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International audience; A reliable determination of the onset of void coalescence is critical to the modelling of ductile fracture. Numerical models have been developed but rely mostly on analyses on single defect cells, thus underestimating the interaction between voids. This study aims to provide the first extensive analysis of the response of microstructures with random distributions of voids to various loading conditions and to characterize the dispersion of the results as a consequence of the randomness of the void distribution. Cells embedding a random distribution of identical spherical voids are generated within an elastoplastic matrix and subjected to a macroscopic loading with constant stress triaxiality and Lode parameter under periodic boundary conditions in finite element simulations. The failure of the cell is determined by a new indicator based on the loss of full rankedness of the average deformation gradient rate. It is shown that the strain field developing in random microstructures and the one in unit cells feature different dependencies on the Lode parameter L owing to different failure modes. Depending on L, the cell may fail in extension (coalescence) or in shear. Moreover the random void populations lead to a significant dispersion of failure strain, which is present even in simulations with high numbers of voids.

A reliable determination of the onset of void coalescence is critical to the modelling of ductile fracture. Numerical models have been developed but rely mostly on analyses on single defect cells, thus underestimating the interaction between voids. This study aims to provide the first extensive analysis of the response of microstructures with random distributions of voids to various loading conditions and to characterize the dispersion of the results as a consequence of the randomness of the void distribution. Cells embedding a random distribution of identical spherical voids are generated within an elastoplastic matrix and subjected to a macroscopic loading with constant stress triaxiality and Lode parameter under periodic boundary conditions in finite element simulations. The failure of the cell is determined by a new indicator based on the loss of full rankedness on the average deformation gradient rate. It is shown that the strain field developing in random microstructures and the one in unit cells feature different dependencies on the Lode parameter L owing to different failure modes. Depending on L, the cell may fail in extension (coalescence) or in shear. Moreover the random void populations lead to a significant dispersion of failure strain, which is present even in simulations with high numbers of voids.

This work constitutes a micromechanical study of ductile fracture.The main methodology consists of acombination of three techniques: Insitu synchrotron radiation computed laminography, digital volume correlation and finite element simulations with advanced meshing and remeshing capabilities. This experimental numerical framework is employed to carry out numerical simulations at the microscale with immersed microstructuresand realistic boundary conditions. The studied material is nodular cast iron, but this methodology has been successfully applied to other materials such as aluminum alloys.Since this is a recent methodology,attention is paid to image immersion as a source of uncertainty. More specifically, the effect of image segmentation on the final mechanical observables, is assessed through comparison of three different segmentation methodologies. The prediction capacity of the numerical simulations is then satisfactorily evaluated through a detailed comparison with experimental measurements. Finally,after evaluating different approaches,the results of the simulations are used to propose and validate a coalescence criterion based on the evolution of the intervoid distance.; Ce travail vise à mieux comprendre et modéliser les mécanismes de rupture ductile pour les microstructures hétérogènes. La principale méthodologie du projet repose sur la combinaison de trois techniques : la laminographie in situ par rayonnement synchrotron,la corrélation d’images volumiques (DVC) et la simulation par éléments finis (FE) avec des fonctionnalités avancées de maillage et de remaillage automatique. Ce cadre expérimental-numérique est utilisé pour réaliser des simulations numériques à l’échelle microscopique avec des microstructures immergées et des conditions aux limites réalistes. L’effet de la segmentation d’image sur les observables mécaniques finales est évalué par comparaison de trois méthodologies différentes. Ce travail permet, pour la première fois, d’accéder aux valeurs de déformation locales au début de la coalescence pour des microstructures réelles et des conditions aux limites exactes. Les résultats des simulations sont utilisés pour définir et valider des critères de rupture locaux fonctions des contraintes/déformations ou un critère de coalescence basé sur l’évolution de la distance entre les pores.

