Modèle viscoplastique pour un monocristal poreux cubique sous chargement purement hydrostatique

Ce travail concerne la modélisation du comportement viscoplastique d'un monocristal poreux, constitué d'une matrice continue, dans laquelle sont distribuées de façon uniforme des cavités dont la taille caractéristique est petite devant celle du cristal environnant. Ce type de microstructure peut se rencontrer dans certains aciers inoxydables austénitiques irradiés, où des cavités peuvent apparaître à l'intérieur des grains de ces polycristaux (voir par exemple [Garner, F. A., 2012. Radiation Damage in Austenitic Steels. Comprehensive Nuclear Materials, 33-95]). La matrice cristalline est prise à symétrie cubique et trois types de familles sont considérées successivement : les cubiques faces centrées, les cubiques centrées et les ioniques. Un chargement en contrainte effective hydrostatique est considéré. La méthode des stratifiés de rang infini de [Idiart, M.I., 2008. Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates. J. Mech. Phys. Solids 56, 2599-2617] est mise en ?uvre. Des développements analytiques permettent d'écrire le potentiel effectif en contrainte en fonction d'une contrainte hydrostatique d'écoulement qui dépend de la microstructure, des paramètres matériaux locaux et du chargement. Des simulations numériques à base de transformées de Fourier rapides (méthode FFT de [Moulinec, H., Suquet, P., 1994. A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. Paris II 318, 1417?1423]) sont réalisées sur des microstructures tridimensionnelles poreuses périodiques sous chargement en contrainte effective hydrostatique. Les trois types de familles énumérées ci-dessus sont considérés successivement. Différentes porosités et différentes valeurs de l'exposant de fluage sont traitées. Un bon accord est obtenu entre les résultats FFT et ceux du modèle basé sur la méthode des stratifiés. Cette comparaison permet de proposer une forme analytique pour la contrainte hydrostatique d'écoulement. Les résultats sont en accord avec des résultats de la littérature ([Han, X., Besson, J., Forest, S., Tanguy, B., Bugat, S., 2013. A yield function for single crystals containing voids. Int. J. Solids Struct. 50, 2115?2131], [Mbiakop, A., Constantinescu, A., Danas, K., 2015. An analytical model for porous single crystals with ellipsoidal voids. J. Mech. Phys. Solids 84, 436?467], [Paux, J., Morin, L., Brenner, R., Kondo, D., 2015. European Journal of Mechanics A/Solids 51, 1-10])

Porous polycrystal plasticity modeling of neutron-irradiated austenitic stainless steels

A micromechanical model for quantifying the simultaneous influence of irradiation hardening and swelling on the mechanical stiffness and strength of neutron-irradiated austenitic stainless steels is proposed. The material is regarded as an aggregate of equiaxed crystalline grains containing a random dispersion of pores (large voids due to large irradiation levels) and exhibiting elastic isotropy but viscoplastic anisotropy. The overall properties are obtained via a judicious combination of various bounds and estimates for the elastic energy and viscoplastic dissipation of voided crystals and polycrystals. Reference results are generated with full-field numerical simulations for dense and voided polycrystals with periodic microstructures and crystal plasticity laws accounting for the evolution of dislocation and Frank loop densities. These results are calibrated with experimental data available from the literature and are employed to assess the capabilities of the proposed model to describe the evolution of mechanical properties of highly irradiated Solution Annealed 304L steels at 330°C. The agreement between model predictions and simulations is seen to be quite satisfactory over the entire range of porosities and loadings investigated. The expected decrease of overall elastic properties and strength for porosities observed at large irradiation levels is reported. The mathematical simplicity of the proposed model makes it particularly apt for implementation into finite-element codes for structural safety analyses.Centro Tecnológico Aeroespacia

Modélisation micromécanique du comportement viscoplastique d’un polycristal poreux : application à un acier inoxydable austénitique irradié

Austenitic stainless steels employed as internals in pressurized water reactor vessels may nucleate intragranluar voids when exposed to prolonged irradiation and high temperature. The voids, almost spherical in shape, modify the mechanical behavior of the material. This work explores three different approaches in order to model viscoplasticity of voided single crystals. The first approach consists in idealizing the voidedcrystal as a hollow sphere assemblage made of crystalline material. The second approach consists in idealizing the voided crystal as a sequential laminate of infinite rank obeying an isotropic lamination sequence. The third approach consists in idealizing the voided crystal as a periodic medium with a complex unit cell, and computing the mechanical fields numerically via a Fast Fourier Transform algorithm. Then, the estimates for porous single crystals are used to model the viscoplasticity of voided polycrystals via a double up scaling process. Finally, in order to apply the present model to an irradiated austenitic stainless steel, the constitutive material parameters are identified with numerical simulations on periodic unit cells where locally the constitutive behavior is described by a phenomenological model especially devoted to this irradiated austenitic stainless steel, taking account of the evolution of irradiation defects. As a general rule, this work aims at delivering innovative, high-performance modeling tools, applicable to a wide variety of crystalline materials together with irradiated austenitic stainless steels.La température élevée et l’irradiation prolongée que subissent les aciers inoxydables austénitiques des internes de cuve des réacteurs à eau pressurisée entraînent potentiellement l’apparition de cavités au sein des grains de la structure polycristalline du matériau considéré. Ces cavités intragranulaires, de forme plutôt sphérique, peuvent modifier les propriétés mécaniques du matériau. Tout d’abord, ce travail de recherche propose de modéliser le comportement viscoplastique de monocristaux poreux, principalement via trois approches différentes. Premièrement, le monocristal poreux est idéalisé comme un assemblage d’une infinité de sphères homothétiques ; deuxièmement, le monocristal poreux est idéalisé comme une microstructure laminée séquentiellement, dont le procédé de laminage est réitéré à l’infini ; troisièmement, le monocristal poreux est idéalisé comme une microstructure périodique dont le comportement est évalué par des simulations numériques basées sur un algorithme de transformées de Fourier rapides. Ensuite, les estimations pour monocristaux poreux sont exploitées via une démarche de double changement d’échelles pour modéliser le comportement viscoplastique d’un polycristal poreux. En vue d’une application à un acier inoxydable austénitique irradié, les paramètres matériau du modèle polycristallin poreux sont identifiés à partir de simulations numériques sur des microstructures périodiques où localement le comportement cristallin est décrit par une loi de comportement spécialement dédiée à cet acier inoxydable austénitique irradié prenant en compte l’évolution des défauts dus à l’irradiation. De manière générale, ce travail cherche à proposer des outils de modélisation innovants, performants, et applicables à une grande variété de configuration cristalline, mais aussi facilement applicables aux aciers inoxydables auténitiques irradiés

