Expérimentation numérique pour l'aide à la spécification de la microstructure et des propriétés mécaniques d'un superalliage base Ni pour des applications moteurs

An optimization loop allowing the optimization of the thermal treatment toward the fatigue life of the turbine disk in PM Ni-base superalloy N18 is built. This loop is constituted of three finite elements calculations and one post-processing of the fatigue life. The first calculation is a thermal calculation which allows the determination of the evolution of the temperature in each point of the disk. The second one is a calculation of the precipitation, which gives the microstructural parameters, i.e. the volume fraction and the size of the different population of precipitates. The third one is the calculation of the mechanical response of the disc to the service loading. The behavior in each Gauss point is a function of the microstructural parameters deduced from the second calculation. To build this loop, a model of precipitation was implemented in ZeBuLoN code and recalibrated for coarse grained N18. Moreover the influence of the intragranular microstructure on the fatigue behaviour was studied through specific mechanical tests performed at 450°C. This study shown the fatigue life function is a priori no dependant from the intragranular microstructure. But it has a very strong influence on the yield stress, which has a direct impact on the mean stress at the stabilised cycle. And the mean stress is one of the key parameters for the fatigue resistance of the material. A multiscale model was built to account for the role of the fine microstructure on the fatigue behaviour. The optimization loop is built with a phenomenological model and shows that a slower cooling, leading to a lower yield stress at the critical point of the disk allows to enhance the fatigue life. Meanwhile, the resistance to brsting also constitutes a major criterion for the design of the disc and this one requires a good mechanical resistance of the material.Une boucle d'optimisation permettant d'optimiser le traitement thermique vis-à-vis de la durée de vie en fatigue d'un disque de turbine haute pression en superalliage à base de nickel N18 a été construite. Cette boucle comporte trois calculs par éléments finis et un post-processing de la durée de vie. Le premier calcul est un calcul thermique qui permet de déterminer l'évolution de la température au cours du traitement thermique en tout point du disque. Le second est un calcul de microstructure qui donne les paramètres microstructuraux, c'est-à-dire le rayon équivalent et la fraction volumique des différentes populations de précipités, en fonction de l'évolution de la température simulée lors du premier calcul. Le troisième calcul consiste à obtenir la réponse mécanique du disque à la sollicitation qu'il subit en service, le comportement en chaque point de Gauss étant dépendant des paramètres microstructuraux résultant du traitement thermique. Afin de construire cette boucle, un modèle de précipitation a été implémenté dans le code ZeBuLoN et calibré pour le N18 à gros grains. De plus, l'influence de la microstructure fine sur le comportement et la résistance en fatigue a été étudiée au moyen d'essais mécaniques spécifiques conduits à 450°C. Ces essais ont montré que la microstructure intragranulaire n'a a priori pas d'influence sur la fonction de durée de vie développée pour les matériaux pour disque. Mais elle a par contre une influence très importante sur la limite d'élasticité du matériau, qui a elle-même une influence directe sur la contrainte moyenne au cycle stabilisé. Et la contrainte moyenne est l'un des paramètres clés gouvernant la résistance en fatigue du matériau. Un modèle multiéchelle a par ailleurs été construit afin de mieux comprendre le rôle de la microstructure fine sur le comportement en fatigue. La boucle d'optimisation intègre un modèle phénoménologique et montre qu'un refroidissement plus lent, aboutissant à une limite d'élasticité plus basse au point critique du disque, permet d'allonger la durée de vie. Cependant, la tenue à l'éclatement constitue aussi un critère dimensionnant du disque et celle-ci requiert quant à elle une bonne résistance mécanique du matériau

Influence of y' precipitate-size and distribution on LCF behavior of a PM disk superalloy

