Mean field modeling of dynamic recrystallization by homogenization of Full field models on 304L
Ludovic Maire, 2015-2018
Mean field (MF) models of dynamic recrystallization (DRX) emerged in the last decades with the intention to implicitly describe the microstructure by considering grains sets as spherical classes. These models have the advantage to provide accurate results in terms of macroscopic results such as recrystallized fraction or grain size but also to provide additional information in terms of grain size distribution and dislocation density distribution [1,2,3,4].
In parallel, finer approaches called full field (FF) models have emerged in the last decades. These approaches consider a complete description of the microstructure topology at the polycrystal scale . A review of the most significant numerical methods can be found in .
Several DRX models based on a full field approach can already be found in the literature [7,8,9]. Although literature already provides a large number of papers on full-field DRX models, major drawbacks are either they are developed in 2D and/or they only consider small deformations (< 20%).
In the present work, a 3D model based on the level-set method in a FE framework is employed to model the DRX phenomenon in austenitic stainless steel 304L at large deformations.
The level-set approach coupled to a remesher provides an accurate tracking of interfaces (i.e. grain boundaries) all along the recrystallization simulation while mean field laws are used for the nucleation and work hardening mechanisms.
The development realized are also dedicated to the elaboration of optimized improved mean field model concerning DRX thanks to the full field developments.
 Montheillet, F., Lurdos, O., and Damamme, G. (2009). Acta Materialia, 57(5):1602–1612.
 Bernard, P., Bag, S., Huang, K., and Logé, R. (2011). Science and Engineering: A, 528(24):7357–7367.
 Cram, D. G., Zurob, H. S., Brechet, Y. J. M., and Hutchinson, C. R. (2009). Acta Materialia, 57(17):5218–5228.
 Maire, L., Moussa, C., Bozzolo, N., Scholtes, B., Pino Muñoz, D., Bernacki, M. (2016). Journal of Materials Science, 51(24):10970-10981.
 Scholtes, B., Shakoor, M., Settefrati, A., Bouchard, P.-O., Bozzolo, N., and Bernacki, M. (2015). Computational Materials Science, 109:388–398.
 Hallberg, H. (2011). Metals, 1(1):16–48.
Globularization phenomenon in α/β titanium alloys: experimental analysis and numerical modeling
Danai Polychronopoulou, 2014-2017
Fragmentation of α lamellae and subsequent spheroidization of α laths in α/β titanium alloys occurring during and after deformation are well known phenomena. In this PhD works, the development of a new finite element methodology to model these mechanisms is considered. This new methodology is based on a level set framework to model the deformation and the ad hoc simultaneous and/or subsequent interfaces kinetics. Validation of these full-field numerical developments thanks to experimental results is also planned.
New 3D Finite-Element Level-Set framework for the modeling of solid-solid phase transformations and grain interfaces for large-scale polycrystals
Chau Thuy Pham, 2017-2020
In order to accurately describe the 3D evolution of polycrystals (recrystallization, phase transformations), full-field methods such as the phase-field (PF) or the level-set (LS) methods have to be employed. In this context, a new FE numerical framework to model grain growth (GG) and recrystallization (ReX) based on a LS description of the interfaces and meshing/remeshing capabilities has been recently developed. Nowadays, the LS approach is used for Rex/GG modeling in the context of uniform grids with a finite-difference formulation or in a FE framework on unstructured mesh. LS method is also particularly interesting for the modeling of Smith-Zener pinning or promising to deal with high anisotropy level of grain interface properties.
Interestingly, if the LS approach was recently extended to other self-diffusion mechanisms such as spheroidization in titanium alloys or sintering in powder metallurgy, solid-solid phase transformations (SSPT) was not yet adressed despite the obvious interest to couple phases and grains evolutions in the same LS numerical framework. In the proposed PhD project, the existing LS framework will be extended in order to model SSPT. The new proposed formalism will be investigated in context of austenite-ferrite transformations for a steel and evolution of second phase particles for a nickel based superalloys. Moreover it will be compared to pre-existing PF strategy dedicated to this topic.
Finally, the resulting developments will be prepared for integration in the DIGIMU® software package.
- New 3D Finite-Element meshing/remeshing approach for large-scale dynamic polycrystals
Sebastian Florez, 2017-2020
In order to accurately describe the 3D evolution of polycrystals (recrystallization, phase transformations…), full-field methods such as the phase-field or the level-set methods have to be employed. Despite the recent introduction of HPC techniques in metallurgy, the main weakness of these methods still lies in their computational cost. Optimized 3D meshing and remeshing strategies are an interesting alternative for overcoming this problem, as illustrated in the figure below. Nevertheless, it seems that state-of-the-art methodologies involving unstructured Finite-Element (FE) meshes will remain incapable of carrying out large-scale computations ( 10000 to 100000 grains) with reasonable computational facilities.
In the proposed PhD project, a new 3D mesh adaptation technique that combines explicit meshing of interfaces and implicit level set (LS) description will be investigated to reach this objective. Front-capturing approaches based on the plain LS method can suffer from spurious deformations of inter-grain interfaces due to numerical diffusion, particularly during the remeshing operations required to follow the interface motion. Comparatively, the new technique has been shown to drastically reduce the volume loss at remeshing in the context of biphasic materials, with a beneficial impact on the overall computational cost. This quite prospective approach will be complemented with a more classical investigation of anisotropic mesh adaptation procedures driven by new geometric error estimators that are specific to 3D polycrystals.
