Study of fracture toughness - microstructure relationships of new high performance oxide dispersion strengthened steels

ODS steels are considered for the development of components for fourth generation reactors. They offer high tensile and creep strength and good resistance to irradiation [1-3]. This high level of reinforcement is accompanied by a reduction in ductility and toughness. Tube shaping changes the microstructure, so the properties of the material in its final form should be evaluated. The work of B. Rais [4] made it possible to compare the different tests and to develop a test and an analysis method for measuring toughness on thin tubes.

This present PhD will use this new test to evaluate the toughness of various ODS grades. Varied microstructures from historical and recent productions will assessed to identify the mechanisms, the key parameters driving toughness and to identify the microstructural parameters which drive the response of the material. In this work we will be interested in ferritic / martensitic grades, some of which come from a manufacturing process which is the subject of a patent application [5-6] and for which we observe for the first time remarkable properties in resilience, associated with good hot mechanical properties.

The study will be based on a comparison of experience and finite element modeling. This applied research work will allow the student to acquire solid skills in fracture mechanics and fine characterization of materials (SEM, EBSD, etc.). A good understanding of the mechanical properties/microstructure relationships will make it possible to understand the origin of the observed properties and to propose new optimizations on the microstructures to improve the mechanical behavior and/or the shaping of the material.

Student profile: Engineer or M2 Mechanics/Materials

On the role of the elastic deformation field on the formation of irradiation defects in pure metals

In the context of extending the operational lifetime of nuclear power plants (NPPs), currently operating in France, a materials ageing surveillance strategy is in place. It is essential for ensuring their mechanical properties. During the operation of the plant, materials are subjected to irradiation. Under this exposure, the internal structure of materials evolves, leading to the creation of numerous defects that degrade macroscopic properties and may result in a limitation of the long-time operation (LTO) of components. The proposed work is a fundamental study conducted on model materials, aiming to better understanding the behavior under irradiation of metallic alloys. It will contribute to the predictive modelling of materials, covering defects created at the nanoscale up to the level of nuclear components.

The irradiation of materials with high-energy particles such as neutrons, ions, or electrons generates a large number of defects called point defects (PD). These mobile PDs can migrate and aggregate to form 2D or 3D-objects like prismatic loops or cavities respectively. They can also be eliminated at PD sinks. The system is then submitted to PDs flows directed towards these sinks. These flows are then responsible for phenomena such as radiation-induced segregation (RIS) or precipitation (RIP) of solute atoms [1] [2]. The presence of clusters of PDs and of PD flows alters the microstructure and can deteriorate the physical response of the irradiated materials. In particular, the formation of prismatic loops degrades the mechanical properties of materials as they can impede dislocations and induce embrittlement [3]. In a previous study, we focused on vacancy defects in the form of cavities and investigated the facetting of defects formed in a weakly anisotropic metal, aluminum, using in-situ irradiations in a high-resolution transmission electron microscope (HRTEM).
The work aims to go further in the role of the elastic deformation field on the morphology of irradiation defects. More precisely, it aims to carry out a systematic study on different metals with different anisotropy coefficients. We have chosen reference metals with body-centered cubic (BCC) and face-centered cubic (FCC) structures with low or high anisotropy coefficients. The study will concern Cr and Fe with a BCC structure, and Al and Cu with a FCC structure and may be extrapolated to alloys of higher complexity such as high entropy alloys (HEA). The work will be mainly experimental but will also include a theoretical part. The effects of the crystal anisotropy on the morphology of prismatic loops will be carried out by phase field modelling [4]. The spatial arrangement of the loops will be studied by Object Kinetic Monte-Carlo (OKMC) simulations [5], as recently done in aluminium.
The work will be mainly experimental. We will studied [100]-oriented single crystals to avoid any surface effect on the shape of the objects formed. They will be irradiated with heavy ions at temperatures normalized with respect to their melting temperature either in-situ within the Jannus Orsay platform, or ex-situ within the Jannus Saclay platform [6]. Loops will be imaged by conventional TEM or STEM with a FEI Tecnai and Jeol NeoARM type microscopes. The latter is equipped with a double spherical aberration corrector. The work will be carried out within the framework of the joint research laboratory (LRC) MAXIT.
The work will also include a modelling part. The effects of crystallographic anisotropy on the morphology of prismatic loops will be investigated using a phase-field code [4]. The spatial arrangement of the loops will be studied using Object Kinetic Monte Carlo (OKMC) [5], as recently done in aluminum.
This work follows a 2-year postdoctoral fellowship scheduled to conclude in December 2023, during which deep learning (DL) approaches were developed to accelerate the automatic detection of defects created under irradiation [7]. The utilization of these approaches will significantly enhance the statistical robustness and precision of the results.

