Couplage thermomécanique et approche non entière de l'irréversibilité en viscoélasticité

A. Oustaloup (Pr - Président), A. Le Méhauté (Docteur d'Etat -Rapporteur), A. Chrysochoos (Pr - Rapporteur), A. Galtier (Ingénieur de Recherche –Arcelor-IRSID), S. André (MdC), C. Cunat (Pr)This report is about the elaboration of constitutive viscoelastic relations in rheology of solids which are consistant in thermodynamics. The DNLR strategy (Distribution of Non-Linear Relaxation) based on the thermodynamics of irreversible processes will be used. The first section of this study is considering the viscoelastic relaxation. The theory of fluctuations and the concept of equipartition of produced entropy is governing the writing of the DNLR Relaxation spectra. The irreversible process is described by a self similar representation. Its recursive proprieties will allow to establish the relation between DNLR approach and rheological models with fractional derivative. The second section analyzes the thermomecanic coupling terms and developes a modelisation of thermic transferts in a sample which is subjected to mechanical loadings. The 1D analytical calculations will be valided with finites elements simulations. After a description of the experimental non intrusive set-up composed by an infrared mono-detector to mesure temperature and a videotraction system for strain measurement, the last section will present a first validation of our modelisation, rising experimental data coming from a S355 steel subjected to mechanical cyclic loadings. The main interest of this part is to present an exemple of a coherent strategy for the thermomechanical characterization of a material.Ce mémoire concerne l'élaboration de lois constitutives viscoélastiques en rhéologie des solides qui sont consistantes sur le plan thermodynamique. On utilise la stratégie DNLR (Distribution of Non-Linear Relaxation) basée sur la Thermodynamique des Processus Irréversibles à variables internes. La première partie s'intéresse à la relaxation viscoélastique. La théorie des fluctuations et le concept d'équipartition de l'entropie produite régissent l'écriture du spectre de relaxation DNLR. L'irréversibilité est décrite par un schéma auto-similaire dont les propriétés récursives permettent de faire le lien entre l'approche DNLR et les modèles rhéologiques à dérivées non entières. La seconde partie analyse les différents termes associés aux couplages thermomécaniques et développe une modélisation des transferts thermiques dans une éprouvette soumise à des sollicitations mécaniques. Une simulation par éléments finis permet de valider le calcul analytique 1D. Enfin après avoir décrit le protocole expérimental mis en place (basé sur la combinaison d'un système de mesure non intrusif de déformation [vidéo-traction] et de température [mono-détecteur infrarouge]), la dernière partie propose une première validation du modèle à partir de données expérimentales obtenues sur une nuance d'acier S355 soumis à des essais mécaniques cycliques. Cette étude a surtout valeur d'exemple pour une stratégie de caractérisation cohérente d'un matériau sur le plan thermomécaniqu

Couplage thermomécanique et approche non entière de l'irréversibilité en viscoélasticité

NANCY-INPL-Bib. électronique (545479901) / SudocSudocFranceF

Thermoformage du verre (développement numérique d'un modèle thermomécanique)

Ce travail de thèse est dédié à la modélisation du thermoformage du verre. Le procédé consiste à déformer une plaque de verre sous l'effet de son propre poids. Posée sur un support et placée dans un four, la température de la pièce augmente et sa viscosité diminue, ce qui permet d'obtenir la forme désirée. Les simulations numériques, qui se basent sur un modèle thermomécanique, doivent permettre de mieux comprendre l'influence, sur le produit final, des différents paramètres d'essai, comme le chargement thermique, la géométrie et le matériau du moule ou encore la forme initiale de la pièce. Pour ce faire, le logiciel commercial Abaqus®, qui utilise une méthode de résolution des calculs par éléments finis, prend en charge les aspects mécaniques et conductifs. En revanche, comme le verre est un milieu semi-transparent, la modélisation du transfert radiatif est complexe et nécessite le développement d'un code se basant sur une méthode de Monte Carlo dite réciproque. La méthode a été validée en deux dimensions sur des cas-tests de la littérature scientifique. Le code a ensuite été implémenté dans le logiciel Abaqus® afin de réaliser des simulations de thermoformage sur moule et en suspension. Le verre est considéré comme un matériau élasto-visco-plastique obéissant à un modèle de Maxwell simple et la thermodépendance de la viscosité est prise en compte par une loi WLF. Une attention particulière a été accordée au modèle radiatif. Différentes hypothèses, issues de la littérature scientifique, sont testées afin de vérifier leur validité dans notre cas d'étudeThis dissertation is dedicated to the modelling of the glass sagging process. This operation consists in forming a sheet or a plate of glass by heating it in a furnace. Glass temperature rises and reaches a work temperature at which viscosity is low enough to allow glass to sag under its own weight due to gravity. Numerical simulation, based on a thermomechanical model, can help to better understand the influence of the different parameters on the final product, such as the thermal loading, the shape and material of the mould or even the initial geometry of the glass plate. Thus, the commercial software Abaqus® is used to solve the problem by a finite elements method. However, it cannot render the complexity of the radiative heat transfer in glass. So, a Monte Carlo code based on a reciprocal method was developed and validated using benchmarks from the scientific literature. Then, the code was implemented into Abaqus® in order to simulate glass sagging on a mould or glass forming by the draping process. Glass is considered as an elasto-viscoplastic material which obeys a Maxwell model. Viscosity is dependant to temperature according to a WLF law. Special care was devoted to the radiative heat transfer. Different hypothesis are reviewed and performed to check their validity when applied to our numerical set-upNANCY-INPL-Bib. électronique (545479901) / SudocSudocFranceF

