Luc Chevalier

Digital image correlation used to analyze the multiaxial behavior of rubber-like materials

We present an experimental approach to discriminate models describing the mechanical behavior of polymeric materials. A biaxial loading condition is obtained in a multiaxial testing machine. An evaluation of the displacement field obtained by digital image correlation allows us to evaluate the heterogeneous strain field observed during these tests. We focus on the particular case of hyper-elastic models to simulate the behavior of a rubber-like material. Different expressions of hyper-elastic potential are used to model experiments under uniaxial and biaxial loading conditions.

WAXD study of induced crystallization and orientation in poly(ethylene terephthalate) during biaxial elongation

This study presents an experimental investigation into the strain-induced crystalline microstructure, under biaxial elongation in poly(ethylene terephthalate) (PET), using wide angle X-ray diffraction (WAXD). We examined how the microstructure of a polymer subjected to a complex strain field evolves in terms of its crystalline ratio, its molecular orientation and the size of its crystallite. PET injection-molded specimens have been subjected to biaxial elongation tests, both equibiaxial and sequential, at different drawing speeds, draw ratios and temperatures above and close to Tg. The strain field was determined using a home-developed image correlation technique that has allowed us to determine all the strain components at each point of the specimen, even with a non-homogeneous strain field. To minimize the effect of quiescent crystallization, specimens are quickly heated with infrared and the temperature was regulated during the test. At the end of the deformation process, the specimens were quenched to room temperature. Their microstructures were later investigated, using both differential densimetry and WAXD with a synchrotron beam. Influences of strain rate, temperature and strain path sequence on the size of the crystallites and their orientation are evaluated. q 2002 Published by Elsevier Science Ltd.

Tools for multiaxial validation of behavior laws chosen for modeling hyper-elasticity of rubber-like materials

We present an experimental approach to discriminate hyper-elastic models describing the mechanical behavior of rubber-like materials. An evaluation of the displacement field obtained by digital image correlation allows us to evaluate the heterogeneous strain field observed during these tests. We focus on the particular case of hyper-elastic models to simulate the behavior of some rubber-like materials. Assuming incompressibility of the material, the hyper-elastic potential is determined from tension and compression tests. A biaxial loading condition is obtained in a multiaxial testing machine and model predictions are compared with experimental results.

Induced crystallization and orientation of poly(ethylene terephthalate) during uniaxial and biaxial elongation

Stretching PET at a high strain rate above the glass transition temperature has a positive effect on the strength of the material. In a recent paper [1] , we presented the influence of stretch and blow molding parameters on the properties of the final product, especially on the crystallinity induced by stretching. In this paper, we focus on the effects of loading, temperature, elongation and strain rate on macromolecular orientation and crystallization kinetics. We present experimental results from uniaxial and biaxial elongation tests carried out on injected PET specimens. To minimize the effect of quiescent crystallization, specimens are quickly heated with infrared lamps before the test and temperature is regulated during the test. Both uniaxial and biaxial tests are analyzed using a cross correlation technique [2] that compares a picture used as reference and the picture of the deformed specimen. This technique allows us to determine all strain components at each point of the specimen, even when the strain field is not homogeneous. In a second part, we present measurements of macromolecular orientation and crystallinity ratio performed after each test. The infrared dichroism technique is used to determine the orientation of the microscopic morphology of PET before and after the testing. DSC measurements and density measurements are carried out to calculate the crystallinity ratio. Influences of strain rate, temperature and strain path sequence are evaluated in order to build a database for recent models of induced crystallization [3],[4],[5] .

Crystallization of polymers under strain : from molecular properties to macroscopic models

The crystallization of thermo-plastic polymers under strain is considered both theoretically and experimentally. The thermo-mechanical model presented here is performed in the framework of the so-called generalized standard materials. In our model we couple in a very natural way the kinetics of crystallization with the mechanical history experienced by the polymer. The viscoelastic properties of the polymer are described using molecular theories. Therefore, in this model of strain-induced crystallization, the kinetics of crystallization is explicitly linked to the polymer chain conformation. Our model is intended to be valid for both for shearing and elongation, or any other complex strain field. Two different viscoelastic molecular models are considered here, corresponding to Maxwell and Pom-Pom constitutive equations. The model is implemented in a dedicated finite element code and the case of injection molding is considered.To validate our strain-induced crystallization model, which explicitly takes into account the molecular conformation, experiments investigating the material behavior at the molecular scale are required. Several measurement techniques can be used to achieve this task, including infrared spectroscopy, optical polarimetry, X-ray scattering or diffraction, etc. In this paper, the wide angle X-ray diffraction (WAXD) is used to investigate the crystalline texture of the polymer. We consider here the case of poly(ethylene terephthalate) (PET) subjected to a biaxial elongation above its T-g. The strain field is determined using a home-developed image correlation technique that allows us to infer all the strain components at each point of the specimen, even in the case of a non-homogeneous strain field. To minimize the effect of quiescent crystallization, specimens are quickly heated with infrared and the temperature was regulated during the test. At the end of the deformation process, the specimens were quenched to room temperature. Their microstructure was later investigated using the WAXD technique. In order to undertake local and accurate WAXD measurements Synchrotron radiation facilities are used.

