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International audience; Semi-cristalline poymers (SCPs) such as High-Density-Poly-Ethylenes (HDPE) present a spherulitic microstructure. During mechanical loading micro-mechanisms of deformation in spherulites and their effect on the macroscopic response have to be clarified. We intend to use the AMITEX code [1] developed at CEA Saclay, firstly to solve the local mechanical equations on such a complex microstructure, and secondly, to couple it with a modelling approach of phase transformation type to explore the thereby opened simulation paths allowing for a better understanding of the damaging processes which explain the macroscale behaviour.The AMITEX code is based on an FFT method [2] and takes into account behaviour laws in UMAT format. To describe mechanical behaviour of crystal-amorphous two-phase spherulite structure we created a UMAT with a transversal isotropic law based on a DLR model [3]. This model allows predicting the local and overall behaviour between amorphous isotropic viscoelastic regions and orthotropic elastic crystallites accounting for their radial arrangement from spherulites centers. A phase field model was developed in AMTEX source code to describe phase changes in crystal-amorphous two-phase arrangements during loading. First computations of behaviour using the mechanical model coupled with the phase field method reveal a deterioration of crystal phases and crystal/amorphous interactions occurring during strain which can now beinvestigated more deeply with respect to the model parameters.

International audience; A mechanobiological model of bone remodeling is developed involving mineralization in a moving diffuse interface separating the marrow containing the bone cells responsible for the remodeling from the newly formed bone. A scalar phase field quantifies the degree of mineralization within the interface at the level of the bone microstructure, varying continuously between the nil lower value (no mineral) and unity for the fully mineralized phase corresponding to new bone. The field equations for the mechanical, chemical, and interfacial phenomena are written under the umbrella of thermodynamics of irreversible processes. A strain gradient model is developed to account for the impact of the underlying hierarchical microstructure on the effective response of bone. Second gradient terms are motivated by the high strain and stress concentrations close to defects, both at mesoscopic and microscopic scales. The combination of the balance equations for the microforce associated to the phase field and the kinetic equations lead to the Ginzburg–Landau equation for by the phase field with a source term accounting for the dissipative microforce.

The process of bone remodeling includes a cycle of repair, renewal, and optimization. This adaptation process, in response to variations in external loads and chemical driving factors, involves three main types of bone cells: osteoclasts, which remove the old pre-existing bone; osteoblasts, which form the new bone in a second phase; osteocytes, which are sensing cells embedded into the bone matrix, trigger the aforementioned sequence of events. The remodeling process involves mineralization of the bone in the diffuse interface separating the marrow, which contains all specialized cells, from the newly formed bone. The main objective advocated in this contribution is the setting up of a modeling and simulation framework relying on the phase field method to capture the evolution of the diffuse interface between the new bone and the marrow at the scale of individual trabeculae. The phase field describes the degree of mineralization of this diffuse interface; it varies continuously between the lower value (no mineral) and unity (fully mineralized phase, e.g. new bone), allowing the consideration of a diffuse moving interface. The modeling framework is the theory of continuous media, for which field equations for the mechanical, chemical, and interfacial phenomena are written, based on the thermodynamics of irreversible processes. Additional models for the cellular activity are formulated to describe the coupling of the cell activity responsible for bone production/resorption to the kinetics of the internal variables. Kinetic equations for the internal variables are obtained from a pseudo-potential of dissipation. The combination of the balance equations for the microforce associated to the phase field and the kinetic equations lead to the Ginzburg–Landau equation satisfied by the phase field with a source term accounting for the dissipative microforce. Simulations illustrating the proposed framework are performed in a one-dimensional situation showing the evolution of the diffuse interface separating new bone from marrow.

The plastic deformation processes that occur in a tensily deformed High Density Polyethylene specimen were studied from full-field strain and strain rate measurements obtained by 3D DIC (Digital Image Correlation). The tensile tests were performed every 10 ° C from room temperature to 120 ° C . For temperatures below 60 ° C , it is shown that the strain localization effect becomes less pronounced when the temperature increases. For temperatures higher than 60 ° C , the material is found to exhibit double yielding behavior. By analyzing the DIC data in Lagrangian representation, it was possible to quantitatively highlight the strain localization effect that is specifically associated with the second yield. The second yield strain ( e Y 2 ) was measured and appeared to be nearly independent of temperature. For temperatures smaller than 60 ° C , it was found that the threshold strain corresponding to e Y 2 also marks the onset of the deformation process phase during which the volume strain strongly increases. On the basis of previous WAXS (Wide Angle X-ray Scattering) studies of our research team and on literature we concluded that the critical strain e Y 2 corresponds to the onset of the lamellar morphology destruction. At high strain levels, the neck stabilization phase was shown to proceed according to a strain driven scheme characterized by threshold strains that are temperature-independent. The experimental values of the threshold strain marking the onset of the stabilization phase are found to be in good agreement with those found using the Haward-Thackray model.