This work constitutes a micromechanical study of ductile fracture.The main methodology consists of acombination of three techniques: Insitu synchrotron radiation computed laminography, digital volume correlation and finite element simulations with advanced meshing and remeshing capabilities. This experimental numerical framework is employed to carry out numerical simulations at the microscale with immersed microstructuresand realistic boundary conditions. The studied material is nodular cast iron, but this methodology has been successfully applied to other materials such as aluminum alloys.Since this is a recent methodology,attention is paid to image immersion as a source of uncertainty. More specifically, the effect of image segmentation on the final mechanical observables, is assessed through comparison of three different segmentation methodologies. The prediction capacity of the numerical simulations is then satisfactorily evaluated through a detailed comparison with experimental measurements. Finally,after evaluating different approaches,the results of the simulations are used to propose and validate a coalescence criterion based on the evolution of the intervoid distance.; Ce travail vise à mieux comprendre et modéliser les mécanismes de rupture ductile pour les microstructures hétérogènes. La principale méthodologie du projet repose sur la combinaison de trois techniques : la laminographie in situ par rayonnement synchrotron,la corrélation d’images volumiques (DVC) et la simulation par éléments finis (FE) avec des fonctionnalités avancées de maillage et de remaillage automatique. Ce cadre expérimental-numérique est utilisé pour réaliser des simulations numériques à l’échelle microscopique avec des microstructures immergées et des conditions aux limites réalistes. L’effet de la segmentation d’image sur les observables mécaniques finales est évalué par comparaison de trois méthodologies différentes. Ce travail permet, pour la première fois, d’accéder aux valeurs de déformation locales au début de la coalescence pour des microstructures réelles et des conditions aux limites exactes. Les résultats des simulations sont utilisés pour définir et valider des critères de rupture locaux fonctions des contraintes/déformations ou un critère de coalescence basé sur l’évolution de la distance entre les pores.

International audience; A model of coalescence by internal necking of primary voids is developed which accounts for the presence of a second population of cavities. The derivation is based on a limit-analysis of a cylindrical cell containing a mesoscopic void and subjected to boundary conditions describing the kinematics of coalescence. The second population is accounted locally in the matrix surrounding the mesoscopic void through the microscopic potential of Michel and Suquet (1992) for spherical voids. The macroscopic criterion obtained is assessed through comparison of its predictions with the results of micromechanical finite element simulations on the same cell. A good agreement between model predictions and numerical results is found on the limit-load promoting coalescence.

International audience; A micromorphic single crystal plasticity model is formulated at finite deformations as an extension of Mandel’s classical theory based on a multiplicative decomposition of the deformation gradient. It involves a single microslip degree of freedom in addition to the usual displacement components. Two main variants of the constitutive equations are proposed. The first one relies on a Lagrangian microslip gradient and leads to a Laplace term in the isotropic hardening law. In contrast, the second formulation, based on a generalized strain measure defined with respect to the intermediate configuration, is shown to induce both isotropic and kinematic enhanced hardening. The first formulation is implemented in a 3D finite element code. The model is applied first to strain localization phenomena in a single crystal in tension undergoing single slip. The regularization power of the model is illustrated by mesh-independent simulations of the competition between kink and slip bands. The model is then used to investigate void growth and coalescence in FCC single crystals. Cylindrical and spherical voids are considered successively. The simulations show, for the first time in the case of spherical voids embedded in a single crystal matrix, that smaller voids grow slower than bigger ones, and that the onset of void coalescence is delayed for smaller voids. These results are related to the fact that the field of plastic slip is found to be more diffuse around smaller voids.

International audience; Voids can be observed at various scales in ductile materials, frequently of sizes lower than the grain size, leading to either microscopicallyor macroscopically porous single crystals materials. Under mechanical loading, two local deformation modes ofporous ductile (single crystals) materials have been identified and referred to as void growth and void coalescence, the latter beingcharacterized by strong interactions between adjacent voids. A simple semi-analytical coalescence criterion for porous singlecrystals with periodic arrangement of voids is proposed using eective isotropic yield stresses associated with a criterion derivedfor isotropic materials. The potential influence of shear stress with respect to the coalescence plane is also accounted for in anextended coalescence criterion. Eective yield stresses are defined using Taylor theory of single crystal deformation, and rely ultimatelyon the computation of average Taylor factors. Arbitrary sets of slip systems can be considered. The coalescence criterion isassessed through comparisons to numerical limit-analysis results performed using a Fast-Fourier-Transform based solver. A goodagreement is observed between semi-analytical predictions and numerical results for various configurations including dierent setsof slip systems (Face-Centered-Cubic, Hexagonal-Close-Packed), crystal orientations, void shapes and loading conditions. Thecompetition between void growth and void coalescence is described for specific conditions, emphasizing the strong influence ofboth crystal orientation and void lattice, as well as their interactions.

