Nearly uniform sampling of crystal orientations

International audienceA method is presented for generating nearly uniform distributions of three-dimensional orientations in the presence of symmetry. The method is based on the Thomson problem, which consists in finding the configuration of minimal energy of N electrons located on a unit sphere – a configuration of high spatial uniformity. Orientations are represented as unit quaternions, which lie on a unit hypersphere in four-dimensional space. Expressions of the electrostatic potential energy and Coulomb's forces are derived by working in the tangent space of orientation space. Using the forces, orientations are evolved in a conventional gradient-descent optimization until equilibrium. The method is highly versatile as it can generate uniform distributions for any number of orientations and any symmetry, and even allows one to prescribe some orientations. For large numbers of orientations, the forces can be computed using only the close neighbourhoods of orientations. Even uniform distributions of as many as 10 6 orientations, such as those required for dictionary-based indexing of diffraction patterns, can be generated in reasonable computation times. The presented algorithms are implemented and distributed in the free (open-source) software package Neper

Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing

International audienceA methodology is presented for the generation and meshing of large-scale three-dimensional random polycrystals. Voronoi tessellations are used and are shown to include morphological properties that make them particularly challenging to mesh with high element quality. Original approaches are presented to solve these problems: (i) "geometry regularization", which consists in removing the geometrical details of the polycrystal morphology, (ii) "multimeshing" which consists in using simultaneously several meshing algorithms to optimize mesh quality, and (iii) remeshing, by which a new mesh is constructed over a deformed mesh and the state variables are transported, for large strain applications. Detailed statistical analyses are conducted on the polycrystal morphology and mesh quality. The results are mainly illustrated by the high-quality meshing of polycrystals with large number of grains (up to 105), and the finite element method simulation of a plane strain compression of ε = 1.4 of a 3000-grain polycrystal. The presented algorithms are implemented and distributed in a free (open-source) software package: Neper

Simulation of uniaxial tensile behavior of quasi-brittle materials using softening contact models in DEM

This study proposes new contact models to be incorporated into discrete element method (DEM) to more accurately simulate the tensile softening in quasi-brittle materials, such as plain concrete and masonry with emphasis on fracture mechanism and post-peak response. For this purpose, a plain concrete specimen (double notched) and stack bonded masonry prism under direct tensile test are modeled. Furthermore, mixed mode crack propagation is investigated in concrete and brickwork assemblages. Two modeling approaches are proposed, the simplified and detailed meso modeling, both based on DEM. In the simplified meso-model, a smooth contact surface is considered between two separate blocks, whereas the internal structure of the material is explicitly represented as a tessellation into random polyhedral blocks in the detailed meso-model. Furthermore, recently developed tensile softening contact constitutive models implemented into a commercial discrete element code (3DEC) are used to simulate the softening behavior of concrete and masonry. As an important novel contribution, it is indicated that the proposed computational models successfully capture the complete (pre- and post-peak) material behavior and realistically replicate the cracking mechanism. Additionally, a sensitivity analysis demonstrates the influence of the various micro-contact parameters on the overall response of the examined materials.Authors would like to express their gratitude to Itasca Educational Partnership Program (IEP) for their kind support and providing 3DEC softwar

Thermal conductivity of MoS2 polycrystalline nanomembranes

Heat conduction in 2D materials can be effectively engineered by means of controlling nanoscale grain structure. Afavorable thermal performance makes these structures excellent candidates for integrated heat management units. Here we show combined experimental and theoretical studies for MoS₂ nanosheets in a nanoscale grain-size limit.Wereport thermal conductivity measurements on 5 nm thick polycrystalline MoS₂ by means of 2-laser Raman thermometry. The free-standing, drum-like MoS₂ nanomembranes were fabricated using a novel polymer- and residue-free, wet transfer, in which we took advantage of the difference in the surface energies between MoS₂ and the growth substrate to transfer the CVD-grown nanosheets. The measurements revealed a strong reduction in the in-plane thermal conductivity down to about 0.73 ± 0.25 W m⁻¹ K⁻¹. The results are discussed theoretically using finite elements method simulations for a polycrystalline film, and a scaling trend of the thermally conductivity with grain size is proposed

