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Refractory masonry with dry joints is widely used in the steel-making industry for the linings of several high-temperature components (>1500 ∘ C) including steel ladles and furnaces. To properly optimize the design and performance of these linings, thorough numerical models that consider the presence of joints, joints closure and reopening and the nonlinear elastic-viscoplastic behaviour (creep and stress relaxation) of refractories at high temperature are required. The present study reports on the formulation, numerical implementation, and application of a homogenized multi-scale elastic-viscoplastic model for the simulation of refractory masonry linings with dry joints. Refractory bricks are considered to exhibit linear elasticity as well as rate-dependent plasticity. Four joint patterns are predefined based on the state of bed and head joints. The homogenized elastic-viscoplastic behaviour of each joint pattern is determined using finite element based nonlinear homogenization approach. The transition criteria between the four patterns are defined in terms of macroscopic stresses and strains. Verification of the developed homogenized constitutive laws is carried out by comparing the numerical results of the detailed micro models (brick and joints are considered) with the homogeneous equivalent material models. Furthermore, comparisons with experimental results of refractory masonry walls subjected to biaxial compression load at room and high temperature are carried out. Good agreements between the experimental and numerical results are obtained. Then, the validated models are employed to predict the mechanical behavior of refractory masonry structures subjected to different loading conditions. The present numerical model is able to simulate the orthotropic, compressible, rate-dependent homogenized behaviour of mortarless refractory masonry structures, and accounts for joints closure and reopening due to loading and unloading.

The interface between bricks and mortar is often the weakest part of masonry structures. For refractory linings, the interface strength must be measured at high temperature. Adapted slant shear tests and a new dedicated tensile test set up are proposed here for this purpose. To test the ability of the proposed method, it was applied on two representative brick/mortar couples from room temperature up to 1450 °C. Slant shear tests were conducted to measure ultimate compression and shear stresses and to identify temperature dependent parameters of the Mohr-Coulomb failure criterion. Tensile tests were performed to identify the tensile cut-off. Depending on the brick/mortar couples, the failure can appear at the interface or in the mortar. Cohesion and tensile strength decrease sharply over 900 °C.

International audience; Mortarless refractory masonry structures are widely used in the steel industry for the linings of many high-temperature industrial applications including steel ladles. The design and optimization of these components require accurate numerical models that consider the presence of joints, as well as joint closure and opening due to cyclic heating and cooling. The present work reports on the formulation, numerical implementation, validation, and application of homogenized numerical models for the simulation of refractory masonry structures with dry joints. The validated constitutive model has been used to simulate a steel ladle and analyze its transient thermomechanical behavior during a typical thermal cycle of a steel ladle. A 3D solution domain and enhanced thermal and mechanical boundary conditions have been used. Parametric studies to investigate the impact of joint thickness on the thermomechanical response of the ladle have been carried out. The results clearly demonstrate that the thermomechanical behavior of mortarless masonry is orthotropic and nonlinear due to the gradual closure and reopening of the joints with the increase and decrease in temperature. In addition, resulting thermal stresses increase with the increase in temperature and decrease with the increase in joint thickness.

International audience

International audience; Mortarless refractory masonry is widely used in the steel industry for the linings of high-temperature components such as steel ladles and furnaces. Successful design of these large-sized structures requires a proper understanding of the interaction between material discontinuity introduced by the presence of mortarless joints, joints closure and reopening due to loading/unloading, and their effect on the thermomechanical response of the structure. In the present study, 3D thermomechanical models have been developed to analyze the effects of joints reopening on the thermomechanical behavior of mortarless masonry walls. Four joint patterns, with their corresponding equivalent elastic properties, have been defined based on the state of head and bed joints (open or closed). The effective elastic properties of each joint pattern have been calculated with the help of the finite element method and the strain energy-based homogenization technique. The joints reopening and closure criteria have been defined as a function of macroscopic stresses and strains. The developed material model has been implemented in a commercial finite element software and then used to analyze the thermomechanical behavior of refractory masonry walls. The numerical model has been validated by comparing the numerical results with experimental data (biaxial compression test of a flat wall). Both results are in good agreement.

