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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.

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.

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; 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; 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.

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; Severe plastic deformation by equal channel angular extrusion (ECAE) is an ingenious deformation process used to modify texture and microstructure without reducing sample cross-section. The application of single ECAE pass to polypropylene (PP) was meticulously investigated at room temperature using a 90° die-angle tooling. The ECAE-induced deformation behaviour was examined in relation to the load versus ram-displacement curves. Depending on extrusion conditions, PP displayed various types of plastic flow. For ram velocities beyond 4.5 mm/min, severe shear bands consisting of successive translucent and opaque bands were observed, accompanied on the top surface by more or less pronounced periodic waves. Although the application of a back-pressure significantly reduced the wave and shear-banding phenomena, slightly inhomogeneous shear deformation was still observed. Shear bands were only suppressed by decreasing extrusion velocity. The strain-induced crystalline microstructure was investigated by X-ray scattering. Shear-banded samples exhibited a strong texturing of the (hk0) planes along the shear direction in the translucent bands whereas perfect crystalline isotropy appeared in the opaque bands. Application of back-pressure and/or reducing ram velocity resulted in uniform texturing along the extruded sample. Yet, texturing changed from single shear to twin-like shear orientation about the shear direction. Mechanical properties changes of the extruded samples due to back-pressure and extrusion velocity effects were analyzed via uniaxial tensile tests. The tensile samples displayed multiple strain localizations in shear-banded materials whereas quite homogeneous deformation appeared for non-banded ones. These effects were connected with the crystalline texturing. The results also revealed significant increase in the strain hardening after ECAE. Digital image correlation technique suitable for large deformation was used for determining the full-field strain of the tensile samples in relation to tensile strain and ECAE conditions.

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.

To provide a better understanding of the relationship between nanostructure and overall material stiffness in the case of polymer/clay nanocomposites, both analytical and finite element modeling were considered. A micromechanical analytical approach based on a multiscale framework is presented in which special attention is devoted to the constrained region around reinforcements. The thickness of the constrained region is seen as a characteristic length scale and the effect of particle size is explicitly introduced in the model. Moreover, the constrained region presents graded properties. The hierarchical morphology of intercalated silicate stacks is also explicitly introduced in the micromechanical model from an equivalent stiffness method in which the silicate stacks are replaced by homogeneous particles with constructed equivalent anisotropic stiffness. The orientational averaging process is used to derive the overall stiffness tensor of nanocomposite materials containing randomly oriented reinforcements. The respective influence of volume fraction, aspect ratio, size and orientation of the reinforcements, matrix properties, number of silicate layers per stack, and interlayer spacing on the overall nanocomposite stiffness is analyzed. The overall stiffness of polymer/clay nanocomposite systems is also evaluated by means of finite element simulations and the results compare favorably with model predictions. From an experimental point of view, relevant morphological and mechanical data were obtained on polyamide-6 nanocomposites prepared using a modified montmorillonite Cloisite 30B and an unmodified sodium montmorillonite Cloisite Na+. The amount of constrained region around reinforcements was estimated using results issued from dynamic mechanical analyses and differential scanning calorimetry. Comparison to the model clearly underlines the contribution of the constrained region to the stiffness improvement. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

International audience; Equal channel angular extrusion (ECAE) is a relatively novel forming process to modify microstructure via severe plastic deformation without modification of the sample cross section. In this study, an optimized design of die geometry is presented, which improves homogeneity of the plastic deformation and decreases the pressing force required for extrusion. Then, a typical semicrystalline polymer (high density polyethylene) was subjected to multipass ECAE using two different processing routes: route A where the sample orientation is kept constant between passes and route C where the sample is rotated by 180 deg. Compression tests at room temperature and under different strain rates were used to identify the material parameters of a phenomenological elastic-viscoplastic model. Two-dimensional finite element analysis of ECAE process was carried out, thus allowing to check out the homogeneity of the plastic strain distribution. The effects of die geometry, number of passes, processing route, and friction coefficient on the plastic strain distribution were studied. The simulations were performed for three channel angles (i.e., 90 deg, 120 deg, and 135 deg), considering different corner angles. According to simulation results, recommendations on the angular extrusion of the polymer are provided for improving die and process performance.

International audience; In this study the non-linear finite element method is used to analyse the effect of presence of microcavity near a crack tip on the variation of the shape and the size of the plastic zone ahead of the crack tip in the case of confined plasticity. The FE Code Franc2D/L is used to carry out this objective. The effect of the interdistance crack tip-microcavity on the plastic zone size is highlighted. The obtained results show that the presence of the microcavity affects in very significant way the shape and the size of the crack plastic zone. The relative distance between the crack tip and the microcavity has a very important effect on the size of the confined plastic zone.