Suivi de microtextures dans l'aluminium en grande déformation à chaud

This work aims to better understand the development of deformation crystallographic textures in aluminium alloys, and thus to improve their modeling. An original method used is to follow the rotations of individual grains in a polycrystal during deformation.The experimental approach, called "microtexture tracking", is based on the use of a "split sample" deformed at 400°C in several passes of plane strain compression, combined with the EBSD technique for the local orientation analysis of the grains on the median surface of the sample during deformation. 176 grains could be followed, up to a strain of 1.2.The data (typically 3000 orientations per grain) provide the average grain rotations, which directly contribute to the texture development. They are described in terms of rotation angle and axis, but also rotation path. In-grain disorientations are characterized and related to strain accommodation mechanisms. Moreover, an effect of grain interaction is examined to extend the modeling accuracy.A wide range of models are studied, notably the Taylor model and a Taylor-type model (RSI). It is shown that the Taylor model provides a first-order agreement for the rotations of the individual grains. The discrepancies can be attributed partly to grain interaction. The RSI model accounts for grain interaction, but not sufficiently. These new and original data are now available to improve crystal plasticity models.Ce travail vise à améliorer la compréhension du développement des textures cristallographiques de déformation dans les alliages d'aluminium, et ainsi améliorer leur modélisation. La méthode originale adoptée consiste à suivre les rotations de grains individuels dans un polycristal en cours de déformation.L'approche expérimentale, nommée "suivi de microtextures", s'appuie sur l'utilisation d'un "échantillon tranché" déformé en compression plane à 400°C, appliquée en plusieurs passes, et de la technique EBSD pour l'analyse des orientations locales des grains sur la surface médiane de l'échantillon au cours de la déformation. 176 grains ont ainsi pu être suivis, jusqu'à une déformation de 1.2. Les données obtenues (classiquement 3000 orientations par grain) donnent accès aux rotations moyennes des grains, lesquelles contribuent directement à la formation de la texture. Elles sont décrites en termes d'angle et d'axe de rotation, mais aussi de chemins de rotation. Les désorientations intragranulaires sont caractérisées et rattachées aux mécanismes d'accomodation des déformations. De plus, un effet d'interaction intergranulaire est mis en évidence afin d'améliorer les modèles.Une large gamme de modèles sont étudiés, notamment le modèle de Taylor et un modèle de type Taylor (RSI). Nous montrons que le modèle de Taylor fournit un accord au premier ordre pour les rotations des grains individuels. Les désaccords peuvent être attribués en partie à l'interaction intergranulaire. Le modèle RSI permet de rendre compte de cette interaction, mais pas suffisamment. Ces données, nouvelles et originales, sont maintenant disponibles pour améliorer les modèles de plasticité cristalline

A numerical modelling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity

International audienceA FE modelling of the elastoplastic interactions occurring within a 3D polycrystal subjected to diffusive phase transformation is proposed. The parent polycrystal is represented by a Voronoi tessellation, where grains differ in shape, size and crystallographic orientation. Grains of the new phase nucleate at favourable sites of the parent polycrystal then grow isotropically, following specific kinetics. This process can result in various product polycrystal morphologies where grains are distinguished by their morphologies and their crystallographic orientations, and have crystalline properties different from those of the parent grains. Application is performed on the austenite-to-ferrite transformation of a low carbon steel, by analysing different basic cases of transformation history with different constitutive modellings. Microplasticity and its related internal stresses are shown to develop during the phase transformations and to affect significantly the elastoplasticity of the product medium

Optimal polyhedral description of 3D polycrystals: method and application to statistical and synchrotron X-ray diffraction data

