A multi-model X-FEM strategy dedicated to frictional crack growth under cyclic fretting fatigue loadings.

International audienceA 2D X-FEM/LATIN numerical model (eXtended Finite Element Method/Large Time Increment method) is proposed in this paper for the analysis of fretting fatigue problems and the simulation of the crack propagation under such loadings. The half-analytical two-body contact analysis allows to capture accurately the pressure and the cyclic tractions exerted at the interface that induce non-proportional multi-axial loading. These distributions are then used as input data for determining critical location for crack initiation and crack inclination based on Dang Van's criterion. The frictional contact conditions of the fretting fatigue cracks have an important impact on the crack behaviour. In this respect, contact with friction between the crack faces is finely modeled within the X-FEM frame. The obtained results are compared and validated with a half-analytical reference model. The numerical simulations reveal the robustness and the efficiency of the proposed approach for a wide range of fretting loadings and friction coefficients values along crack faces. The crack growth directions are then predicted accurately based on the use of criteria adapted to multi-axial non-proportional fatigue. Four cases dealing with crack propagation are then presented. It is shown how the crack length, the tangential loading modify the crack path during the propagation process

An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods

International audienceAbstract: A 3D graded coating/substrate model based on multigrid techniques within a finite difference frame work is presented. Localized refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for (i) a homogeneous material and (ii) a graded material. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < E-c/E-s < 10) of the coating on the contact parameters (P-h, a). Three-dimensional examples are then presented to illustrate the efficiency and the large range of possibilities of the model. The influence of different gradations of Young's modulus, constant, linear and sinusoidal, through the coating thickness on the maximum tensile stress is analyzed, showing that the sinusoidal gradation best accommodates the property mismatch of two successive layers. A final case is designed to show that full 3D spatial property variations can be accounted for. Two spherical inclusions of different size made from elastic solids with Young's modulus and Poisson's ratio are embedded within an elastically mismatched finite domain and the stress field is computed

Damage law identification of a quasi brittle ceramic from a bending test using digital image correlation

International audienceAlthough ceramics are generally considered as to be elastic brittle solids, some of them are quasi brittle. These ceramics show a non linear mechanical behaviour resulting most of the time in a difference between their tensile and compressive stress-strain laws. The characterization of their fracture strengths might be biased if elastic linear formulae are used to analyze classical tests like bending tests. Based on Digital Image Correlation (DIC), an efficient technique to measure full field displacements, a methodology is proposed to characterize and model materials with dissymmetric behaviours between tension and compression. Applying specific basis functions for DIC displacement decompositions for bending, compressive and tensile tests, a stress-strain model and its damage law are identified and then validated for aluminium titanate, a damageable micro cracked ceramic at room temperature. This identification method using DIC can obviously be applied to other quasi brittle materials

Modélisation du contact normal et tangentiel entre deux matériaux anisotropes

Un modèle de contact basé sur des méthodes semi analytiques, s'appuyant sur des solutions analytiques élémentaires a été développé. Il repose sur des techniques numériques adaptées aux spécificités des sollicitations tribologiques, notamment l'aspect multi échelle. Il permet de quantifier les champs de déplacements et de contraintes d'un matériau élastique anisotrope, en contact avec un second matériau anisotrope. Il est intéressant d'observer l'influence des directions privilégiées d'un matériau ainsi que celle de leurs orientations

Etude et modélisation de l'endommagement du contact revêtu soumis à des sollicitations de fretting-fatigue

Ce travail présente une analyse de l'endommagement des contacts revêtus en fretting-fatigue. Un modèle d'endommagement a été développé et couplé à notre modèle de contact semi-analytique. Ce modèle, basé sur la mécanique des milieux continus, permet de décrire le comportement élastique-endommageable du revêtement. Il s'appuie sur un critère d'endommagement écrit en déformation, pour modéliser l'évolution des propriétés du matériau entre son état sain (initial) et son état endommagé (final). Cette modélisation a permis d'analyser l'influence de plusieurs paramètres sur l'évolution de l'endommagement au cours du chargement cyclique

Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model

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Calcul de la durée de vie en fretting d'une attache pale/disque de turbomachine soumise à un chargement vibratoire

