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In the present paper, we present an approach combining physically-based constitutive modeling and experiments to study the thermo-mechanical response of amorphous thermoplastics whose final objective is the prediction of the thermally-induced strain recovery. The underlying thermo-mechanical mechanisms are described by elastoviscoplastic-viscohyperelastic constitutive relations allowing to account for the variation with temperature of the inter and intramolecular barriers to deformation and their abrupt change when the temperature traverses the glass transition. The model fit shows a good agreement with experimental observations on polycarbonate in terms of temperature and strain-rate dependent stress-strain response. The material kinetics with temperature is designed and introduced into the model to predict the thermally-activated strain recovery process during heating. In our approach, the intramolecular resistance of the entangled molecular chain network orientation/relaxation is used as the driving stress that continuously activates the strain recovery process during zero-stress creep above glass transition. The model predictions are shown under zero-stress creep recovery for different previous loading histories in terms of strain-rate and strain-level. The simulated results are in satisfactory agreement with experimental observations at different heating temperatures showing the relevance of the proposed approach.

International audience; The present contribution aims to examine the erosion behavior of soda-lime-silica glass in connection with damage interaction and angle effects. Experimental observations are reported on glass plates subjected to sandblasting process using alumina abrasive particles for different sandblasting durations and impact angles. The damage and erosion mechanisms are computed through a numerical model of the sandblasted glass plate. The glass internal stiffness degradation due to impact process is accounted for by an anisotropic stress-based continuum damage mechanics model. The glass erosion is simulated by means of a vanishing element technique using the critical values of damage components as failure criterion. A parametric numerical study is carried out to bring insights into damage interaction and angle effects on the material loss.

International audience; Polymers operating in various weathering conditions must be assessed for lifetime performance. Particularly, ultraviolet (UV) radiations alters the chemical structure and therefore affect the mechanical and fatigue properties. The UV irradiation alters the polymer chemical structure, which results into a degradation of the mechanical and fatigue behavior of the polymer. The polymer properties degradation due to UV irradiation is the result of a competitive process of chain scission versus post-crosslinking. Although few studied investigated the effect of UV irradiation on the mechanical behaviour of thermoplastics, fewer examined the UV irradiation effect on the fatigue life of polymers. This study focuses on investigating the effect of UV irradiation on the fatigue properties of bulk semi-crystalline polymer; the low density Polyethylene (LDPE). Tensile specimens were exposed to different dose values of UV irradiation then subjected to fatigue loading. The fatigue tests were achieved under constant stress amplitude at a frequency of 1Hz. The results show an important decrease of the fatigue limit with increasing absorbed UV irradiation dose.

Rubbers are nowadays widely used in many structural systems, and more particularly in transportation applications, hence, their reliability must be checked especially when they are subjected to cyclic loadings. This paper aims to discuss the state of the art of rubbers multiaxial fatigue criteria. The capability of the continuum damage mechanics based model to estimate the elastomers fatigue life under multiaxial loading is checked using a set of constant amplitude multiaxial fatigue tests conducted on a carbon-black filled styrene-butadiene rubber (SBR). Furthermore, for variable amplitude tests, the predictive capability of damage rules is achieved.

The fretting fatigue behavior of Al–Mg–Si alloy (6082-T6) was investigated using a configuration of a cylindrical pad of Z160CDV12. Experimental tests were performed under constant amplitude loading and variable loading Finite Element Analyses using ABAQUS commercial code were also performed to calculate stress distribution in the contact zone. Two multiaxial fatigue parameters, Smith-Watson-Topper “SWT”, and Crack Energy Density “ΔCED” were coupled with the linear law developed by Palmgren-Miner and the nonlinear Damage Stress Model (DSM). The estimates obtained with the modified (DSM) model are in good agreement with the experiments and seem very promising to predict fatigue life under conditions of fretting fatigue.

International audience; In this contribution, we attempt to derive a tool allowing the prediction of the stretch ratio at failure in rubber components subjected to thermal ageing. To achieve this goal, the main idea is to combine the fracture mechanics approach and the intrinsic defect concept. Using an accelerated ageing procedure for an Ethylene-Propylene-Diene Monomer (EPDM), it is first shown that the average molar mass of the elastically active chains (i.e. between crosslinks) can be used as the main indicator of the macromolecular network degradation. By introducing the time-temperature equivalence principle, a shift factor obeying to an Arrhenius law is derived, and master curves are built as well for the average molar mass as for the ultimate mechanical properties. Fracture mechanics tests are also achieved and the square root dependence of the fracture energy with the average molar mass is pointed out. Moreover, it is shown that the mechanical response could be approximated by the phantom network theory, which allows to relate the strain energy density function to the average molar mass. Assuming that the fracture of a smooth specimen is the consequence of a virtual intrinsic defect whose the size can be easily estimated, the stretch ratio at break can be therefore computed for any thermal ageing condition. The estimated values are found in a very nice agreement with EPDM experimental data, making this approach a useful tool when designing rubber components for moderate to high temperature environments.

