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Richaud E.,CNRS Process and Engineering in Mechanics and Materials Laboratory
European Polymer Journal | Year: 2013

Irganox 1010 stabilized PE was monitored by carbonyl build-up and DSC under oxygen. A scheme for PE stabilization by phenols was implemented and its kinetic parameters were calculated from experimental results. This model was validated from its ability to simulate kinetics curves for carbonyl build up, induction period changes with stabilizer concentration, and stabilizer depletion curve in thermal ageing. The use of OIT measurement for quantifying stabilizer is also discussed. Kinetic analysis showed that OIT is actually proportional to stabilizer concentration in virgin samples but this is not true for aged samples because of negative influence of oxidation unstable by-products. The model was also employed for discussing some scenarii proposed as explanation of heterogeneity observed during thermal oxidation of stabilized polyolefins. © 2013 Elsevier Ltd. All rights reserved. Source

Diani J.,CNRS Process and Engineering in Mechanics and Materials Laboratory
Rubber Chemistry and Technology | Year: 2016

Directional laws, also called micro-sphere laws, are based on the rubber elasticity theory and are designed to fit rubber mechanical stress-strain responses at large strain. Because they depend on material directions, directional changes may be introduced accounting for anisotropic damage or residual stretch such as resulting from Mullins softening or accounting for anisotropic strain hardening such as induced by crystallization. Directional laws provide a relevant alternative to strain invariants laws when the material isotropy evolves or when its anisotropy is difficult to guess a priori. In the current contribution, the building process involved when defining directional laws is presented. The major assumptions resulting from this process are reviewed. Finally, recent directional laws from the literature are discussed, highlighting the interest and potential of such a constitutive framework. Source

Laamouri A.,University of Sousse | Sidhom H.,University of Tunis | Braham C.,CNRS Process and Engineering in Mechanics and Materials Laboratory
International Journal of Fatigue | Year: 2013

This paper is aimed at evaluating the residual stress relaxation and its effect on the fatigue strength of AISI 316L steel ground surfaces in comparison to electro-polished surfaces. An experimental evaluation was performed using 3-point and 4-point bending fatigue tests at Rσ = 0.1 on two sets of notched specimens finished by electro-polishing and grinding. The residual stress fields were measured at the notch root of specimens, before and after fatigue tests, by means of the X-ray diffraction technique. It was found a degradation of about -35% for the 4-point bending fatigue limit at 2 × 106 cycles of the ground specimens in comparison to the electro-polished ones. This degradation is associated with a slight relaxation of the grinding residual stresses which remain significant tensile stresses at the stabilized state. While under the 3-point bending test, these residual stresses relax completely and provoke a noticeable increase of the fatigue limit estimated at about 50% in comparison to the 4-point bending fatigue test. The numerical evaluation of residual stress relaxation was carried out by FE analyses of the cyclic hardening behaviour of the ground layer. The isotropic and nonlinear kinematic model proposed by Chaboche was used and calibrated for the base material and the ground layer. The results show that residual stresses relax to a stabilized state characterized by elastic-shakedown response. This stabilization is occurred after the first cycle of the 4-point bending test corresponding to the higher stress concentration (Kt-4p = 1.66), while it requires many cycles under the 3-point bending test corresponding to the lower stress concentration (Kt-3p = 1.54). The incorporation of stabilized residual stress values into the Dang Van's criterion has permitted to predict with an acceptable accuracy the fatigue limits under both bending modes. © 2012 Elsevier Ltd. All rights reserved. Source

Cruz C.,CNRS Process and Engineering in Mechanics and Materials Laboratory | Chinesta F.,Ecole Centrale Nantes | Regnier G.,CNRS Process and Engineering in Mechanics and Materials Laboratory
Archives of Computational Methods in Engineering | Year: 2012

Kinetic theory is a mathematical framework intended to relate directly the most relevant characteristics of the molecular structure to the rheological behavior of the bulk system. In other words, kinetic theory is a micro-to-macro approach for solving the flow of complex fluids that circumvents the use of closure relations and offers a better physical description of the phenomena involved in the flow processes. Cornerstone models in kinetic theory employ beads, rods and springs for mimicking the molecular structure of the complex fluid. The generalized bead-rod-spring chain includes the most basic models in kinetic theory: the freely jointed bead-spring chain and the freely-jointed bead-rod chain. Configuration of simple coarse-grained models can be represented by an equivalent Fokker-Planck (FP) diffusion equation, which describes the evolution of the configuration distribution function in the physical and configurational spaces. FP equation can be a complex mathematical object, given its multidimensionality, and solving it explicitly can become a difficult task. Even more, in some cases, obtaining an equivalent FP equation is not possible given the complexity of the coarse-grained molecular model. Brownian dynamics can be employed as an alternative extensive numerical method for approaching the configuration distribution function of a given kinetic-theory model that avoid obtaining and/or resolving explicitly an equivalent FP equation. The validity of this discrete approach is based on the mathematical equivalence between a continuous diffusion equation and a stochastic differential equation as demonstrated by Itô in the 1940s. This paper presents a review of the fundamental issues in the BD simulation of the linear viscoelastic behavior of bead-rod-spring coarse grained models in dilute solution. In the first part of this work, the BD numerical technique is introduced. An overview of the mathematical framework of the BD and a review of the scope of applications are presented. Subsequently, the links between the rheology of complex fluids, the kinetic theory and the BD technique are established at the light of the stochastic nature of the bead-rod-spring models. Finally, the pertinence of the present state-of-the-art review is explained in terms of the increasing interest for the stochastic micro-to-macro approaches for solving complex fluids problems. In the second part of this paper, a detailed description of the BD algorithm used for simulating a small-amplitude oscillatory deformation test is given. Dynamic properties are employed throughout this work to characterise the linear viscoelastic behavior of bead-rod-spring models in dilute solution. In the third and fourth part of this article, an extensive discussion about the main issues of a BD simulation in linear viscoelasticity of diluted suspensions is tackled at the light of the classical multi-bead-spring chain model and the multi-bead-rod chain model, respectively. Kinematic formulations, integration schemes and expressions to calculate the stress tensor are revised for several classical models: Rouse and Zimm theories in the case of multi-bead-spring chains, and Kramers chain and semi-flexible filaments in the case of multi-bead-rod chains. The implemented BD technique is, on the one hand, validated in front of the analytical or exact numerical solutions known of the equivalent FP equations for those classic kinetic theory models; and, on the other hand, is control-set thanks to the analysis of the main numerical issues involved in a BD simulation. Finally, the review paper is closed by some concluding remarks. © 2012 CIMNE, Barcelona, Spain. Source

Richaud E.,CNRS Process and Engineering in Mechanics and Materials Laboratory | Flaconneche B.,French Institute of Petroleum | Verdu J.,CNRS Process and Engineering in Mechanics and Materials Laboratory
Polymer Testing | Year: 2012

This paper reports solubility and diffusivity data for soy and rapeseed methyl esters in polyethylene together with comparisons with methyl oleate and linoleate. These data showed that there is no significant difference in diffusivity and solubility between all these penetrants. Data were used to discuss the reliability of predictive models for diffusion and solubility of additive type molecules into semi-crystalline thermoplastic polymers. Permeability data were monitored by a new device, the results from which are in reasonable agreement with theoretical considerations on solubility and diffusivity. They also showed that biodiesels are less aggressive towards polyethylene than diesel from a petrochemical source. © 2012 Elsevier Ltd. All rights reserved. Source

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