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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; 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 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.

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.

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; 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.

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; 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.

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; 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; 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; In this work, the large deformation behaviour under monotonic loading and unloading of a high density polyethylene (HDPE) is studied. To analyze the nonlinear time-dependent response of the material, mechanical tests were conducted at room temperature under constant true strain rates and stress relaxation conditions. A physically-based inelastic model written under finite strain formulation is proposed to describe the mechanical behaviour of HDPE. In the model, the inelastic mechanisms involve two parallel elements: a visco-hyperelastic network resistance acting in parallel with a viscoelastic–viscoplastic intermolecular resistance where the amorphous and crystalline phases are explicitly taken into consideration. The semicrystalline polymer is considered as a two-phase composite. The influence of the crystallinity on the loading and unloading behaviour is investigated. Numerical results are compared to experimental data. It is shown that the model is able to accurately reproduce the experimental observations corresponding to monotonic loading, unloading and stress relaxation behaviours at different strain levels. Finally, the model capabilities to capture cyclic loading–unloading behaviour up to large strains are discussed. To demonstrate the improved modelling capabilities, simulations are also performed using the original model of Boyce et al. [Boyce, M.C., Socrate, S., Llana, P.G., 2000. Constitutive model for the finite deformation stress–strain behavior of poly(ethylene terephthalate) above the glass transition. Polymer 41, 2183–2201] modified by Ahzi et al. [Ahzi, S., Makradi, A., Gregory, R.V., Edie, D.D., 2003. Modeling of deformation behavior and strain-induced crystallization in poly(ethylene terephthalate) above the glass transition temperature. Mechanics of Materials 35, 1139–1148].

International audience; The present work focuses on the development of a physically-based model for large deformation stress–strain response and anisotropic damage in rubber-toughened glassy polymers. The main features leading to a microstructural evolution (regarding cavitation, void aspect ratio, matrix plastic anisotropy and rubbery phase deformation) in rubber-toughened glassy polymers are introduced in the proposed constitutive model. The constitutive response of the glassy polymer matrix is modelled using the hyperelastic–viscoplastic model of (Boyce et al., 1988) and (Boyce et al., 2000). The deformation mechanisms of the matrix material are accounted for by two resistances: an elastic–viscoplastic isotropic intermolecular resistance acting in parallel with a visco-hyperelastic anisotropic network resistance, each resistance being modified to account for damage effects by void growth with a variation of the void aspect ratio. The effective contribution of the hyperelastic particles to the overall composite behaviour is taken into account by treating the overall system in a composite scheme framework. The capabilities of the proposed constitutive model are checked by comparing experimental data with numerical simulations. The deformation behaviour of rubber-toughened poly(methyl methacrylate) was investigated experimentally in tension at a temperature of 80 °C and for different constant true strain rates monitored by a video-controlled technique. The reinforcing phase is of the soft core–hard shell type and its diameter is of the order of one hundred nanometers. The particle volume fraction was adjusted from 15% to 45% by increments of 5%. The stress–strain response and the inelastic volumetric strain are found to depend markedly on particle volume fraction. For a wide range of rubber volume fractions, the model simulations are in good agreement with the experimental results. Finally, a parametric analysis demonstrates the importance of accounting for void shape, matrix plastic anisotropy and rubber content.

International audience; Equal channel angular extrusion (ECAE) is a relatively novel deformation process used to produce severe plastic deformation by simple shear of materials with the aim to improve their mechanical properties. In this study, the influence of ram speed, friction, processing route, number of passes and back-pressure on pressing force and inhomogeneous behaviour during ECAE of high density polyethylene and polypropylene was investigated by finite element modelling (FEM) and experimental testing. Digital image correlation method was used to measure the surface deformation of the sample during ECAE process. A good correlation was found between the FEM simulations and the experimental results. The strain distribution is not homogeneous and a large residual curvature is remaining after complete extrusion without back-pressure. In order to improve the homogeneity of strain distribution, it is suggested, based on the present results, to use a tool with a low corner angle in combination with the application of a back-pressure on the sample end at the exit channel.