To improve our understanding of the rheology of solid semi-crystalline polymers, descriptions of the deformation-induced microstructural reorganization mechanisms with precise and local quantitative data are needed. The novel results presented in this paper for high-density polyethylene (HDPE) were obtained in situ on a coherent synchrotron beamline specifically developed to allow very fast scanning of a specimen under tensile test. From the recorded small angle X-ray scattering (SAXS) patterns, a quantitative index characterizing the microstructure local anisotropy was calculated. With the scanning operating mode, many different material points could be studied. These material points were subjected to various deformation paths in the plastic regime due to the necking development and its propagation. Their positions and strain evolutions were obtained through digital image correlation (DIC). With an appropriate analysis coupling the bulk-averaged SAXS and DIC surface measurements, the microstructural anisotropy index is shown to have a given value at a given true strain. This means that the microstructure morphology is only governed by the current strain level. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017.

Spectral solvers are mesh-free, fast and very efficient simulation tools which emerged in the last two decades for solving continuum mechanics problems for heterogenous materials. Applied exclusively on particle-type composites, this paper demonstrates that they can model woven laminated composites with very valuable issues as they are able to capture with high spatial resolution the details of the stress and strain fields in the fabric periodic cell. Assessment of the modelling tool is given within in-plane shear mechanical testing: (i) at the mesoscale, through the comparison of local full-field strain maps obtained experimentally with Digital Image Correlation; (ii) at the macroscale, through the estimation of macroscopic properties from direct computation and comparison to their measured values. As shown in the last part of the paper, this tool provides in-depth knowledge of the strain-stress tensor in the microstructure as it offers an opportunity for precise local 3-D investigation. It should be a matter of high concern in the future as it allows the rapid design of new composite structures.

International audience; L'objectif général de ce travail est d'étudier l'évolution de la microstructure de tous les points matériels d'une éprouvette en polyéthylène haute densité (PEHD, polymère semi-cristallin) sollicitée en traction. Du fait du phénomène de striction, plusieurs points matériels de l'éprouvette peuvent parvenir à un même niveau de déformation après avoir subi des histoires de déformation très différentes. Dans cette étude nous analysons l'influence des cinétiques de déformation sur l'évolution de la microstructure de notre PEHD. La caractérisation de la microstructure sur l'ensemble de l'éprouvette a été obtenue in situ sur synchrotron grâce à un balayage SAXS ultra-rapide. En réalisant également des expériences de corrélation d'images 3D, il a été possible de construire un observable quantitatif qui permet d'analyser la dépendance de l'anisotropie de la microstructure pour les différents points matériels (représentation lagrangienne) ou géométriques (représentation eulérienne) d'une même éprouvette en fonction de la déformation locale.

International audience; This work is devoted to the study of the deformation mechanisms of a high-density polyethylene deformed in tension. Specific treatments were applied to synchrotron wide-angle X-ray scattering patterns obtained in situ with the aim of quantifying: (i) the evolution of the apparent crystal sizes during the deformation process, (ii) the reorientation dynamics of the fragmented crystals while aligning their chains along the drawing axis during the establishment of the fibrillar morphology, and (iii) the reorientation dynamics of the amorphous chains. In addition, the volume strain evolution was measured using 3D digital image correlation. The cavitation phenomenon was found to mainly occur during the lamellae fragmentation phase. At the end of the deformation process, when the lamellar structure is destroyed, the fragmented crystals have new degrees of freedom and become free to rotate to align their chains along the drawing axis. Crystal fragmentation is then no longer needed to allow material deformation, and there is no further volume strain increase.

Point sources exhibit low threshold electron emission due to local field enhancement at the tip. The development and implementation of tip emitters have been hampered by the need to position them sufficiently apart to achieve field enhancement, limiting the number of emission sites and therefore the overall current. Here we report low threshold field (< 0.1V/um) emission of multiple electron beams from atomically thin edges of reduced graphene oxide (rGO). Field emission microscopy (FEM) measurements show evidence for interference from emission sites that are separated by a few nanometers, suggesting that the emitted electron beams may be coherent. Based on our high-resolution transmission electron microscopy, infrared spectroscopy and simulation results, field emission from the rGO edge is attributed to a stable and unique aggregation of oxygen groups in the form of cyclic edge ethers. Such closely spaced electron beams from rGO offer prospects for novel applications and understanding the physics of linear electron sources., 20 pages, 4 figures, Submitted