Advantage for the student: The PhD is situated in a laboratory composed by 25 researchers and approximately 25 students (PhD, postdoctoral fellows), creating a simulating scientific environment. The activities involve both experimental and simulation sides, offering the opportunity to interact with experts from both sides.

[1] M. Nastar, L. T. Belkacemi, E. Meslin, et M. Loyer-Prost, « Thermodynamic model for lattice point defect-mediated semi-coherent precipitation in alloys », Communications Materials, vol. 2, no 1, p. 1-11, mars 2021, doi: 10.1038/s43246-021-00136-z.
[2] L. T. Belkacemi, E. Meslin, B. Décamps, B. Radiguet, et J. Henry, « Radiation-induced bcc-fcc phase transformation in a Fe3%Ni alloy », Acta Materialia, vol. 161, p. 61-72, 2018, doi:
[3] M. Lambrecht et al., « On the correlation between irradiation-induced microstructural features and the hardening of reactor pressure vessel steels », Journal of Nuclear Materials, vol. 406, no 1, p. 84-89, 2010, doi:
[4] A. Ruffini, Y. Le Bouar, et A. Finel, « Three-dimensional phase-field model of dislocations for a heterogeneous face-centered cubic crystal », Journal of the Mechanics and Physics of Solids, vol. 105, p. 95-115, août 2017, doi: 10.1016/j.jmps.2017.04.008.
[5] D. Carpentier, T. Jourdan, Y. Le Bouar, et M.-C. Marinica, « Effect of saddle point anisotropy of point defects on their absorption by dislocations and cavities », Acta Materialia, vol. 136, p. 323-334, sept. 2017, doi: 10.1016/j.actamat.2017.07.013.
[6] A. Gentils et C. Cabet, « Investigating radiation damage in nuclear energy materials using JANNuS multiple ion beams », Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 447, p. 107-112, mai 2019, doi: 10.1016/j.nimb.2019.03.039.
[7] T. Bilyk, A. M. Goryaeva, E. Meslin, M.-C. Marinica, Quantification of radiation damage in high entropy alloys by deep learning approach, 2-7/10/2022, MMM2022, Baltimore, USA

Impact of irradiation parameters on the alpha’ phase formation in oxide dispersion strengthened steels

Ferritic-martensitic oxide dispersion strengthened steels (ODS steels) are materials of great interest in the nuclear industry. Predominantly composed of iron and chromium, these materials can become brittle due to the precipitation of a chromium-rich phase, called a', under irradiation. This phase, known to be sensitive to irradiation conditions, provides an ideal topic for a deeper exploration of the capability to emulate neutron irradiation with ions. Indeed, while ion irradiations are frequently used to understand phenomena observed during neutron irradiations, the question of their representativeness is often raised.

In this thesis, we aim to understand how the irradiation parameters can affect the characteristics of the a' phase in ODS steels. To do so, various ODS steels will be irradiated under different conditions (flux, dose, temperature, and type of particles, such as ions, neutrons, electrons), and subsequently analyzed at the nanoscale. The a' phase (size, chromium content) obtained for each ion irradiation condition will be compared to the one after neutron irradiation.

