Numerical modelling of large ductile crack progagation and assessment of margins comparing to engineering approach
Predicting failure modes in metal structures is an essential step in analyzing the performance of industrial components where mechanical elements are subjected to significant stress (e.g., nuclear power plant components, pipelines, aircraft structural elements, etc.). To perform such analyses, it is essential to correctly simulate the behavior of a defect in ductile conditions, i.e., in the presence of significant plastic deformation before and during propagation.
Predictive numerical simulation of ductile tearing remains an open scientific and technical issue despite significant progress made in recent years. The so-called local approach to fracture, notably the Gurson model (and its modified version GTN), is widely used to model ductile tearing. However, its use has limitations: significant computation time, simulation stoppage due to the presence of completely damaged elements in the model, and non-convergence of the result when the mesh size is reduced.
The aim of this thesis is to develop the ductile tear simulation model used at LISN so that it can be applied to large crack propagation on complex structures. It also aims to compare the results obtained with engineering methods that are simpler to implement.
Fatigue crack growth modelling with residual stress - Improvement of the Gtheta method
Residual stresses are self-balanced stress fields found in certain mechanical components in the absence of external loading. Caused by welding, for example, these stresses can potentially affect the behaviour of the structure and its resistance to fracture. When demonstrating the integrity of a mechanical component, particularly in the context of nuclear safety, it is crucial to precisely understand the role of these stress fields on the component's resistance. In the case of fatigue crack propagation, to accurately model all the phenomena involved (stress redistribution, evolution of plasticity, closure effect), it will be necessary to improve numerical tools, such as meshing and crack propagation methods (AMR, X-FEM...) and the J-integral interpolation in the case of through-cracks (Gtheta method). The thesis will consist of two complementary parts: (a) numerical development aimed at improving the Gtheta method in Castem FE code, associated with a 3D crack propagation modelling using AMR, and (b) continuation of component scale tests on fatigue crack propagation in different configurations of residual stress fields.
Effect of water radiolysis on the hydrogen absorption flux by austenitic stainless steels in the core of a nuclear pressurized water reactor
In pressurized water nuclear reactors, the core components are exposed to both corrosion in the primary medium, pressurized water at around 150 bar and 300°C, and to neutron flux. The stainless steels in the core are damaged by a combination of neutron bombardment and corrosion. In addition, radiolysis of the water can have an impact on the mechanisms and kinetics of corrosion, the reactivity of the medium and, a priori, the mechanisms and kinetics of hydrogen absorption by these materials. This last point, which remains unexplored, may prove problematic, as hydrogen in solid solution in steel can lead to changes in (and degradation of) the mechanical properties of the steel or induce premature cracking of the part. The pioneering work developed in this highly experimental thesis will focus on the impact of radiolysis phenomena on the mechanisms and kinetics of corrosion and, above all, hydrogen pick-up in 316L stainless steel exposed to the primary environment under irradiation. Hydrogen will be traced by deuterium, and neutron irradiation simulated by electron irradiation on particle accelerators. An existing permeation cell will be modified into a unique setup to allow in operando measurement by mass spectrometry of the deuterium permeation flux through a sample exposed to the simulated primary water under radiolysis conditions. The distribution of hydrogen in the material, as well as the nature of the oxide layers formed, will be analysed in detail using state-of-the-art techniques available at the CEA and in partner laboratories. The doctoral student will ultimately be required to (i) identify the mechanisms involved (corrosion and hydrogen entry), (ii) estimate their kinetics and (iii) model the evolution of hydrogen flux in the steel in connection with radiolysis activity.
Kinetics of segregation and precipitation in Fe-Cr-C alloys under irradiation : coupling magnetic, chemical and elastic effects
Ferritic steels are being considered as structural materials in future fission and fusion nuclear reactors. These alloys have highly original properties, due to the coupling between chemical, magnetic and elastic interactions that affect their thermodynamic properties, the diffusion of chemical species and the diffusion of point defects in the crystal. The aim of the thesis will be to model all of these effects at the atomic scale and to integrate them into Monte Carlo simulations in order to model the segregation and precipitation kinetics under irradiation, phenomena that can degrade their properties in use. The atomic approach is essential for these materials, which are subjected to permanent irradiation and for which the laws of equilibrium thermodynamics no longer apply.
