Amorçage et propagation de fissures dans les milieux ductiles non locaux

Within the framework of industrial structures design, a novel methodology is presented which allows to model ductile damage evolution followed by crack initiation and propagation. This study is divided into three parts. First, damage evolution should be properly described with a continuous model up to the onset of fracture. However, solving finite element problems involving elasto-plasticity coupled with damage softening faces two major difficulties: mesh dependence and volumetric locking. In this work, a four-field mixed nonlocal formulation is proposed in order to solve simultaneously both problems within the small strain framework. Then, accuracy is improved and computational costs are minimized thanks to a mesh adaptivity procedure based on an error indicator. The strategy combines a direct transfer of the smoothed fields at the old Gauss points to the new ones with a viscous model, so that computation can continue on the adapted mesh after reducing the time step. Finally, once the first stage of damage evolution is described accurately, a new strategy using remeshing techniques is proposed for crack initiation and propagation. The crack path is represented by an auxiliary mesh with a regular crack tip. The discontinuity is oriented according to a criterion depending on the gradient of the smoothed damage field. A numerical application is presented on a double notched specimen both in 2D and in 3D. Future work should focus on applying this methodology to more realistic models involving stress triaxiality within the finite strain framework.Cette étude s'inscrit dans le domaine de la conception et du dimensionnement de structures industrielles. Elle consiste à proposer une méthodologie permettant de simuler l'endommagement ductile de structures métalliques, suivi de l'amorçage et de la propagation de fissures. La démarche s'organise en trois temps. La première étape consiste à pouvoir décrire correctement l'évolution de l'endommagement jusqu'à l'amorçage de la fissure, par un modèle continu. Or, l'utilisation de modèles de comportement ductiles endommageables classiques avec la méthode des éléments finis conduit à de nombreux problèmes, tels que la dépendance pathologique à la finesse et à l'orientation du maillage ou le verrouillage volumique. Une nouvelle formulation mixte non locale à quatre champs est proposée dans le cadre des petites perturbations afin de surmonter ces problèmes. L'étape suivante vise à améliorer la qualité du calcul. Pour cela, une procédure d'adaptivité de maillage reposant sur un indicateur d'erreur est mise en place afin de permettre d'atteindre le niveau de qualité désiré par l'utilisateur, tout en minimisant les coûts de calculs. Associée au lissage des champs aux anciens points de Gauss avant projection directe aux nouveaux points de Gauss et à l'ajout de viscosité dans le modèle, elle permet de reprendre les calculs sur le nouveau maillage plus adapté après quelques divisions du pas de temps. Enfin, une fois toute la phase d'endommagement décrite avec précision, la dernière partie est consacrée au développement d'une stratégie d'amorçage et de propagation de fissure utilisant l'adaptation de maillage. Pour cela, le chemin de fissure est représenté par un maillage auxiliaire dont le front est le plus régulier possible. Pour déterminer l'orientation de cette discrétisation, un critère reposant sur le gradient de l'endommagement lissé est formulé. Cette stratégie est mise en oeuvre sur un cas test académique en dimensions deux et trois. Par la suite, il serait intéressant de pouvoir appliquer cette méthodologie avec des modèles plus réalistes faisant intervenir le taux de triaxialité, et ce en grandes déformations

Modélisation de la propagation de fissure en fatigue dans les superalliages base Nickel par une approche locale de la rupture

International audienceThis study concerns the analysis of cracking in Nickel-base superalloys used in the hot zones of aeronautical turbines. For this purpose, a time-incremental fatigue crack propagation model using damages coupled to the elasto-viscoplastic behavior of the material is developed using a local approach to fracture. In order to take into account for both complex phenomena occuring in the vicinity of the crack tip, possible instabilities of cracking, and the type of loading; damages caused by creep, ductility and oxidation may interact with fatigue. To obtain mesh-independent results when performing Finite Element calculations, non-local methods are then considered.Cette étude concerne l’analyse de la fissuration dans les superalliages base Nickel employés dans les zones chaudes des turbines aéronautiques. Dans ce but, un modèle de propagation de fissure en fatigue incrémental en temps, via des endommagements couplés au comportement élasto-viscoplastique du matériau, est développé à l’aide d’une approche locale de la rupture. Afin de rendre compte à la fois des phénomènes complexes présents en pointe de fissure, des éventuelles instabilités de fissuration, et du type de chargement ; des endommagements induits par le fluage, la ductilité et l’oxydation peuvent interagir avec la fatigue. Une régularisation du modèle via une approche non-locale garantira sa robustesse lors de calculs de structures par éléments finis