Many multiaxial fatigue parameters are available to estimate the onset of the crack initiation in mechanical components subjected to fretting fatigue conditions. This study focuses on the ability of the cracking energy density parameter to predict the fretting fatigue life. To estimate this, obtained predictions are compared with those given by another commonly used parameter, namely the Smith–Watson–Topper parameter. First, fretting fatigue experiments were achieved using a new designed setup with a mono-contact configuration (aluminum/steel). A finite element model was used to compute the stress/strain fields around the contact zone. Because of the high stress gradient in the contact zone, the estimates of the two fatigue parameters, when using the mechanical quantities on the most loaded material point, lead to too conservative predicted values. It was therefore necessary to define a kind of process zone in which crack nucleation takes place. Using an averaging method to compute stress and strain in this zone, the obtained results show a quite good agreement between the estimated fatigue life and experimental data, whatever the used fatigue indicator. The size of this zone was then compared with the material microstructure and seems to be in the same magnitude that the average grain size.

International audience; The present work focuses on the continuum-based micromechanical modeling of the elastic-plastic stress-strain response including damage mechanisms of polymer-clay nanocomposites. The micromechanical elastic-plastic-damage model includes both the actual microstructure of the said composites using a multi-scale approach and the microstructural evolution related to damage accumulation under applied macroscopic deformation. The interfacial debonding between clay nanoparticles and polymer matrix, and the polymer matrix voiding are the two prevalent damage events considered. The tensile stress-strain response and micromechanical deformation processes of polyamide-6 and polypropylene-based systems reinforced with modified montmorillonite clay at various concentrations are experimentally investigated by a video-controlled technique. The usual shear yielding deformation mode of neat polyamide-6 is altered by the presence of clay platelets which induce a dilatational process due to interfacial debonding. In addition to matrix shear yielding, a dual-dilatational deformation mechanism by crazing and interfacial debonding is revealed in polypropylene-clay nanocomposites. Using the intrinsic deformation micromechanisms and elastic-plastic properties of the polymer matrix, and the nanocomposite structural characteristics, the micromechanical model is found to successfully describe the experimental results of the two nanocomposite materials in terms of tensile stress-strain response and inelastic volumetric strain.

International audience; A clay-induced crystal transformation has been widely pointed out in semi-crystalline polymer-clay nanocomposites, from the α-form to the γ-form in the particular case of polyamide 6 (PA6). The proposition of a predictive model taking explicitly into account the polymer crystalline structure is still needed for a reliable prediction of the structure-property relationship and for a better understanding of the reinforcement mechanism in such systems. The aim of this paper is to present an approach issued from the continuum-based micromechanical framework using self-consistency condition to predict the overall stiffness of PA6-clay nanocomposites. Besides the effect of clay particle characteristics, the micromechanical model introduces the contribution of α- and γ-form crystals in the overall stiffness by considering the PA6 matrix as a heterogeneous medium containing distinct amorphous and crystalline phases. A closed-formulation of the micromechanical model is derived using the Walpole spectral decomposition of the stiffness tensors for the two monoclinic crystalline phases. Two possible representations of the microstructure are considered: the first one considers that all the phases are independent and the second one that the γ-crystalline phase constitutes an interphase region around clay particles. The micromechanical model using the two morphological representations is used to predict the overall stiffness of PA6 nanocomposites reinforced with montmorillonite clay (adjusted from 1 wt% up to 20 wt%) for which the polymer crystalline structure was characterized by infrared spectroscopy and calorimetry. The respective role of clay particles and of two crystalline species in the stiffening of exfoliated and intercalated PA6-clay nanocomposites is discussed with respect to the micromechanical model.

International audience; The large deformation time-dependent mechanical response of rubber-like materials under cyclic loading is characterized by stress-softening, hysteresis and permanent set. To describe this set of first-order phenomena a constitutive model integrating the physics of polymer chains and their alteration under cyclic loading is proposed. The time-dependency is considered using a Zener-type framework in which the chain extensibility limit is described with both physical and phenomenological approaches. The efficiency of the proposed constitutive model is illustrated by comparisons with experimental data obtained on a styrene-butadiene rubber submitted to cyclic tension loading up to failure both in constant and variable amplitudes.

Cavitation phenomenon is studied in rubber-like materials by combining experimental, theoretical and numerical approaches. Specific tests are carried out on a Styrene Butadiene Rubber to point out main characteristics of cavitation phenomenon. Hydrostatic depression is numerically modelled using finite element method. Numerical results are compared to Ball’s and Hou & Abeyaratne’s models with regard to cavity nucleation in the material. Both models well fit experimental observations suggesting that the cavitation nucleation in elastomers depends on the confinement degree of the specimen. Finally, critical hydrostatic pressure and critical global deformation are proved to govern cavitation nucleation in the studied material. Critical loadings are identified by comparing experimental and numerical load–displacement curves.