Influence of the fiber/matrix strength on the mechanical properties of a glass fiber/thermoplastic-matrix plain weave fabric composite

International audienceIn this work, we analyze the influence of different fiber surface treatments on the mechanical properties of plain weave composites. The reinforcement is a glass fibers fabric and the matrix is an acrylic polymer. Until very recently, this thermoplastic polymer family was not used in composite industry. It is therefore necessary to study if the existing fiber surface treatments are suitable for acrylic resins or if new ones have to be found. At the macroscale, composite materials corresponding to different fiber surface treatments were characterized with: (i) monotonic in-plane shear tests and (ii) heat-build up fatigue measurements on specimens with +/- 45 degrees fiber orientations with respect to the tensile force. At the mespscale (fabric scale), the development of damage was experimentally analyzed from (i) 3-D DIC (Digital Image Correlation) full-field strain measurements with spatial resolution smaller than the textile repeating unit and (ii) X-ray microtomography. We show that the analyzed composite materials exhibit linear viscoelastic behavior until a given stress threshold above which damage develops in the material. It was also found that the application on the fibers of a coupling agent specifically developed for promoting the bond between glass fibers and acrylic resins improves the composite mechanical properties, in particular the fatigue properties

Finite element simulation of the slumping process of a glass plate using 3D generalized viscoelastic Maxwell model

International audienceGlass slumping process is widely developed toward several industrial applications and also for high-technology uses. It is however difficult to properly predict the glass behavior during the forming process using numerical methods. This study aims at better understanding some of the issues related to finite element modeling of the slumping process. A numerical implementation of the generalized Maxwell model (GMM) is performed to reproduce the 3D viscoelastic behavior of a soda-lime-silica glass plate during the process. The material routine is first verified against experimental and analytical quasistatic isothermal creep recovery tests. Then, FE simulations of glass slumping reveal two important points: for the so-called sag-bending process, the simple Maxwell rheological model is sufficient to take into account the deviatoric part of the glass behavior, whereas a Zener model is required for the bulk behavior. However, in the Drop-Ring-Glass-Slumping application, working with a simple Maxwell or the 6 arms GMM does not give the same results. The applied severe contact condition or the fact that axisymmetric simulation is retained could be the origin of this discrepancy

Identification Of The True Elastic Modulus Of High Density Polyethylene From Tensile Tests Using An Appropriate Reduced Model Of The Elastoviscoplastic Behavior

43pagesThe rheological parameters of materials are determined in the industry according to international standards established generally on the basis of widespread techniques and robust methods of estimation. Concerning solid polymers and the determination of Young's modulus in tensile tests, ISO 527-1 or ASTM D638 standards rely on protocols with poor scientific content: the determination of the slope of conventionally defined straight lines fitted to stress-strain curves in a given range of elongations. This paper describes the approach allowing for a correct measurement of the instantaneous elastic modulus of polymers in a tensile test. It is based on the use of an appropriate reduced model to describe the behavior of the material. The model comes a thermodynamical framework and allows to reproduce the behavior of an HDPE Polymer until large strains, covering the elastoviscoplastic and hardening regimes. Well-established principles of parameter estimation in engineering science are used to found the identification procedure. It will be shown that three parameters only are necessary to model experimental tensile signals: the instantaneous ('Young's') modulus, the maximum relaxation time of a linear distribution (described with a universal shape) and a strain hardening modulus to describe the 'relaxed' state. The paper ends with an assessment of the methodology. Our results of instantaneous modulus measurements are compared with those obtained with other physical experiments operating at different temporal and length scales

Advantages of a 3-parameter reduced constitutive model for the measurement of polymers elastic modulus using tensile tests

International audienceExact measurements of the rheological parameters of time-dependent materials are crucial to improve our understanding of their intimate relation to the internal bulk microstructure. Concerning solid polymers and the apparently simple determination of Young’s modulus in tensile tests, international standards rely on basic protocols that are known to lead to erroneous values. This paper describes an approach allowing a correct measurement of the instantaneous elastic modulus of polymers by a tensile test. It is based on the use of an appropriate reduced model to describe the behavior of the material up to great strains, together with well-established principles of parameter estimation in engineering science. These principles are objective tools that are used to determine which parameters of a model can be correctly identified according to the informational content of a given data set. The assessment of the methodology and of the measurements is accomplished by comparing the results with those obtained from two other physical experiments, probing the material response at small temporal and length scales, namely, ultrasound measurements with excitation at 5 MHz and modulated nanoindentation tests over a few nanometers of amplitude

Glass sagging simulation with improved calculation of radiative heat transfer by the optimized reciprocity Monte Carlo method

International audienceGlass sagging is used to process glass industrial products such as windscreens, mirrors or lenses. A 2D glass sagging process, simulated with the Finite Element Method (FEM), is presented in this work. Different thermal cases are reviewed with special care brought to radiative transfer model, with an optimized reciprocity Monte Carlo method used as the reference. Results show that ignoring radiative transfer is a too rough hypothesis. This leads to large errors on the glass temperature distribution, on the forming process and on the final shape in case of glass sagging without mold. However, predefining glass temperature or using Rosseland approximation give acceptable results, less accurate than Monte Carlo simulations especially for a fine prediction of the transfer as a function of time, but with smaller CPU times