Optimization of the Thickness of PET Bottles during Stretch Blow Molding by Using a Mesh-free (Numerical) Method

Abstract The stretch-blow molding process of polyethylene terephthalate (PET) bottles generates some important modifications in the mechanical properties of the material. Considering, the process temperature (T > Tg) that is usually used, the material exhibits a very high viscosity and involves a strain hardening effect associated with the microstructure evolution. An anisotropic viscoplastic model coupled with induced properties, identified from experimental results of uniaxial and biaxial tensile tests previously published by Chevalier and Marco (2006), is presented in a first part of the paper. Secondly, we perform a numerical simulation to simulate the free inflation of a preform under an internal pressure with different parameters. Because the final strains are up to 300 to 400%, it generates important distortion of node distribution and we chose to use the mesh-free Constrained Natural Elements Method (C-NEM) for numerical simulation. The final goal is to use these simulations in order to fit the best parameter set leading to a quasi-homogeneous distribution of the thickness along the bottle. Homogeneous thickness implies homogeneous biaxial stretching and more uniform induced properties for the final bottle and this is an important industrial goal.

Simplified Modelling of the Infrared Heating Involving the Air Convection Effect before the Injection Stretch Blowing Moulding of PET Preform

Initial heating conditions and temperature effects (heat transfer with air and mould, self-heating, conduction) have important influence during the ISBM process of PET preforms. The numerical simulation of infrared (IR) heating taking into account the air convection around a PET preform is very time-consuming even for 2D modelling. This work proposes a simplified approach of the coupled heat transfers (conduction, convection and radiation) in the ISBM process based on the results of a complete IR heating simulation of PET sheet using ANSYS/Fluent. First, the simplified approach is validated by comparing the experimental temperature distribution of a PET sheet obtained from an IR camera with the numerical results of the simplified simulation. Second, we focus on the more complex problem of the rotating PET preform heated by IR lamps. This problem cannot be modeled in 2D and the complete 3D approach is out of calculation possibilities actually. In our approach, the IR heating flux coming from IR lamps is calculated using radiative laws adapted to the test geometry. Finally, the simplified approach used on the 2D plane sheet case to model the air convection is applied to the heat transfer between the cylindrical preform and ambient air using a simple model in Comsol where only the preform is meshed. In this case, the effect of the rotation of the preform is taken into account in the radiation flux by a periodic time function. The convection effect is modeled through the thermal boundary conditions at the preform surface using the heat transfer coefficients exported from the simulations of the IR heating of a PET sheet with ANSYS/Fluent. The temperature distribution on the outer surface of the preform is compared to the thermal imaging for validation.

On a Simplified Model for Numerical Simulation of Wear During Dry Rolling Contacts

We deal with rolling contact between quasi-identical bodies. As normal and tangential problems are uncoupled in that case, the simplified approach to determine contact area and normal loading distribution for rolling contact problems is presented in Sec. 2. In Sec. 3, the solution of the tangential problem is used to update the rolling profiles and enables to follow the wear evolution versus time. The method used to solve the normal problem is called semi-Hertzian approach with diffusion. It allows fast determination of the contact area for non-Hertzian cases. The method is based on the geometrical indentation of bodies in contact: The contact area is found with correct dimensions but affected by some irregularities coming from the curvatures discontinuity that may arise during a wear process. Diffusion between independent stripes smoothes the contact area and the pressure distribution. The tangential problem is also solved on each stripe of the contact area using an extension of the simplified approach developed by Kalker and called FASTSIM. At the end, this approach gives the dissipated power distribution in the contact during rolling and this power is related to wear by Archards law. This enables the profiles of the bodies to be updated and the evolution of the geometry to be followed.

Simplified modeling of the convection and radiation heat transfers during the infrared heating of PET sheets and preforms Nomenclature

Abstract Initial heating conditions and temperature effects have an important influence during the injection stretch blow molding process of PET preforms. The paper provides a simplified modeling of the infrared (IR) flux provided by the IR lamps and the convection heat transfer with air, for the finite element simulation of the heating of PET samples. This modeling enables fast thermal simulations in industrial context. First, a complete 2D simulation of the air convection around a PET sheet sample is conducted using ANSYS/FLUENT to compute the local convection heat transfer coefficient. The distribution of this coefficient along the PET wall is then interpolated by a best linear fit function of the wall position to provide the boundary condition of the convection heat transfer thereafter. This boundary condition, coupled with the calculation of the infrared flux absorbed by the PET sheet sample, allows a 3D calculation of the time evolution of the sample temperature. This calculation is validated by comparing the experimental temperature distribution of the PET sheet obtained from an IR camera with the numerical results of the simulation. Second, we focus on the modeling of the heating of a cylindrical PET preforms by IR lamps. In our approach, the IR heating flux is calculated using the spectral and surfaceto-surface radiation laws adapted to the sample geometry. The air convection effect around the preform is modeled using the heat transfer coefficient identified from the 2D plane sheet case. It is applied on the boundaries of a simpler model in Comsol where only the preform is meshed. The temperature distribution on the outer surface of the preform is compared to experimental measurements by thermal imaging. A good agreement is observed which validates the whole approach used.

Identification of a Visco‐Elastic Model for PET Near Tg Based on Uni and Biaxial Results

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature Tg, the stress‐strain curve presents a strain softening effect vs strain rate but a strain hardening effect vs strain under conditions of large deformations. The main goal of this work is to propose a viscoelastic model to predict the PET behaviour when subjected to large deformations and to determine the material properties from the experimental data. The viscoelastic model is written in a Leonov like way and the variational formulation is carried out for the numerical simulation using this model. To represent the non‐linear effects, an elastic part depending on the elastic equivalent strain and a non‐Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained through the comparison with the experimental uniaxial and biaxial tests.