Showing papers by "Marc Bernacki published in 2018"

On the Coupling between Recrystallization and Precipitation Following Hot Deformation in a γ-γ′ Nickel-Based Superalloy

Abstract: Postdynamic recrystallization and γ′ precipitation during cooling from γ′ supersolvus temperature after hot compression were studied in the AD730 (AD730 is a trademark of Aubert et Duval Company in Paris, France) γ-γ′ nickel-based superalloy. Emphasis was on not only both phenomena as distinct mechanisms but also on their mutual influence in terms of physical mechanisms. The growth of γ′ precipitates is hastened in the unrecrystallized grains compared to the recrystallized ones. This could possibly be attributed to the higher dislocation content acting as high-diffusivity paths. Postdynamic recrystallization is not prevented by Smith–Zener pinning of the recrystallization front by the γ′ precipitates. Instead, the recrystallization front dissolves γ′ precipitates, which then reprecipitate discontinuously or continuously and coherently with the surrounding γ matrix in the recrystallized grains.

On the calibration of elastoplastic parameters at the microscale via X-ray microtomography and digital volume correlation for the simulation of ductile damage

Abstract: An identification framework is introduced herein to calibrate material parameters at the microscale in order to analyze ductile damage. It is applied to study a dog-bone sample, which is made of spheroidal graphite cast iron, loaded in tension and imaged via in situ microtomography. The region of interest is analyzed via Digital Volume Correlation (DVC) to measure kinematic fields. Finite Element (FE) simulations, which account for the studied microstructure that is explicitly meshed thanks its 3D image, are driven by Dirichlet boundary conditions extracted from DVC measurements. The plastic behavior of the ferritic matrix is calibrated via integrated DVC. The three mechanisms of ductile damage are then analyzed in view of the predictions of numerical simulations at the microscopic scale .

DIGIMU V3.0 : première solution commerciale pour la modélisation physique des évolutions d’un polycristal durant les procédés thermomécaniques de mise en forme des matériaux métalliques

Abstract: L’etat microstructural d’un materiau metallique joue un role preponderant sur ses proprietes d’usage et son comportement mecanique durant la mise en forme. Il devient aujourd’hui necessaire de maitriser ces evolutions tout au long des procedes industriels afin de remplir des cahiers des charges exigeants et de repondre efficacement aux nouveaux marches. Les logiciels de simulation de mise en forme des materiaux dont disposent les industriels permettent d’utiliser des modeles metallurgiques principalement bases sur des equations phenomenologiques ou des modeles a champ moyen. Cependant, le domaine de validite de ces modeles associes a un jeu de parametres est souvent limite a un materiau et un procede. Reidentifier en permanence ces parametres par des etudes experimentales est synonyme de couts prohibitifs. Ces vingt dernieres annees, des solutions de modelisation academiques en champ complet sont apparues. Ces methodes sous-entendent une modelisation directe des evolutions d’un polycristal sur un volume elementaire representatif a l’echelle mesoscopique. La modelisation des mecanismes physiques a l’œuvre rendant ces simulations plus generiques.

Experimental-Numerical Validation Framework for Micromechanical Simulations

Abstract: A combined experimental-numerical framework is presented in order to validate computations at the microscale. It is illustrated for a flat specimen with two holes, which is made of cast iron and imaged via in situ synchrotron laminography at micrometer resolution during a tensile test. The region in the reconstructed volume between the two holes is analyzed via Digital Volume Correlation (DVC) to measure displacement fields. Finite Element (FE) simulations, whose mesh is made consistent with the studied material microstructure, are driven by measured Dirichlet boundary conditions. Damage levels and gray level residuals for DVC measurements and FE simulations are assessed for validation purposes.

A novel monolithic Lagrangian approach for modelling crack propagation using anisotropic mesh adaptation

Abstract: A monolithic Lagrangian finite element method is explored to model crack propagation. This approach is based on the level-set method coupled with anisotropic remeshing to define the crack faces and tip. Moreover, the Gθ method is used for computing the strain energy release rate and the propagation direction. Furthermore, a new technique for computing the convection velocity, which is a mixture between the propagation speed and the mechanical velocity, is introduced.