International audience; This work describes a computational homogenization methodology to estimate the effective elastic-plastic response of random two-phase composite media. It is based on finite element simulations using three-dimensional cubic cells of different size but smaller than the deterministic representative volume element (DRVE) of the microstructure. We propose to extend the approach developed in the case of elastic heterogeneous media by Drugan and Willis (1996) and Kanit et al. (2003) to elastic-plastic composites. A specific polymer blend, made of two phases with highly contrasted properties, is selected to illustrate this approach; it consists of a random dispersion of elastic rubber spheres in an elastic-plastic glassy polymer matrix. It is found that the effective elastic-plastic response of this particulate composite can be accurately determined by computing a sufficient number of small subvolumes of fixed size extracted from the DRVE and containing different realizations of the random microstructure. In addition, the response of an individual subvolume is found anisotropic whereas the average of all subvolumes leads to recover the isotropic character of the DRVE. The necessary realization number to reach acceptable precision is given for two examples of particle volume fractions.

International audience; This contribution is focused on the Mullins effect in polyethylene. An ultra-low-density polyethylene with 0.15 crystal content, a low-density polyethylene with 0.3 crystal content and a high-density polyethylene with 0.72 crystal content are subjected to cyclic stretching over a large strain range. Experimental observations are first reported to examine how the crystal content influences the Mullins effect in polyethylene. It is found that the cyclic stretching is characterized by a stress-softening, a hysteresis and a residual strain, whose amounts depends on the crystal content and the applied strain. A unified viscohyperelastic-viscoelastic-viscoplastic constitutive model is proposed to capture the polyethylene response over a large strain range and its crystal-dependency. The macro-scale polyethylene response is decomposed into two physically distinct sources, a viscoelastic-viscoplastic intermolecular part and a viscohyperelastic network part. The local inelastic deformations of the rubbery amorphous and crystalline phases are considered by means of a micromechanical treatment using the volume fraction concept. Experimentally-based material kinetics are designed by considering the Mullins effect crystal-dependency and are introduced into the constitutive equations to capture the experimental observations. It is shown that the model is able to accurately reproduce the Mullins effect in polyethylene over a large strain range. The inherent deformation mechanisms are finally presented guided by the proposed constitutive model.

Using the fracture mechanics framework, a fracture criterion based upon the intrinsic defect concept was developed to predict the failure of rubber parts under biaxial monotonic loading. This fracture criterion requires as input data the fracture toughness of the material in terms of critical value of the J integral, the constitutive law of the material and the breaking stretch of a smooth specimen under uniaxial tension. To develop this criterion a generalized expression of the J integral under biaxial loading is proposed on the basis of finite element calculations on a RVE containing a small circular defect. The estimated failure elongations were found in very nice agreement with experimental data on two kinds of rubber materials. Moreover, we have also shown that this criterion could be extended to the failure analysis of thermoplastic polymers.

International audience; This contribution presents a continuum damage mechanics model for the high-cycle fatigue life prediction of rubber-like materials. The proposed model is an extension of that proposed by Wang et al. (2002) for multiaxial loadings. The damage strain energy release rate is first derived from a generalized Ogden strain energy density and then from the cracking energy density. A new multiaxial fatigue predictor is proposed and presented in its most general form with the aim of being applicable to all hyperelastic materials. The effects of variable amplitude and mean stretch are explicitly accounted for in the damage evolution law. The fatigue damage behavior of a carbon-filled styrene-butadiene rubber is experimentally investigated under tension, torsion and combined tension-torsion loadings both in constant and variable amplitudes, including the effects of different R ratios (i.e. different minimum and maximum stretches). The proposed model, which requires few damage parameters to be identified, is used to predict the number of cycles to failure and, a satisfactory agreement between predicted values and experimental data is clearly highlighted for the different loading paths.

International audience; This work deals with fracture of elastomers by cavitation. So, tension tests were achieved on specific volumetric specimens, the shape of which should induce void nucleation in the bulk of the material. Macroscopic behaviour of this material was related to the cavitation phenomenon. It was particularly proved that the slope break of the stress–strain curves coincides with the apparition of voids. Then, all experimental tests were numerically modelled using Finite Element Method (FEM) and results were analysed. Numerical study highlighted, among others, effects of specimen shape factor and those of filler volume fraction on the nucleation and growth of cavities.

International audience; Although several theories were more or less recently proposed to describe the Mullins effect, i.e. the stress-softening after the first load, the nonlinear equilibrium and non-equilibrium material response as well as the continuous stress-softening during fatigue loading need to be included in the analysis to propose a reliable design of rubber structures. This contribution presents for the first time a network alteration theory, based on physical interpretations of the stress-softening phenomenon, to capture the time-dependent mechanical response of elastomeric materials under fatigue loading, and this until failure. A successful physically based visco-hyperelastic model is revisited by introducing an evolution law for the physical material parameters affected by the network alteration. The general form of the model can be basically represented by two parallel networks: a nonlinear equilibrium response and a time-dependent deviation from equilibrium, in which the network parameters become functions of the damage rate (defined as the ratio of the applied cycle over the applied cycle to failure). The mechanical behavior of styrene-butadiene rubber was experimentally investigated, and the main features of the constitutive response under fatigue loading are highlighted. The experimental results demonstrate that the evolution of the normalized maximum stress only depends on the damage rate endured by the material during the fatigue loading history. The average chain length and the average chain density are then taken as functions of the damage rate in the proposed network alteration theory. The new model is found to adequately capture the important features of the observed stress–strain curves under loading–unloading for a large spectrum of strain and damage levels. The model capabilities to predict variable amplitude tests are critically discussed by comparisons with experiments.

