Chapter 2 contains the continuum mechanical notions for the description of the plastic behavior of sheet metal under large deformations at room temperature. As such, it includes the kinematics of a continuum body, strain and stress definitions, and a general elasto-plastic constitutive model description. This last point is complemented by the definition of anisotropy, as well as the description of some yield criteria and hardening laws. Next, Chapter 3 defines the stress strain states required to be experimentally reproduced in order to describe the initial yield locus and its displacement in the stress axis representation during plastic deformation. A review of the available experimental equipment capable of reproducing the required stress strain states is presented in order to choose the best for further construction. After consideration, those deemed the highest performing are the Miyauchi device, able to perform simple shear tests and the bi-axial testing machine, able to perform plane strain and simple shear tests separately or simultaneously. This chapter presents the mechanical features of the Miyauchi device and the bi-axial test machine that were built at the M&S Laboratory, followed by a description of the optical strain gauge chosen that allows the computation of the strain field throughout the specimens deformation area. Chapter 4 focuses on the validation of the experimental equipment. First, the homogeneity of the stress and strain fields is verified. Then, the availability of performing the plane strain, simple shear, Bauschinger and orthogonal tests is checked. The repeatability (precision) of the tests is corroborated and the accuracy is validated by comparison with finite elements simulations. In Chapter 5, the identification methods are proposed and DC06 (0,8mm thick), DP1000 (1,6mm thick) and S320GD (0,69mm thick) steels are identified according to those methods. The initial yield surface for DC06 is identified by two methods (one using the strain measurements, the other using stress measurements) for two yield criteria, which are then compared with a texture-based yield criterion and the experimental points. The initial yield surface for the other two materials is described by the Hill 1948 yield criterion identified using strain measurements. The yield surface evolution (hardening) for DC06 and S320GD is described by the Teodosiu and Hu hardening law due to the observed mechanical behavior, i.e., the Bauschinger effect and strong influence of the pre-strain when strain-path changes take place. DP1000 exhibits a high Bauschinger effect and its flow stress is not influenced by the amount of pre-strain when reversing the load; hence, its behavior is described by a kinematic hardening law. Finally, in Chapter 6, conclusions about the present work are established and equipment improvement and further topics for research are proposed, namely, the study of texture evolution, the material axis rotation and the experimental validation of new yield criteria.

No description available.

This thesis is concerned with the theoretical and computational aspects of generating solutions to problems involving materials with fading memory, known as viscoelastic materials. Viscoelastic materials can be loosely described as those whose current stress configuration depends on their recent past. Viscoelastic constitutive laws for stress typically take the form of a sum of an instantaneous response term and an integral over their past responses. Such laws are called hereditary integral constitutive laws. The main purpose of this study is to analyse adaptive finite element algorithms for the numerical solution of the quasistatic equations governing the small displacement of a viscoelastic body subjected to prescribed body forces and tractions. Such algorithms for the hereditary integral formulation have appeared in the literature. However the approach here is to consider an equivalent formulation based on the introduction of a set of unobservable interval variables. In the linear viscoelastic case we exploit the structure of the quasistatic problem to remove the displacement from the equations governing the internal variables. This results in an elliptic problem with right hand side dependent on the internal variables, and a separate independent system of ordinary differential equations in a Hilbert space. We consider a continuous in space and time Galerkin finite element approximation to the reformulated problem for which we derive optimal order a priori error estimates. We then apply the techniques of the theory of adaptive finite element methods for elliptic boundary value problems and ordinary differential equations, deriving reliable and efficient a posteriori error estimates and detailing adaptive algorithms. We consider the idea of splitting the error into space and time portions and present results regarding a splitting for space time projections. The ideas for splitting the error in projections is applied to the finite element approximation and a further set of a posteriori error estimates derived. Numerical studies confirm the theoretical properties of all of the estimators and we show how they can be used to drive adaptive in space and time solution algorithms. We consider the extension of our results for the linear case to the constitutively nonlinear case. A model problem is formulated and the general techniques for dealing with a posterior error estimation for nonlinear space time problems are considered.