Synthesis, characterization and modeling of (Mn,Co)3O4 thin films applied to corrosion layers and spintronics

Spinel-type transition metal oxides (AB2O4) appear spontaneously during the generalized corrosion of steels or alloys in aqueous or gaseous environments at high temperatures. This spinel phase forms a continuous corrosion layer and thus regulates corrosion processes by controlling conductivity and material transport between the material and the oxidizing medium. They are also applied voluntarily as protective coatings against degradation phenomena. In particular, the Mn-Co-O spinel system is very promising as protective conductive layers on ferritic stainless steel used to fabricate interconnects in solid oxide fuel cells for green hydrogen production. The composition of the spinel phase determines the protective performance of the coatings. This feature is particularly delicate for materials used in high-temperature electrolyzers, as electronic transport must be optimal (high electrolysis), but must not be accompanied by material transport (low cation diffusion).
In contrast, electronic transport properties of spinel-type transition metal oxides are generally not well understood. Measurements are made on complex corrosion layers (or coatings) of variable composition, low crystallinity, complex microstructure and low thickness. Furthermore, spinel oxides exhibit magnetic properties and composition-dependent cationic disorder that are usually ignored, even though they have a strong impact on electronic transport. The properties highlighted here are the ones that also hold significant importance within the field of spintronics. Thus, tuning the chemical composition of these spinel-structured oxides (normal, inverse or mixed) offers a wide range of magnetic (ferrimagnetic, antiferromagnetic) and electronic (semimetallic, semiconductor, insulator) properties. In particular, CoMn2O4 is expected to exhibit a complex magnetic configuration [1], mainly related to the arrangement of Co2+ and Mn3+ cations in interstitial sites, which needs to be analyzed in detail. Unlike corrosion layers, these physical studies require the synthesis of thin films of well-controlled composition and high crystallinity.
The aim of the thesis is to build up knowledge of physicochemical and structural properties of (Mn,Co)3O4 in order to contribute to the elaboration of Mn-Co-O phase diagrams and electronic transport models based on the relationship between order/disorder, magnetic properties and resistivity of (Mn,Co)3O4. Eventually, the whole (Fe,Cr,Mn,Co)3O4 system will be also considered. The study will be carried out on thin films of perfectly controlled composition and high crystallinity, and will be enhanced by numerical simulations. The experimental and theoretical work will be based on the results of previous studies on (Ni,Fe,Cr)3O4 epitaxial thin films [2,3].
The thesis will be divided as follows:
- Growth of thin films and multilayers by MBE (Molecular Beam Epitaxy) (J.-B. Moussy)
- Spectroscopic characterization using XPS (X-ray photoemission spectroscopy) (F. Miserque)
- Fine structure characterization by DRX and X-ray absorption (XMCD) (P. Vasconcelos)
- Modeling of core-level spectra (XPS, XAS and XMCD) and atomistic modeling (A. Chartier)
- Magnetic characterization by SQUID/VSM magnetometry and electric transport characterization (J.-B. Moussy)

[1] Systematic analysis of structural and magnetic properties of spinel CoB2O4 (B= Cr, Mn and Fe) compounds from their electronic structures, Debashish Das, Rajkumar Biswas and Subhradip Ghosh, Journal of Physics: Condensed Matter 28 (2016) 446001.
[2] Stoichiometry driven tuning of physical properties in epitaxial Fe3-xCrxO4 thin films, Pâmella Vasconcelos Borges Pinho, Alain Chartier, Denis Menut, Antoine Barbier, Myrtille O.J.Y. Hunault, Philippe Ohresser, Cécile Marcelot, Bénédicte Warot-Fonrose, Frédéric Miserque, Jean-Baptiste Moussy, Applied Surface Science 615 (2023) 156354.
[3] Elaboration, caractérisation et modélisation de films minces et multicouches à base d’oxydes (Ni,Fe,Cr)3O4 appliquées à la corrosion et à la spintronique, A. Simonnot, thèse en cours.

Experimental study and modelling of high temperature oxidation of Cr coated zirconium alloy substrate

This thesis concerns the research and development of materials more resistant in extreme conditions at high temperature. It is more specifically dedicated to the development of a new concept of nuclear fuel cladding : Cr coated Zr-based claddings. The purpose of this work is to adpat the Ekinox-Zr code, initially developped for the description of diffusion phenomena in uncoated Zr claddings, to Cr-coated Zr-based claddings and create a new code : “Ekinox-Zr-Cr”. This work will be divided into two parts : a modelling/simulation one and an experimental one dedicated to the determination of the diffusion coefficients of Cr, Zr and O species inside the different phases of the system. These data constitute essential parameters for the modelisation. High temperature oxidation experiments on Cr-coated claddings will also be used in order to improve our knowledge on the different mechanisms involved and compare them to the results obtained with the Ekinox-Zr-Cr code created during this study.