International audience; Although few investigations recently proposed to describe the overall elastic response of polymer–clay nanocomposite materials using micromechanical-based models, the applicability of such models for nanocomposites is far from being fully established. The main point of criticism to mention is the shelving of crucial physical phenomena, such as interactions and length scale effects, generally associated by material scientists, in addition to the nanofiller aspect ratio, to the remarkable mechanical property enhancement of polymer–clay nanocomposites. In this Part I of two-part paper, we present a micromechanical approach for the prediction of the overall moduli of polymer–clay nanocomposites using a self-consistent scheme based on the double-inclusion model. This approach is used to account for the inter-inclusion and inclusion–matrix interactions. Although neglected in the models presented in the literature, the active interaction between the nanofillers should play a key role in the reinforcing effect of nano-objects dispersed in a polymer matrix. The present micromechanical model incorporates the nanostructure of clay stacks, modeled as transversely isotropic spheroids, and the so-called constrained region, modeled as an interphase around reinforcements. This latter is linked to the interfacial interaction between matrix and reinforcements that forms a region where the polymer chain mobility is reduced. To account for length scale effects, interphase thickness and particle dimensions are taken as explicit model parameters. Instead of solving iteratively the basic homogenization equation of the self-consistent scheme, our formulation yields to a pair of equations that can be solved simultaneously for the overall elastic moduli of composite materials. When the interphase is disregarded for spheroids with zero aspect ratio, our formulation coincides with the Walpole solution (J Mech Phys Solids 1969;17:235–251). Using the proposed general form, a parametric study is presented to analyze the respective influence of aspect ratio, number of silicate layers, interlayer spacing and nanoscopic size of the transversely isotropic spheroids on the overall elastic moduli of nanocomposite materials.

International audience; Experimental observations are reported on the finite deformation stress-strain response during loading-unloading of polyethylene materials covering the range of crystal volume fractions 0.15–0.72. Hyperelastic-viscoplastic constitutive equations, based on a two-phase interpretation of the microstructure, are derived. It is shown that the constitutive model adequately describes the experimental observations under loading-unloading conditions.

International audience; Polylactic acid (PLA) films were subjected to accelerated ultra-violet (UV) ageing. The UV irradiation leads to the alteration of the chemical structure which influences directly the mechanical response of the polymer. The chemical modification of the polymer was followed by gel permeation chromatography. Uniaxial tension tests were conducted at 50 °C and for different strain rates in order to characterize the large deformation response of PLA. The influence of UV irradiation on the alteration of the large deformation response of PLA was examined. A physically based elastic–viscoplastic model was used to describe the mechanical response of virgin PLA. The photodegradation effect was incorporated into the constitutive model to capture the stress–strain behaviour up to failure of aged PLA. To that end, the measured molecular weight was used as a direct input into the model. The model is shown to be in good agreement with experimental results over a wide range of UV irradiation doses.

In this work, a micromechanical model is proposed in order to predict the yield stress of polymer-based nanocomposites filled with spherical nanoparticles. The adopted approach integrates an inhomogeneous interphase around the nanoparticles. A characteristic length scale corresponding to the thickness of the interphase allows accounting for the particle size effects. The key role of particle size and features of inhomogeneous interphase on the overall initial yield surface of nanocomposites is theoretically studied.

International audience; Establishing structure–property relationships for nanoparticle/polymer composites is a fundamental task for a reliable design of such new systems. A micromechanical analytical model is proposed in the present work, in order to address the problem of stiffness and yield stress prediction in the case of nanocomposites consisting of silica nanoparticles embedded in a polymer matrix. It takes into account an interphase corresponding to a perturbed region of the polymer matrix around the nanoparticles. Its modulus is continuously graded from that of the silica nanoparticle to that of the polymer matrix. Considering the thickness of the third phase as a characteristic length scale, the influence of particle size on the overall nanocomposite behaviour is examined. The key role of the interphase on both the overall stiffness and yield stress is studied and the model output is compared to experimental data of various silica spherical nanoparticle/polymer composites extracted from the literature. The model is also used to examine the influence of interphase features on the overall nanocomposite behaviour. A finite element analysis is then achieved and the numerical results are validated using the analytical predictions. Local stress and strain distributions are analysed in order to understand the phenomena occurring at the nano-scale.