International audience; This paper provides multi-level modeling of microcracked viscoelastic masonries generally present in historical masonries or refractory linings. It is an extension of the Cecchi and Tralli (2012) or Cecchi & Barbieri (2008) and Cecchi & Taliercio (2013) works for the typical Burgers and Modified Maxwell models followed by both undamaged and microcracked masonries. For the sake of simplicity and in order to provide rigorous analytical global estimates, only the mortar is assumed to be viscoelastic and microcracked. Bricks are assumed to be undamaged, elastic or quasi-rigid. The distribution of microcracks is assumed to be isotropic. The effective behavior of the viscoelastic microcracked masonry is provided by two steps. The first one relies on the coupling between the Griffith’s brittle fracture theory and linear mean-field homogenization scheme in order to account for the effect of microcracks on the macroscopic deformation of the mortar and establishes a linear relation between apparent macroscopic stress and strain. This step allows to easily and fast determine the effective creep function of the microcracked mortar without recourse to ’complex’ or heavy numerical inversion of the Laplace–Carson transform. The second step is based on the coupling between asymptotic analysis and homogenization theory applied for a periodic masonry. The proposed models provide analytical solutions - explicit functions of the crack density parameter - for the effective orthotropic behavior of a microcracked viscoelastic periodic masonry cell. This study proves that the Cecchi & Tralli’s and Cecchi & Taliercio’s extension estimates are close and that the later are softer. Such overall properties are used to perform finite element computations on a compressed masonry panel as a first application. These models allow then the prediction of mostly stressed and deformed areas in microcracked masonry structures. This study demonstrates that modeling a mortar (at its undamaged or microcracked state) with this Burgers formulation is only suitable for a masonry with too high values of the Maxwell’s relaxation time otherwise it yields to vanishing effective properties with the increase of time and crack density leading thus to a premature collapse of the masonry. On the other hand, the Modified Maxwell model permits the masonry to preserve a certain resistance for every range value of Maxwell’s relaxation time. These conclusions are valid for masonry either with elastic or quasi-rigid undamaged bricks.

This paper aims to model the effective viscoelastic properties of micro-cracked materials based on the homogenization micro-macro approach. The isotropic case with random orientation and parallel distribution of micro-cracks in Burger and generalized Kelvin non-ageing linear viscoelastic solids was recently considered. To complete these works, this paper develops a model to estimate viscoelastic properties of materials that are constituted of two phases: a non-cracked phase described by Generalized Maxwell model and micro-cracks. The methodology consists in an approximation by using the same Generalized Maxwell model of the non-cracked phase for the overall cracked material. The crucial advantage of this technique is to avoid the complexity of the inverse Laplace–Carson (LC) transform. The approximation is carried out in short- and long-term behaviors in the LC space and validated in transient situation with exact solution obtained from the inverse LC transform in simple loading condition. Useful explicit formulas are provided for calculation of effective viscoelastic properties of isotropic micro-cracked media.

International audience; In order to support the optimization of mortarless brick linings of steel producing furnaces it is proposed in this paper to investigate only the compressibility of dry refractory joints. To this end, optical measurements based on the Digital Image Correlation method were carried out during compression of Magnesia-Carbon brick samples with dry joints. The second main objective is to assess the accuracy of the secant linearization schemes (the classical secant procedure and its modified extension) to reproduce the reference local and global behaviour of refractory mortarless linings accounting for the identified inelastic convex powerlaw behaviour of the Magnesia-Carbon dry joint. The reference nonlinear solution is obtained by means of finite elements method. Under normal compressive loading, unlike for usual (concave) power-law viscoplastic composites for which the secant schemes are known to provide too stiff results, it was found that the modified secant scheme leads to good overall predictions. The classical secant procedure underestimates the reference local and overall behaviour. To improve the latter result, an empirical improved secant formulation was proposed and implemented. It leads to better estimates at local and global levels.

