Lead-cooled Fast Reactors (LFRs) represent a promising solution within the Generation IV nuclear systems, thanks to their inherent safety features, high thermal efficiency, and potential for sustainable fuel cycles. However, the extreme operating conditions typical of LFRs, high temperatures, lead corrosion, and irradiation, pose significant challenges to structural materials. In this context, ceramic coatings, particularly alumina-based f ilms, have emerged as attractive candidates due to their excellent chemical stability, wear resistance, and compatibility with lead environments. This thesis focuses on the mechanical characterization of an yttria-doped alumina thin f ilm deposited by Pulsed Laser Deposition (PLD) on AISI 316L stainless steel substrates. The specimens were prepared and tested in collaboration with the X-Nano research facil ity, where nanoindentation tests were carried out at room temperature and after thermal annealing. Particular attention was given to the as-deposited condition at room temper ature, which served as the reference case for numerical modeling. To extract key mechanical properties, such as hardness and reduced modulus, the load–displacement curves were analyzed using the Oliver and Pharr method. In parallel, a two-dimensional axisymmetric Finite Element Model (FEM) was developed in Abaqus to simulate the indentation process. The model included an elastic–perfectly plastic mate rial response for both the coating and the substrate, and used a diamond conical indenter geometry equivalent to a Berkovich tip, with a semi-apex angle of 70.3°. The multilayer system was modeled assuming perfect adhesion at the film–substrate interface, meaning that no sliding or interfacial debonding was allowed and displacements remained continu ous across the interface. This assumption, often adopted in similar studies, is justified by the absence of experimental evidence of delamination and contributes to the numerical stability of the simulations. The formulation was based on the hypothesis of large displacements, which is particu larly relevant for accurately capturing the evolution of the contact area and the local deformation field beneath the indenter tip, especially in the post-yield regime. Inverse analysis was implemented in two stages. First, a deterministic approach based on a trust-region optimization algorithm was used to calibrate the elastic modulus and yield strength of the coating. Then, a Bayesian framework was applied to quantify the un certainty of the identified parameters and to evaluate the robustness of the identification with respect to input noise and prior assumptions. The study combined deterministic and Bayesian inverse analyses, balancing computational efficiency and uncertainty quantifica tion. From acomputational perspective, the inverse analyses required repeated evaluation of the model sensitivity via forward finite differences. Each iteration involved three finite element simulations to estimate the Jacobian matrix, resulting in a moderate but manageable computational burden. The results highlight the robustness and reliability of the proposed identification strate gies. The deterministic analysis yields parameter estimates in good agreement with exper imental trends, while the Bayesian approach demonstrates stability under various noise levels and prior assumptions. Final results are compared with literature data, showing consistency with reported yield strengths for amorphous alumina coatings and slightly lower elastic modulus, likely due to the doping effect and structural morphology of the PLD-deposited layer. The methodology developed in this study represents a first step toward the robust me chanical characterization of ceramic coatings for extreme environments. Future work should aim to extend the numerical framework to full three-dimensional models, which would provide a more realistic representation of the actual indentation process, albeit at a higher computational cost. To manage this complexity, model reduction techniques such as Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF) or Arti f icial Neural Networks (ANN) could be integrated. Furthermore, incorporating additional experimental data,such as the residual imprint geometry, into the inverse analysis could improve parameter accuracy and offer a more comprehensive validation of the results.