International audience; La très grande majorité des matériaux d'intérêt industriel ont un caractère commun générique : ils sont très souvent hétérogènes et/ou constitués de différentes phases. La maîtrise de la microstructure de ces alliages passe par une meilleure compréhension des mécanismes de formation de ces phases et par la modélisation des cinétiques dans des conditions diverses (température, contrainte externe, irradiation…). Les alliages Al-Sc, riches en aluminium, sont très utilisés dans l'industrie en raison leurs propriétés mécaniques. Après homogénéisation à haute température, on observe en effet, l'apparition d'une forte densité de petits précipités cohérents, répartis de façon homogène avec la matrice d'aluminium. Ces précipités ordonnés sont de composition Al 3 Sc et possèdent la structure L1 2. Ils bloquent le mouvement des dislocations ainsi que celui des joints de grains, ce qui durci l'alliage et lui confère un fort pouvoir anti-recristallisant. L'addition de zirconium, en plus du scandium, améliore encore les propriétés mécaniques du matériau. Les précipités obtenus dans cet alliage sont en effet, plus fins et leur distribution est plus dense que dans les alliages Al-Sc. L'origine de ces observations expérimentales est attribuée à la composition chimique hétérogène des précipités qui apparaissent dans l'alliage ternaire. Ces précipités, de structure L1 2 et de composition Al 3 (Zr x Sc 1-x), sont en effet formés, d'un coeur riche en scandium et d'une coquille riche en zirconium. Pour comprendre les phénomènes qui ont lieu dans ces matériaux, il est nécessaire de mettre au point un modèle mathématique capable de décrire les cinétiques de précipitation et de coalescence. La méthode de champ de phase a émergée récemment comme un outil performant pour étudier l'évolution microstructurale dans les alliages. Ce modèle décrit un alliage à l'échelle mésoscopique. Il permet d'appréhender l'évolution de la taille, de la forme et de la distribution des précipités dans le matériau. Le principe de cette méthode est de décrire l'état de la matière à l'aide d'une ou plusieurs variables de champ, conservatives ou non-conservatives. L'évolution temporelle de ces variables est pilotée par la minimisation de l'énergie libre du système. Dans un problème de transformation de phase avec mise en ordre, les variables de champ sont les concentrations des éléments ainsi que les paramètres d'ordre correspondant aux structures étudiées.

The coarsening kinetics of γ’ precipitates in binary and ternary Al3Sc1-xZrx alloys is studied by using the two- and three-dimensional phase-field simulations. Our focus is on the influence of diffusion coefficients of Sc and Zr atoms on the transformation path kinetics from disordered f.c.c. matrix to two phases equilibrium state with γ’ precipitates and f.c.c. disordered matrix. Our simulation results demonstrate that in the case of binary alloys taking into account the concentration dependence of the mobility of atoms decreases the coarsening rate. In the case of ternary alloys we show that the Al3Sc particles precipitate first following by appearance of a Zr-rich shell. Our simulations results are in good agreement with experimental observations.

International audience

International audience; Al-Sc-based alloys exhibit a unique combination of high strength and plasticity, corrosion resistance and weldability [1-4]. Mechanical properties of these alloys depend on their microstructure and their phase composition, so its knowledge provides an opportunity to improve material properties by thermal treatment. The addition of Sc to aluminium is a very effective mean to form small ordered L12 precipitates which increase the tensile strength and inhibit recrystallisation.. Recently it was demonstrated that these precipitates remain coherent up to sizes of. 40 nm in diameter [1]. To further improve the properties of Al-Sc alloys, the effects of ternary additions to Al-Sc alloys have been investigated [5]. Previous studies have shown that addition of Zr in Al-Sc alloys improve the stability these systems to coarsening [20-21]. It was determined that Zr segregates to the α-Al/Al3Sc heterophase interface and acts as a barrier for the diffusion of Sc across the interface, which leads to a lowering of the coarsening rate [22-23] as compared to binary Al-Sc alloys. Harada and Dunand [7] shown that zirconium addition reduces the lattice parameter of Al3Sc and concomitantly the inter- face free and elastic strain energies. The purpose of this work is to study the microstructural evolution in binary Al-Sc and in ternary Al-Sc-Zr alloys. Phase field approach based on the Cahn-Hilliard and Ginzburg-Landau equations [12-18] has been used. It is shown that L12 particles have a heterogeneous structure with the Al3Sc core surrounded by a Zr-rich shell .