Endommagement par cavitation dans les élastomères : analyses expérimentale et numérique

Dans ce travail nous avons étudié le phénomène d’endommagement par cavitation dans les matériaux caoutchoutiques en combinant les approches expérimentale, théorique et numérique. Dans un premier temps, nous avons réalisé des essais spécifiques de dépression hydrostatique et de mesure de variation de volume. Les résultats obtenus ont mis en évidence le phénomène de cavitation dans les matériaux Styrène Butadiène Rubber (SBR) et caoutchouc naturel (NR). La nucléation, la taille et le nombre des vacuoles observées, en post-mortem, sur les faciès de rupture, semblent dépendre du facteur de forme des éprouvettes qui traduit le degré de confinement de celles-ci. Dans un deuxième temps, nous avons modélisé à l’aide de la Méthode des Éléments Finis (MEF) tous les essais expérimentaux et, ensuite, nous avons tenté de prédire la nucléation des cavités dans les matériaux étudiés en utilisant deux modèles théoriques. Les modèles en question sont le modèle de Ball et celui de Hou et Abeyaratne. Ces deux modèles ont conduit à des prédictions quasi-similaires qui, de plus, s’avèrent en bon accord avec les observations expérimentales. En effet, ces prédictions ont montré que le phénomène de cavitation dans les élastomères est intimement lié au degré de confinement des éprouvettes. Ces calculs numériques ont aussi, particulièrement, illustrés que ce phénomène semble être gouverné par une pression hydrostatique critique locale et par une valeur critique de la déformation globale dans l’échantillon

Identification des paramètres de modèles viscoplastique-viscohyperélastique : Application à un polymère semi-cristallin sur une large gamme de cristallinités

Ce travail est dédié aux stratégies d’identification des paramètres de modèles viscoplastique-viscohyperélastique appliqués aux polymères. Une méthode numérique d’identification, basée sur une procédure d’optimisation évolutionnaire, est présentée. L’application est faite sur un polyéthylène, contenant différents taux de cristallinités, sollicité en grandes déformations à différentes vitesses de déformation vraies. Dans une première approche, les paramètres d’un modèle viscoplastique-viscohyperélastique, permettant de reproduire la réponse mécanique du polymère semi-cristallin, sont identifiés en supposant le matériau homogène. En considérant le polymère semi-cristallin comme un milieu hétérogène, les résultats de l’identification des paramètres d’un modèle viscoplastique-viscohyperélastique, basé sur une représentation à deux phases de la microstructure, sont présentés et analysés en terme de variations

Micromechanical based model for predicting aged rubber fracture properties

Environmental aging induces a slow and irreversible alteration of the rubber material’s macromolecular network. This alteration is triggered by two mechanisms which act at the microscale: crosslinking and chain scission. While crosslinking induces an early hardening of the material, chain scission leads to the occurrence of dangling chains responsible of the damage at the macromolecular scale. Consequently, the mechanical behavior as well as the fracture properties are affected. In this work, the effect of aging on the mechanical behavior up to fracture of elastomeric materials and the evolution of their fracture properties are first experimentally investigated. Further, a modeling attempt using an approach based upon a micro-mechanical but physical description of the aging mechanisms is proposed to predict the mechanical and fracture properties evolution of aged elastomeric materials. The proposed micro-mechanical model incorporates the concepts of residual stretch associated with the crosslinking mechanism and a so-called “healthy” elastic active chain (EAC) density associated with chain scission mechanism. The validity of the proposed approach is assessed using a wide set of experimental data either generated by the authors or available in the literature

The energy release rate of a crack in the interfacial zone of particulate-reinforced composites