The finite element (FEM) and the boundary element methods (BEM) are well known powerful numerical techniques for solving a wide range of problems in applied science and engineering. Each method has its own advantages and disadvantages, so that it is desirable to develop a combined finite element/boundary element method approach, which makes use of their advantages and reduces their disadvantages. Several coupling techniques are proposed in the literature, but until now the incompatibility of the basic variables remains a problem to be solved. To overcome this problem, a special super-element using boundary elements based on the usual finite element technique of total potential energy minimization has been developed in this paper. The application of the most commonly used approaches in finite element method namely quarter-point elements and J-integrals techniques were examined using the proposed coupling FEM–BEM. The accuracy and efficiency of the proposed approach have been assessed for the evaluation of stress intensity factors (SIF). It was found that the FEM–BEM coupling technique gives more accurate values of the stress intensity factors with fewer degrees of freedom.

International audience; The 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.

Both natural and man-made materials, often exhibit heterogeneous structure, depending on the scale of observation. This heterogeneous aspect acts as an important factor on their macroscopic mechanical behaviour response. One of the most reliable ways to obtain a quantitative relation between different scales is the use of the homogenisation methods. The fundamental assumption in these methods is the existence of a unit cell that is representative for the microstructure of the material under consideration, the so-called representative volume element (RVE). Modelling the mechanical behaviour of heterogeneous elastic–viscoplastic solids under finite strains framework, by using numerical homogenisation methodology is the main goal purchased in this work. Generally, the macroscopic quantities are formulated as average values of the corresponding microscopic state variables. The average of a quantity is taken over the region occupied by the unit cell [R. Hill, Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids 11 (1963) 357–372]. The method which is proposed here, has been validated by comparing results of F.E. simulations with the experimental results. The composite elements consist of a polymeric continuous matrix of polymethylmethacrylate filled with rubber particles, to obtain the so-called RT-PMMA (rubber toughened PMMA). An hyper-elastic–viscoplastic description was developed to account for both finite strains and time and history dependence mechanical behaviour that exhibits most of polymers. With regard to the influence of the damage in such kinds of composites materials, the evolution of the cavitation mechanism, identified as one of the possible damage process, is also examined.

The assumption of imperfect interface using the multi-scale approach enables a more realistic description of composite behavior. In a heterogeneous material, the junctions between the constituents do not always play their full role because defects may appear in these highly constrained regions. In this work, the interface is considered as an elastic medium with vanishing thickness. It can lead to a jump in the displacement but continuity of the traction across the interface is possible. The interface is modelled analytically and is given two stiffness parameters which characterise its normal and tangential extension. A simple polynomial form of the displacement jump is used to implement this condition together with the approach of Eshelby. The overall elastic moduli of a two-phase composite is computed by taking into account the existence of imperfect interfaces. The same interfacial model is modelled using the finite element analysis for predicting the macroscopic response of the composite.

International audience; A computational homogenization study of three-dimensional cubic cells is presented to estimate the overall yield surface of random porous media covering a wide range of stress triaxiality ratios. The representativity of the overall yield surface estimates is examined using cubic cells containing randomly distributed and oriented voids with different volume fractions and shapes (spherical and oblate/prolate). The computational results are compared with some existing Gurson-type yield criteria. The extension of the Gurson-Tvergaard model recently proposed by Fritzen et al. (2012) for spherical cavities is shown in good agreement with the computational results for all investigated porosities.

This paper dealing with the fracture of rubber-like materials is a continuation of our previous works (Ait Hocine et al., 1996, 1998). Single specimen methods for measuring the J-integral and, so, its critical value J c (fracture surface energy) are investigated combining experimental data and finite elements analysis. It shown that the formula of J established by Rivlin et al. in the case of the SENT geometry can be extended to the DENT specimen containing small crack lengths (a/w≤0.3). Moreover, considering DENT and pure-shear (PS) specimens, alternative expressions of this parameter, based on the η factor, are proposed and a good agreement is obtained between the numerical calculations and the experimental data whenever available. The critical values of J are found constant for the two tested materials. Finally, it's pointed out that, at the onset of crack growth, the strain energy density along the crack axis is independent on both the crack length and the specimen geometry.

In this paper, we have verified the validity of some formulations allowing the determination of the fracture surface energy in the case of rubber-like materials. The J-integral is chosen as a fracture characterizing parameter which is experimentally determined by considering a multiplying form that; numerically evaluated using a finite element method. The numerical results are compared to the experimental data and a good agreement has been pointed out for the deeply cracked specimen (a/w≥0.5). Below this limit, a significant divergence is observed which is attributed to a lack of accuracy of the experimental data processing.

International audience; The mechanical response of high-density polyethylene (HDPE) was examined under different stress states. The biaxial yielding of HDPE material was investigated from a series of biaxial shear/tension and shear/compression tests using butterfly-shaped specimens deformed with an Arcan apparatus equipped with a digital image correlation (DIC) system for local strain measurements. In order to investigate a wider range of stress states, notched round bar specimens with different curvature radii were also tested using a video-controlled tensile testing apparatus. More conventional mechanical loading paths (uniaxial tension/compression and simple shear tests) were also examined to provide better insights on the stress state effects. The present investigation is more particularly focused on the yield envelope determination of HDPE material. A combined DIC and analytical approach was proposed to measure the yield strengths of butterfly-shaped specimens in the region where the yielding occurs. The relevance of classical yield criteria, exhibiting dependence on both the deviatoric and hydrostatic stresses, is verified. Considering HDPE as a heterogeneous medium consisting of a percolated crystalline matrix and a discrete amorphous phase, a micromechanics-based yield locus is tested. The experimental biaxial yield data are found to support this theoretical yield criterion and thus the suggested morphological representation for high-crystalline polymers.

