Добірка наукової літератури з теми "Quantification of elastic anisotropy by two different approaches"

Abstract. Crystallographic texture (or fabric) evolution with depth along ice cores can be evaluated using borehole sonic logging measurements. These measurements provide the velocities of elastic waves that depend on the ice polycrystal anisotropy, and they can further be related to the ice texture. To do so, elastic velocities need to be inverted from a modeling approach that relate elastic velocities to ice texture. So far, two different approaches can be found. A classical model is based on the effective medium theory; the velocities are derived from elastic wave propagation in a homogeneous medium characterized by an average elasticity tensor. Alternatively, a velocity averaging approach was used in the glaciology community that averages the velocities from a given population of single crystals with different orientations. In this paper, we show that the velocity averaging method is erroneous in the present context. This is demonstrated for the case of waves propagating along the clustering direction of a highly textured polycrystal, characterized by crystallographic c axes oriented along a single maximum (cluster). In this case, two different shear wave velocities are obtained while a unique velocity is theoretically expected. While making use of this velocity averaging method, reference work by Bennett (1968) does not end with such an unphysical result. We show that this is due to the use of erroneous expressions for the shear wave velocities in a single crystal, as the starting point of the averaging process. Because of the weak elastic anisotropy of ice single crystal, the inversion of the measured velocities requires accurate modeling approaches. We demonstrate here that the inversion method based on the effective medium theory provides physically based results and should therefore be favored.

Two data evaluation concepts for X-ray stress analysis based on energy-dispersive diffraction on polycrystalline materials with cubic crystal structure, almost random crystallographic texture and strong single-crystal elastic anisotropy are subjected to comparative assessment. The aim is the study of the residual stress state in hard-to-reach measurement points, for which the sin2ψ method is not applicable due to beam shadowing at larger sample tilting. This makes the approaches attractive for stress analysis in engineering parts with complex shapes, for example. Both approaches are based on the assumption of a biaxial stress state within the irradiated sample volume. They exploit in different ways the elastic anisotropy of individual crystallites acting at the microscopic scale and the anisotropy imposed on the material by the near-surface stress state at the macroscopic scale. They therefore complement each other, in terms of both their preconditions and their results. The first approach is based on the evaluation of strain differences, which makes it less sensitive to variations in the strain-free lattice parameter a 0. Since it assumes a homogeneous stress state within the irradiated sample volume, it provides an average value of the in-plane stresses. The second approach exploits the sensitivity of the lattice strain to changes in a 0. Consequently, it assumes a homogeneous chemical composition but provides a stress profile within the information depth. Experimental examples from different fields in materials science, namely shot peening of austenitic steel and in situ stress analysis during welding, are presented to demonstrate the suitability of the proposed methods.

Various approaches are reviewed for determining elastic anisotropy and its coupling to crystallographic texture, with special reference to ultrasonic measurements. Two new methods are described for measuring the anisotropy of P-wave velocity using laser-ultrasonics. Making measurements across the diameter of a cylindrical specimen as it is rotated makes it possible to maintain a very constant known path length. This permits extremely accurate measurements with a precision of better than 0.01%. Results on 316 stainless steel in different conditions are compared with calculated values obtained from EBSD textures together with measured densities and crystalline coefficients from the literature. Excellent agreement is obtained when applying the Hill geometrical average procedure. A similar approach is adopted to measure the variation of wave velocity in a martensitic steel, after tempering at a range of temperatures. Changes in the anisotropy associated with thermal softening are discussed. The second method uses Galvano mirrors to steer the generating laser to different positions over a sheet surface, allowing wave velocities to be determined along different directions in the anisotropic material.

The mechanical behavior of soils has been traditionally described using continuum-mechanics-based models. These are empirical relations based on laboratory tests of soil specimens. The investigation of the soils at the grain scale using discrete element models has become possible in recent years. These models have provided valuable understanding of many micromechanical aspects of soil deformation. The aim of this work is to draw together these two approaches in the investigation of the plastic deformation of non-cohesive soils. A simple discrete element model has been used to evaluate the effect of anisotropy, force chains, and sliding contacts on different aspects of soil plasticity: dilatancy, shear bands, ratcheting etc. The discussion of these aspects raises important questions such as the width of shear bands, the origin of the stress-dilatancy relation, and the existence of a purely elastic regime in the deformation of granular materials.