International audienceThe influence of γ' precipitate distribution on tensile and low cycle fatigue (LCF) behaviors of a powder metallurgy (PM) disk superalloy was investigated at 450°C. Four γ' particle distributions were obtained through various cooling paths and/or aging treatments in coarse grain size superalloy N18. The mechanical tests show that the main influence of the intragranular microstructure concerns the 0.2% yield stress (0.2%YS) and the ultimate tensile stress. Wide variations of the 0.2%YS affect the mean stress under non symmetrical loading but have only little effect on fatigue life, the lower the 0.2%YS, the longer the fatigue life. The fatigue life of N18 at 450°C is independent of the intragranular microstructure as long as the mean stress effect is correctly taken into account. As expected with the coarse grain size N18, no crack initiation at pores or inclusions was observed. A precipitation model was coupled with a critical resolved shear stress calculation providing 0.2%YS value for a given heat treatment sequence. Finally, this computation procedure was implemented in a numerical modeling of the LCF life of a disk taking into account the heat treatment applied to its wrought preform

Numerical simulations and modeling of the effective plastic flow surface of a biporous material with pressurized intergranular bubbles: application to irradiated uranium dioxide

International audienceIn this work, the specific microstructure of the irradiated uranium dioxide (UO2) is modeled as a biporous material with 2 populations of bubbles: intragranular bubbles of spherical shape, and an intergranular population of bubbles elongated along the grain boundaries. The effective plastic flow surface of such a biporous material is investigated through full-field numerical simulations. The effect of the intragranular cavities is modeled by a GTN (Gurson-Tvergaard-Needleman) matrix. Full-field numerical simulations are performed with a FFT-based (Fast Fourier Transforms) method (originally developed by [Moulinec and Suquet, 1994]) on 3-dimensional and periodic cells. A particular attention is paid to this specific microstructure and the effect of the distribution of the intergranular bubbles on the effective plastic flow surface. Different microstructures with different porosities and sizes for the intergranular bubbles are considered here (the mean size of the grains being fixed).Three loading conditions are imposed on the cells: a purely hydrostatic overall stress, a purely deviatoric overall stress, and an ‘intermediate’ overall stress (triaxiality ratio of 4). It is shown that the effect of the relative size of the intergranular bubbles depends on the direction of the loading. Then, a comparison is made with the analytical model of [Vincent et al., 2014] and a correction of the intergranular porosity is introduced in this model and identified to take into account the non-isotropic distribution of the intergranular bubbles. The corrected intergranular porosity is composed of two terms: the first one is predominant for low intergranular porosities, and the second one is predominant for high intergranular porosities. It is checked that the correction introduced in the analytical model can also be used for pressurized cavities such as encountered in irradiated UO2

Numerical simulations and modeling of the effective plastic flow surface of a biporous material with pressurized intergranular voids

International audienceThis study is devoted to the effective plastic flow surface of a biporous polycrystalline material, with an intragranular porosity consisting of spherical voids, and an intergranular porosity consisting of larger elongated voids along the grain boundaries. These two populations of voids (or bubbles) with well separated scales and shapes are saturated by a fluid and therefore are subjected to internal pressures. The effect of the intragranular voids is modeled through a GTN (Gurson-Tvergaard-Needleman) criterion in the matrix. Numerical simulations are performed with a FFT-based (Fast Fourier Transforms) method. A particular attention is paid to the effect of the distribution of the intergranular bubbles on the effective plastic flow surface. Different microstructures with different volume fractions and sizes for the intergranular bubbles are tested under three loading conditions (the mean size of the grains being fixed). Two main results are exhibited. First, it is shown that the effect of the relative size of the intergranular bubbles on the effective plastic flow surface depends on the loading direction. Secondly, a comparison is made with the analytical model of (Vincent et al., 2014) and a correction of the porosity relative to the intergranu-lar bubbles is introduced in this analytical model in order to take into account the specific distribution of the intergranular bubbles along the grain boundaries. This correction is expressed as a sum of two power law functions, each of them being significant either for low or for large values of the porosity of intergranular bubbles

Étude du comportement mécanique de microstructures à porosité bimodale pressurisée par transformées de Fourier rapides