International audience; Above the glass transition temperature, a semi-crystalline polymer can behave like an elastomer or a stiff polymer according to the crystal content. For a reliable design of such polymeric materials, it is of prime importance to dispose a unified constitutive modeling able to capture the transition from thermoplastic-like to elastomeric-like mechanical response, as the crystal content changes. This work deals with polyethylene materials containing a wide range of crystal fractions, stretched under large strains at room temperature and different strain rates. A large-strain viscoelastic-viscoplastic approach is adopted to describe the mechanical response of these polymers. In order to identify the model parameters, an analytical deterministic scheme and a practical, "engineering-like", numerical tool, based on a genetic algorithm are developed. A common point of manipulated constitutive models is that the elementary deformation mechanisms are described by two parallel resistances; one describes the intermolecular interactions and the other deals with the molecular network stretching and orientation process. In a first approach, the semi-crystalline polymers are considered as homogeneous media; at each crystal content, the semi-crystalline polymer is thus considered as a new material and a new set of model parameters is provided. In a second approach, the semi-crystalline polymer is seen as a two-phase composite, and the effective contribution of the crystalline and amorphous phases to the overall mechanical response is integrated in the constitutive model, which allows simulating the transition from thermoplastic-like to elastomeric-like mechanical response. In this case, one set of model parameters is needed, the only variable being the crystal volume fraction. The identification results obtained using deterministic and numerical methods are discussed.

International audience; A thermo-visco-hyperelastic constitutive model, in accordance with the second thermodynamics principle, is formulated to describe the self-heating evolution in elastomeric materials under cyclic loading. The mechanical part of the model is based upon a Zener rheological representation in which the specific free energy potential is dependent on an added internal variable, allowing the description of the time-dependent mechanical response. The large strain mechanical behavior is described using a Langevin spring, while the continuous stress-softening under cyclic loading is taken into account by means of a network alteration kinetics. The thermo-mechanical coupling is defined by postulating the existence of a dissipation pseudo-potential, function of the viscous dilatation tensor. The proposed model is fully three-dimensional and is implemented into a finite element code. The model parameters are identified using experimental data obtained on a styrene-butadiene rubber under a given strain rate for different strain conditions. Predicted evolutions given by the model for other strain rates are found in good agreement with the experimental data.

International audience; The macroscopic yield response of random porous media containing two populations of spherical voids is investigated via large volume computations. The computed yield surface is compared to analytical criteria recently developed for the above-mentioned porous media. To overcome the observed discrepancies, the analytical models are modified by introducing additional parameters which are numerically derived. These parameters depend neither on the void volume fraction nor on the void size. Large volume computations are also used to build the yield surface for porous media containing a single population of randomly distributed spherical voids. The results show that, for an identical fraction of porosities, there is no significant difference between a double and a single population of voids. This result implies that the yield response of porous media containing two populations of voids may be also described by analytical criteria developed in the case of a single population.

International audience; The purpose of this study is to give an insight on the existing fatigue criteria for rubbers and their capability to predict the fatigue life of a carbon-filled styrene-butadiene rubber (SBR) under constant and variable amplitude tests. Strain, stress and energy-based predictors are compiled using combinations of tension and torsion tests. Stress and cracking energy-based predictors are found to have the best prediction capability for constant amplitude tests. Variable amplitude tests highlight the nonlinear nature of the damage by fatigue of the SBR material. A comparison between several cumulative laws is provided.

International audience; Polymer clay nanocomposites (PCNs) have been seen as the most novel materials in engineering applications since they exhibit significant improvement in mechanical and physical properties. Indeed, with few amount of organoclay, PCNs exhibit enhanced mechanical, optical, thermal and liquid or gas barrier properties compared to pure polymers and to their counterpart microcomposites. Thus, organoclays are extensively used as precursors in the preparation of PCNs. They are the best candidate in reinforcing PCNs because of the lightweight and the high availability of clay minerals in the nature. However, structure and physical phenomena arising at molecular level in organoclays, and subsequently in PCNs, are not completely or difficultly accessible with existing experimental techniques. In this work, molecular dynamics (MD) simulation was conducted using the combination of two force fields (CLAYFF and CHARMM) to evaluate the thermodynamics and structural properties of organoclay such as heat capacities, isothermal bulk modulus, density, basal spacing and chains arrangement in the interlayer spacing. Our results regarding the basal spacing and density are in fairly good agreement with available experimental data. This allows us to validate the use of the two force fields to represent interactions in organoclays. The effect of the cation exchange capacity (CEC) on the basal spacing and the thermodynamics properties is assessed. We found, through our MD simulation, that the calculated isothermal bulk modulus is in good agreement with the density value of organoclays with two different CEC.