The aim of the current study was to analyse the particle size distribution of a liposome dispersion, which contained small egg phosphatidylcholine vesicles and had been prepared by high-pressure homogenisation, by various size analysis techniques. Such liposomes were chosen since they can be looked at as a prototype of drug nano-carriers. Three sub-micron particle size analysis techniques were employed: (1) fixed-angle quasi-elastic laser light scattering or photon correlation spectroscopy (PCS), (2) size exclusion chromatographic (SEC) fractionation with subsequent (off-line) PCS size-analysis and quantification of the amount of particles present in the sub-fractions, and (3) field-flow-fractionation coupled on-line with a static light scattering and a refractive index (RI)-detector. When designing liposome-based drug carrier systems, a reliable and reproducible analysis of their size and size distribution is of paramount importance: Not only does liposome size influence the nanocarrier's in-vitro characteristics such as drug loading capacity, aggregation and sedimentation but also it is generally acknowledged that the pharmacokinetic behaviour and biodistribution of the carrier is strongly size-dependent. All three approaches of liposome size analysis used here were found to yield useful results, although they were not fully congruent. PCS indicated either a broad, mono-modal, log-normal size distribution in the range of below 20 to over 200 nm in diameter, or alternatively, a bimodal distribution with two discrete peaks at 30 to 70 nm and 100 to over 200 nm. Which of the two distribution models represented the best fit depended primarily on the data collection times used. In contrast, both fractionating techniques revealed a size distribution with a large, narrow peak well below 50 nm and a minor, broad, overlapping peak or tail extending to over 100 nm in diameter. The observed differences in liposome size distribution may be explained by the inherent limitations of the different size analysis techniques, such as the detection limit and the fact that PCS is overemphasizing bigger particle sizes.

An image contrast given in the scanning electron microscope(SEM) is due to differences in a detected number of secondary electrons (SE) coming from the specimen surface. The difference arises from the topographic, compositional and voltage features at the specimen surface. Two kinds of approaches have been taken for the quantification of SE images. One is to simulate electron trajectories in vacuum toward the detector, assuming the typical angular and energy distributions of electrons emitted from the specimen surface. However, the typical angular and energy distributions are not always applicable if a topographic or a compositional feature is present at the surface. The other is to simulate electron trajectory in the specimen. It is possible to obtain angular, energy, and spatial distributions of electrons emitted from the specimen surface. However, in order to discuss the SEM contrast based on these data, one has to assume that, for example, all slow electrons (<50eV) may be collected by the SE detector, or fast electrons ((>50eV) electrons may take a straight trajectory in the vacuum specimen chamber of the SEM. In a practical SEM picture of, for example, an etch-pit, different crystallographic plane surface shows different contrast even if the angle of the primary electron incidence toward all those surfaces is the same. This is because of the acceptance of the signal detection system. In a present study we combined two electron trajectory simulations mentioned above and calculated electron trajectories both in and out of the specimen, to simulate the trajectory from the point of the signal generated until the signal is detected.Although several simulation models of electron scatterings in a specimen have been reported to estimate the SE intensity at the surface, the model should be available to trace low energy (<50eV) electron trajectories. The model used here is basically the same as that reported in previous papers, and only a brief explanation is given in the following. Here, we made several assumptions as; [l]the energy loss of the primary and excited fast electrons is proportion to the number of SEs generated in the specimen, [2]the generated SE has an energy distribution as described by the Streitwolf equation, [3]the energy of the generated SEs are transferred to free electrons of the atom by the elastic-binary-collision, then one SE excited by the primary electron produces a ternary electron after the collision, and each one of the SE and the ternary electron produces higher order electrons in a cascade fashion. The simulation continues until the energy of each electron is less than the surface potential barrier. Angular and energy distributions and number of electrons emitted at the surface agree quite well with each experimental result in a typical case.

AbstractUncertainty quantification and reliability assessment for uniaxial tension of some hyper‐elastic material characterized by a few different constitutive equations is analyzed in this paper. The stretch of hyper‐elastic material is adopted as the Gaussian input with given expected value's range relevant to the experimentation and constant standard deviation. This goal is achieved with the use of the stochastic perturbation technique to calculate the first two probabilistic moments of the increasing tensile stress. Additionally, the Shannon probabilistic entropy fluctuations are determined for this test. Finally, reliability index is calculated using the stress‐based limit function and two reliability approaches–the First Order Reliability Method and the Bhattacharyya relative entropy.

