Multiscale modeling of the effective viscoplastic behavior of Mg 2 SiO 4 wadsleyite: bridging atomic and polycrystal scales

The viscoplastic behavior of polycrystalline Mg2SiO4 wadsleyite aggregates, a major high pressure phase of the mantle transition zone of the Earth (depth range: 410–520 km), is obtained by properly bridging several scale transition models. At the very fine nanometric scale corresponding to the dislocation core structure, the behavior of thermally activated plastic slip is modeled for strain-rates relevant for laboratory experimental conditions, at high pressure and for a wide range of temperatures, based on the Peierls–Nabarro–Galerkin model. Corresponding single slip reference resolved shear stresses and associated constitutive equations are deduced from Orowan’s equation in order to describe the average viscoplastic behavior at the grain scale, for the easiest slip systems. These data have been implemented in two grain-polycrystal scale transition models, a mean-field one (the recent Fully-Optimized Second-Order Viscoplastic Self-Consistent scheme of [1]) allowing rapid evaluation of the effective viscosity of polycrystalline aggregates, and a full-field (FFT based [2, 3]) method allowing investigating stress and strain-rate localization in typical microstructures and heterogeneous activation of slip systems within grains. Calculations have been performed at pressure and temperatures relevant for in-situ conditions. Results are in very good agreement with available mechanical tests conducted at strain-rates typical for laboratory experiments.This work was supported by the European Research Council under the Seventh Framework Programme (FP 7), ERC (grant number 290424 RheoMan) and under the Horizon 2020 research and innovation programme (grant number 787198 TimeMan)

A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method

The correspondence principle is customarily used with the Laplace–Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599–1606) have shown the equivalence between the collocation method used to invert Laplace–Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered

Synchrotron X-ray diffraction experiments with a prototype hybrid pixel detector

International audienceA prototype X-ray pixel area detector (XPAD3.1) has been used for X-ray diffraction experiments with synchrotron radiation. The characteristics of this detector are very attractive in terms of fast readout time, high dynamic range and high signal-to-noise ratio. The prototype XPAD3.1 enabled various diffraction experiments to be performed at different energies, sample-to-detector distances and detector angles with respect to the direct beam, yet it was necessary to perform corrections on the diffraction images according to the type of experiment. This paper is focused on calibration and correction procedures to obtain high-quality scientific results specifically developed in the context of three different experiments, namely mechanical characterization of nanostructured multilayers, elastic-plastic deformation of duplex steel and growth of carbon nanotubes

Numéro thématique des Comptes Rendus Mécanique en lʼhonneur dʼAndré Zaoui

La Mécanique des Matériaux a connu, en France et dans le monde, un développement spectaculaire au cours des dernières décennies, rendu à la fois nécessaire par les besoins d’innovation et de sûreté de secteurs industriels comme l’énergie et les transports, et possible par les avancées contemporaines en Physique et en Mécanique des Milieux Continus. Tout matériau est, par nature, hétérogène à une et souvent plusieurs échelles. La prise en compte, à une échelle pertinente, de cette hétérogénéité gouvernant les interactions entre mécanismes élémentaires est bien souvent la clef de la compréhension et de la prédiction du comportement mécanique des matériaux à leur échelle macroscopique d’usage. La Micromécanique des Matériaux, à laquelle ce numéro thématique des Comptes Rendus Mécanique est consacré, a précisément pour objet d’aborder ces problèmes de transition d’échelles. Ce numéro thématique est tout naturellement l’occasion d’honorer l’un des acteurs emblématiques du domaine, André Zaoui, qui a contribué de façon essentielle à l’établissement de la démarche micro–macro sur des bases théoriques rigoureuses validées par une approche expérimentale ambitieuse. Par ses travaux personnels, par la création, en avance sur son temps, d’une équipe de recherche dédiée aux expériences micromécaniques, par ses enseignements et ses actions de structuration de la recherche, André Zaoui a initié, puis constamment encouragé,ce domaine en France, l’ancrant solidement dans un dialogue fructueux entre expériences à petite échelle et modélisation

Additive layer manufacturing of titanium matrix composites using the direct metal deposition laser process

Titanium Matrix Composites (TMC's) containing various volume fractions of (TiB+TiC) particles have been deposited from powder feedstocks consisting of a blend of pre-alloyed (Ti-6Al-4V+B4C) powders, using the direct metal deposition (DMD) laser process and the in-situ chemical reaction 5Ti+B4C→4TiB+TiC. Process optimization has allowed to obtain a homogeneous distribution of tiny TiB whiskers within the Ti-6Al-4V α/β matrix, with a full solubilization of C for low B4C contents (0.5 wt% and 1.5 wt%), and the formation of a small amount of globular TiC particles at higher B4C content (3%). Comparisons with Ti-6Al-4V DMD walls revealed a substantial grain refinement on TMC's due to enhanced grain nucleation on TiB whiskers, even for low B4C contents. Last, mechanical investigations indicated an increase of 10–15% of Vickers hardness, and a constant 10% increase of Young modulus on a large temperature range (20–600 °C) for all B4C conten

Peculiar effective elastic anisotropy of nanometric multilayers studied by surface Brillouin scattering