A new level set - finite element formulation for anisotropic grain growth

Abstract: Grain growth in metallic materials is often detrimental to the desired properties of finished components. As such, predicting the evolution of a microstructure undergoing grain growth under specic conditions of temperature and stress is crucial to controlling the microstructure, and therefore the properties, of formed metal parts. Even so, a grain boundary is a complex 5 dimensional object [1] that evolves in order to minimize thermodynamic potentials [2] and whose movement is thermally activated. The intrinsic properties of these boundaries vary based on crystallographic variables, the misorientation M, as well as topological ones, the normal to the grain boundary n, which vary in space. This means that quantities commonly associated to grain boundaries such as grain boundary energy, , or mobility, m, are not constants for a given material at a given temperature, but functions of the grain boundary character B = (M, n). Models for driving forces do exist for normal dependent grain boundary energies (n) [2]. However, the dependence of the grain boundary energy to crystallographic variables (M), and more notably the gradients of this component of the energy, is not clearly formulated in the classical models for grain growth. This work aims to formulate, develop and implement a grain growth simulation framework that can take into account aspects of the gradient of anisotropy of grain boundary energy using a level-set (LS) description of the microstructure and a finite element (FE) resolution of the physical problem. This framework is tested for high ratios of anisotropies, with the max-min ratio of energy values of the order of ten (the order of a twin boundary with respect to a general grain boundary). The behavior of anisotropic systems in this new formulation is different and closer to analytical values as compared with anisotropic systems in the classical formulation of the problem. The new formulation is able to predict the equilibrium angles of triple junctions associated with the energies of the boundaries that meet at the triple point. In polycrystal simulations, the results in terms of microstructural evolutions and their kinetics follow new tendencies as compared with results from classical formulations.

Prediction of the grain size evolution during thermal treatments at the mesoscopic scale: a numerical framework and industrial examples

Abstract: Recently, an original full field model working at the mesoscopic scale using the level set (LS) method in a finite element (FE) framework has been introduced. This approach has demonstrated its potential for the simulation of grain growth and recrystallization problems. Through the development of the DIGIMU® software, this methodology is now considered for industrial applications. The paper presents (i) the recent developments made on the LS approach and (ii) some examples of large scale simulations in two and three dimensions considering thermal treatments applied on materials. Grain boundaries motion considering the presence or not of second phase particles (like precipitates) are investigated.

Modélisation en champ complet des phénomènes de recristallisation et de croissance de grains par une approche level-set : un outil de simulation avancée adapté à un usage industriel

Abstract: La simulation thermomecanique de la mise en forme des materiaux metalliques est predictive, d'un point de vue macroscopique, si la dependance de la contrainte d'ecoulement vis-a-vis de la deformation, de la vitesse de deformation, et de la temperature est decrite par une loi de comportement adaptee. Les proprietes mecaniques et le comportement rheologique des materiaux metalliques dependent fortement de la densite de dislocations et des structures constituees au sein du reseau de dislocations. Il apparait donc naturel d'incorporer ces aspects metallurgiques dans les outils de simulation numerique afin de decrire les principaux mecanismes physiques a l'oeuvre dans le materiau deforme : ecrouissage, restauration, migration des joints de grains, germination et croissance de grains recristallises, que ce soit en conditions statiques (au cours du chauffage ou traitement thermique), dynamiques (pendant une deformation a chaud) ou post-dynamiques. Cette etape est necessaire au developpement de modeles avec un fondement physique qui soient capables de predire l'evolution du materiau lui-meme, ou plus exactement de sa microstructure. Des modeles macroscopiques et homogeneises sont assez frequemment utilises dans l'industrie, notamment parce qu'ils ne necessitent pas de moyens de calculs particuliers, qu'ils sont assez simples et rapides a mettre en oeuvre [1, 2]. Ces avantages doivent neanmoins etre nuances par le fait que ces modeles necessitent de realiser au prealable un grand nombre de mesures experimentales impliquant des moyens d'analyse parfois assez lourds, afin d'identifier les valeurs de parametres adaptes a chaque cas (materiau/procede). De plus, le principe meme de l'homogeneisation peut empecher de decrire les phenomenes metallurgiques locaux apparaissant de maniere heterogene dans la microstructure. Depuis une quinzaine d'annees, des modeles a plus fine echelle, appeles modeles en champ complet, ont ete developpes pour decrire explicitement la microstructure et simuler son evolution [3-5] a l'echelle du polycristal. L'idee sous-jacente est que le reseau de joints de grains, sa morphologie et sa topologie jouent un role primordial dans l'evolution de la microstructure, il faut donc le prendre en compte de maniere aussi fine que possible. Une nouvelle approche en champ complet, basee sur la description des interfaces au moyen de fonctions distance (level-set) dans un contexte elements-finis (EF), a ete introduite pour modeliser la recristallisation statique (incluant le phenomene de germination) en deux puis trois dimensions, et a ensuite ete etendue a la modelisation de la croissance de grains [6-8]. L'un des avantages de cette methode est que le phenomene d'ancrage de joints de grains par des particules de seconde phase (« Smith-Zener pinning »), qui apparait dans de nombreux alliages industriels, est pris en compte de maniere naturelle, sans introduire d'hypothese simplificatrice ou de parametre specifique [9]. L'inconvenient majeur des modeles en champ complet est qu'ils sont souvent tres couteux d'un point de vue numerique, ce qui peut meme devenir redhibitoire pour certains calculs en trois dimensions. Par ailleurs, ils reposent sur de nombreux parametres dont la