Finite element analysis of damage in ductile structures using a nonlocal model combined with a three-field formulation

International audienceSolving finite element problems involving elasto-plasticity coupled with damage softening faces two major difficulties: mesh dependence and volumetric locking. In this study, a specific finite element is proposed which allows to solve simultaneously both problems within the small strain framework. It combines a mixed treatment based on a three-field formulation (displacements, assumed pressure, and assumed dilatation) to solve the volumetric locking and a nonlocal implicit gradient-enhanced formulation to avoid localization of damage. Simulations on a double-notched specimen are presented which allow to compare the nonlocal formulation and the mixed nonlocal formulation. Triangular elements with quadratic shape functions for the displacements and linear shape functions for the assumed dilatation, assumed pressure, and nonlocal variable are used. First results show that the mixed nonlocal method regular

A new marching ridges algorithm for crack path tracking in regularized media

International audienceTracking algorithms are used to predict crack paths in structures modeled with the finite element method, in such a way that the paths do not depend on the selected mesh. For regularized media, the simplest methods rely on scalar variables, somehow related to material degradation. Despite their simplicity, they suffer from a major limitation: they allow the crack to initiate and propagate in only one direction. Consequently, such approaches usually fail in case of crack branching or crack initiation inside the structure. To overcome this difficulty, we propose a new crack path tracking algorithm. It is designed to simultaneously detect several local maxima of a degradation-related variable by following the associated ridge lines. That is why the algorithm proposed in this paper could be referred to as a marching ridges algorithm. The performance of the proposed approach is illustrated by three numerical examples within different frameworks. The first ones show that the algorithm can be used to insert crack increments during a ductile failure computation with a quasi-static implicit resolution procedure, in 2D and 3D. The last example proves that the algorithm can be used as a post-processing tool to capture dynamic crack branching from a damage distribution image only

A non-local approach for Reissner–Mindlin shell elements in dynamic simulations: Application with a Gurson model

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Plastic and fracture behavior of a dual phase steel sheet under quasi-static and dynamic loadings

International audienceCrack prediction is an important step of car design: its accuracy is crucial to avoid additional development costs and delays. The prediction of steel or aluminium sheets tearing is particularly challenging, and its simulation is not always reliable yet. This could be explained by the use of too simple fracture criteria based on a critical plastic strain that are uncoupled with the constitutive behavior (i.e. the material response is not affected by damage). To overcome this problem, coupled damage models are proposed in the literature. To select the appropriate constitutive equations to model the plastic and fracture behavior of a given material, various characterization tests are needed. A comprehensive experimental campaign that covers a wide range of stress states and loading rates was conducted. All tests can be performed on a tensile machine. From the results, an original set of constitutive equations was chosen from the literature to propose an extended Gurson-based damage model. A practical parameter identification procedure is proposed to calibrate the model on a few relevant specimen geometries. The model is then validated on another set of specimen geometries: comparisons between test results and simulations show a good agreement in terms of loaddisplacement curves for both quasi-static and dynamic loading conditions

Analyse de l'impact du filtrage de conditions au bord bruitées sur un calcul éléments fins

International audienceLors d'une comparaison entre un essai mécanique et sa simulation numérique, il est primordial d'assurer que cette dernière soit représentative du premier. Pour y parvenir, on peut imposer à la simulation une condition au bord issue d'une mesure. Néanmoins, cette solution conduit à imposer de manière incontrolée le bruit de mesure conduisant à des contraintes numériques artificielles. Ce bruit peut être filtré et cette contribution illustre l'impact du bruit et analyse différentes methodes de filtrage pour une application aux essais de traction sur matériaux à comportement ductil

Forces configurationnelles et localisation de front de fissure

International audienceEn exploitant un procédé de post-traitement de calcul de taux de restitution d'énergie, une stratégie pour la recherche de front de fissure est présentée. La position d'un éventuel front de fissure au sein d'un domaine spatial (sur lequel au moins une information de déformation et de comportement est donnée) est recherchée à partir de la maximisation de la dérivée d'une quantité énergétique par rapport à une transformation de domaine. Plusieurs applications sont présentées, sur l'exploitation de résultats d'essais en corrélation d'image et sur une simulation d'endommagement non-local