Viscoplasticity of voided cubic crystals under hydrostatic loading

A micromechanical study of the viscoplasticity of voided cubic crystals is presented. The microscopic void distribution is isotropic and the macroscopic loading is hydrostatic. Three different approaches are considered. The first approach consists in idealizing the voided crystal as a hollow sphere assemblage and bounding from above the corresponding dissipation potential à la Gurson. The second approach consists in idealizing the voided crystal as a sequential laminate of infinite rank and computing the corresponding dissipation potential exactly. Finally, the third approach consists in idealizing the voided crystal as a periodic medium with a complex unit cell and computing the mechanical fields numerically via a Fast Fourier Transform (FFT) algorithm. Predictions are reported for a wide range of crystals deforming by power-law creep and rate-independent plasticity. When the plastic anisotropy is weak, a fairly good agreement between all three approaches is observed. When the plastic anisotropy is strong, by contrast, discrepancies arise. In the extreme case of plastically deficient crystals, the various predictions can exhibit different asymptotics. While estimates based on hollow-sphere assemblages predict that any deficient voided crystal is rigid under hydrostatic loading, FFT simulations and sequential laminates suggest that some deficient voided crystals with more than two linearly independent systems may dilate. Overall, estimates based on sequential laminates are found to be superior to Gurson-type estimates based on hollow sphere assemblages and to predict the hydrostatic response of cubic voided crystals with reasonable accuracy, even for relatively strong plastic anisotropies.Fil: Joëssel, Louis. Institut de Radioprotection Et de Sureté Nucléaire; FranciaFil: Vincent, Pierre Guy. Institut de Radioprotection Et de Sureté Nucléaire; FranciaFil: Garajeu, Mihail. Centre National de la Recherche Scientifique; Francia. Aix Marseille Universite; FranciaFil: Idiart, Martín Ignacio. Universidad Nacional de La Plata. Facultad de Ingeniería. Departamento de Aeronáutica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentin

Porous polycrystal plasticity modeling of neutron-irradiated austenitic stainless steels

International audienceA micromechanical model for quantifying the simultaneous influence of irradiation hardening and swelling on the mechanical stiffness and strength of neutron-irradiated austenitic stainless steels is proposed. The material is regarded as an aggregate of equiaxed crystalline grains containing a random dispersion of pores (large voids due to large irradiation levels) and exhibiting elastic isotropy but viscoplastic anisotropy. The overall properties are obtained via a judicious combination of various bounds and estimates for the elastic energy and viscoplastic dissipation of voided crystals and polycrystals. Reference results are generated with full-field numerical simulations for dense and voided polycrystals with periodic microstructures and crystal plasticity laws accounting for the evolution of dislocation and Frank loop densities. These results are calibrated with experimental data available from the literature and are employed to assess the capabilities of the proposed model to describe the evolution of mechanical properties of highly irradiated Solution Annealed 304L steels at 330°C. The agreement between model predictions and simulations is seen to be quite satisfactory over the entire range of porosities and loadings investigated. The expected decrease of overall elastic properties and strength for porosities observed at large irradiation levels is reported. The mathematical simplicity of the proposed model makes it particularly apt for implementation into finite-element codes for structural safety analyses

Viscoplasticity of voided cubic crystals under hydrostatic loading

International audienceA micromechanical study of the viscoplasticity of voided cubic crystals is presented. The microscopic void distribution is isotropic and the macroscopic loading is hydrostatic. Three different approaches are considered. The first approach consists in idealizing the voided crystal as a hollow sphere assemblage and bounding from above the corresponding dissipation potential à la Gurson. The second approach consists in idealizing the voided crystal as a sequential laminate of infinite rank and computing the corresponding dissipation potential exactly. Finally, the third approach consists in idealizing the voided crystal as a periodic medium with a complex unit cell and computing the mechanical fields numerically via a Fast Fourier Transform (FFT) algorithm. Predictions are reported for a wide range of crystals deforming by power-law creep and rate-independent plasticity. When the plastic anisotropy is weak, a fairly good agreement between all three approaches is observed. When the plastic anisotropy is strong, by contrast, discrepancies arise. In the extreme case of plastically deficient crystals, the various predictions can exhibit different asymptotics. While estimates based on hollow-sphere assemblages predict that any deficient voided crystal is rigid under hydrostatic loading, FFT simulations and sequential laminates suggest that some deficient voided crystals with more than two linearly independent systems may dilate. Overall, estimates based on sequential laminates are found to be superior to Gurson-type estimates based on hollow sphere assemblages and to predict the hydrostatic response of cubic voided crystals with reasonable accuracy, even for relatively strong plastic anisotropies. © 2018 Elsevier Lt