Fahmi Zaïri

Elasto-viscoplastic constitutive equations for the description of glassy polymers behavior at constant strain rate

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.

Constitutive modelling of the large inelastic deformation behaviour of rubber-toughened poly(methyl methacrylate): effects of strain rate, temperature and rubber-phase volume fraction

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.

A two-phase hyperelastic-viscoplastic constitutive model for semi-crystalline polymers: Application to polyethylene materials with a variable range of crystal fractions

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

Damage mechanisms in bioactive glass matrix composites under uniaxial compression

The damage and crack resistance improvement of bioactive glass is of prime importance, particularly when applied to the repair of load-bearing bones. The present contribution is focused on the prediction of damage mechanisms and crack resistance under uniaxial compression of bioactive glass matrix composites reinforced with a particulate phase. In order to characterize the effects of voids and particles on the damage mechanisms and the macro-response, a two-step homogenization is performed by considering the two phases existing at two different scales: micro/meso through the homogenization of the porous matrix and then meso/macro through the periodic micro-field approach. The damage in the bioactive glass matrix is computed via an anisotropic stress-based damage model, implemented into a finite element program. Failure resulting of excessive damage accumulation in the bioactive glass matrix is predicted by a critical damage criterion combined with a vanishing element technique. The implication of particles in the toughening mechanism as well as the damage and crack resistance improvement in this class of porous biomaterials is highlighted via a parametric study using the proposed numerical model.

Mullins effect in polyethylene and its dependency on crystal content: A network alteration model

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

Damage interaction and angle effects on the erosion behavior of soda-lime-silica glass:

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.