La présente étude vise à comprendre le comportement chimico-hydro-mécanique des argiles raides à travers deux formations géologiques, l'argile de Boom et les argiles yprésiennes, qui sont censées être des formations hôtes potentielles pour le stockage de déchets radioactifs en Belgique. Le comportement volumique a été étudié tant à l'état intact qu'à l'état reconstitué, et sous différentes conditions : K0 et isotrope, sous des boucles de chargement - déchargement. Les résultats obtenus montrent que le comportement volumique de ces argiles est gouverné par la compétition entre l'effet physico-chimique et l'effet mécanique, caractérisée par une contrainte seuil qui correspond à la contrainte de gonflement en termes de changements de structure. Une loi de comportement volumique a été ainsi développée afin de décrire cet aspect. La perméabilité a été déterminée, comparée avec les résultats dans la littérature et corrélée avec les paramètres comme l'indice des vides. La variation de la perméabilité avec la profondeur ont mis en évidence le rôle déterminant des macro-pores dans le transfert des fluides. Le comportement volumique et la perméabilité des argiles de Boom et yprésiennes intactes sont aussi influencés par la variation de la composition chimique de l'eau de pore, qui modifie la double couche diffuse et favorise l'agrégation des particules argileuses. Les caractéristiques élastiques, la surface de charge et l'enveloppe de rupture ont été identifiées pour le comportement déviatorique des argiles de Boom et yprésiennes. Un modèle élasto-plastique conceptuel a été développé permettant de tenir compte des effets du gonflement et de la compétition entre l'effet mécanique et l'effet physico-chimique / The present research aims to understand the chemo-hydro-mechanical behavior of stiff clays through two geological formations, the Boom Clay and the ypresian clays which are considered as possible host formations for the radioactive wastes disposal in Belgium. The volume change behavior was studied in both intact and reconstituted states, and under different conditions: under K0 and isotropic loading, under loading/unloading loops. The results show that the volume change behavior is governed by the competition between the physico-chemical effect and the mechanical effect, characterized by a threshold stress which corresponds to the swelling stress in terms of structure changes. A constitutive law was developed to capture this aspect. The permeability was determined, compared with the results in literature and correlated with the parameters as void ratio. The permeability variation with depth shows the important role of macro-pores in fluids' transfer. The volume change behavior and permeability of intact Boom Clay and ypresian clays are also influenced by pore water chemical composition changes which modify the diffuse double layer and give rise to the aggregation of clay particles. The elastic parameters, yield curve and failure envelope of Boom Clay and ypresian clays were identified. A conceptual elasto-plastic model was developed, accounting for the swelling effects and the competition between the physico-chemical effect and the mechanical effect

Les travaux de cette thèse se sont intéressés à l’obtention du comportement d’un composite sergé 2x2 verre/PA66 via un outil numérique basé sur une double homogénéisation : la première concerne les torons et la seconde le volume élémentaire représentatif du composite. A partir d’une campagne de caractérisation expérimentale sur le PA66, nous avons dans un premier temps identifié l’influence à la fois de l’hygrométrie et de la température sur le comportement de la matrice en quasi-statique. Ensuite, nous avons élaboré, implémenté et validé une loi de comportement isotrope élasto-plastique endommageable. Cette loi a servi à identifier par homogénéisation le comportement des torons en supposant un collage parfait des fibres et de la matrice ainsi qu’une homogénéité de l’eau dans le toron. Grâce à ces comportements identifiés et à l’élaboration d’une loi de comportement anisotrope élasto-plastique endommageable, nous avons pu déterminer les caractéristiques élastiques dans un premier temps et les comportements longitudinaux et en cisaillement dans un second temps. Les comparaisons aux résultats expérimentaux menés sur le composite offrent des résultats satisfaisants et permettent de penser que l’outil numérique développé, permettrait, à termes, d’aider à une conception rapide incluant ce genre de matériau en diminuant le nombre d’essais expérimentaux à faire. Des perspectives enfin sont proposées notamment pour l’extension aux comportements en dynamique (crash). / The objective of this PhD thesis is to create a methodology to simulate the behavior of a 2x2 glass/PA66 twill composite using homogenization. To achieve this goal, we use two steps: first one is dedicated to represent the yarn behavior and the second one to represent the behavior of the composite RVE. An experimental characterization campaign about the PA66 has been done in order to quantify the influence of both hygrometry and temperature on the behavior of the matrix in quasi-static. Then, we formulated, implemented and validated an isotropic elasto-plastic damageable constitutive law. It was used to identify by homogenization the behavior of the yarns by assuming a perfect bonding of the fibers and the matrix as well as a water homogeneity inside the yarn. Thanks to the identified behavior of the yarns and by formulating a compatible constitutive law (anisotropic elasto-plastic damageable), we have determined for the woven composite on one hand the elastic properties and in the other hand the longitudinal/transversal and shear nonlinear behaviors. The comparisons of the numerical and experimental results offer satisfactory results. It provides good outlook in short-term in regard of structures design which include this type of woven composite materials. The main advantage of the methodology is to decrease the number of required experimental tests. Some outlook dedicated to crash studies are finally suggested.

