dimensional multiscale approaches and some established and emerging applications have been discussed.

“…Their microstructure, at the grain scale, is characterized by grains morphology, size distribution, anisotropy and crystallographic orientation, by the presence of flaws and porosity and by physical and chemical properties of the intergranular interfaces [6], which have direct influence on the initiation and evolution of damage. Polycrystalline microstructures have been studied using experimental [7,8,9,10,11,12,13,14,15] and computational techniques [4,16,17]. Much research has been carried out for developing numerical models for polycrystalline microstructures and their failure processes.…”

Section: Introductionmentioning

confidence: 99%

Multiscale modeling of polycrystalline materials: A boundary element approach to material degradation and fracture

Computer Methods in Applied Mechanics and Engineering

Aliabadi

2015

In this work, a two-scale approach to degradation and failure in polycrystalline materials is proposed. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modelled using a three-dimensional boundary element formulation in which the presence of damage is taken into account employing an initial stress approach for modelling the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighborhood of the selected points. A three-dimensional grain-boundary formulation is used to simulate intergranular degradation and failure in the microstructure, whose morphology is generated using Voronoi tessellations. Intergranular degradation and failure are modelled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVE as periodic boundary conditions, while overall macro-stresses are obtained as volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. To avoid pathological damage localization at the macro-scale, integral non-local counterparts of the strains are employed. The multiscale processing algorithm is described. Some multiscale simulations are performed to investigate the capability of the method.