Delayed hydride cracking (DHC) of nuclear fuel cladding: experiments, modelling and numerical simulations of microstructure effects

Corrosion of nuclear fuel cladding by the water in the primary circuit as it passes through the reactor leads to hydriding. Delayed hydride cracking (DHC) is likely to occur later, during dry storage. Such cracking requires a pre-existing defect and a thermo-mechanical history that enables the following iterative mechanism to be set in motion: hydrogen diffusion, precipitation of hydrides at the crack tip and rupture of the embrittled zone. During a previous thesis carried out in the host laboratory, an original procedure combining experiments and numerical simulations using finite elements was used to determine the toughness of unirradiated relaxed Zircaloy-4 cladding in the event of DHC, and to report on the effect of mechanical loading and temperature on the incubation time and cracking speed between 150°C and 250°C. The aim of this thesis is to apply this procedure to a more modern cladding material (recrystallised M5) and to develop fine-scale microstructure modelling that can account for the effects of texture (crystallographic and morphological), propagation direction and plane, and irradiation on DHC.
Corrosion of nuclear fuel cladding by the water in the primary circuit as it passes through the reactor leads to hydriding. Delayed hydride cracking (DHC) is likely to occur later, during dry storage. Such cracking requires a pre-existing defect and a thermo-mechanical history that enables the following iterative mechanism to be set in motion: hydrogen diffusion, precipitation of hydrides at the crack tip and rupture of the embrittled zone. During a previous thesis carried out in the host laboratory, an original procedure combining experiments and numerical simulations using finite elements was used to determine the toughness of unirradiated relaxed Zircaloy-4 cladding in the event of DHC, and to report on the effect of mechanical loading and temperature on the incubation time and cracking speed between 150°C and 250°C. The aim of this thesis is to apply this procedure to a more modern cladding material (recrystallised M5) and to develop fine-scale microstructure modelling that can account for the effects of texture (crystallographic and morphological), propagation direction and plane, and irradiation on DHC.

Experimental characterisation and numerical simulation of intergranular oxide fracture: Application to Irradiation Assisted Stress Corrosion cracking

Metal alloys used in industrial applications can form oxide layers in the presence of a corrosive environment. These oxides may be distributed on the surface and/or localized at the grain boundaries. In the latter case, the oxidized grain boundaries may experience brittle fracture under mechanical loading, potentially leading to intergranular cracking of the material. This mechanism is, for example, a possible scenario for the failure of austenitic stainless steel bolts used in the internals structure of Pressurized Water Reactors (PWRs). Under the effect of mechanical loading, neutron irradiation and the presence of a corrosive environment, these bolts fail through a phenomenon known as irradiation-assisted stress corrosion cracking. To model this phenomenon, we need to determine the fracture properties of intergranular oxides, and to take into account the coupling between cracking, oxidation and irradiation. In this thesis, experimental and numerical work will be combined. Firstly numerical simulations based on the variational approach to fracture approach will be assessed in order to design micro-beam micromechanics experiments aimed at reliably determining the fracture properties of oxides, and also to study the couplings between cracking, oxidation and irradiation. In particular, the cracking-oxidation coupling that prefigures the transition between initiation and propagation will be investigated in detail. These experiments will then be carried out on model and industry-relevant steels, and interpreted using numerical simulations. Finally, all the results obtained in this work will be incorporated into simulations of polycrystalline aggregates, in order to assess the possibility of quantitatively predicting intergranular cracking in the context of irradiation-assisted stress corrosion.
By the end of the PHD, the doctoral student will have acquired both experimental skills - micromechanical tests - and numerical skills - numerical simulations of fracture - at the cutting edge of the state of the art and applicable to a large number of problems in the mechanics of materials.
A Master's 2 / end-of-studies internship preparatory to the PHD is available in 2024.