Modélisation de la propagation de fissure en fatigue par une approche locale de la rupture

International audienceIn the aeronautical field, fatigue crack propagation analysis is commonly performed at the macroscopic level through a global energetic approach that considers the material in its elastic domain. Within this framework, the plastic zone is assumed to be confined at the crack tip, in the singularity area. However, recent observations on specimens made of Nickel-based superalloys at 550◦C [1] tend to highlight nonlinear phenomena occurring in the process zone, ahead of the crack tip. This plasticity leads to deterioration mechanisms, and to a disturbed crack front, with flat to slant fracture in mode I loading or “tunneling effect” under holding-times. To deal with such complex fracture problems, elastic fracture mechanics is not anymore adapted. To model fatigue crack propagation in a Ni-based superalloy used in the high-pressure stages of aeroengines [2], the present study proposes to use a local approach to fracture. It consists in estimating more accurately the stress and strain fields in the crack tip area where plasticity occurs. The knowledge of these mechanical fields offers the possibility to characterize the fracture processes by the use of either a damage criterion in post-processing or a fully coupled damage model. This last one can be phenomenological and established within the Thermodynamics of Irreversible Processes and the Continuum Damage Theory frameworks [3, 4], by fully coupling the elasto-viscoplastic behavior and damage. This damage is the combination of different deterioration mechanisms. The most relevant one is fatigue damage which represents persistent slip bands that appear after several reversal loadings. In addition, creep damage also needs to be taken into account, representing holding-period degradation processes at the grain boundaries. Finally, ductile damage can have a contribution for the highly loaded plastic zone in the vicinity of the crack tip. Fatigue damage is, most of the time, cyclically estimated by the use of a damage law written in terms of loading parameters such as the loading ratio or the stress amplitude. The innovative aspect of the present study is to model fatigue damage in an incremental manner to avoid using cycle-counting algorithms. The main issue with incremental fatigue damage is to describe properly the mean-stress effect. As part of the solution, this study proposes to take into account, in the constitutive equations, the microcracks’ closure effect [3]. Another issue is associated with the fact that there is a full coupling between damage and the elastoviscoplastic behavior. In this case, the structure will progressively exhibit a softening behavior. Then, the well-posedness of the equilibrium problem is not verified anymore and the constitutive equations lose their ellipticity. When performing Finite Element calculations, this leads to spurious localization problems. To obtain mesh-independent results, non-local methods [4, 5] are thus considered.Cette étude concerne l’analyse de la fissuration dans les superalliages base Nickel employés dans les zones chaudes des turbines aéronautiques. Dans ce but, un modèle de propagation de fissure en fatigue incrémental en temps, via des endommagements couplés au comportement élasto-viscoplastique du matériau, est développé à l’aide d’une approche locale de la rupture. Afin de rendre compte à la fois des phénomènes complexes présents en pointe de fissure, des éventuelles instabilités de fissuration, et du type de chargement ; des endommagements induits par le fluage, la ductilité et l’oxydation peuvent interagir avec la fatigue. Une régularisation du modèle via une approche non-locale garantira sa robustesse lors de calculs de structures par éléments finis

A non-local damage approach compatible with dynamic explicit simulations and parallel computing

International audienceIn the automotive industry, crack prediction is an important step of the design: its accuracy is crucial to avoid additional development costs and delays. However, its simulation is not always reliable yet which could be explained by the use of too simple fracture criteria. A possible solution could be the improvement of the fracture behavior prediction through the use of coupled damage models. Unlike the fracture criteria, damage models consider the loss of resistance on the elements behavior, which gives a better definition of the strain localization and crack path. However, due to stress softening, the problem becomes ill posed, generating damage localization on a single row of elements. The results are then dependent on the mesh size and the mesh orientation. To obtain mesh independent results, a possible solution is to resort to regularization methods, but only a few of them are compatible with dynamic explicit simulations, especially for ductile failure. This paper proposes to extend the implicit second gradient non-local regularization approach to crash simulations. This is achieved by modifying the second gradient equation to ensure its robustness for dynamic explicit simulations. This extended second gradient approach is implemented by enriching under-integrated continuum elements so as to naturally preserve the parallel computing ability. A comparison between simulations and experimental results obtained with specimens machined in a dual-phase steel sheet is realized to validate the proposed approach. Numerical results obtained with different mesh sizes and mesh orientations illustrate the mesh independence and are in very good agreement with the experiments in terms of both load–displacement curves and crack path