The candidate should have a good background in statistical physics or materials science, and be interested in numerical simulations and computer programming. The thesis will be carried out at CEA Saclay's physical metallurgy laboratory (SRMP), in a research environment with recognised experience in multi-scale modelling of materials, with around fifteen theses and post-doctoral contracts in progress on these topics.
A Master 2 internship on the same subject is proposed for spring 2025 and is highly recommended.
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.
Numerical simulation of turbulence models on distorted meshes
Turbulence plays an important role in many industrial applications (flow, heat transfer, chemical reactions). Since Direct Simulation (DNS) is often an excessive cost in computing time, Reynolds Models (RANS) are then used in CFD (computational fluid dynamics) codes. The best known, which was published in the 70s, is the k - epsilon model.
It results in two additional non-linear equations coupled to the Navier-Stokes equations, describing the transport, for one, of turbulent kinetic energy (k) and, for the other, of its dissipation rate (epsilon). ). A very important property to check is the positivity of the parameters k and epsilon which is necessary for the system of equations modeling the turbulence to remain stable. It is therefore crucial that the discretization of these models preserves the monotony. The equations being of convection-diffusion type, it is well known that with classical linear schemes (finite elements, finite volumes, etc ...), the numerical solutions are likely to oscillate on distorted meshes. The negative values of the parameters k and epsilon are then at the origin of the stop of the simulation.
We are interested in nonlinear methods allowing to obtain compact stencils. For diffusion operators, they rely on nonlinear combinations of fluxes on either side of each edge. These approaches have proved their efficiency, especially for the suppression of oscillations on very distorted meshes. We can also take the ideas proposed in the literature where it is for example described nonlinear corrections applying on classical linear schemes. The idea would be to apply this type of method on the diffusive operators appearing in the k-epsilon models. In this context it will also be interesting to transform classical schemes of literature approaching gradients into nonlinear two-point fluxes. Fundamental questions need to be considered in the case of general meshes about the consistency and coercivity of the schemes studied.
During this thesis, we will take the time to solve the basic problems of these methods (first and second year), both on the theoretical aspects and on the computer implementation. This can be done in Castem, TrioCFD or Trust development environments. We will then focus on regular analytical solutions and application cases representative of the community.
Thermally activated glide of screw dislocations in bcc metals
Thermally activated glide of dislocation is a key point for understanding the plastic deformation of metals. The screw dislocation in bcc metals is an archetypical case for which a large quantity of experimental data has been published in the scientific literature. It is then possible to compare these data to the theoretical predictions realized from the Vineyard statistical theory [1,2]. Such a theory is an essential tool allowing to perform a scale transition from atomistic computations [3] toward macroscopic scale at which are realized the deformation tests.
The aim of our research will be to test Vineyard theory in comparison with molecular dynamics simulations [4]. Some preliminary computations have shown a significant discrepancy that is not present when we repeat the comparison for point-like defect as vacancies or self-interstitial atoms. The discrepancy of the theory will have to be reduce within a new theoretical development. Our new theory should allow some predictions in agreement with macroscopic tensile test in bcc metals [5].
[1] Vineyard G.H., J. Phys. Chem. Solids 3, 121 (1957).
[2] Proville L., Rodney D., Marinica M-C., Nature Mater. 11, 845 (2012).
[3] Proville L., Ventelon L., Rodney D., Phys. Rev. B 87, 144106 (2013).
[4] Proville L., Choudhury A., Nature Mater. 23, 47 (2024).
[5] Caillard D., Acta Mater. 58, 3504 (2010).
Staggered schemes for the Navier-Stokes equations with general meshes
The simulation of the Navier-Stokes equations requires accurate and robust numerical methods that
take into account diffusion operators, gradient and convection terms. Operational approaches have
shown their effectiveness on simplexes. However, in some models or codes
(TrioCF, Flica5), it may be useful to improve the accuracy of solutions locally using an
error estimator or to take into account general meshes. We are here interested in staggered schemes.
This means that the pressure is calculated at the centre of the mesh and the velocities on the edges
(or faces) of the mesh. This results in methods that are naturally accurate at low Mach numbers .