This paper provides finite elements predictions for the effective tangent properties of microcracked viscoelastic masonry. This model relies on two steps. The first one is based on the identification at the short and long terms of an approximate analytical creep function for the mortar. Following (Nguyen et al., 2011) for a microcracked homogeneous material, this step rests on the coupling between the Griffith’s brittle fracture theory and stress-based dilute homogenization scheme. It allows to avoid recourse to ‘heavy’ numerical inversion of the Laplace–Carson transform. The second step provides orthotropic overall properties of masonry by means of finite elements method used to carry out periodic homogenization on masonry. This step relies on the calculation of the localization strain tensors in each phase (brick and mortar). This paper proposes an alternative model to an incremental homogenization of masonry which is heavier to carry out since it depends on additional parameters such as time increment and prestresses in viscoelastic phases added to the crucial computation step of strain localization tensors in each phase. In this work, for the sake of simplicity and as a first approach, only time-dependent crack densities (Shrive et al., 1997; Reda Taha and Shrive, 2006) are considered at short and long-terms. Results provided by the proposed finite elements model can be considered as reference solution enabling a rigorous assessment of recently analytical model proposed by Nguyen et al. (2014) and Rekik et al. (2016) as a generalization of the Cecchi & Taliercio model (Cecchi and Taliercio, 2013) initially available for uncracked masonries. This comparison is carried out for different mortar thicknesses and brick’s dimensions. The case of a compressed wall is also considered at the long term.

International audience; To support optimisation of refractory masonry structures compressibility of dry joints of magnesia-carbon and magnesia-chromite bricks have been investigated. Laboratory scale tests and finite element modelling have been performed. Measurements done in wide temperature range have shown that the exponential form of the joint closure curve results from gradual closure of initially non-parallel surfaces. The stress needed to close the joint was found to be proportional to the material stiffness. Temperature influences the joint closure by changing the stiffness of material and by reducing the initial joint gap due to thermal expansion.

In shaping of composite reinforcements, tensile stresses are the major stresses, while in plane shear strains are the major strains. However the knowledge of the bending behaviour would give more precisely simulation of forming especially for stiffer and thicker textiles. A new cantilever test using optical measurement has been developed to identify non elastic behaviour by taking into account the history of the strains. Associated to the test, an inverse identification method has been developed. Based on the simulation of the test using finite element analysis, the method enables to test the validity of a postulated bending model and to optimize the values of its parameters if validated. An hysteretic bending model has been tested for a carbon Non Crimp Fabric reinforcement to show the advantage of the complete approach.

In this work, a bone adaptation law based on fully coupled stimulus function taking into account strain–damage effects and spatial function influence based on ruptured osteocytes processes concept have been developed and implemented into Abaqus code. Contrary to previous works where the spatial function was considered without damage influence, in the present model, we propose a novel idea to describe osteocytes ruptured processes using damaged spatial function. Also, the stimulus reference value for bone resorption threshold is considered cycles depending variable and an experimental fitted relation between the strain reference value and the cycle’s number was proposed. In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. The idea is that the real cycles number are reduced (divided) into equivalent cycles blocks. Damage accumulation is computed over the cycles blocks and extrapolated over the real correspond cycles. To illustrate the capabilities of the remodeling algorithm, four mechano-regulation laws have been implemented and tested corresponding to four stimuli functions: (i) strain based stimulus without damage influence, (ii) fully coupled strain–damage without spatial function influence, (iii) fully coupled strain–damage with non damaged spatial function influence and (iv) fully coupled strain–damage with damaged spatial function influence.

The MRS-100 system combines at the same time the simplicity of a linear sliding gate and the advantages of a round plate. This sliding gate is based on 3 innovating approaches: a sliding gate built around a refractory plate, a mechanism that avoids the cracking of plates and finally, an optimisation of the round plate through a programmable sequential rotation at the ladle stand. This MRS-100 system leads to a safe use, an improvement of the tasks at the working station and a reduction of the user costs.

Some refractory linings of metallurgical vessels consist of masonry without mortar. To describe the mechanical behaviour of these large-sized structures, it is necessary to use an equivalent material instead of a model that comprises all the bricks and joints involved. The properties of the equivalent material depend on the opening and closure mechanism of joints. In this paper, four joint states which are the combination of open/closed states of bed and head joints are identified, and the corresponding equivalent elastic properties are determined accordingly using homogenisation techniques. The transition criterion between these joint states is based on the unilateral contact conditions written in terms of macroscopic strain. The developed model is then compared to an in-plane biaxial compression test. The numerical and experimental results are in good agreement.