Finally, the resulting developments will be applied to industrial-scale cases and prepared for integration in the DIGIMU® software package.
- Enhancement of a full field finite element framework to model recrystallization in context of strong anisotropies of mobility and grain boundary energy
David Ruiz, 2017-2020
In order to accurately describe the 3D evolution of polycrystals (recrystallization, phase transformations…), full-field methods such as the phase-field (PF) or the level-set (LS) methods have to be employed. In this context, a new FE numerical framework to model grain growth (GG) and recrystallization (ReX) based on a LS description of the interfaces and meshing/remeshing capabilities has been recently developeda. Nowadays, the LS approach is used for Rex/GG modeling in the context of uniform grids with a finite-difference formulation or in a FE framework on unstructured mesh. LS method is also particularly interesting for the modeling of Smith-Zener pinning.
These PhD works will be dedicated to the enhancement of the existing formalism in order to be able, in a smart and efficient way, to deal with strong and local anisotropies of mobility and grain boundary energy. This aspect is today a strong numerical difficulty for existing full field numerical approaches. Moreover a new modular crystal plasticity finite element method will be employed/ improved during the PhD. DRX (as illustrated in the figure) and SRX phenomema for different austenitic stainless steels will be investigated with these developments and validated thanks to existing experimental results.
Finally, the resulting developments will be prepared for integration in the DIGIMU® software package.
Towards a precise description of the mobility and its numerical integration in finite element modeling of recrystallization mechanisms
Brayan Murgas, 2018-2021
In order to accurately describe the 3D evolution of polycrystals (recrystallization, phase transformations…), full-field methods such as the phase-field (PF) or the level-set (LS) methods currently represent the best option. In this context, a new FE numerical framework to model grain growth (GG) and recrystallization (ReX) based on a LS description of the interfaces and meshing/remeshing capabilities has been recently developed in a static context  or a dynamic one . LS method is also particularly interesting for the modeling of Smith-Zener pinning. These PhD works will be dedicated to the enhancement of the existing numerical formalism in order to be able, in a smart and efficient way, to deal with strong and local anisotropies of mobility. This aspect is today a big numerical challenge for existing full field numerical approaches but also an open question from a metallurgical point of view. These developments will be motivated, criticized and validated thanks to experimental investigations on 304L and 316L stainless steels. Finally, the resulting developments will be impleted in the DIGIMU software packing.
 B. Scholtes, R. Boulais-Sinou, A. Settefrati, D. Pino Muñoz, I. Poitrault, A. Montouchet, N. Bozzolo, and M. Bernacki. 3D level set modeling of static recrystallization considering stored energy fields. Computational Materials Science, 122:57-71, 2016.
 L. Maire, B. Scholtes, C. Moussa, N. Bozzolo, D. Pino Muñoz, A. Settefrati, and M. Bernacki. Modeling of dynamic and post-dynamic recrystallization by coupling a full field approach to phenomenological laws. Materials & Design, 133:498-519, 2017.
Influence of grain boundary pinning on recrystallized grain size homogeneity : multiscale modelling and application to nickel based superalloys used in aeronautic industry
Karen Alvarado, 2018-2021
During the last six decades, Smith-Zener pinning phenomenon has been widely studied and many different analytical models have been proposed in the literature. In this context, abnormal grain growth (AGG) is a versatile phenomenon and its prediction is extremely complex. AGG can be seen as a particular metallurgical configuration where few grains grow much faster than the mean grain growth rate, leading to a bimodal grain size distribution or eventually to a single population of very large grains. At stable subsolvus configuration, if only capillarity force is considered, this phenomenon is always driven by a kind of growing advantage for some grains comparatively to their neighbours (grain size, high anisotropy of boundary energy and/or boundary mobility) but this phenomenon can also be triggered by critical stored energy distributions. In the last case, even if AGG remains the accepted term in the literature, we should rather discuss of a particular regime of ReX. Recently, a new level-set (LS) numerical approach to consider inert second phase particles (SPP) in a FE framework has been proposed and used to perform 2D GG and static recrystallization (SRX) simulations for Inconel™ 718. Such approach seems very promising in context of AGG. Indeed, the Smith-Zener drag effect is naturally modeled by the modification of the local mean curvature when the grain boundaries pass through the particles. AGG in 2D framework, critical stored energy context and stable subsolvus configuration were also discussed thanks to this method . Next steps that we will consider in the proposed work will be to deal with realistic and large 3D simulations by considering all the different metallurgical mechanims which can lead to overgrown grains. Possible evolutions of second phase particles and resulting interactions with grain interfaces in context of near-solvus static TT will be studied. Homogenization will also be considered in order to build improved mean field models. Moreover a large piece of the proposed work will also be dedicated to experimental investigations. Firstly, large databases capitalized by the DIGIMU industrial partners concerning microstructure evolutions of Inconel™ 718 during TMT will be used to discuss the full field simulations and the proposed new main field models. Secondly, in order to validate more finely the different modeled mechanims for more prospective materials, TMT and microstructural characterizations will be realized for two other nickel-based superalloys: N19™ and AD730™.
 A. Agnoli, M. Bernacki, R. Loge, J.-M. Franchet, J. Laigo, and N. Bozzolo. Selective growth of low stored energy grains during sub-solvus annealing in the inconel 718 nickel base superalloy. Metallurgical and Materials Transactions A, 46(9):4405-4421, 2015.