International audience; Polyethylene-based polymers as biomedical materials can contribute to a wide range of biomechanical applications. Therefore, it is important to identify, analyse, and predict with precision their mechanical behaviour. Polyethylene materials are semi-crystalline systems consisting of both amorphous and crystalline phases interacting in a rather complex manner. When the amorphous phase is in the rubbery state, the mechanical behaviour is strongly dependent on the crystal fraction, therefore leading to essentially thermoplastic or elastomeric responses. In this study, the finite deformation stress-strain response of polyethylene materials is modelled by considering these semi-crystalline polymers as two-phase heterogeneous media in order to provide insight into the role of crystalline and amorphous phases on the macro-behaviour and on the material deformation resistances, i.e. intermolecular and network resistances. A hyperelastic-viscoplastic model is developed in contemplation of representing the overall mechanical response of polyethylene materials under large deformation. An evolutionary optimization procedure based on a genetic algorithm is developed to identify the model parameters at different strain rates. The identification results show good agreement with experimental data, demonstrating the usefulness of the proposed approach: the constitutive model, with only one set of identified parameters, allows reproducing the stress-strain behaviour of polyethylene materials exhibiting a wide range of crystallinities, the crystal content becoming the only variable of the model.

The general purpose of our study is the determination of the energy parameter J when dealing with fracture of rubber-like materials. The energy parameter J is expressed in a multiplicative form in which a calibration factor is introduced in order to take into account the finite dimensions of the specimen. The parameter J, issued from fracture tests performed on S.E.N.T specimen of an E.P.D.M rubber is compared with the the J integral which is computed using a finite element procedure for the non-linear elastic materials with large deformation. The numerical results are in good agreement with the experimental data when considering the deeply cracked specimen (a/w ≥ 0.5). Below this limit, a divergence is pointed out which is attributed to a lack of accuracy of the identification procedure used to determine the experimental calibration factor. When this one is determined using the numerical J integral results, a better concordance is obtained.

International audience; Micromechanical 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.

International audience; In this paper, fracture mechanics concepts are reviewed and their relevance to examine the toughness of highly deformable materials such as high-density polyethylene (HDPE) pipe materials is discussed. Using two different specimen configurations (single edge notched bending and compact tension), it was found that the J−R approach is unable to give pertinent indications on fracture toughness of HDPE. Alternatively, applying the essential work of fracture approach to double edge notched tension specimen, seems a more appropriate way to measure the fracture strength of HDPE and therefore to analyze the fracture process of such materials. Nevertheless, the severe necking occurring at the crack tip and in the plastic zone makes difficult the crack growth measurement, which clearly depends on the strain state and on the stress triaxiality level.

International audience; Finite element analyses are used to simulate the response of glass impacted by solid particles. The Sun-Khaleel stress-based continuum damage mechanics (CDM) model is used to describe the constitutive behavior of glass. The contribution of different cracking systems in the strength degradation of glass is explicitly taken into account by the anisotropic CDM model which is enhanced by coupling with a vanishing element technique. Focusing on the initiation and propagation of the ring/cone crack, a combined numerical and experimental approach is proposed to estimate the CDM stress limits. The changes in contact characteristics due to erosion damage mechanism in glass are then studied using the developed predictive tool. In accordance with available experimental observations, it is found that the impact-induced damage reduces the energy restitution coefficient and increases the contact time.

International audience; The mechanical stress–strain behaviour of polyethylene (PE) materials under finite strains is studied both experimentally and theoretically. In order to gain insight into the structure and physical properties of investigated PE materials, a series of thermal (DSC and DMTA) and microstructural (small-angle X-ray scattering and AFM) characterizations have been undertaken. The influence of crystallinity on the various features of the tensile stress–strain response is considered over a large strain range, implying thermoplastic-like to elastomer-like mechanical behaviour. A physically-based hyperelastic–viscoplastic approach was adopted to develop a pertinent model for describing the mechanical behaviour of PE materials under finite strains. The semicrystalline polymer is being treated as a heterogeneous medium, and the model is based on a two-phase representation of the microstructure. The effective contribution of the crystalline and amorphous phases to the overall intermolecular resistance to deformation is treated in a composite framework, and coupled to a molecular network resistance to stretching and chain orientation capturing the overall strain hardening response. In order to extract the individual constitutive response of crystalline and amorphous phases, a proper identification scheme based on a deterministic approach was elaborated using the tensile test data of PE materials under different strain rates. Comparisons between the constitutive model and experiments show fair agreement over a wide range of crystallinities (from 15% to 72%) and strain rates. The constitutive model is found to successfully capture the important features of the observed monotonic stress–strain response: the thermoplastic-like behaviour for high crystallinity includes a stiff initial response, a yield-like event followed by a gradual increase of strain hardening at very large strains; for the elastomer-like behaviour observed in the low crystallinity material, the strain hardening response is largely predominant. Strain recovery upon unloading increases with decreasing crystallinity: this is quantitatively well reproduced for high crystallinity materials, whereas predictions significantly deviate from experiments at low crystallinity. Model refinements are finally proposed in order to improve the ability of the constitutive equations to predict the nonlinear unloading response whatever the crystal content.