In this work, fracture of elastomers is analyzed using global and local approaches, combining experiments, analytical developments, and finite element calculations. The J-integral is chosen as a global parameter characterizing crack initiation in such materials. Particular attention is paid to single specimen methods for measuring the fracture surface energy. More precisely, models developed in the literature are summarized and, because of the lack of accuracy of these models, an original pertinent expression of J is proposed by analogy with linear elastic fracture mechanics frameworks. However, the J-integral is not able to predict the kinetic or the propagation direction of a crack. Thus, some local parameters are examined: principal strains, principal stresses, and the strain energy density (SED) factor. Results revealed that all these parameters represent reasonable indicators of the crack propagation direction in elastomers. Moreover, unlike maximal principal stress and SED factor, maximal principal strain seems to govern the crack initiation in this kind of materials. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

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.

Equal channel angular extrusion (ECAE) is a powerful tool to modify microstructure via high plastic deformation without altering sample geometry. This article investigates the behavior of a polypropylene processed by ECAE. A finite element analysis in which the material constitutive law is coupled with damage by means of Gurson-Tvergaard damage potential allowed to model experimental tests achieved on this material. Such a modeling allows the prediction of the extrusion load, strain and stress fields, and void volume fraction distribution. The need for the use of a back-pressure is highlighted.

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.

Videomeasurements were used to estimate the damage in chopped random glass fiber polymer–matrix composites. In order to predict the overall mechanical behaviour, voiding evolution induced by fiber debonding is incorporated into a micromechanics-based constitutive model. The comparison between the experimental data and the numerical predictions shows a very good agreement.

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.

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

The aim of this paper is to propose a new fracture criterion of rubber-like materials under plane stress loading. Our experimental data already published [A. Hamdi, M. Nait Abdelaziz, N. Ait Hocine, P. Heuillet, N. Benseddiq, Fracture criteria of rubber like-materials under plane stress conditions. Polym. Test. 25(9) (2006) 994–1005] are herein completed by results obtained from pure shear tests and then further analysed. In this analysis, we used a theoretical approach based on a reference axis change principle, introduced earlier by Neviere et al. [A strain based design criterion for solid propellant rocket motors. Proceedings OTAN, Symposium on Combat Survivability of Air, Sea and Land Vehicles, Alborg, Denmark, 2002, pp. 23–26] for the case of solid propellant materials. Logarithmic extensions evaluated in a specific coordinates system were introduced in the analytical development, which leads to identifying a relevant rubber fracture criterion. The ultimate experimental extensions were compared with the predictions of this criterion and good agreement was observed.

In this work, we attempt to derive a fracture criterion for filled and unfilled elastomer vulcanizates and thermoplastics from a set of experimental data. Firstly, fracture criteria reported in the literature have been applied to experimental data obtained from tests including various loading modes (simple tension, equal biaxial tension and biaxial tension) and performed on four materials: a natural rubber (NR), a styrene butadiene rubber (SBR), a polyurethane (PU) and a thermoplastic elastomer (TPE). Then, a new failure criterion based on an equivalent elongation concept is proposed. This equivalent elongation seems to be linearly dependent on a given biaxiality ratio n = ( ln ( λ 2 b ) / ln ( λ 1 b ) ) , which leads to expressing the principal elongations at break as functions of both the biaxiality n and two experimental parameters. Quite good agreement is highlighted when comparing the failure experimental data with the proposed criterion for the tested elastomers.

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.

This study concerns the fracture of rubbers. The objective is to verify the validity of the J-integral expression we proposed for such materials (Ait Hocine et al., 2002). In this expression, the parameter J is represented as a multiplicative form of a geometrical η* (or η) factor and elastic work per unit area as it has been already done in the Linear Elastic Fracture Mechanics (LEFM) (Turner, 1973). The whole problem rests in the fact that the factor η* (or η) is unknown whereas in LEFM, expressions of ηel factors are available for several kinds of specimen geometry. Thus, in this work, an experimental and a numerical analysis have been achieved and we have shown, for both the studied materials and the considered specimens, that these unknown factors could be replaced by those issued from the LEFM or from the work of Kim and Joe (1989) on rubber-like materials. The results obtained confirm the validity of our model representing a single specimen method of an experimental evaluation of the elastomers fracture energy.

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.