Abstract The determination of the transverse tip deflection of an elastic, hollow, tapered, cantilever, box beam under a uniform loading applied over half the length of the beam presented in the V&V10.1 standard is used to compare the application of the validation procedures presented in the V&V10.1 and V&V20 standards. Both procedures aim to estimate the modeling error of the mathematical/computational model used in the simulations taking into account the variability of the modulus of elasticity of the material used in the beam and the rotational flexibility at the clamped end of the beam. The paper discusses the four steps of the two error quantification procedures: (1) characterization of the problem including all the assumptions and approximations made to obtain the experimental and simulation data; (2) selection of the validation variable; (3) determination of the different quantities required by the validation metrics in the two error quantification procedures; (4) outcome of the two validation procedures and its discussion. The paper also discusses the inclusion of experimental, input, and numerical uncertainties (assumed or demonstrated to be negligible in V&V10.1) in the two validation approaches. This simple exercise shows that different choices are made in the two alternative approaches, which lead to different ways of characterizing the modeling error. The topics of accuracy requirements and validation comparisons (model acceptance/rejection) for engineering applications are not addressed in this paper.

AbstractMany geoscientific problems require us to exploit synergies of experimental and numerical approaches, which in turn lead to questions regarding the significance of experimental details for validation of numerical codes. We report results of an interlaboratory comparison regarding experimental determination of mechanical and hydraulic properties of samples from five rock types, three sandstone varieties with porosities ranging from 5% to 20%, a marble, and a granite. The objective of this study was to build confidence in the participating laboratories’ testing approaches and to establish tractable standards for several physical properties of rocks. We addressed the issue of sample-to-sample variability by investigating the variability of basic physical properties of samples of a particular rock type and by performing repeat tests. Compressive strength of the different rock types spans an order of magnitude and shows close agreement between the laboratories. However, differences among stress–strain relations indicate that the external measurement of axial displacement and the determination of system stiffness require special attention, apparently more so than the external load measurement. Furthermore, post-failure behavior seems to exhibit some machine-dependence. The different methods used for the determination of hydraulic permeability, covering six orders of magnitude for the sample suite, yield differences in absolute values and pressure dependence for some rocks but not for others. The origin of the differences in permeability, in no case exceeding an order of magnitude, correlate with the compressive strength and potentially reflect a convolution of end plug–sample interaction, sample-to-sample variability, heterogeneity on sample scale, and/or anisotropy, the last two aspects are notably not accounted for by the applied evaluation procedures. Our study provides an extensive data set apt for “benchmarking” considerations, be it regarding new laboratory equipment or numerical modeling approaches.

AbstractIn this paper, we have investigated necking formability of anisotropic and tension-compression asymmetric metallic sheets subjected to in-plane loading paths ranging from plane strain tension to near equibiaxial tension. For that purpose, we have used three different approaches: a linear stability analysis, a nonlinear two-zone model and unit-cell finite element calculations. We have considered three materials –AZ31-Mg alloy, high purity α-titanium and OFHC copper– whose mechanical behavior is described with an elastic-plastic constitutive model with yielding defined by the CPB06 criterion (15) which includes specific features to account for the evolution of plastic orthotropy and strength differential effect with accumulated plastic deformation (48). From a methodological standpoint, the main novelty of this paper with respect to the recent work of N’souglo et al. (42) –which investigated materials with yielding described by the orthotropic criterion of Hill (24)– is the extension of both stability analysis and nonlinear two-zone model to consider anisotropic and tension-compression asymmetric materials with distortional hardening. The results obtained with the stability analysis and the nonlinear two-zone model show reasonable qualitative and quantitative agreement with forming limit diagrams calculated with the finite element simulations, for the three materials considered, and for a wide range of loading rates varying from quasi-static loading up to 40000 s− 1, which makes apparent the capacity of the theoretical models to capture the mechanisms which control necking formability of metallic materials with complex plastic behavior. Special mention deserves the nonlinear two-zone model, as it does not need prior calibration –unlike the stability analysis– and it yields accurate predictions that rarely deviate more than 10% from the results obtained with the unit-cell calculations.