In this work, the energy release rate is computed for a curved crack in a two-phase particulate composite Al/SiC. The crack lies in a flexible interface between the spherical particle and the surrounding matrix. Applying classical approaches to calculate the energy release rate of that kind of crack is not an easy task, especially as the problem is of three-dimensional nature and the material is heterogeneous. Thus, the principles of the so-called θ-method are used to deal with these difficulties. Using the variational formulation, the method is rewritten for the case of cracks lying in compliant interfaces, which permits to obtain the expression of the energy release rate in the form of a domain integral. The expression is eventually discretized in the framework of the finite element method in order to have a usable form for the simulations. The validation of the method is made in the first place by considering the simpler case of a crack around a cylindrical inclusion, for which an analytical solution exists. The energy release rate is then evaluated for the cracked Al/SiC composite with compliant interfaces while making some micromechanical parameters vary, like the mechanical properties of the constituents. The evolution of the energy release rate is also represented with respect to growing crack lengths

Tribological, thermal and mechanical coupling aspects of the dry sliding contact

An original experimental set-up, made of two coaxial rings in relative motion, a sapphire and steel, enabled temperature measurements on both sides of the third body at the friction interface. Hot spots have been identified and temperature gradient across the third body accurately measured. Infrared camera and thermocouples have shown to be an effective tool for this research. Investigations conducted using SEM enabled detailed analysis of friction interfaces of both components, the sapphire and steel rings. Two types of third body (layers) have been identified, the compact, smooth micro-plates—where the actual contact occurs, and granular—which seem to accumulate in depressions or against material obstacles. There are also clear indications that the hot spots and depressions on steel friction surface are directly related. These areas of contact seem to be ‘shrinking' in height after the application and complete component cooling. The investigation of the third body phenomenon and its influence on interface temperatures has direct relation to the observations made in automotive disc brakes. A thermal numerical model, which was also developed, introduced the third body as a uniform layer with energy storage and conduction. The obtained thermal gradients seem to be accurate, when compared with measurements conducted. The results are also similar to those found in literature. In addition, when only a fraction (1/1000th and 1/2000th) of the total nominal friction surface was considered to be in the actual contact, experimental temperature results were exactly within the predicted range. This indicates that the actual contact area varies during application

A unified mechanical based approach to fracture properties estimates of rubbers subjected to aging

In this work, the influence of aging on the mechanical properties at break of rubber materials are examined. When subjected to physical-chemical aging, the structure of the rubber network is deeply modified through two main mechanisms: crosslinking and chain scission. These aging mechanisms act both on the mechanical behaviour and on the fracture properties of the rubber materials. The goal of this work is to propose a predictive mechanical tool able to give estimates of these mechanical properties. To address this issue, an hyperelastic constitutive model based upon the energy limiter approach, was coupled with physical-chemical parameters in order to capture the whole mechanical behaviour of the damaged materials beyond the fracture. That allows fracture stress and strain estimates. A wide set of materials and experimental data extracted from the literature or obtained in our team were selected based upon the aging mechanism they can exhibit. We found that the elastically active chains concentrations and the swelling rate can be used as relevant indicators of damage either for crosslinking or chain scission process. These parameters are then introduced as damage parameters in the mechanical modelling. The proposed approach leads to very satisfactory predictions, either to capture the whole mechanical behaviour in uniaxial tension or in terms of stress and strain at break estimates

Fracture of elastomers under static mixed mode: the strain energy density factor

International audienceThis work deals with the fracture of rubbers under a mixed mode loading (I + II) and it is an extension of our previous papers on that subject [Aït Hocine N, Naït Abdelaziz M, Imad A (2002) Int J Fract 117:1–23; Aït Hocine N, Naït Abdelaziz M (2004) In: Sih GC, Kermanidis B, Pantelakis G (eds) 6th international conference for mesomechanics. Patras (Greece), May 31–June 4, pp 381–385]. An experimental and a numerical analysis were carried out using a Styrene Butadiene Rubber (SBR) filled with 20 and 30% of carbon black. Sheets with an initial central crack (CCT specimens) inclined with a given angle compared to the loading direction were used. The J-integral and its critical values J c (fracture surface energy) were determined by combining experimental data and finite element results. These critical values, determined at the onset of crack growth, were found to be quite constant for each elastomer tested, which suggests that J c represents a reasonable fracture criterion of such materials. Then, the strain–stress field and the strain-energy-density factor S, earlier introduced by Sih [Sih GC (1974) Int J Fract 10(3):305–321; Sih GC (1991) Mechanics of fracture initiation and propagation. Kluwer Academic Publishers, Dordrecht, 428 pp] were numerically calculated around the crack tip. According to the experimental observations, the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values S min of the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the maximum principal stretch and the one of the strain-energy-density factor can be used as indicators of the crack propagation direction