WOS; International audience; Void coalescence in ductile voided solids subjected to dynamic loading is investigated numerically. Finite element simulations of an axisymmetric unit cell, taking inertia and finite strain effects into account, are used to describe the coalescence process in a porous material containing a periodic distribution of initially spherical voids. The numerical results suggest that inertia yields a stabilizing effect and slows down the necking of the ligaments between neighbouring voids. Besides, for sufficiently high stress triaxiality and loading rate, coalescence is found to occur by direct impingement, instead of ligament necking. This result correlates with experimental observations in spall fracture and dynamic crack propagation.

As part of the current context of requiring ever more efficient grades of steels in terms of resistance to stress and to damage, the Dual-Phase steels (DP) present an acceptable strength/ductility compromise. It is nevertheless necessary to have a better understanding of the mechanisms leading to the fracture of such steels. Damage mechanisms were studied in this PhD using X-ray tomography. In-situ tensile tests were carried out on several grades of DP steel, a ferritic steel and a martensitic steel in order to characterize each step of ductile damage. Qualitative observations and quantitative data on the nucleation of damage, the void growth and the coalescence of cavities were collected during these tests. This quantitative data was then used for the development and/or the validation of damage models. A prediction of the kinetic of nucleation was proposed and the Huang’s correction of the void growth model of Rice and Tracey accounting for the triaxiality was experimentally validated. For the first time, the step of void coalescence leading to fracture of materials was quantitatively characterized in an industrial material and coalescence criteria were locally applied on couples of neighboring cavities present in the studied specimen. The use of analytical models enabled a better understanding of the properties influencing the studied damage phenomena. The effect of the kinematic part of the strain hardening on void nucleation and void growth was notably emphasized and validated by performing complex loading tests., Dans le cadre du développement de nuances d’aciers toujours plus performantes en termes de résistance à l’effort et à l’endommagement, les aciers Dual-Phase (DP) présentent un bon compromis résistance/ductilité. Cependant, il est nécessaire de disposer de meilleures connaissances concernant les mécanismes menant à la rupture de tels aciers. Les mécanismes d’endommagement ont ainsi été étudiés dans cette thèse à l’aide de la tomographie aux rayons X. Des essais de traction in-situ ont été réalisés sur plusieurs nuances d’aciers DP, un acier ferritique et un acier martensitique afin de caractériser chaque étape de l’endommagement ductile. Des observations qualitatives et des données quantitatives concernant la germination de l’endommagement, la croissance des cavités et la coalescence ont été recueillies lors de ces essais. Ces données quantitatives ont ensuite été utilisées pour le développement et/ou la validation de modèles d’endommagement. Une prédiction de la cinétique de germination a ainsi été proposée et la version du modèle de croissance de cavités de Rice et Tracey corrigée par Huang et prenant mieux en compte l’effet de la triaxialité a été validée expérimentalement. L’étape de coalescence des cavités menant à la rupture des matériaux a pour la première fois été caractérisée de façon quantitative dans un matériau industriel et des critères de coalescence ont été appliqués localement sur les couples de cavités présentes dans le matériau. L’utilisation de ces modèles analytiques a permis une meilleure compréhension des propriétés agissant sur les phénomènes mis en jeu. L’effet de la part cinématique de l’écrouissage sur la germination et la croissance de l’endommagement a notamment été souligné et validé par des essais de chargements complexes.

International audience; This study is devoted to the mechanical behavior of polycrystalline materials with two populations of voids, small spherical voids located inside the grains and larger spheroidal voids located at the grain boundaries. In part I of the work, instantaneous effective stress-strain relations were derived for fixed microstructure. In this second part, the evolution of the microstructure is addressed. Differential equations governing the evolution of the microstructural parameters in terms of the applied loading are derived and their integration in time is discussed. Void growth results in a global softening of the stress-strain response of the material. A simple model for the prediction of void coalescence is proposed which can serve to predict the overall ductility of polycrystalline porous materials under the combined action of thermal dilatation and internal pressure in the voids.

International audience; A theory of anisotropic ductile fracture is outlined and applied to predict failure in a low alloy steel. The theory accounts for initial anisotropy and microstructure evolution (plastic anisotropy, porosity, void shape, orientation and spacing) and is supplemented by a recent micromechanical model of void-coalescence. A rate-dependent version of the theory is employed to solve boundary value problems. The application to the studied steel relies on material parameters inferred from quantitative metallography measurements. The quantitative prediction of damage accumulation and crack initiation in notched bars is achieved without any adjustable factor and is discussed under various stress states and loading orientations.