Experimental characterization and cluster dynamics simulation of the effect of helium on irradiation defects and associated swelling in austenitic stainless steels of pressurized water reactors internals vessel

The microstructure of the materials of the internal structure of Pressurized Water Reactors (PWRs), which play a key role notably in maintaining the fuel assemblies, will evolve under irradiation. A better understanding of these evolutions could allow a better prediction of the behavior in operation of these materials in austenitic stainless steels (Fe-Cr-Ni) of the 300 series, in particular the 304 grade. Swelling is one of these potential evolutions and the question of its existence at high doses is of importance with the aim of extending the operating time of PWRs.
The objective of this work is to provide a better understanding of the mechanisms of swelling and microstructural evolutions through an analytical study of the effect of helium (influence of the rate of helium implanted up to high dose, temperature, and concomitant presence of hydrogen ...). Fine characterizations (grain scale and bottom), coupled with simulations in cluster dynamics, will be carried out on austenitic stainless steels irradiated with ions.
This study will be conducted mainly at the CEA, in the “Service de Recherche en Matériaux et procédés Avancés” (SRMA) and “ Section de Recherches de Métallurgie Physique ” (SRMP). It will benefit from the available ion irradiation devices (JANNuS), microstructural characterizations (notably Transmission Electron Microscopy and Atom Probe Tomography) and modeling (cluster dynamics simulation) tools. It will be supervised by M. Legros (CEMES) and T. Jourdan (SRMP) and driven par J. Malaplate and A. Renault-Laborne (SRMA). This broad subject will allow the candidate to acquire training on the behavior of materials under irradiation and also strong skills in the field of microstructural characterization of materials and simulation.
This subject is aimed at a student in materials science, with skills/appetite in the field of materials characterization and simulation. A Master 2 internship is proposed prior to this subject.

Impact of microstructure in uranium dioxide (UO2) on ballistic and electronic damage

During reactor irradiation, fuel pellets undergo a partial evolution of their microstructure. At high levels of burnup, a subdivision of grains into smaller grains in the peripheral areas of the fuel pellets - called high burn-up structure (HBS) - is observed. Similar changes also occur in the central regions of the pellets at elevated temperatures. These evolutions result from the combination of several factors, including the loss of energy from fission products. The effect of this damage could vary depending on the crystal orientation and grain size.
The main objective is therefore to understand how crystal orientation and grain size influence the damage caused by irradiation. Ion irradiation experiments will be conducted on single- and poly-crystalline UO2 samples at the JANNUS Saclay facility. In situ and ex situ characterizations using Raman and Rutherford backscattering (RBS-C) spectroscopy, transmission and scanning electron microscopy with Electron backscatter diffraction (EBSD) will be carried out.

Development of a physically based multi-scale numerical model for the fuel rod cladding of pressurized water reactors

The fuel rods of pressurized water nuclear reactors are made of uranium oxide pellets stacked in zirconium alloy tubes. In reactor, these materials undergo mechanical loading that lead to their irreversible deformation. In order to guarantee the safety and increase the performance of nuclear reactors, this deformation must be modeled and predicted as precisely as possible. In order to further improve the predictivity of the models, the polycrystalline nature of these materials as well as the physical deformation mechanisms must be taken into account. This is the objective of this study, which consists of developing a physically based multi-scale numerical model of the fuel rod cladding.

The mechanical behavior of metallic materials is usually modeled by considering the material as homogeneous. In fact metallic materials are made of many crystalline grains clustered together. The behavior of the material is therefore the result of the deformation of individual grains but also their interactions between each other. In order to take into account the polycrystalline nature of the material, mean-field self-consistent polycrystalline models have been developed for many years. These models are based on the theory of homogenization of heterogeneous materials. Recently, a polycrystalline model, developed in a linear and isothermal framework, has been coupled with an axisymmetric 1D finite element calculation to simulate the in-reactor deformation of cladding tubes. A complex mechanical loading history, mimicking the stresses and strains experienced by the cladding has been simulated.

The objective of this PhD work is to extend the field of application of this model in particular by applying it to a non-linear framework in order to simulate high stress loadings, to extend it to anisothermal conditions but also to carry out 3D finite element simulations with at each element and each time step a simulation using the polycrystalline model. These theoretical and numerical developments will finally be applied to the simulation of the behavior of fuel rods in a power ramp situation thanks to its integration into a software platform used for industrial applications. This approach will allow to better assess the margins available to operate the reactor in a more flexible manner, allowing it to adapt to changes in the energy mix in complete safety.