Temperature and filler effects on the relaxed response of filled rubbers: Experimental observations on a carbon-filled SBR and constitutive modeling

International audienceThe self-heating temperature of filled rubbers under cyclic loading at environmental conditions is well-known. This increase in temperature seriously affects the constitutive stress–strain behavior by producing a thermal softening of the rubber compound. Although this feature is well-recognized and considered as important to its function, few constitutive thermo-mechanical models attempt to quantify the stress–temperature relationship. In this work, a physically-based model is developed to describe the large strain relaxed response of filled rubbers over a wide range of temperatures. The non-linear mechanical behavior is described via a Langevin formalism in which the temperature and filler effects are, respectively, included by a network thermal kinetics and an amplification of the first strain invariant. Experimental observations on the relaxed state of styrene-butadiene rubber hourglass-shaped specimens with a given carbon-black content are reported at different temperatures. A hybrid experimental–numerical method is proposed to determine simultaneously the local thermo-mechanical response and the model parameters. In addition, the predictive capability of the proposed constitutive thermo-mechanical model is verified by comparisons with results issued from micromechanical simulations containing different arrangements of the microstructure. The results show that the model offers a satisfactory way to predict the relaxed response of filled rubbers at different temperatures

A thermo-visco-hyperelastic model for the heat build-up during low-cycle fatigue of filled rubbers: Formulation, implementation and experimental verification

International audienceIn a previous contribution (Ovalle Rodas et al., 2014), a finite strain thermo-visco-elastic constitutive model, in accordance with the second thermodynamics principle, has been developed to predict the heat build-up field in rubbers during low-cycle fatigue. Using a viscous dilatation tensor, related to the time-dependent response of the rubber material, as an internal variable of the specific free energy potential, both the mechanical behavior and the heat build-up have been predicted for different strain rates and stretches. In the present contribution, the finite strain thermo-mechanical constitutive model is extended by using a stretch amplification factor to account for the effect of carbon-black filler on the heat build-up. Experimental observations on the mechanical response and the heat build-up during fatigue tests of carbon-black filled styrene-butadiene rubber (SBR) containing different filler contents are reported at room temperature. The increasing effect of the filler content on the heat build-up is evidenced. The proposed constitutive model is implemented into a finite element code and the same thermo-mechanical boundary conditions regarding the experimental tests are simulated. The model parameters are identified using experimental data issued from SBR filled with a given carbon-black content under a given strain rate and different stretches. Predicted evolutions given by the proposed constitutive model for other strain rates and amounts of carbon-black are found in good agreement with the experimental data

Molecular dynamics study of the polymer clay nanocomposites (PCNs): Elastic constants and basal spacing predictions

International audienceMicromechanical approaches seem to be limited in the prediction of polymer nanocomposite properties, since the active molecular interactions between nanofillers and polymer matrix as well as those between nanofillers themselves, are far from being explicitly taken into consideration. The molecular interactions between nanofillers and polymer matrix lead to the so-called interphase region, where polymer chains mobility is reduced in the vicinity of nanofillers interface. Many assumptions are made on this interphase region to incorporate implicitly nanofillers/polymer interactions in micromechanical models. Experimental characterizations of this interphase and the confined interlayer polymer in the intercalated structure are not available to date. In this work, we have used isothermal-isostress (NσT) molecular dynamics simulation to predict the isothermal elastic constants of nylon-6 clay nanocomposites in the case of intercalated structure. The effect of the number of monomers in the nylon-6 chains on the basal spacing is evaluated. Isothermal bulk modulus is determined via isothermal-isobaric (NPT) molecular dynamics simulation. We also provide through this work an insight into molecular interactions in intercalated nylon-6 clay nanocomposites