Les joints de dilatation jouent un role important dans les garnissages refractaires. Ils permettent de diminuer les contraintes durant la montee en temperature. Il est alors necessaire de les prendre en compte lors d'un calcul mecanique. Dans le cas ou le garnissage est une maconnerie (composee de briques), il n'est pas possible de modeliser chaque brique et joint. La solution proposee est de remplacer la maconnerie par un materiau qui aurait le meme comportement. Du fait qu'il est difficile de realiser des essais sur un ensemble de briques (dans le but d'identifier les parametres du materiau equivalent), ces chargements ont ete simules sur une cellule elementaire en utilisant un modele developpe a l'echelle des composants, a laquelle les joints sont representes par un contact. Une identification inverse a permis d'obtenir les parametres d'un materiau equivalent simplifie qui a ete valide a l'aide d'un essai thermomecanique sur une structure reelle.

International audience; It is a common practice to design refractory linings with the help of thermal computations, thermochemistry analyses and strong workman know-how. Their mechanical design is often limited to simple thermo-elastic computations. Sometimes computations are refined considering non-linear mechanical behaviour, even if corrosion often induces additional chemical strain and strong change in service of the mechanical behaviour of the refractory. The aim of this presentation is to briefly recast the irreversible thermodynamic framework in order to underline the implications of some basic thermodynamic concepts in term of refractory behaviour modelling. Then, the use of these concepts to develop fully 3D finite element simulations accounting simultaneously for thermal, mechanical and chemistry phenomena will be illustrated on the particular case of SiC-based refractory. Comparison between long duration oxidation test at high temperature and model prediction allows the validation of the proposed approach. Then, an extension to the industrial case of refractory lining in Waste to Energy plant will be illustrated. The interest of taking into account the thermo-chemo-mechanical coupling effects is shown.

International audience; In refractory masonry lining of industrial furnaces the compressibility of mortars is critical for the thermo-mechanical integrity of the structure.Compressive stress-strain behaviour of refractory mortars has been measured during drying at room temperature and in the service temperaturerange of 300-1400◦C. The results have been explained using fractographic analysis and distinct element method computer modelling. The mortarfailure has been shown to occur due to formation of shear bands of micro-cracks. The propagation of cracks preferably follows the shortest pathbetween larger pores and is influenced by grain cohesion and interlocking. Tests with mortars featuring calcium aluminate cement, mono aluminiumphosphate, water glass and bentonite clay binders have indicated that besides increasing the cohesion between the grains the binder reduces theinternal friction that promotes higher compressibility. It has been found that the mortar with clay has the highest compressibility. The mortar withcement shows the most stable behaviour.

International audience; Silicon carbide-based refractory castables (SiC-RC) have high mechanical and chemical resistances at high temperature. Nevertheless when subjected to both high temperature and aggressive oxidizing environment, due to phase transformation, a chemical strain appears that leads to additional stresses in industrial parts and may cause degradation. In this paper, macroscopic constitutive equations are proposed to model the complex relationship between stress, strain, temperature and oxidizing atmosphere in porous SiC-RC. To model the kinetics of the chemical swelling, oxygen content in the porosity of the heterogeneous material is estimated. It depends on both the oxidation reaction of SiC-based grains and the diffusion of oxygen through the connected porosity in the castable. The macroscopic chemical strain associated to the local SiO2 formation takes only place when the local small voids cannot absorb the reaction product anymore. Besides, the reduction of porosity is accompanied by a reduction in the gas permeability and consequently a reduction in the diffusion of oxygen. The multi-physical model is implemented in the finite element code Abaqus . It accounts for heat transfer,reactive oxygen transport and chemically induced strain. A validation test was carried out on a cylindrical sample subjected to high temperature with a thermal gradient in ambient air. Comparison between experimental results, microscopic observations and numerical results showed that the model provides a good description of the main physical phenomena.

In steel ladles (steel industry) or in coal-fired power plants (energy production), the refractory linings anchored to the steel structure (casing) are subjected to significant thermal loadings which lead to cracking (owing to the difference between the thermal expansion coefficients). A first approach allows us to analyse the problem at a local scale: a smeared crack model permits the computation of the damage which is observed in an experimental test. But since a structure contains thousand of anchors, it is not possible to compute it with this model. An approach was therefore developed with a two-layered shell equivalent to the anchored lining and the casing. This model is identified with an inverse method and uses results from the first approach, validated by a bending test performed on a refractory lining specimen. The damage computing of a structure shows that it is very important to take the expansion joints into account.