Fretting has been the subject of numerous experimental investigations. It occurs when two surfaces rub against each other at very low amplitude (some tens of microns of sliding distance). If the tangential force Q is lower than the product of the friction coefficient ? and the normal force P, two different zones can be observed within the contacting zone. At the center, both surfaces are sticked to each other while they have a relative motion in the annular zone. This is the partial slip regime. The corresponding dominant failure is crack initiation located at the edges of the contact area. Fretting is present in a blade-disc attachment of a turboshaft engine. It is due to the superimposition of two fatigue stresses: a low frequency loading (LCF), induced by the centrifugal force from the rotation of the disc, and a high frequency loading (HCF), which is a sinusoidal force induced by vibrations. It's a difficult phenomenon to model and industries are not capable of predicting it with good accuracy yet. Instead, they are forced to use huge safety factors. Therefore, the prediction of the lifetime of a blade disc assembly under fretting has now become a major issue in the field of turboshaft engineering.   A major difficulty of providing such a prediction comes from the complication of determining the stress and strain fields in the vicinity of the contact. The finite element parameters needed to compute the intense stress gradient in this zone have been found out using a simplified 2D finite element model of a classical fretting test device. This model was also used for a sensitivity analysis of the damage using the Dang Van fatigue criterion. An important set of results was obtained. These results provide a better understanding of the mechanism of fretting damage, and enriching information for decision support concerning future experimental campaigns.   The second step of our work was to set up a calculation process to compute the stress field under a fretting contact induced by a superimposed LCF + HCF solicitation in a fir-tree root. The combination of this process with the Dang Van fatigue criterion allows the calculation of a criticality parameter related to the life cycle. This modeling process was first applied on a model representing an innovative test device, designed at Safran Helicopter Engines, allowing the superimposition of a static and a vibratory loading on a dovetail test specimen. The model reproduces experimental observations with a very good accuracy. This modeling process was then applied to the model representing a real fir-tree root geometry. The results correlate with the feedback from in-service engines. The simulation results from the test device and the fir-tree root models were compared. This comparison made possible the determination of the dovetail geometry and the experimental conditions to apply that are most representative of the phenomenon that induces fretting failure in a blade-disc attachment

Identification de comportements à la rupture, de mécanismes d'endommagement et de dissipations d'énergie à partir de méthodes de corrélation d'images

Il est proposé d'étudier la propagation d'une fissure à partir de deux méthodes de mesure de champ. Par rapport à la corrélation d'images (DIC), la méthode Integrated-DIC utilise des hypothèses sur la cinématique globale pour améliorer la précision de la mesure et la méthode Regularized-DIC s'appuie sur des hypothèses sur le comportement mécanique du matériau pour filtrer les solutions non admissibles. Ces deux techniques optiques sont comparées à la méthode des complaisances pour analyser la propagation d'une fissure lors d'un test de flexion entaillée sur une céramique endommageable

Calcul 3D massif revêtu -Techniques multi-grilles avec raffinement local (MGL)

Un outil de simulation 3D élastique linéaire pour l'analyse du comportement de matériaux revêtus est proposé. Les équations de Lamé généralisées sont discrétisées par différences finies et résolues à l'aide des techniques MGL. Des systèmes de plus de 400 millions d'inconnues sont résolus pour des temps de calcul acceptables. Ainsi le problème de contact entre massifs revêtus est abordé avec la finesse nécessaire pour traiter des variations de propriétés sur des épaisseurs faibles (0,01<e/a<2). Une étude paramétrique montre l'influence de l'amplitude et de la forme des variations de propriétés

Local Fretting Regime Influences on Crack Initiation and Early Growth

International audienceAn investigation of fatigue crack initiation and propagation under fretting conditions is described in which both experimental and theoretical approaches are used. Fretting tests were conducted on an aerospace aluminium alloy. The approach presented here aims to describe the propagation of a fretting crack through a step-by-step understanding of the different stages of its life (1) Stage I crack initiation, i.e., sites, growth directions and fracture mode, (2) Stage I-to-Stage II transition as a result of the competition between failure modes, i.e the branching depth and the growth direction after branching. This methodology was successfully applied to fretting fatigue data obtained under the Partial Slip Regime (PSR). Pertinent parameters were proposed to deal with items (1) and (2) depending on the ranges of shear and tensile stresses and their respective roles in crack growth. This step-by-step methodology is used here to analyze the influence on crack initiation and propagation of the local fretting regime and the associated mechanical stress-strain state