Accurate three-dimensional stress-strain constitutive properties are essential to understanding complex deformation and failure mechanisms for materials with highly anisotropic mechanical properties. The large number of different methods and specimen types currently required to generate three-dimensional allowables for structural design slow down the material characterization. Also, some of the material constitutive properties are never measured due to prohibitive cost of the specimens needed. A method for measurement of three-dimensional constitutive properties using short-beam specimens subject to three-point bend load has been recently developed. This method is based on the Digital Image Correlation (DIC) full-field deformation measurement and closed-form stress approximation. The purpose of this work is to improve the accuracy of the constitutive properties through accurate stress solution. A method is developed based on a combination of full-field strain measurement and nonlinear finite element stress analysis in the material characterization. The nonlinear shear stress-strain relations are the major concern in this work. An iterative procedure is applied to update the nonlinear shear properties using iterative finite element simulations. The accuracy of the numerical procedure is verified by comparing the finite element strain results with full-field measurements. The procedure is further verified using the V-notched beam test results. Excellent agreement has been achieved in the verification. Simplicity of the short-beam specimens and accuracy of the constitutive property approximations make the present method attractive for measurement of three-dimensional stress-strain relations for anisotropic materials at various load rates.

L’augmentation de la puissance électrique consommée à bord des avions a récemment conduit à introduire des convertisseurs électroniques de puissance à base d'interrupteurs à IGBT dans de nombreuses applications aéronautiques. L'utilisation de ces interrupteurs diffère de leurs emplois traditionnels dans les domaines du ferroviaire ou de l'automobile. En effet, les sollicitations environnementales ainsi que les cycles de commandes électriques sont différents de ceux rencontrés jusqu’alors, ce qui amène à remettre en cause les résultats actuels au sujet de la durée de vie et de la fiabilité de ces interrupteurs. Face à ces interrogations, les sociétés THALES et Hispano-Suiza se sont associées au sein du programme de l’avion plus électrique MODERNE (MODular ElectRical NEtwork) initié par Airbus, en vue de développer des solutions à haut niveau de fiabilité pour des applications aéronautiques sévères. C’est dans ce contexte que prennent place les présents travaux, dont les objectifs sont dans un premier temps de proposer de nouvelles architectures de modules susceptibles de présenter de meilleures performances d’intégration, et dans un second temps d’en étudier la fiabilité. Pour répondre à ces questions, un état de l'art des technologies utilisables a été mené. La confrontation de ses technologies aux contraintes et recommandations aéronautiques a conduit au choix de deux approches d'assemblage, proposées avec un jeu de matériaux sélectionnés pour leurs propriétés physiques et en conformité avec les réglementations sur l’utilisation de matériaux polluants. À l'issue d'une analyse de défaillances, différents développements ont été conduits afin de modéliser et caractériser le comportement thermique, mécanique puis à défaillance des modules. Des modèles Éléments Finis de structures représentatives des solutions proposées ont alors été mis au point et exploités pour l'élaboration de règles de conception, sur la base de plans d'expériences couplés à de la simulation numériques. Les informations générées ont servi à la conception de trois prototypes destinés à des applications différentes. Les performances de ces prototypes ont été évaluées, notamment leurs fiabilités obtenues par des calculs mécano-fiabilistes ayant permis l'optimisation de la conception des différents modules. / Within the framework of the electric plane programs, the aircraft industry is facing higher demands of electric power, fact which involves an increasing use of IGBT modules in aeronautical power converters. Although such modules have been well studied and known in railway and the automotive domains, they will be subjected to stresses and operational cycles specific to the aeronautical environment. Consequently, this requires manufacturers to answer some questions about their lifetime and reliability issues. Faced with these questions, THALES and Hispano-Suiza have associated in the more electric aircraft project launched by Airbus (MODERNE - MODular ElectRical NEtwork), with the aim of developing high reliability solutions for harsh aeronautic applications. This work takes place in this context, with the objectives of proposing power modules architectures likely to exhibit better performances and integration level, and then study the reliability of different prototypes. To answer these questions, technological studies of the possible packaging and connecting solutions, faced with aeronautical stresses and requirements led to the choice of two basic assembling approaches. A set of materials selected for their physical properties and their compliance with polluting materials regulations was also proposed. The potential failure modes of these solutions were pointed out and taken into account within experimental and numerical developments, to model and characterize the thermal, mechanical and failure behaviour of the modules. Then, different Finite Element models representative of the proposed technologies structures were developed and investigated for defining design rules on the basis of Designs of Experiments. The whole knowledge generated by the simulations was used to design three prototypes of IGBT module for different applications. The performance of these prototypes have been evaluated and compared to the requirements, including their reliability obtained by mechanical calculations coupled with probabilistic methods which led to their optimization.