The forming of fibre fabric reinforcements without a matrix is possible because of their very specific mechanical behaviour. The lack of some rigidities is due to possible motions between the fibres. For the fabrics used as reinforcement in the R.T.M. process and composed of warp and weft yarns made with untwisted fibres, the tension stiffness is very preponderant compared to the others. The tensile behaviour of such a fabric is biaxial, i.e. the tension-deformation states in warp or weft directions depend on the other direction because of the interweaving. It is given by the knowledge of two surfaces relating the warp and weft tensions to the two strains in these directions (or that of a single surface if the fabric is balanced). In the present paper, three complementary methods are investigated in order to determine these surfaces. A biaxial tensile device on a cross-shaped specimen is first used. 3D finite element simulations of the unit woven cell are then presented. This mesoscopic study permits to understand some phenomena at the elementary woven cell level. Finally a simplified model, which is consistent with the geometry of the plain weave woven mesh is presented. The agreement of the two last methods with experimental results is shown. From these tensile behaviour surfaces, a dynamic explicit approach for the simulations of a fabric sheet forming process is presented. The interests of the method are both its good numerical efficiency, particularly due to the direct use of the biaxial tension surfaces, and its proximity with fabric physics.

The simulation of the drawing process for woven reinforcements aims at evaluating the possibility of forming a shape for a given fabric. The mode of deformation during the forming of woven reinforcements is very specific and different from that for metal sheets. Knowledge of fabric behaviour is necessary. In the present work, this is studied experimentally by means of biaxial tests that bring out the influence of the geometric non-linearity, at the mesh scale, on the macroscopic behaviour of the fabric. Models based on bar and yarn theories, are identified from these tests and used in a specific finite-element formulation for fabrics. These elements are efficient since they take into account only the tension stiffness of the yarns (the only one present in a fabric). Three-dimensional simulations of the elementary mesh supplement this study with local information.

The wall of refractorized vessels are composites, made of metallic casing often containing tubes and a refractory material for the protection against the high temperature environment. The objective of the present paper is to model a two layer shell with a thermomechanical behavior equivalent to those of the 3D lining and that render possible the finite element analysis of the complete vessel. A smeared crack model is used for the damage analysis of the refractory material. The equivalent shell is made up of an exterior orthotropic layer and an interior isotropic damageable layer. The set of thermal and mechanical parameters of the equivalent shell is obtained by an inverse method in conjunction with finite element analyses of the 3D panel subjected to an appropriate set of loadings. Some validation analyses show that the identified parameters lead to shell behavior, which is in good agreement with those of the 3D wall. In the case of a simplified cyclone, it is shown that the equivalent shell permits to compute the thermomechanical behavior of a complete refractorized vessel and especially to follow the damaged zones of the refractory.

Refractory linings are used in order to protect the steel structure in industrial applications such as coal-fired power plants or steel ladles. These linings are subjected to important thermal loading that can lead to cracking (due to the difference between the thermal expansion of steel and the thermal expansion of the refractory). The aim of this study is to build a tool that allows the structural design to be improved so as to decrease the refractory cracking. The first approach is developed on a local scale. A special furnace allows the reproduction of the thermal conditions in a coal-fired plant. Acoustic emission is employed to detect when the refractory is cracking. A finite element analysis, using three-dimensional elements and a smeared-crack model, is conducted to reproduce the experimental observations. The material behaviour is identified using an inverse method. This local approach can be directly used for structural analyses when the geometry of the lining is sufficiently simple. For instance, the computation of a steel ladle is presented. When the geometry of the lining is very complex, it is not possible to compute it with this three-dimensional model. In this case, a simplified approach using a two-layered composite shell, the behaviour of which is equivalent to the three-dimensional behaviour, is briefly described.