La fabrication additive est une technique industrielle révolutionnaire qui suscite un intérêt croissant depuis la fin des années 80 et commence petit à petit à remplacer les procédés conventionnels de fabrication, et même à ouvrir des horizons sur la création de nouveaux types de matériaux.Cette importance lui est attribuée grâce à plusieurs spécificités, à savoir la possibilité presque infinie de construire des pièces avec des géométries complexes et la possibilité de mixer plusieurs types de poudres avec des compositions chimiques différentes pour obtenir des matériaux à propriétés bien déterminées selon l’application finale. Ces matériaux sont souvent appelés matériaux à gradation fonctionnelle (functionally graded materials). La fabrication additive permet même de construire des matériaux composites. Elle est à présent utilisée dans presque tous les domaines industriels : aérospatial, médical, automobile ainsi que celui des composants électroniques. L’extension de la fabrication additive aux alliages métalliques est encore plus récente. Au cours des vingt dernières années, de nombreux procédés de fabrication additive métallique ont été développés. On peut citer la fusion laser sur lit de poudre (appelée SLM ou L-PBF), la Construction Laser Additive Directe (CLAD), le frittage sélectif sous laser (SLS), etc. … Bien qu’elle soit une technique très prometteuse, la fabrication additive, surtout la métallique, reste encore mal maîtrisée. Un gros travail technologique a été réalisé pour optimiser les paramètres de fabrication et améliorer les propriétés, notamment mécaniques, des pièces produites. Pour pouvoir exploiter à fond les atouts de la technique, un important effort de recherche reste cependant à faire pour bien comprendre et contrôler les mécanismes fins mis en jeu par les procédés. En conséquence, la communauté scientifique est actuellement très active dans ce domaine et les publications très nombreuses. D’un point de vue métallurgique, deux points apparaissent primordiaux pour la tenue mécanique des pièces. D’une part la présence de porosités, en plus ou moins forte proportion, dans le matériau déposé, qui peut conduire à une diminution de sa résistance. D’autre part, la texturation cristalline inhérente au procédé utilisé, qui se traduit par un comportement mécanique anisotrope. Les travaux de cette thèse se situent dans ce contexte. Ils ont été menés dans le cadre d’une collaboration entre le LEM3 de Metz et le CEA-LIST de Saclay, intégrée dans un programme de recherche et d’innovation plus large liant le CEA-Tech de Lorraine et la Région Lorraine. Le CEA-LIST est spécialisé -entre autres- dans le développement de méthodes de contrôle non destructif (CND) pour détecter la présence de défauts dans des pièces métalliques. Le LEM3 a une compétence particulière dans la quantification et la compréhension des textures cristallines des alliages métalliques liées à leurs conditions d’élaboration. D’un point de vue scientifique, les objectifs de la thèse étaient doubles : d’une part améliorer notre compréhension de la genèse des textures cristallines lors du dépôt d’un alliage métallique par SLM ; d’autre part, évaluer les conséquences de ces textures sur la propagation des ondes ultrasonores utilisées classiquemen t en CND. D’un point de vue plus pratique, la question qui se posait en début de thèse était : l’anisotropie de propagation élastique des ultrasons liée à la texturation cristalline produite par le procédé SLM nécessite-t-elle de revoir le protocole de contrôle non destructif par ultrasons ?
Additive Manufacturing is a revolutionary industrial technique that has attracted increasing interest since the late 1980s and is gradually beginning to replace conventional manufacturing processes, and even to open horizons for the creation of new types of materials. This importance is attributed to it thanks to several specificities, namely the almost infinite possibility of building parts with complex geometries and the possibility of mixing several types of powders with different chemical compositions to obtain materials with well-defined properties depending on the final applications. These materials are often referred to as functionally graded materials. Additive manufacturing is even used to build composite materials. It is now used in almost all industrial fields: aerospace, medical, automotive and electronic components. The extension of additive manufacturing to metal alloys is even more recent. Over the past 20 years, many metal additive manufacturing processes have been developed. Examples include laser powder bed fusion (called SLM or L-PBF), direct additive laser construction (CLAD), selective laser sintering (SLS), etc... Although that it is a very promising technique, additive manufacturing, especially the metallic one, is still poorly controlled. Considerable technological work has been done to optimise the manufacturing parameters and improve the properties, particularly mechanical ones, of the parts produced. However, to fully use the advantages of the technique, a major research effort remains to be made to fully understand and control the fine mechanisms involved in the processes. As a result, the scientific community is currently very active in this field and the publications are very numerous. From a metallurgical point of view, two points seem to be important for the mechanical strength of the parts. On one hand, the presence of porosities, in a greater or lesser proportion, in the deposited material, which can le ad to a decrease in its resistance. On the other hand, the crystalline texturing inherent in the process used, which results in an anisotropic mechanical behaviour. The work of this thesis is in this context. It was conducted as part of a collaboration between the LEM3 in Metz and CEA-LIST in Saclay, integrated within a wider program of research and innovation joining CEA-Tech Lorraine and the Region of Lorraine. The CEA-LIST is specialized -among other things- in the development of non-destructive control methods (NDT) to detect the presence of defects in metal parts. LEM3 has particular competence in quantifying and understanding the crystalline textures of metal alloys related to their elaboration conditions. From a scientific point of view, the objectives of the thesis were twofold: on the one hand, our objective was to improve our understanding of the genesis of crystalline textures during the deposit of a metal alloy by SLM; On the other hand, we aim to evaluate the consequenc es of these textures on the propagation of the ultrasound waves which are traditionally used in CND. From a more practical point of view, the question that arose at the beginning of the thesis was: does the elastic anisotropy of propagation of ultrasound linked to the crystalline texturing produced by the SLM process require a review of the protocol of non-destructive control by ultrasound?

