Cyclic calculations and life estimation in thermomechanical fatigue

International audienceThe present paper describes a new numerical procedure devoted to the calculation of aeronautic engines and to the fatigue life assessment evaluation. The original aspects consists (1) in a new method used to determine the mechanical steady state of a structure under thermomechanical loading, (2) in a short review of an advanced fatigue model which can reproduce the Woehler curve, including the influence of the mean stress

A microstructure sensitive approach for the prediction of the creep behaviour and life under complex loading paths

International audienceThe prediction of the creep behaviour and life of components of aeronautic engines like high pressure turbine blades is still a challenging issue due to non-isothermal loadings. Indeed, certification procedures of turboshaft engines for helicopters consist of complex thermomechanical histories, sometimes including short and very high temperature excursions close to the γ'-solvus (T~1200°C) of the blade alloy. A better design of those components could be gained using a model that takes into account non-isothermal loadings inducing microstructural changes. Most of the commonly used models consider only a nearly constant (or slowly evolving) microstructure, i.e. far from the rapid microstructure evolutions encountered during close γ'-solvus overheatings where a rapid dissolution/precipitation of the γ'-phase and fast recovery mechanisms were observed by Cormier et al. (2007b). A new constitutive modelling approach was hence recently proposed in a crystal viscoplasticity framework to capture the transient effects of such rapid microstructure evolutions on the creep behaviour and life (Cormierand Cailletaud (2010a)). In this article, an updated version of this model is detailed. Special attention will be paid to (i) the effect of the accumulated plastic strain on the microstructure evolution, (ii) the introduction of an additional damage formulation, and (iii) the creep strain at failure. The performances of the model are illustrated on the basis of isothermal or complex non-isothermal creep experiments performed on nearly [001] oriented samples

A new modelling of the Mullins'effect and viscoelasticity of elastomers based on physical approach

The mechanical behaviour of elastomers is known to be highly non-linear, time-dependent and to exhibit hysteresis and stress-softening known as the Mullins effect (Mullins, 1948) upon cyclic loading. These phenomena are classically studied and modelled independently. Some studies are based on physical approaches (Arruda and Boyce, 1993; Bergström and Boyce, 1998; Marckmann et al., 2002) in which macroscopic constitutive equations are build in regards with the physics of polymeric chains. In this context of physical considerations, the aim of the present paper is to study independently each phenomenon involved in rubber-like materials and to assemble them in a global constitutive equation. First, the hyperelastic behaviour of elastomers is modelled by the physical approach of Arruda and Boyce (1993), widely known as the eight-chains model. This model accurately reproduces the large strains elastic behaviour of elastomers under different types of deformation. Second, the hysteretic time dependent behaviour is approached by the model developed by Bergström and Boyce (1998) that considers the separation of the network in two phases: an elastic equilibrium network and a viscoelastic network that captures the nonlinear rate-dependent deviation from equilibrium. This model is quite simple and successfully reproduces the rate-dependent hysteretic properties of elastomers. Last, as shown in the bibliography, the Mullins stress-softening effect can be considered as a damage phenomenon which only depends on the maximum stretch attained during the deformation history (Govindgee and Simo, 1992). In the present approach, the physical theory of Marckmann et al. (2002) based on an alteration of the polymeric network is adopted. This theory was introduced in the eight-chains hyperelastic model and successfully simulates the decrease of the material stiffness between the first and the second loading curves under cyclic loading. As these three models are based on the physics of the polymeric network, they are gathered in a new efficient constitutive equation. This model is able to reproduces imultaneously the Mullins effect and the time-dependent hysteretic behaviour of elastomers. Finally, the constitutive parameters of this new model are identified by fitting experimental data

Theoretical and numerical limitations for the simulation of crack propagation in natural rubber components

International audienceIn this paper, two commercial software packages dedicated to the simulation of crack propaga-tion in elastomer components were tested: FLEXPAC and MSC-MARC. Firstly, the theoretical limitations ofclassical crack propagation laws were examined to demonstrate that actual numerical predictions are limitedto very simple loading conditions. Secondly, crack propagation approaches implemented in both softwareswere analysed. In order to compare their performances, fatigue experiments are performed. Different rubbercomponents with different pre-cracks were tested under several loading conditions. Crack propagation, i.e.size and direction of the crack, was measured as a function of the number of cycles. Then, these results werecompared with crack direction criteria proposed by the two models. It was demonstrated that loading ampli-tude highly influenced the crack direction and that the models must take this into account in their solver. Fi-nally, limitations of this type of numerical analysis to predict the duration life of rubber components werehighlighted