Resume La simulation des operations de mise en forme des composites minces est necessaire a l'etape de conception car elle permet de valider la faisabilite d'une geometrie et de connaitre la position des renforts. Une methode de simulation par elements finis de l'emboutissage des renforts tisses est presentee dans cette etude. Elle necessite la connaissance du comportement mecanique du renfort. Un modele de comportement geometriquement coherent est propose. Il s'appuie sur des resultats experimentaux obtenus sur une machine de traction biaxiale. Deux exemples de simulations numeriques de la mise en forme des renforts tisses, sont presentes. Le premier afin de demontrer l'influence de la geometrie des outils sur la faisabilite de l'operation de mise en forme et le second qui illustre la potentialite de la methode, comparativement a des algorithmes geometriques, par la prise en compte des phenomenes mecaniques. Une extension de la methode developpee a la mise en forme de composites minces a matrice thermoplastique est enfin proposee.

The knowledge of the mechanical behaviour of dry woven fabrics is necessary in many applications. The aim of this study is to recall the specificity of the mechanical behaviour of dry fabrics and to understand the local phenomena that influence the macroscopic behaviour. For this, 3D finite element analyses of elementary patterns are performed. These calculations are not classical due to the constitution of the yarns made of a lot of small fibres. The possible motions of the yarns allow changes of undulation leading to nonlinear biaxial tensile behaviour and the lack of most of the other stiffnesses. The specificities of the calculation in order to reach this behaviour are described. The model is compared to biaxial tests on several fabrics. Such a model allows to understand the phenomena implicated in the behaviour and the main aspects that lead to the specific behaviour of woven media. It can also bring a help for the design of new fabrics in changing some mechanical and geometrical parameters in order to get prescribed properties.

A general theory of damage mechanics is applied to a fibre-reinforced ceramic matrix composite, SiC/MAS-L, in order to describe its non-linear mechanical behaviour up to failure. This study is limited to the case of quasi-monotonic loading at room temperature. The model, which uses an anisotropic damage theory previously applied to other composites, is a mesoscopic-scale model which has been developed using tension–compression tests on different stacking sequences and applies in the case of multiaxial loading. It includes the marked differences observed between mechanical behaviour in tension and in compression, and is also able to predict the failure values.

International audience; Many bottom linings of refractory structures used in steel making industry are made of masonries with or without mortar. Several designs are possible: parallel, fish bone or radial. To compare the influence of these designs on the level of stress and displacements in the steel shell, the different masonries were modelled by an equivalent homogeneous material. The thermo-mechanical properties of this equivalent material were determined using a periodic homogenization method. They are temperature depending and depend of the joint states (open or closed in the two directions) for masonries with mortarless joints. This masonry model is used to simulate by the finite element method the behaviour of a simplified steel ladle. It demonstrates the influence of different parameters: presence or not of joints, dry joints/mortar joints, thickness of mortar joints, masonry design. It brings a help for the design of refractory masonry linings.

International audience

International audience; The coking process is composed of two main stages: drying process and pyrolysis of coal. A heat and mass transfer model was developed to simulate the drying process of coal. The mechanisms of heat and mass transfer described in the model are: conduction through the coal cake; conduction and convection through the gas in pores; generation, flux and condensation of water vapor. The model has been implemented in finite element software. It requires basic data on the coke oven charge properties and oven dimensions as input. These input data were obtained by experiments or from the literature. The proposed model includes condensation and evaporation allowing us to reproduce the temperature plateau observed experimentally.

Different matrix microcracking mechanisms are observed in ceramic-matrix composites under complex loading conditions. These mechanisms are introduced in the proposed model by using an anisotropic damage theory, which takes into account the effects due to microcrack opening and closure, according to the state of the stress tensor (the behaviour is different in tension and in compression). One difficulty is the identification of this model for the woven SiC SiC composite under study. Classical uniaxial tests (at 0 ° and 45 °) are not sufficient to identify the model completely. A combined biaxial tension test is defined in order to determine the missing parameters. Internal pressure tests on tubes qualitatively validated the model.