The present Note concerns the formulation, implementation and a first application of a micromechanically based hyperelastic damage model. The approach is based on the second order homogenization method proposed by Lopez-Pamies and Ponte Castañeda (2000) for hyperelastic composites and recently developed by Lopez-Pamies and Ponte Castañeda (2007) in the case of porous elastomers. We first implement the method and proceed to its verification by comparison with Finite Element simulations on a unit cell. Taking advantage of this validation and by using standard thermodynamics arguments, we propose an hyperelastic damage model founded on voids growth phenomena. Finally, we provide an example of validation of the model by comparison with experimental data obtained on an EPDM/PP composite.

International audience; We present a 3D implementation and verification of a micromechanical model dedicated to highly compressible hyperelastic composites having a random microstructure. The model is based on the second-order method proposed by Ponte Castañeda and Tiberio [P. Ponte Castañeda, E., Tiberio, J. Mech. Phys. Solids 48 (2000) 1389–1411]. After recalling the basic principles of this non-linear homogenization technique, we describe its application to composites made up of an hyperelastic matrix and deformable (or rigid) spherical inclusions. The inclusions can be either particles or voids. Computational issues related to the implementation of the model are also presented. In order to provide a rigorous verification of the model for a large range of material contrasts, unit cell computations are performed for reinforced or porous hyperelastic materials. It is shown that in the two cases, the predictions of the model are in a good agreement with the reference finite elements solutions. Finally, voids shape effects on the macroscopic behavior of porous hyperelastic materials are analyzed.

Constitutive equations are proposed in order to describe the elasto-viscoplastic damage behaviour of polymers. The behaviour is well accounted for by a modified Bodner–Partom model comprising hydrostatic and void evolution terms. The true stress–strain and volumetric strain behaviour of typical rubber-toughened glassy polymers (RTPMMA and HIPS) were experimentally determined at constant local true strain rate by using a video-controlled technique. Successful agreement is obtained between experimental results and the proposed model.

The present paper is focused on the numerical simulation of a glass plate subjected to static indentation by a spherical indenter. For this purpose, a combined approach of continuum damage mechanics (CDM) and fracture mechanics is performed. Results provided by an axisymmetric finite element model were compared with analytical solutions. A CDM based constitutive model with an anisotropic damage tensor was selected and implemented into a finite element code to study the damage of glass. The numerical results were analysed through the framework of the stress and damage distribution. Various regions with critical damage values were therefore predicted in good agreement with the experimental observations in the literature. In these regions, the directions of crack propagation, including both cracks initiating on the surface as well as in the bulk, were predicted using the strain energy density factor. Predicted directions were found in good agreement with those experimentally obtained in the literature results.

In this study, a modelization of the viscoplastic behavior of amorphous polymers is proposed, from an approach originally developed for metal behavior at high temperature, in which state variable constitutive equations have been modified. A procedure for the identification of model parameters is developed through the use of experimental data from both uniaxial compressive tests extracted from the literature and uniaxial tensile tests performed in this study across a variety of strain rates. The numerical algorithm shows that the predictions of this model well describe qualitatively and quantitatively the intrinsic softening immediately after yielding and the subsequent progressive orientational hardening corresponding to the response of two polymers, amorphous polyethylene terephthalate and rubber toughened polymethyl methacrylate.

The influence of initial yield strain, material nonlinearity characteristics (perfectly plastic, strain hardening and strain softening) and die geometry on the deformation behaviour of a sample in an equal-channel angular extrusion process was simulated by the finite element method. The results indicate that plastic strain heterogeneity and sample bending increase with initial yield strain magnitude while the maximum processing load is reduced. In order to validate the numerical results, experiments were conducted on representative polymers.