Conception et réalisation d'un essai de fatigue sur caoutchouc naturel

International audienceTrelleborg-Modyn est un équipementier automobile spécialiste de l'antivibratoire. Face à la politique actuelle des constructeurs automobiles de réduire les délais de conception des pièces, Modyn cherche à optimiser la boucle de validation expérimentale en se dotant d'un outil permettant de classer qualitativement les mélanges élastomères existants en terme de tenue à la fatigue et d'optimiser les nouveaux mélanges. L'essai de caractérisation mis en place est un essai à déplacement imposé sur des éprouvettes de double cisaillement, pouvant être modélisée en déformations planes et plus représentative des pièces réelles que les éprouvettes en contraintes planes généralement utilisées dans la bibliographie. Cet essai a pour but de construire pour chaque matériau une courbe de fissuration reliant l'énergie de déchirement T à la vitesse de fissuration correspondante dc / dn : • Le calcul T est directement effectué à partir de la définition donnée par Rivlin et Thomas [RIV53], et dépend des dimensions de l'éprouvette et du déplacement maximal imposé, • la vitesse de fissuration est déduite de la mesure de l'évolution de l'effort de réaction et d'un calcul Eléments Finis. Notons que l'essai développé ne nécessite aucun moyen spécifique de suivi optique de la longueur de fissure

Influence of the loading conditions on fatigue properties for filled elastomers

International audienceFatigue characterisation of elastomers is an essential prerequisite of new car project schedules imposed by carmakers. Consequently, durability prediction softwares are needed to reduce the time allowed to design elastomeric parts. Until now, the only theoretical variable used to predict duration life is the tearing energy proposed by Rivlin and Thomas. Classically, fatigue properties are determined using plane stress experiments (trousers or pure shear samples for example) under simple loading conditions. In the present paper, a brief bibliographical review presents the limitations of this approach and the need of more complex loading conditions is emphasised. Then, a new simple shear sample is proposed to simplify the treatment of experimental results, said the calculation of the tearing energy, under complex loading conditions. The test sample is initially notched and is submitted to controlled displacement loading conditions. The procedure adopted to analyse the results is presented. Assuming that the tearing energy and the crack growth rate remain constant during the test, they can be easily calculated using both the decreasing stiffness of the sample during the test and a FE model. Note that no complex system, such as video recording, is necessary to measure the crack length. Then, experimental results are reported. Both filled crystallising and non-crystallising elastomers are studied in order to highlight the influence of the testing temperature and of the imposed displacement ratio (i.e.: minimum/maximum displacement) on the fatigue crack growth rate law. This fatigue crack growth rate law obtained agrees well with previously published papers. Furthermore, other complex tests are in progress to determine the influence of the Mullins stress-softening on fatigue properties. Finally, in regards with these results, it is demonstrated that the tearing energy is not a sufficient variable to completely characterise the fatigue life of elastomers

Conception et réalisation d'un essai de fatigue sur caoutchouc naturel

International audienceTrelleborg-Modyn est un équipementier automobile spécialiste de l'antivibratoire. Face à la politique actuelle des constructeurs automobiles de réduire les délais de conception des pièces, Modyn cherche à optimiser la boucle de validation expérimentale en se dotant d'un outil permettant de classer qualitativement les mélanges élastomères existants en terme de tenue à la fatigue et d'optimiser les nouveaux mélanges. L'essai de caractérisation mis en place est un essai à déplacement imposé sur des éprouvettes de double cisaillement, pouvant être modélisée en déformations planes et plus représentative des pièces réelles que les éprouvettes en contraintes planes généralement utilisées dans la bibliographie. Cet essai a pour but de construire pour chaque matériau une courbe de fissuration reliant l'énergie de déchirement T à la vitesse de fissuration correspondante dc / dn : • Le calcul T est directement effectué à partir de la définition donnée par Rivlin et Thomas [RIV53], et dépend des dimensions de l'éprouvette et du déplacement maximal imposé, • la vitesse de fissuration est déduite de la mesure de l'évolution de l'effort de réaction et d'un calcul Eléments Finis. Notons que l'essai développé ne nécessite aucun moyen spécifique de suivi optique de la longueur de fissure

Approche macromoléculaire pour la modélisation de l'hystérésis et de l'effet Mullins dans les caoutchoucs naturels

National audienceLe dimensionnement en fatigue des pièces élastomère est devenu un point stratégique pour les équipementiers automobiles. Une étude énergétique de la propagation de fissures a été mise en place par la société Modyn – Trelleborg. La première étape de ce travail consiste à modéliser le comportement des élastomères. Les différents phénomènes le caractérisant ont été isolés et étudiés séparement et modélisés par des approches macromoléculaires sur le comportement des chaînes. Le comportement hyperélastique a été modélisé par le modèle huit chaînes d'Arruda et Boyce [ARR93], le comportement hystérétique par le modèle de Bergström et Boyce [BER98] et l'accomodation à l'effet Mullins par le modèle de Marckmann et al. [MAR02]. Les autres phénomènes comme la relaxation ou le fluage n'ont pas été pris en compte à ce jour. Les trois modèles étudiés sont assemblés afin de pouvoir décrie le comportement global du matériau avec un seul modèle

Development and use of a new burner rig facility to mimic service loading conditions of Ni-based single crystal superalloys

Performing representative experiments of in-service operating conditions of Ni-based superalloys used as high pressure turbine blades in aeroengines is a challenging issue due to the complex environmental, mechanical and thermal solicitations encountered by those components. A new burner rig test facility called MAATRE (French acronym for Mechanics and Aerothermics of Cooled Turbine Blades) has been developed at ENSMA – Pprime Institute to mimic as close as possible those operating conditions. This new test bench has been used to perform complex non-isothermal creep tests representative of thermomechanical solicitations seen by some sections of HP turbine blades during engine certification procedure