This study presents a viscosity sensor that converts the vibration amplitude at the resonance frequency of a needle immersed in viscous fluid, into electric current. The goal of this work is to provide a dedicated numerical tool for the sensor design, that couples fluid, structure and magnetism.Copyright © 2012 by ASME

International audience; This paper is devoted to the modelling of a specific ramming mix mainly used in the high-temperature industry due to its high-compacting behaviour. This material has the ability to absorb the deformation of parts submitted to high thermal loads. Triaxial and instrumented die compaction tests were carried out in order to identify the shear and hardening behaviours, respectively. Tests on the ramming mix were led for a temperature range between 20 C and 80 C. The temperature effect is particularly observed on the material response when it is compacted. The main features of the behaviour of the ramming mix can be represented by the theoretical framework of the Modified Cam-Clay model. A single variable allows to accurately reproduce the hardening behaviour depending on the temperature. Moreover, an extension of the model for the hardening behaviour at high pressures is proposed. A good agreement between the experimental data and numerical tests is reached with this model.

In composite reinforcement shaping, textile preform undergo biaxial tensile deformation, in plane shear deformation, transverse compaction and out-of-plane bending deformations. Bending deformations have been neglected in some simulation codes up to now, but taking into account them would give more accurate simulations of forming especially for stiff and thick textiles. Bending behaviour is specific because the reinforcements are structural parts and out of plane properties cannot be directly deduced from in-plane properties, like for continuous material. Because the standard tests are not adapted for stiff reinforcements with non linear behaviour a new flexometer using optical measurements has been developed to test such reinforcements. This new device enables to carry out a set of cantilever tests with different histories of load. A series of tests has been performed to validate the test method and to show the capacities of the new flexometer to identify non linear non elastic behaviour.

National audience

In shaping of composite reinforcements, tensile stresses are the major stresses, while in plane shear strains are the major strains. However the knowledge of the bending behaviour would give more precisely simulation of forming especially for stiffer and thicker textiles. Two standard tests are used to determine it. The cantilever test is limited because of its elastic linear model. The KES fabric bending test allows a more complicated model but its use is difficult for stiff and thick reinforcements. A new cantilever test using optical measurement has been developed to provide the searched flexibility. Tests have been performed on a carbon woven reinforcement and compared with KES measurements. The results allow to validate the experimentation.

Le comportement mécanique des renforts tissés utilisés dans les composites est fortement influencé par l'assemblage par tissage des mèches chaîne et trame. La rigidité principale du tissé est celle de tension. Le comportement en tension est non-linéaire compte tenu des liaisons entre les deux réseaux qui conduisent à des non-linéarités géométriques locales. Ce comportement en tension est analysé dans le présent travail par des essais de traction biaxiale et des simulations 3D de la maille élémentaire. La rigidité de cisaillement dans le plan des renforts tissés est faible jusqu'à un angle limite. On montre par des mesures optiques que ceci correspond à une phase de rotation de corps rigide de chaque mèche. Une deuxième phase correspondant à un blocage et un écrasement latéral des mèches conduit à des rigidités beaucoup plus fortes. On présente deux formes simplifiées de l'équation de la dynamique ne prenant en compte que les travaux virtuels de tension d'une part et de tension cisaillement d'autre part. On montre sur un exemple de simulation d'emboutissage d'un renfort tissé que la prise en compte du cisaillement est importante si l'on dépasse un angle limite.

International audience; A finite element simulation of composite woven reinforcement forming requires the knowledge of the fabric mechanical behaviour. In the presented mesoscopic approach, the tensile and shear mechanical behaviour of the elementary cell (mesoscopic level) are used in a finite element made of woven meshes. The principal stiffness of the fabric is the tensile rigidity. Because of the weaving, the tensile behaviour is non-linear. It is analysed by biaxial tensile tests and 3D finite element computations of the woven unit cells. The in plane shear rigidity of fabrics is very weak up to a limit angle. In this first stage, it is shown by optical measures that the yarns are subjected to rigid rotations. A second stage in which the yarns are laterally crushed leads to larger stiffness. A first simplified form of the dynamic equation is based only on tensile internal virtual work. A second one takes also shear internal work into account. A fabric square box forming simulation is performed with both approaches. It shows the importance to account for shear when the limit shear angle is exceeded.

International audience; Expansion joints play an important role in refractory linings as they reduce stresses during heating. It is therefore necessary to take them into account in a mechanical analysis. In the case where the lining is a masonry construction (made up of bricks), it would require an excessive number of elements to model each brick and joint. The proposed solution is to replace the masonry with a material that has the same behaviour (or very near) as masonry. Since it is difficult to perform experimental tests on a set of bricks (to identify the parameters of the equivalent material), these loads were simulated on an elementary cell using a model developed at a local scale (scale of the components, bricks and joints). At this scale, the joints are represented as contacts (with normal and tangential behaviour). The parameters of a simplified equivalent material were obtained by an inverse identification. This model was validated by a thermomechanical test on a real structure.

