A 2D numerical study of the effect of particle shape and orientation on resistivity in shallow formations

International audienceSurficial heterogeneous soils such as till, alluvial fans or slope deposits are difficult to characterize by geotechnical tests due to the presence of decimeter to meter sized pebbles or rocks. The effective resistivity of such two-component medium composed of a percentage of resistive particles embedded in a conductive matrix is given by the Bussian's equation. The application of this equation allows the concentration of resistive particles to be determined if the resistivity values of each component and of the mixture, as well as the cementation exponent m, are known. However, previous theoretical and experimental studies have shown that the effective resistivity is affected by the shape of the particles. The objective of this study is to numerically determine the 2D effects of particle shape and orientation on the resistivity. Two configurations have been considered in the Finite Element modeling: laboratory like measurements and field layout. For circular particles, the numerical results fit the Bussian's equation with an exponent m of 2. Aligned elongated particles induce an anisotropy which can raise or diminish the exponent m, depending on the particle orientation and on the tortuosity of the current paths. Field experiment simulations showed that m varies 2 between 2.5 and 3.1 for an aspect ratio of 5 and that anisotropy resulting from the particle shape has little effect (m close to 2) when this ratio is lower than 2.5. This increase of m with the aspect ratio is in agreement with the theoretical model of Mendelson and Cohen and is consistent with the results of experimental studies. For laboratory measurement simulations, m values vary between 1.3 and 4 for a particle aspect ratio of 5, whatever the resistivity contrast between the particles and the matrix. The difference of results between the two configurations is explained by the paradox of anisotropy

Chapitre 3: Les joints de grains dans la déformation à froid

Les joints de grains jouent un rôle primordial lors de la déformation élastique et élasto-plastique d'un polycristal. L'influence des joints est traditionnellement appréciée à différentes échelles : - à l'échelle microscopique, on considère les interactions entre les dislocations du réseau cristallin et les défauts propres constituant la microstructure des joints. Ce faisant on perd de vue les interactions à grande distance entre les grains, - à l'échelle macroscopique, on considère que l'influence des joints provient des effets des incompatibilités de déformation élastique et plastique entre les grains d'un agrégat polycristallin. Ce faisant, on perd de vue les phénomènes particuliers qui se produisent au niveau des joints du fait de leurs caractéristiques propres, en n'envisageant que des effets moyens de grains à grains. Les joints de grains sont à l'origine de la déformation hétérogène des grains. Cette hétérogénéité se manifeste par l'existence de " domaines " déformés suivant des systèmes de glissement différents. La non uniformité de la déformation est révélée par les marquages (grilles ou mouchetis) déposés sur la surface du matériau. Les incompatibilités de déformation plastique induisent dans les grains, des contraintes internes qui varient en chaque point des grains et qui peuvent être relaxées par des déformations élasto-plastiques. Les contraintes internes locales et les déformations localisées sont étroitement liées. Elles jouent un rôle prépondérant dans la réponse du matériau à une sollicitation et sur son endommagement. Bien que de grand progrès technologiques aient permis de mieux caractériser la réponse locale des grains, les contraintes internes ne peuvent être mesurées à l'échelle du micromètre. C'est pourquoi la méthode des éléments finis utilisée dans le cadre de la plasticité cristalline, permet une évaluation des contraintes internes ainsi que leur localisation spatiale dans les grains. Les modèles polycristallins sont des outils qui permettent d'étudier la réponse locale d'un matériau à une échelle intermédiaire, dite " mésoscopique ", c'est-à-dire se situant entre 0,1 et 10 micromètres. Cependant, les résultats dépendent : - de l'agrégat censé représenter le matériau, - des conditions aux limites imposées à cet agrégat de taille limitée, - des lois de comportement introduites. Dans ce qui suit, nous ne traiterons que des matériaux métalliques purs et des alliages homogènes (pas de variation de concentration d'éléments chimiques) ne présentant ni inclusions, ni précipités. Nous supposerons également que les joints, présentent une bonne cohésion pour les basses et moyennes températures et ne contiennent pas d'éléments de ségrégation. Le plan général est le suivant : - définition des incompatibilités de déformation, - après des rappels sur la plasticité du monocristal, notion de contraintes internes et des modes de relaxation de ces contraintes. - modélisation polycristalline. - effet de taille de grain sur le comportement à travers la loi de Hall et Petch et modélisation associée (dislocations géométriquement nécessaires). - formation de sous-joints et de joints de grains en recristallisation

Characterisation of soils with stony inclusions using geoelectrical measurements

Characterisation and sampling of coarse heterogeneous soils is often impossible using common geotechnical in-situ tests once the soil contains particles with a diameter larger than a few decimetres. In this situation geophysical techniques - and particularly electrical measurements - can act as an alternative method for obtaining information about the ground characteristics. This paper deals with the use of electrical tomography on heterogeneous diphasic media consisting of resistive inclusions embedded in a conductive matrix. The adopted approach articulates in three steps: numerical modelling, measurements on a small-scale physical model, and field measurements. Electrical measurements were simulated using finite element analyses, on a numerical model containing a random concentration of inclusions varying from 0 to 40 %. It is shown that for electrode spacing 8 times greater than the radius of inclusions, the equivalent homogeneous resistivity is obtained. In this condition, average measured resistivity is a function of the concentration of inclusions, in agreement with the theoretical laws. To apply these results on real data, a small-scale physical model has been built, where electrical measurements were conducted both on the model and on each phase. From these laboratory measurements, a very satisfying estimation of the percentage of inclusions has been obtained. Finally, the methodology applied to a real experimental site composed of alluvial fan deposits made of limestone rocks embedded in a clayey matrix. The estimated percentage of rock particles obtained via electrical measurements was in accordance with the real grain size distribution