A finite element method for two-phase flows based on adaptive interface-fitted meshes

Abstract: A broad range of numerical methods have been devised in the last decades to simulate multi-phase flows. Many of them are based on interface-capturing strategies, where the interface is represented implicitly by a continuous function defined over the whole computational domain (for instance a level-set function). The discrete jump in fluid properties, as well as interfacial phenomena like the surface tension, are then approximately taken into account at the level of the elements/cells intersected by the interface (for instance through Volume-of-Fluid or Cut Finite Element Methods) or in a thicker band of elements/cells around the interface. Local mesh refinement, at least in the normal direction, is often required to accurately capture the behaviour of the interface.

A new topological model for the prediction of dynamic recrystallization

Abstract: During hot deformation of metal alloys, the mechanisms of strain hardening and recovery tend to increase and reduce the energy stored in the material, respectively. When a high enough stored energy level is locally reached, new grains nucleate. In parallel, grain boundaries migrate as a result of stored energy gradients across interfaces and capillary effects. The combination of those mechanisms leads to the so-called dynamic recrystallization (DRX) mechanism.

Simulation de la croissance de grains dans l’olivine par une approche champ complet de type level-set

Abstract: Le phenomene de croissance de grains peut etre vu comme une migration des interfaces entre grains pilotee par la minimisation de l’energie surfacique du reseau de joints de grains. Ces interfaces separent deux domaines d’orientations cristallographiques differentes et possedent une energie par unite de surface dependant du materiau considere, des directions cristallographiques des grains voisins a l’interface consideree et de sa normale. On parle d’energie interfaciale. En general, lorsque la mesure de la desorientation entre deux grains voisins est faible, le joint de grains peut etre decrit comme une succession de dislocations et son energie peut etre calculee a partir de l’energie des dislocations. En etudiant les angles diedres formes par les joints a l’equilibre, il est possible d’etablir des relations entre les energies interfaciales. Le deplacement de ces interfaces met en jeu des deplacements atomiques (diffusion) et est largement favorise par l’agitation thermique. L’etude de ces deplacements en fonction la temperature permet de quantifier, a travers un parametre M appele la mobilite, la « facilite » qu’a un joint de grains a se mouvoir dans la microstructure. Ces deux parametres, et M, sont necessaires a la description de la croissance de grains par capillarite. Ce sont des parametres anisotropes mais qui peuvent etre approches par des constantes (fonction de la temperature pour la mobilite) lorsque le materiau considere est peu texture et contient peu de joints de grains speciaux. Cette hypothese a pour effet de simplifier la determination experimentale de ces quantites et les simulations numeriques. Cette hypothese, realiste dans le cas de l’olivine pure consideree dans ce travail, sera utilisee dans la suite.