The goal of this work is to numerically show by using finite element method the influence of key factors on the mechanical response of a workpiece in equal channel angular extrusion (ECAE) process. Various geometrical parameters (channel angle, outer corner angle and inner radius) and material properties were considered in the numerical calculations with a view to the use of the process to polymers.

The process of fatigue failure of materials is generally described by two phases: crack initiation and crack propagation. This study concerns the crack initiation in rubbers submitted to a cyclic loading. A parameter based on the strain energy density (SED) and predicting the onset of primary crack and its probable orientation has been identified for such materials according to the investigations of Mars and Fatemi. More precisely, this criterion has been analytically developed in the cases of simple tension, biaxial tension and simple shear loadings by assuming large 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 in order to be applied to structures under any kind of the strain states. A good agreement was obtained between FE and analytical results for the usual strain states. Finally, to evaluate lifetime 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 localize the crack initiation. The obtained results proved the efficiency of the criterion to describe the fatigue life of rubbers under multiaxial loading.

The plastic response of a polymer during equal channel angular extrusion (ECAE) at room temperature has been investigated by numerical simulations. The objective of this paper is to provide some basic understanding of the plastic flow in the polymer during one ECAE pass considering various process parameters such as extrusion velocity, friction conditions and die geometry. The distribution of strains, strain rates and stresses, the deformation behaviour of the sample and the load–displacement curves were analysed for slow and fast extrusion by taking into account material non-linearity of a typical semicrystalline polymer (HDPE).

In this work, experimental tests in tension on a RT-PMMA material have been achieved under various constant true strain rates and at room temperature. The volumetric dilatation was determined in real time during the deformation by videomeasurements. The experimental results have revealed the presence of both the nucleation and growth deformation mechanisms. Modified viscoplastic constitutive equations for homogeneous glassy polymers at isothermal loading, including strain softening and strain hardening, are proposed. Such a model is based upon an approach originally developed for metals at high temperature. Next, this modified model is coupled with a micromechanics formulation, using the Gurson–Tvergaard model, to investigate the macroscopic mechanical response of the RT-PMMA. The constitutive relation includes strain softening, strain hardening, strain rate sensitivity and void evolution. In the test conditions, the modified viscoplastic model coupled with the original Gurson–Tvergaard model produce quantitative agreement with experimental observations.

Ductile fracture of an 2024-T351 aluminium alloy has been investigated using a central crack panel (CCP). In order to predict rupture, two models using the local approach to fracture mechanics were verified: the uncoupled Rice and Tracey void growth model and the coupled Rousselier model based on continuum damage mechanics. A finite element analysis has been performed in order to verify the capability of these models to predict the crack extension.

International audience; A combined approach including experimental investigation and constitutive modelling was followed in this work to study the stress–strain behaviour of rubber-toughened glassy polymers. The large inelastic deformation response of rubber-toughened poly(methyl methacrylate) (RT-PMMA) was experimentally studied under uniaxial compression tests at different strain rates and temperatures. The studied composite system consists of spherical core–shell (PMMA hard shell and soft rubber core) particles embedded in a PMMA matrix. The influence of particle concentration (ranging from 0% to 45%) on the macroscopic behaviour was also investigated from small to large strain. The physically based hyperelastic–viscoplastic constitutive model of Boyce–Socrate–Llana was extended to describe the stress–strain behaviour of rubber-toughened glassy polymers. The model accounts for the effective contribution of the two polymeric phases to the overall composite macroscopic behaviour, by including in the original model the hyperelastic deformation of rubber particles. The capabilities of the model to describe the rate-dependent yield and post-yield behaviour of PMMA over a wide range of temperatures and strain rates are pointed out. The model is able to successfully capture the significant features of the stress–strain behaviour including the initial linear elasticity, the gradual rollover to yield, the strain softening after yield (when it exists) followed by the strain hardening. Its predictive capabilities are further tested by comparison with compression data on RT-PMMA for different rubber contents.