International audience; In order to predict the nanostructure as well as the particle size dependence of the elastic-plastic stress-strain response of polymer/clay nanocomposites, a micromechanical model based upon a multiscale approach starting from the nanostructure is proposed. The multiscale micromechanical model takes into account the interphase between the polymeric matrix and the inorganic reinforcement, and the intercalated nanostructure. Considering the interphase thickness as a characteristic length scale, the nanoparticle size effect is explicitly introduced in the present model. The intercalated nanostructure is taken into account according to an equivalent stiffness method in which the clay stacks are replaced by homogeneous nanoparticles with predetermined equivalent anisotropic stiffness. The physical and mechanical properties of nylon-6/montmorillonite nanocomposites (with clay weight fractions ranging from 1 up to 7.5%) are investigated by means of differential scanning calorimetry, dynamic mechanical analysis, thermogravimetric analysis and video-controlled tensile mechanical tests. The microstructure was characterized by transmission electron microscopy. The amount of interphase was estimated from the thermal analysis. The reinforcing effect of clay is discussed with respect to the multiscale micromechanical model. A parametric study is carried out to investigate the effect of nanoparticle shape and size and nanoparticle structural parameters (i.e. number of clay layers in the nanoparticle and interlayer spacing) on the elastic-plastic stress-strain response of polymer/clay nanocomposites. Comparison of the model results with the experimental data demonstrates that the evaluation of the reinforcing effect of clay involves considering the elastic stiffness and yield stress simultaneously. It was further found that the model correctly predicts the elastic-plastic stress-strain data.

International audience; Polyamide-6 (PA6) based nanocomposites were prepared using a modified montmorillonite (MMT) Cloisite 20A as nanofillers. The silicate weight fraction of the prepared nanocomposites, determined by burning off the PA6 matrix, was ranged from 0.2 wt% up to 7.5 wt%. The thermomechanical properties of both the neat PA6 and the PA6 filled with MMT nanoclay were measured by means of uniaxial tension tests and dynamic mechanical thermoanalysis, their crystallinity analyzed by differential scanning calorimetry and their morphology observed by transmission electron microscopy. The elastic stiffness of PA6–clay nanocomposites was examined under two moisture levels and was analyzed with the theory formulated in the Part I of this work. Predicted results are found in good agreement with our experiments. The model capabilities are also critically discussed by comparisons with both experiments issued from the literature and the Mori–Tanaka approach widely used in recent literature. It is demonstrated that the proposed micromechanical model is more efficient than the Mori–Tanaka approach. Moreover, the obtained results support the idea that the elastic stiffness of polymer–clay nanocomposites is governed by the same mechanisms as microcomposites, the effects of particle dimension or constrained region being of a second order.

International audience; Numerical and experimental aspects of rubber fatigue crack initiation are investigated in this study. A parameter based on the strain energy density (SED) and predicting the onset of primary crack and its probable orientation was identified for such materials according to the investigations of Mars and Fatemi [1]. In a last work, we have analytically developed this criterion for simple tension (UT), biaxial tension (BT) and simple shear (SS) loadings in the framework of finite strains. The results denote the possibility to predict the orientation plane in which the primary crack would be expected to occur in a material. Then, it was implemented in a finite elements (FE) program. FE and analytical results for the usual strain states were compared and perfect agreement was highlighted. In this study, the load history dependence of the criterion is also pointed out and discussed. Finally, to evaluate life time up to crack nucleation, we have achieved a set of experimental fatigue tests using uniaxial tension (UT) and pure shear (PS) test specimens containing a hole in order to localise the crack initiation. We have also exploited a literature database issued from uniaxial and torsion fatigue tests. The obtained results prove the efficiency of the criterion to describe the fatigue life of rubbers under multiaxial loading.

International audience; In the present contribution, the relationship between the fatigue life of styrene-butadiene rubber (SBR) and the stretch amplitude was established. Focusing on the multiaxial loading effect on the life duration of SBR, experimental tests were conducted using cylindrical specimens subjected to tension and torsion loadings under constant and variable amplitudes. Based upon the continuum damage mechanics approach, a three-dimensional model was derived and coupled with the cracking energy density criterion to predict the fatigue life of SBR. The capabilities of the model, which requires only three damage parameters to be identified, were analysed and a good agreement between predicted values and experimental data were clearly highlighted for tension and torsion loadings both in constant and variable amplitudes.

International audience; The purpose of this study is to propose a fatigue criterion based on the continuum damage mechanics (CDM) theory to predict the fatigue life of rubber-like materials. The fatigue life of a styrene-butadiene rubber was investigated under tension and twist loadings. Using a generalized Ogden strain energy density function, a CDM model was derived in order to express the fatigue life as a function of an equivalent stress. Since the obtained model was unable to fit all the experimental results, a modified version, which shows a fair agreement with our data, is finally proposed.