International audienceA methodology is presented for optimal polyhedral description of 3D polycrystals from experimental properties. This is achieved by determining, by optimization, appropriate attributes of the seeds of Laguerre tessellations. The resulting tessellations are optimal in the sense that no further improvements are possible using convex geometries. The optimization of Laguerre tessellation combines a new, computationally-efficient algorithm for updating tessellations between iterations to a generic optimization algorithm. The method is applied to different types of experimental data, either statistical, such as grain size distributions, or grain-based, as provided by synchrotron X-ray diffraction experiments. It is then shown how the tessellations can be meshed for finite-element simulations. The new method opens the way to more systematic and quantitative analyses of microstructural effects on properties. The presented algorithms are implemented and distributed in the free (open-source) software package Neper

Suivi de microtextures dans l'aluminium en grande déformation à chaud

Ce travail vise à améliorer la compréhension du développement des textures cristallographiques de déformation dans les alliages d'aluminium, et ainsi améliorer leur modélisation. La méthode originale adoptée consiste à suivre les rotations de grains individuels dans un polycristal en cours de déformation. L'approche expérimentale, nommée "suivi de microtextures", s'appuie sur l'utilisation d'un "échantillon tranché" déformé en compression plane à 400 degrés Celsius, appliquée en plusieurs passes, et de la technique EBSD pour l'analyse des orientations locales des grains sur la surface médiane de l'échantillon au cours de la déformation. 176 grains ont ainsi pu être suivis, jusqu'à une déformation de 1.2. Les données obtenues (classiquement 3000 orientations par grain) donnent accès aux rotations moyennes des grains, lesquelles contribuent directement à la formation de la texture. Elles sont décrites en termes d'angle et d'axe de rotation, mais aussi de chemins de rotation. Les désorientations intragranulaires sont caractérisées et rattachées aux mécanismes d'accomodation des déformations. De plus, un effet d'interaction intergranulaire est mis en évidence afin d'améliorer les modèles. Une large gamme de modèles sont étudiés, notamment le modèle de Taylor et un modèle de type Taylor (RSI). Nous montrons que le modèle de Taylor fournit un accord au premier ordre pour les rotations des grains individuels. Les désaccords peuvent être attribués en partie à l'interaction intergranulaire. Le modèle RSI permet de rendre compte de cette interaction, mais pas suffisamment. Ces données, nouvelles et originales, sont maintenant disponibles pour améliorer les modèles de plasticité cristalline.This work aims to better understand the development of deformation crystallographic textures in aluminium alloys, and thus to improve their modeling. An original method used is to follow the rotations of individual grains in a polycrystal during deformation. The experimental approach, called "microtexture tracking", is based on the use of a "split sample" deformed at 400 Celsius degrees in several passes of plane strain compression, combined with the EBSD technique for the local orientation analysis of the grains on the median surface of the sample during deformation. 176 grains could be followed, up to a strain of 1.2. The data (typically 3000 orientations per grain) provide the average grain rotations, which directly contribute to the texture development. They are described in terms of rotation angle and axis, but also rotation path. In-grain disorientations are characterized and related to strain accommodation mechanisms. Moreover, an effect of grain interaction is examined to extend the modeling accuracy. A wide range of models are studied, notably the Taylor model and a Taylor-type model (RSI). It is shown that the Taylor model provides a first-order agreement for the rotations of the individual grains. The discrepancies can be attributed partly to grain interaction. The RSI model accounts for grain interaction, but not sufficiently. These new and original data are now available to improve crystal plasticity models.ST ETIENNE-ENS des Mines (422182304) / SudocSudocFranceF

A numerical modelling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity

International audienceA FE modelling of the elastoplastic interactions occurring within a 3D polycrystal subjected to diffusive phase transformation is proposed. The parent polycrystal is represented by a Voronoi tessellation, where grains differ in shape, size and crystallographic orientation. Grains of the new phase nucleate at favourable sites of the parent polycrystal then grow isotropically, following specific kinetics. This process can result in various product polycrystal morphologies where grains are distinguished by their morphologies and their crystallographic orientations, and have crystalline properties different from those of the parent grains. Application is performed on the austenite-to-ferrite transformation of a low carbon steel, by analysing different basic cases of transformation history with different constitutive modellings. Microplasticity and its related internal stresses are shown to develop during the phase transformations and to affect significantly the elastoplasticity of the product medium