Les propriétés des polymères sont intéressantes pour des applications pneumatiques, de verres organiques, de joints, … Leurs propriétés mécaniques sont néanmoins mal comprises. Dans ce manuscrit, le comportement mécanique du PMMA et du CR39 est étudié en fonction du temps.Il en résulte des courbes maîtresses à partir d’expérience de relaxation de contrainte et de fluage d’indentation. D'autre part, le comportement mécanique au contact est analysé sur des expériences de fluage et recouvrance d’indentation et de rayures analysées pour la première fois dans cette thèse. Finalement, des lois de comportements sont construites, leurs précisions sont comparées grâce à des calculs par éléments finis aux expériences en contact. / Polymer's low weight, deformability and easy manufacturing make them attractive materials for tire, organic glasses, sealing applications … Their mechanical properties are nonetheless poorly understood. In particular, two fields are searched over this thesis: time dependency and contact behavior for two transparent polymer: PMMA and CR39. The mechanical behavior time dependency is observed by the construction of stress relaxation and contact master curves. The mechanical contact behavior is analyzed by indentation creep and recovery experiments. Moreover the immediate scratch recovery is measured in the thesis. Finally, the uniaxial data is used to build constitutive laws, which accuracy is compared by Finite Element Modeling to contact tests.

Synthetic vascular grafts are useful to bypass diseased arteries. The long-term failure of synthetic grafts is primarily due to intimal hyperplasia at the anastomotic sites. The accelerated intimal hyperplasia may stem from a compliance mismatch between the host artery and the graft since commercially available synthetic conduits are much stiffer than an artery. The objective of this thesis is to design a method for fabricating a vascular graft that mechanically matches the patients native artery over the expected physiologic range of pressures. The creation of an optimized mechanical graft will hopefully lead to an improvement in patency rates. The mechanical equivalency between the graft and the host artery is defined locally by several criteria including the diameter upon inflation, the elasticity at mean pressure, and axial force. A single parameter mathematical for a thin-walled tube is used to describe of the final mechanical behavior of a synthetic graft. For the general problem, the objective would be to fabricate a mechanics-matching vascular graft for each host artery. Typically, fabrication parameters are set initially and the properties of the fabricated graft are measured. However, by modeling the entire fabrication process and final mechanical properties, it is possible to invert the situation and let the typical output mechanical values be used to define the fabrication parameters. The resultant fabricated graft will then be mechanically matching. As a proof-of-concept, several prototype synthetic grafts were manufactured and characterized by a single Invariant to match a canine artery. The resultant graft equaled the diameter upon inflation, the elasticity at mean pressure, and axial force of the native canine artery within 6%. An alternative to making an individual graft for each artery is also presented. A surgeon may choose the best graft from a set of pre-manufactured grafts, using a computer program algorithm for best fit using two parameters in a neighborhood. The design optimization problem was solved for both canine carotid and human coronary arteries. In conclusion, the overall process of design, fabrication and selection of a mechanics matching synthetic vascular graft is shown to be reliable and robust.