Polycrystal model of the mechanical behavior of a Mo-TiC30vol.% metal-ceramic composite using a 3D microstructure map obtained by a dual beam FIB-SEM

The mechanical behavior of a Mo-TiC30 vol.% ceramic-metal composite was investigated over a large temperature range (25^{\circ}C to 700^{\circ}C). High-energy X-ray tomography was used to reveal the percolation of the hard titanium carbide phase through the composite. Using a polycrystal approach for a two-phase material, finite element simulations were performed on a real 3D aggregate of the material. The 3D microstructure, used as starting configuration for the predictions, was obtained by serial-sectioning in a dual beam Focused Ion Beam (FIB)-Scanning Electron Microscope (SEM) coupled to an Electron Back Scattering Diffraction system (3D EBSD, EBSD tomography). The 3D aggregate consists of a molybdenum matrix and a percolating TiC skeleton. As most BCC metals, the molybdenum matrix phase is characterized by a change in the plasticity mechanisms with temperature. We used a polycrystal model for the BCC material, which was extended to two phases (TiC and Mo). The model parameters of the matrix were determined from experiments on pure molydenum. For all temperatures investigated, the TiC particles were considered as brittle. Gradual damage of the TiC particles was treated, based on an accumulative failure law that is approximated by an evolution of the apparent particle elastic stiffness. The model enabled us to determine the evolution of the local mechanical fields with deformation and temperature. We showed that a 3D aggregate representing the actual microstructure of the composite is required to understand the local and global mechanical properties of the studied composite

Etude de l'interface NiTi/silicone

National audienceLa présente étude vise à élaborer et caractériser mécaniquement un composite architecturé, constitué de Nickel-Titane (NiTi) et de silicone. Afin de pouvoir envisager l'utilisation d'un tel composite, une bonne adhésion à l'interface entre ces deux matériaux doit être assurée. L'interface entre Nickel-Titane (NiTi) et polymères a été le sujet de nombreuses études récentes. Concernant plus particulièrement les élastomères, utilisés dans le cadre de la présente application, les études sont bien plus rares. Ce travail a donc consisté à étudier l'interface entre fil de NiTi et deux silicones chargés, l'un étant biocompatible. Plusieurs méthodes d'amélioration de l'interface entre ces deux matériaux ont été testées : une désoxydation des fils, un primaire favorisant l'adhésion, et un traitement plasma. Des essais de pull-out ont été réalisés pour déterminer l'influence de ces différentes méthodes. Les résultats ont montré qu'une forte amélioration de l'adhésion était obtenue en utilisant un primaire, un traitement plasma ou encore une combinaison de ces deux traitements 1 . Dans le cadre d'applications biomédicales, une attention particulière a été portée à l'étude des paramètres du traitement plasma. Une structure composée d'un tube tricoté de NiTi enrobé de silicone a ensuite été élaborée 2 à l'aide d'un traitement plasma par argon. Des essais de traction et gonflement ont été réalisés sur ce composite architecturé

Effects of temperature on the mechanical behavior of filled and unfilled silicone rubbers

International audienceIn this contribution, the influence of the temperature on the mechanical behavior of a filled and an unfilled silicone rubber was analyzed. Firstly, the crystallization and melting temperatures were determined by differential scanning calorimetry. Secondly, mechanical tests were carried out at different temperatures above that of crystallization, up to 150°C. Results show that both silicone rubbers exhibit an entropic behavior in this temperature range. Thirdly, the temperature influence on the stress softening and mechanical hysteresis is studied and analyzed

Effects of temperature on the mechanical behavior of filled and unfilled silicone rubbers

International audienceIn this contribution, the influence of the temperature on the mechanical behavior of a filled and an unfilled silicone rubber was analyzed. Firstly, the crystallization and melting temperatures were determined by differential scanning calorimetry. Secondly, mechanical tests were carried out at different temperatures above that of crystallization, up to 150°C. Results show that both silicone rubbers exhibit an entropic behavior in this temperature range. Thirdly, the temperature influence on the stress softening and mechanical hysteresis is studied and analyzed

Modeling of hysteresis by means of a directional approach. Constitutive Models

International audienceThis paper focuses on the mechanical hysteresis in elastomers, i.e. the difference between loading and unloading paths. This property can be time-dependent as well as time-independent, depending on the physical phenomena that come into play. Similarly, mechanical hysteresis can be affected or not by material anisotropy. In this context, the present study is devoted to the modeling of time-independent hysteresis, in the framework of material anisotropy, accommodated to the Mullins effect. For this purpose, directional model is used to predict the tridimensional response of such materials. The proposed model is based on the stress decomposition into two parts. The first one represents the hyperelasticity of the macromolecular network, whereas the second part represents the friction in the network, i.e. the hysteretic part. Experiments were carried with filled silicone rubber and results show that the model predictions and experimental curves fit well