Prediction of fatigue behaviour in fusion and generation IV reactor materials: numerical, experimental, and machine learning study

This doctoral dissertation presents a comprehensive and multidisciplinary investigation into the fatigue behaviour of Reduced Activation Ferritic/Martensitic (RAFM) steels and CuCrZr alloys under conditions relevant to nuclear fusion reactors, with a particular focus on the DEMO (Demonstration Power Plant) reactor. The study integrates advanced viscoplasticity modelling, finite element implementation, and machine learning (ML) techniques to predict fatigue life and cyclic softening behaviour under both irradiated and non-irradiated conditions. Fusion energy is widely regarded as a promising alternative to fossil fuels due to its inherent safety, sustainability, and minimal environmental impact. Unlike fission, fusion does not produce long-lived radioactive waste and carries no risk of meltdown. The European fusion roadmap outlines a phased approach to achieving commercial fusion energy, progressing through ITER (International Thermonuclear Experimental Reactor), DEMO, and IFMIF-DONES (International Fusion Materials Irradiation Facility – DEMO Oriented Neutron Source). DEMO is envisioned as the first fusion power plant to generate net electricity and demonstrate tritium self-sufficiency, serving as a critical bridge between experimental devices and commercial reactors. The structural components of DEMO, particularly the breeding blanket (BB) and divertor, are subjected to extreme operational conditions, including high thermal loads, intense neutron irradiation, and cyclic mechanical stresses. These conditions lead to complex degradation mechanisms such as thermal fatigue, irradiation-induced embrittlement, and cyclic softening. Therefore, the development of robust predictive models for fatigue life and material degradation is essential to ensure the structural integrity and operational longevity of reactor components. The objective of this research is to develop a viscoplasticity model for RAFM steels and CuCrZr alloys that accurately captures their fatigue deformation behaviour under fusion-relevant conditions. This model should be implemented into a finite element analysis (FEA) framework using ABAQUS UMAT subroutines. Another objective is to predict fatigue life using both empirical methods (e.g., Manson- Coffin-Basquin equation) and data-driven machine learning approaches. Finally, this research focuses to model cyclic softening behaviour using deep neural networks (DNNs) and physics-informed ML techniques, addressing the scarcity of experimental data for irradiated materials. Low-cycle fatigue (LCF) tests were conducted on EUROFER97-3, a widely studied RAFM steel, at SCK CEN. Tests were performed at room temperature (RT) and 350 °C across various strain amplitudes and strain ratios. The experimental data revealed significant cyclic softening behaviour, which was used to develop a modified Chaboche viscoplasticity model. This model incorporates strain memory effects to capture the material’s response to cyclic loading more accurately. Similarly, LCF tests were performed on CuCrZr, a copper alloy used in heat sink applications due to its high thermal conductivity and good mechanical strength. Tests were conducted at RT and 350 °C with a strain ratio of -1. Analysis of internal stresses showed that the back stress followed the cyclic stress behaviour of CuCrZr, exhibiting initial hardening followed by softening. The effective stress also showed a similar trend, though with less pronounced variation. These insights were used to further refine the viscoplasticity model to better describe the fatigue behaviour of CuCrZr. The developed model was implemented into ABAQUS using a fully implicit backward Euler integration scheme. Validation simulations on EUROFER97-3 confirmed the model’s accuracy and computational efficiency. Sensitivity analyses on mesh size and time increment were conducted to ensure robustness and reliability for practical engineering applications. A comprehensive LCF database comprising 458 tests (408 non-irradiated and 50 irradiated specimens) was compiled from open literature. The database includes various RAFM steels such as EUROFER97, JLF-1, F82H, ARAA, In-RAFM, and CLAM, tested under a wide range of conditions including different specimen sizes, test media (air and vacuum), temperatures (RT to 650 °C), and strain ranges. Statistical analysis using Analysis of Variance (ANOVA) revealed several key findings: specimen size significantly affects fatigue life at elevated temperatures but not at room temperature; test medium influences fatigue life at RT for both small and large specimens, and at high temperatures for large specimens; and smaller specimens (diameter < 4 mm) generally exhibit shorter fatigue lives, likely due to higher surface-to-volume ratios and increased sensitivity to surface defects. These findings underscore the importance of accounting for geometric and environmental factors in fatigue life prediction models. Several empirical methods based on the Manson-Coffin-Basquin equation were benchmarked, including those proposed by Manson, Muralidharan, Baumel, Meggiolaro, Lee, and Wächter. Among these, the method by Meggiolaro et al. demonstrated the highest accuracy, particularly after applying scaling factors to account for test medium and specimen size. The modified Meggiolaro method achieved 95% accuracy within a factor of three of experimental values, even for irradiated materials. This method provides a practical and reliable tool for fatigue life prediction using only basic tensile properties such as ultimate tensile strength and Young’s modulus. To enhance predictive capabilities, machine learning models were trained on the LCF dataset. Two scenarios were tested: one including yield strength as an input feature, and another using only fatigue test conditions such as temperature, strain range, and irradiation dose. Four ML algorithms were evaluated: Random Forest (RF), Support Vector Regression (SVR), Multi-Layer Perceptron (MLP), and Gradient Boosting Regression (GBR). RF and GBR demonstrated the highest accuracy, with R² scores exceeding 0.9 and over 85% of predictions falling within a factor of two of actual values. Interestingly, including yield strength did not significantly improve prediction accuracy, suggesting that fatigue test conditions alone are sufficient for accurate modelling. This finding simplifies the input requirements for ML-based fatigue life prediction and enhances the model’s applicability in scenarios where tensile properties are unavailable or difficult to measure. To address the scarcity of experimental data on irradiated materials, deep neural networks (DNNs) were employed to predict cyclic softening curves. Four modelling strategies were compared: direct prediction of isotropic hardening parameters, pointwise prediction of stress reduction using accumulated inelastic strain, transfer learning from parameter prediction to curve prediction, and physics-informed DNNs incorporating constitutive laws into the loss function. The fourth method, a data-assisted physics- informed neural network, yielded the best accuracy and lowest scatter. It effectively combined the strengths of data-driven and physics-based approaches, ensuring both predictive accuracy and physical consistency. This hybrid approach is particularly valuable in fusion applications, where experimental data are limited and physical laws must be respected. To enhance the interpretability of the ML models, SHAP (SHapley Additive exPlanations) analysis was conducted. The results revealed that strain range and irradiation dose are the most influential factors on cyclic softening, followed by specimen diameter and test medium. These insights not only validate the model’s predictions but also provide guidance for experimental design and material selection in future fusion reactor development. This dissertation successfully integrates physics-based modelling and machine learning to enhance fatigue life prediction for fusion reactor materials. The developed models offer accurate, efficient, and scalable alternatives to costly and time-consuming irradiation experiments. They support the design and lifetime assessment of DEMO’s structural components and contribute to the broader goal of realizing commercial fusion energy. Key contributions include a validated viscoplasticity model for RAFM steels and CuCrZr, implemented in ABAQUS; a modified empirical model (Meggiolaro et al.) with scaling factors for accurate fatigue life prediction; high-performing ML models (RF and GBR) for fatigue life prediction using minimal input features; and a novel DNN framework for predicting cyclic softening behaviour, including physics-informed enhancements. Limitations and future work include the need for more temperature-dependent data to improve generalizability of the viscoplasticity model, and validation beyond the tested strain ranges to ensure robustness under extreme conditions. Future research should focus on expanding the temperature and strain range coverage, integrating the models into full-scale simulations of in-vessel components (IVCs), and exploring real-time predictive maintenance applications using ML.