International audience; The paper presents an approach to model the behaviour of a representative volume element (unit cell) of textile reinforcement in in-plane deformation (bi-axial tension and shear) and in compression. The model is a further development of a virtual textile concept implemented in the WiseTex software, and is based on the concept of hierarchical description of textile properties and systematic application of the principle of minimum energy to calculate the textile geometry in the relaxed and deformed state. With the internal geometry of the unit cell built, the model computes overall parameters of the deformed textile, such as fibre volume fraction, porosity etc. The internal geometry is visualised and such properties as pore structure in typical cross-sections are analysed. The load-deformation curves for compression, tension and shear are computed via the balance between change of the internal energy of the unit cell and mechanical work of the applied loads. The internal geometry description is further fed into flow modelling software, which allows computing local permeability of the deformed reinforcement, and micro-mechanical modelling to calculate homogenised local stiffness of the composite.

International audience; Refractory linings are used to protect the exterior metallic part of some vessels containing very hot fluids. They are submitted to high thermomechanical loading that can lead to cracking. A local approach is first presented in order to analyse the refractory lining as a 3D domain. A smeared crack model is used to compute the damage in the refractory. Comparison with experiments on a refractory wall containing metal parts is performed in order to validate the 3D numerical computations. Some type of refractorised vessels (e.g. some steel ladles) can directly be analysed from this 3D modelling. Since some other refractorised vessel contains a very large number of metallic parts (such as tubes or anchors), it cannot be possible to compute such a global structure with this 3D analysis. Consequently, an approach has been developed based on a two-layer shell equivalent to the lining including the metallic casing with tubes and the refractory. The thermal and mechanical parameters of the model are identified with an inverse method, using results of 3D calculations performed with the local model defined previously. An experimental validation is made by a bending test, performed on a large refractory lining specimen. In the case of a cyclone of coal-fired power plant, the equivalent shell permits to compute the damage of the refractory in the global structure.

International audience; Les structures réfractorisées peuvent présenter des dégradations en cours de fonctionnement. Afin de limiter ces dégradations en améliorant la conception, il est nécessaire de disposer d'outils de calcul (par éléments finis) adaptés. Pour des structures simples, telles que des poches à acier, un calcul 3D est réalisable. Par contre, pour des structures plus complexes, telles que des centrales à charbon, l'utilisation d'un élément simplifié est indispensable. Il s'agit ici d'un élément coque bi-couche dont le comportement est équivalent à celui de l'ensemble ossature métallique/garnissage réfractaire.

International audience; Simulation of the forming processes of thin composite structures is necessary at the design level in order to check the feasibility of the shape and to know the position of the reinforcements. A finite element analysis of fabric shaping process needs the knowledge of the mechanical behavior of the woven reinforcement. This behavior is non linear because of the shape variation of the weaving pattern when it is loaded. Experimental results are obtained from biaxial tests in the case of balanced and unbalanced fabric. A constitutive model consistent with the geometry of the woven pattern is proposed. It is based on experimental results achieved by biaxial tensile tests. 3D simulations of the unit woven cell submitted to biaxial tensions are also performed and compared to experiments.

For ceramic composites, continuum damage mechanics models are built, which include information coming from both the “micro” and “macro” scales. These models are constitutive relations which, when included in a structural analysis code, are able to predict the damage state of the studied structure at any time and at any point until final fracture.

Darcet material (a mix of bismuth, lead and tin) can be used in the shaping process of copper joints in T since it is a soft material and it melts down at low temperature (96°C). This process is studied using a finite element simulation that requires the Darcet material behaviour. This behaviour is very particular, depending on the temperature, strain rate and age of the material. It is determined under these different conditions with compression tests, and a behaviour model is proposed. It is introduced in a finite element model that allows one to determine the median branch length of the copper joint versus the stamping length. The influence of different parameters can be studied with this model to optimise the process.

International audience