New schemes have recently been presented in this context and have shown their
robustness and accuracy. However, these discretisations can be very costly in terms of memory and
computation time compared with MAC schemes on regular meshes
We are interested in the "gradient" type methods. Some of them are based on a
variational formulation with pressure unknowns at the mesh centres and velocity vector unknowns on
the edges (or faces) of the cells. This approach has been shown to be effective, particularly in terms of
robustness. It should also be noted that an algorithm with the same degrees of freedom as the
MAC methods has been proposed and gives promising results.
The idea would therefore be to combine these two approaches, namely the "gradient" method with the same degrees of freedom as MAC methods. Initially, the focus will be on recovering MAC schemes on regular meshes. Fundamental
questions need to be examined in the case of general meshes: stability, consistency, conditioning of
the system to be inverted, numerical locking. An attempt may also be made to recover the gains in
accuracy using the methods presented in for discretising pressure gradients.
During the course of the thesis, time will be taken to settle the basic problems of this method (first and
second years), both on the theoretical aspects and on the computer implementation. It may be carried
out in the Castem, TrioCFD, Trust or POLYMAC development environments. The focus will be on
application cases that are representative of the community.
Development of a transport chemistry model for spent fuel in deep geological disposal under radiolysis of water
The direct storage of spent fuel (SF) represents a potential alternative to reprocessing as a means of managing nuclear waste. The direct storage of spent fuel in a deep geological environment presents a number of scientific challenges, primarily related to the necessity of developing a comprehensive understanding of the processes involved in the dissolution and release of radionuclides. The objective of this thesis is to develop a comprehensive scientific model that can accurately describe the intricate physico-chemical processes involved, such as the radiolysis of water and the interaction between irradiated fuel and its surrounding environment. The objective is to propose an accurate reactive transport model to enhance long-term predictions of storage performance. This thesis employs a back-and-forth process between modeling and experimentation, with the goal of refining the understanding of alteration mechanisms and validating hypotheses with experimental data. Based on existing models, such as the operational radiolytic model, the work will propose improvements to reduce the current simplifying assumptions. The candidate will contribute to major industrial and societal issues related to nuclear waste management and will help to provide solutions to the associated safety issues.
Radiative heat transfer: efficient numerical resolution of associated problems in Beerian or non-Beerian media for the validation of simplified models
This research proposal focuses on the study, through modeling and numerical simulation, of heat transfer within a heterogeneous medium composed of opaque solids and a transparent or semi-transparent fluid. The considered modes of transfer are radiation and conduction.
Depending on the scale of interest, the radiance is the solution of the Radiative Transfer Equation (RTE). In its classical form, the RTE describes heat transfer phenomena at the so-called local scale, where solids are explicitly represented in the domain. At the mesoscopic scale of an equivalent homogeneous medium, however, the radiance is governed by a generalized RTE (GRTE) when the medium no longer follows the Beer–Lambert law. In this work, we focus on the numerical resolution of the RTE in both configurations, ultimately coupled with the energy conservation equation for temperature.
In deterministic resolution of the RTE, a standard approach for handling the angular variable is the Discrete Ordinates Method (Sn), which relies on quadrature over the unit sphere. For non-Beerian media, solving the GRTE is a very active research topic, with Monte Carlo methods often receiving more attention. Nevertheless, the GRTE can be linked to the generalized transport equation, as formulated in the context of particle transport, and a spectral method can be applied for its deterministic Sn resolution. This is the direction pursued in this PhD project.
The direct application of this work is the numerical simulation of accidents in Light Water Reactors (LWR) with thermal neutrons. Modeling radiative heat transfer is crucial because, in the case of core uncovering and fuel rod drying, radiation becomes a major heat removal mechanism as temperatures rise, alongside gas convection (steam). This topic is also relevant in the context of the nuclear renaissance, with startups developing advanced High Temperature Reactors (HTR) cooled by gas.
The goal of this thesis is the analysis and development of an innovative and efficient numerical method for solving the GRTE (within a high-performance computing environment), coupled with thermal conduction. From an application standpoint, such a method would enable high-fidelity simulations, useful for validating and quantifying the bias of simplified models used in engineering calculations.
Successful completion of this thesis would prepare the student for a research career in high-performance numerical simulation of complex physical problems, beyond nuclear reactor physics alone.