We show in this paper by using a two-scale transition model that the elastic anisotropy of a thin film specimen can be tuned by appropriate stacking design. The anisotropic behaviour is illustrated for two monophase thin films, namely W which is perfectly elastically isotropic and Au which is strongly elastically anisotropic, and for a nanometric W/Au multilayers. The experimental measurements show that the model capture the elastic anisotropy rather well even for a nanometric multilayer stacking (period of 12 nm) and that the elastic anisotropy of W/Au multilayer is more pronounced than the ones of the two components for a fraction of 50%. This enhanced anisotropy is discussed in view of the multilayer microstructur

Experimental characterization of the intragranular strain field in columnar ice during transient creep

A digital image correlation (DIC) technique has been adapted to polycrystalline ice specimens in order to characterize the development of strain heterogeneities at an intragranular scale during transient creep deformation (compression tests). Specimens exhibit a columnar microstructure so that plastic deformation is essentially two-dimensional, with few in-depth gradients, and therefore surface DIC analyses are representative of the whole specimen volume. Local misorientations at the intragranular scale were also extracted from microstructure analyses carried out with an automatic texture analyzer before and after deformation. Highly localized strain patterns are evidenced by the DIC technique. Local equivalent strain can reach values as much as an order of magnitude larger than the macroscopic average. The structure of the strain pattern does not evolve with strain in the transient creep regime. Almost no correlation between the measured local strain and the Schmid factor of the slip plane of the underlying grain is observed, highlighting the importance of the mechanical interactions between neighboring grains resulting from the very large viscoplastic anisotropy of ice crystals. Finally, the experimental microstructure was introduced in a full-field fast Fourier transform polycrystal model; simulated strain fields are a good match with experimental ones

Modelling capsizing icebergs in the open ocean

At near-grounded glacier termini, calving can lead to the capsize of kilometre-scale (i.e. gigatons) unstable icebergs. The transient contact force applied by the capsizing iceberg on the glacier front generates seismic waves that propagate over teleseismic distances. The inversion of this seismic signal is of great interest to get insight into actual and past capsize dynamics. However, the iceberg size, which is of interest for geophysical and climatic studies, cannot be recovered from the seismic amplitude alone. This is because the capsize is a complex process involving interactions between the iceberg, the glacier and the surrounding water. This paper presents a first step towards the construction of a complete model, and is focused on the capsize in the open ocean without glacier front nor ice-mélange. The capsize dynamics of an iceberg in the open ocean is captured by computational fluid dynamics (CFD) simulations, which allows assessing the complexity of the fluid motion around a capsizing iceberg and how far the ocean is affected by iceberg rotation. Expressing the results in terms of appropriate dimensionless variables, we show that laboratory scale and field scale capsizes can be directly compared. The capsize dynamics is found to be highly sensitive to the iceberg aspect ratio and to the water and ice densities. However, dealing at the same time with the fluid dynamics and the contact between the iceberg and the deformable glacier front requires highly complex coupling that often goes beyond actual capabilities of fluid-structure interaction softwares. Therefore, we developed a semi-analytical simplified fluid-structure model (SAFIM) that can be implemented in solid mechanics computations dealing with contact dynamics of deformable solids. This model accounts for hydrodynamic forces through calibrated drag and added-mass effects, and is calibrated against the reference CFD simulations. We show that SAFIM significantly improves the accuracy of the iceberg motion compared with existing simplified models. Various types of drag forces are discussed. The one that provides the best results is an integrated pressure-drag proportional to the square of the normal local velocity at the iceberg’s surface, with the drag coefficient depending linearly on the iceberg’s aspect ratio. A new formulation based on simplified added-masses or computed added-mass proposed in the literature, is also discussed. We study in particular the change of hydrodynamic-induced forces and moments acting on the capsizing iceberg. The error of the simulated horizontal force ranges between 5 and 25 per cent for different aspect ratios. The added-masses affect the initiation period of the capsize, the duration of the whole capsize being better simulated when added-masses are accounted for. The drag force mainly affects the amplitude of the fluid forces and this amplitude is best predicted without added-masses.he authors acknowledge funding from ANR (contract ANR-11- BS01-0016 LANDQUAKES), ERC (contract ERC-CG-2013-PE10-617472 SLIDEQUAKES), DGA-MRIS and IPGP - Univer-sit´e de Paris ED560 (STEP’UP), which has made this work possible. The authors acknowledge Justin Burton for providing us with the data from laboratory experiments. The authors are also very grateful to Franc¸ois Charru, Emmanuel de Langre and Evgeniy A. Podolskiy for fruitful discussions, and the reviewers (Jason M. Amundson and Bradley P. Lipovsky) for helpful comments

Controlled biaxial deformation of nanostructured W/Cu thin films studied by X-ray diffraction

The deformation behaviour of 150. nm thick W/Cu nanocomposite deposited on polyimide substrates has been analysed under equi-biaxial tensile testing coupled to X-ray diffraction technique. The experiments were carried out using a biaxial device that has been developed for the DiffAbs beamline of SOLEIL synchrotron source. Finite element analysis has been performed to study the strain distribution into the cruciform shape substrate and define the homogeneous deformed volume. X-ray measured elastic strains in tungsten sub-layers could be carried out for both principal directions. The strain field was determined to be almost equi-biaxial as expected and compared to finite element calculations