ABSTRACT: Westerly granite (WG) is well known rock, believed to be isotropic. We studied four samples of WG heated between 100°C and 600°C, by ultrasonic sounding on spherical samples under hydrostatic pressure up to 400 MPa, neutron diffraction on identical samples and scanning electron microscopy (SEM). Thermal treatment studies are important for localities like nuclear waste storages, geothermal projects, rock and earthquake mechanics. All measurements were done at room temperature. The 3D distribution of P-wave velocities at high pressures reflects intrinsic structure and even though the anisotropy is low, the orientation of the minimum velocity corresponds to the highly preferred orientation of plagioclase (010) and biotite (001). Image analyses showed that there is also preferred orientation of microcracks regardless of their size and thermal treatment level. Neutron diffraction measurements of the samples heated to 100°C and 600°C confirm weak intrinsic elastic anisotropy, which remain unchanged due to the thermal treatment. We can assume that in Westerly granite there are two types of anisotropy: crystal preferred orientation which was formed during igneous crystallization and second one is due to the oriented microcracks which have been formed during tectonic exhumation or during sample excavation in the quarry. Both seems to be unrelated. 1. INTRODUCTION Westerly granite has been studied for decades and its properties are very well known. There were studied mechanical properties, elastic properties, development of cracks introduced by uniaxial or triaxial loading, thermal heating, study of permeability, study of fracturing process by acoustic emission, modelling of crack systems and plenty of others. Westerly granite is considered as fine grained, homogeneous material, isotropic and therefore it is often discussed or even used as a standard for comparison with other granitic rocks. Quantification of elastic properties of granites is important to determine crustal seismic velocities and stress orientation. Generally, it is assumed that granitic rocks are elastically isotropic. In this paper, we study influence of thermal cracks and crack induced anisotropy on P-wave propagation in spherical samples of Westerly granite at different confining pressures. Experimental elastic wave velocity distributions in Westerly granite are compared to the model based on neutron diffraction data on mineral composition and mineral preferred orientations. Due to high penetration depth of thermal neutrons, information on a large representative volume of geomaterial is obtained; and the method of neutron diffraction allows to investigate same bulk samples that were used for elastic wave propagation study. Thus, ultrasonic sounding (US) and neutron diffraction form a pair of complementary methods suitable for in-depth analysis of elastic anisotropy of rocks.

Abstract Coal geomechanical properties are of importance in various applications, including drilling in coal seams, ensuring long-term borehole stability, and predicting the permeability evolution in coal seam gas reservoirs. However, coal is highly cleated and fragile. Obtaining standard drill cores for the laboratory test becomes exceptionally challenging. Also, the anisotropic characterizations of coal mechanical properties are often overlooked despite being essential in understanding directional drilling to increase gas production. In this study, nanoindentation tests were conducted to investigate the anisotropic nanomechanical properties of coal macerals and then the nano-scale data was used to predict the corresponding macroscopic mechanical properties. Overall, 900 indents were made on three types of coal polished surfaces perpendicular to the bedding plane, face, and butt cleats, respectively. The load-displacement curves obtained from the nanoindentation tests were used to calculate the elastic modulus and hardness. We then employed the dilute and Mori-Tanaka homogenization schemes to upscale the nano-scale results. To validate our findings, we compared our predicted values with the results obtained from direct laboratory measurements across different scales. According to the nanoindentation tests, the averaged elastic modulus is 5.89 GPa, 5.75 GPa, and 5.11 GPa, for the directions perpendicular to the bedding (Z), face cleats (Y), and butt cleats (X), respectively. Three coal macerals are identified. The elastic modulus of vitrinite is averaged as 4.55 GPa, 4.75 GPa, and 4.58 GPa for Z, Y, and X directions, respectively. For liptinite and inertinite, their elastic moduli are 4.35 GPa, 4.70 GPa, and 4.24 GPa, as well as 8.76 GPa, 7.80 GPa, and 6.51 GPa, respectively. It was observed that the elastic modulus of inertinite was anisotropic, with the measurement perpendicular to the bedding plane being greater than in the two directions parallel to the bedding plane. There was, however, no significant anisotropy identified for vitrinite and liptinite. This work provides direct measurements of the anisotropic mechanical properties of coal at the nano-scale, and establishes a correlation among the elastic modulus at different scales, especially at the nano-scale. By estimating the coal's mechanical properties from measurements on smaller samples, we provide an alternative approach to understanding the bulk anisotropic features of coals, which benefits various operations, especially directional drilling and permeability.