Nuclear reactor pressure vessels, subjected to neutron irradiation for several decades, undergo a progressive embrittlement process. The Master Curve theory provides a comprehensive framework for evaluating the structural integrity of irradiated reactor pressure vessel steels, relying on fracture toughness tests performed on specimens with standardized geometries. The Master Curve allows the estimation of a reference temperature in the ductile-to-brittle transition range, referred to as T0, which provides a quantitative indicator for monitoring irradiation-induced embrittlement over time. However, the volumes of usable steel, after spending several decades in a reactor, are extremely valuable, which usually results in having only a few samples. A significant challenge then arises: how can we guarantee an accurate estimation of T0 from a small number of tests? This questions the role of experimental design variables on the uncertainty in the estimation of T0, as well as the available means to quantify and reduce the associated uncertainty.
 
To address these challenges, the thesis focuses on two complementary objectives. The main objective is to develop a numerical decision-making tool that optimizes the planning of experimental campaigns. The aim is to identify for each test to be conducted, the test temperature that minimizes the estimation uncertainty of T0. To implement this tool, it is necessary to develop a digital twin able to faithfully replicate fracture toughness test campaigns, which represents the second objective. The numerical model here is based on finite element simulations that require a material behavior law, as well as a Beremin-type brittle fracture model whose parameters are identified by Bayesian calibration.
 
The core of this work lies in the development of a comprehensive Bayesian optimization method to optimize experimental designs for fracture toughness tests. The problem is formulated as a constrained combinatorial optimization, aiming to identify temperature sequences that minimize the uncertainty in the estimation of T0. The original approach proposed to solve the optimization problem here is to model the temperature sequences using homogeneous first-order discrete-time Markov chains. The optimal temperature sequence is then characterized by an optimized transition matrix. The cross-entropy method allows for such identification, and the proposed global approach is thus named MCP-CEM (Master Curve Planning based on Cross-Entropy Method). The resulting transition matrix then serves as a directly interpretable decision-making tool because it indicates, for each test to be performed, which temperature is best to minimize the estimation uncertainty of T0. Throughout this thesis work, particular attention has been devoted to the simulation of fracture tests on the mini-CT geometry, which has been proposed over the past decade as a promising option for increasing the number of available tests.