National audienceLe comportement des matériaux poreux est étudié depuis longtemps car la présence des cavités peut mener à l'endommagement voire à la rupture du matériau. Des développements récents tendent à préciser l'effet de taille, de répartition ou de forme de ces pores sur le comportement élasto-plastique [1,2,3]. Le présent travail concerne l'effet d'une répartition bimodale de porosités sous pression : une porosité intragranulaire sphérique de petite taille et une porosité intergranulaire non-sphérique de grande taille

Étude du comportement mécanique de microstructures à porosité bimodale pressurisée par transformées de Fourier rapides

National audienceLe comportement des matériaux poreux est étudié depuis longtemps car la présence des cavités peut mener à l'endommagement voire à la rupture du matériau. Des développements récents tendent à préciser l'effet de taille, de répartition ou de forme de ces pores sur le comportement élasto-plastique [1,2,3]. Le présent travail concerne l'effet d'une répartition bimodale de porosités sous pression : une porosité intragranulaire sphérique de petite taille et une porosité intergranulaire non-sphérique de grande taille

Étude du comportement mécanique de microstructures à porosité bimodale pressurisée par transformées de Fourier rapides

National audienceLe comportement des matériaux poreux est étudié depuis longtemps car la présence des cavités peut mener à l'endommagement voire à la rupture du matériau. Des développements récents tendent à préciser l'effet de taille, de répartition ou de forme de ces pores sur le comportement élasto-plastique [1,2,3]. Le présent travail concerne l'effet d'une répartition bimodale de porosités sous pression : une porosité intragranulaire sphérique de petite taille et une porosité intergranulaire non-sphérique de grande taille

Numerical simulations and modeling of the effective plastic flow surface of a biporous material with pressurized intergranular bubbles: application to irradiated uranium dioxide

International audienceIn this work, the specific microstructure of the irradiated uranium dioxide (UO2) is modeled as a biporous material with 2 populations of bubbles: intragranular bubbles of spherical shape, and an intergranular population of bubbles elongated along the grain boundaries. The effective plastic flow surface of such a biporous material is investigated through full-field numerical simulations. The effect of the intragranular cavities is modeled by a GTN (Gurson-Tvergaard-Needleman) matrix. Full-field numerical simulations are performed with a FFT-based (Fast Fourier Transforms) method (originally developed by [Moulinec and Suquet, 1994]) on 3-dimensional and periodic cells. A particular attention is paid to this specific microstructure and the effect of the distribution of the intergranular bubbles on the effective plastic flow surface. Different microstructures with different porosities and sizes for the intergranular bubbles are considered here (the mean size of the grains being fixed).Three loading conditions are imposed on the cells: a purely hydrostatic overall stress, a purely deviatoric overall stress, and an ‘intermediate’ overall stress (triaxiality ratio of 4). It is shown that the effect of the relative size of the intergranular bubbles depends on the direction of the loading. Then, a comparison is made with the analytical model of [Vincent et al., 2014] and a correction of the intergranular porosity is introduced in this model and identified to take into account the non-isotropic distribution of the intergranular bubbles. The corrected intergranular porosity is composed of two terms: the first one is predominant for low intergranular porosities, and the second one is predominant for high intergranular porosities. It is checked that the correction introduced in the analytical model can also be used for pressurized cavities such as encountered in irradiated UO2

Numerical modelling of the microstructure effect on fatigue behaviour of Ni-base superalloys for turbine disk

International audienceNickel-based alloy like N18 can present various types of precipitate distributions according to the applied heat treatment. A model involving a three scale homogenization procedure is developed to characterize the influence of this microstructure on fatigue life. The microstructural parameters are the size and the volume fraction of the secondary and tertiary precipitates of gamma phase. Experimental results at 450 °C, specially designed to calibrate the model, allow to understand the role of tertiary precipitation. The first identification of the three scale homogenization model is shown