I reattori veloci raffreddati a piombo (LFR, Lead-cooled Fast Reactors) rappresentano una delle soluzioni più promettenti tra i sistemi nucleari di IV generazione, grazie alle loro intrinseche caratteristiche di sicurezza, all’elevata efficienza termica e al potenziale per cicli del combustibile sostenibili. Tuttavia, le condizioni operative estreme tipiche degli LFR—alte temperature, corrosione da piombo fuso e irraggiamento neutronico—pongono notevoli sfide ai materiali strutturali. In questo contesto, i rivestimenti ceramici, in particolare i film sottili a base di allumina drogata con ittria, si sono dimostrati candidati interessanti per la protezione superficiale, grazie alla loro elevata stabilità chimica, resistenza all’usura e compatibilità con ambienti contenenti piombo. Il presente lavoro si concentra sulla caratterizzazione meccanica di un film sottile di allu mina drogata con ittria, depositato su substrati in acciaio inossidabile AISI 316L mediante Pulsed Laser Deposition (PLD). I campioni sono stati preparati e testati in collaborazione con il laboratorio X-Nano, dove sono state condotte prove di nanoindentazione a temper atura ambiente e dopo trattamenti termici. Particolare attenzione è stata dedicata alla condizione “as-deposited” a temperatura ambiente, utilizzata come caso di riferimento per la modellazione numerica. Per estrarre le principali proprietà meccaniche—come la durezza e il modulo elastico ri dotto—le curve carico–spostamento sono state analizzate con il metodo di Oliver e Pharr. Parallelamente, è stato sviluppato un modello agli elementi finiti bidimensionale assial simmetrico in Abaqus per simulare il processo di indentazione. Il modello includeva un comportamento elasto–plasticamente perfetto per il rivestimento e il substrato, e impie gava una geometria conica equivalente a una punta Berkovich con un angolo semi-apicale di 70,3°. L’interfaccia film–substrato è stata modellata assumendo un’adesione perfetta, ovvero senza scorrimenti o delaminazioni, con continuità del campo di spostamento. Tale ipotesi, comune in letteratura e giustificata dalla mancanza di evidenze sperimentali di delaminazione, contribuisce alla stabilità numerica del modello. La formulazione ha adottato l’ipotesi di grandi spostamenti, particolarmente rilevante per descrivere accuratamente l’evoluzione dell’area di contatto e del campo di deformazione locale sotto la punta dell’indenter, specialmente nella fase post-snia. L’analisi inversa è stata implementata in due fasi. In primo luogo, è stato utilizzato un approccio deterministico basato su un algoritmo di ottimizzazione a regione di fiducia per calibrare il modulo elastico e la tensione di snervamento del rivestimento. Succes sivamente, è stato applicato un framework bayesiano per quantificare l’incertezza dei parametri identificati e valutare la robustezza del metodo rispetto al rumore sperimentale e alle assunzioni a priori. Lo studio ha quindi combinato approcci inversi deterministici e bayesiani, bilanciando efficienza computazionale e capacità di quantificare l’incertezza. Dal punto di vista computazionale, le analisi inverse hanno richiesto la valutazione ripetuta della sensibilità del modello tramite differenze finite. Ogni iterazione ha comportato tre simulazioni FEM per la stima della matrice Jacobiana, comportando un onere com putazionale moderato ma gestibile. I risultati ottenuti confermano la robustezza e l’affidabilità delle strategie di identificazione proposte. L’analisi deterministica ha fornito stime coerenti con l’andamento sperimentale, mentre l’approccio bayesiano ha mostrato buona stabilità anche al variare del rumore e delle condizioni iniziali. I parametri finali sono stati confrontati con dati di letteratura, mostrando una buona coerenza con i valori di snervamento per film di allumina amorfa e un modulo elastico leggermente inferiore, probabilmente influenzato dalla presenza dell’ittria e dalla morfologia della struttura depositata tramite PLD. La metodologia sviluppata in questa tesi rappresenta un primo passo concreto verso una caratterizzazione meccanica affidabile dei rivestimenti ceramici in ambienti estremi. Gli sviluppi futuri dovrebbero mirare a estendere il framework numerico a modelli tridimen sionali completi, che offrirebbero una rappresentazione più realistica del processo di in dentazione, seppur a fronte di un maggiore costo computazionale. Per contenere questa complessità, sarà possibile integrare tecniche di riduzione del modello come la Proper Orthogonal Decomposition (POD), le Radial Basis Functions (RBF) o le reti neurali ar tificiali (ANN). Inoltre, l’integrazione di ulteriori dati sperimentali—come la geometria residua dell’impronta—potrebbe migliorare l’accuratezza dei parametri e offrire una vali dazione più completa dei risultati.
Alumina-Yttria films for Lead-Cooled Fast Reactors. Mechanical characterization by nanoindentation and bayesian estimation
Tripodi, Chiara
2024/2025
Abstract
Lead-cooled Fast Reactors (LFRs) represent a promising solution within the Generation IV nuclear systems, thanks to their inherent safety features, high thermal efficiency, and potential for sustainable fuel cycles. However, the extreme operating conditions typical of LFRs, high temperatures, lead corrosion, and irradiation, pose significant challenges to structural materials. In this context, ceramic coatings, particularly alumina-based f ilms, have emerged as attractive candidates due to their excellent chemical stability, wear resistance, and compatibility with lead environments. This thesis focuses on the mechanical characterization of an yttria-doped alumina thin f ilm deposited by Pulsed Laser Deposition (PLD) on AISI 316L stainless steel substrates. The specimens were prepared and tested in collaboration with the X-Nano research facil ity, where nanoindentation tests were carried out at room temperature and after thermal annealing. Particular attention was given to the as-deposited condition at room temper ature, which served as the reference case for numerical modeling. To extract key mechanical properties, such as hardness and reduced modulus, the load–displacement curves were analyzed using the Oliver and Pharr method. In parallel, a two-dimensional axisymmetric Finite Element Model (FEM) was developed in Abaqus to simulate the indentation process. The model included an elastic–perfectly plastic mate rial response for both the coating and the substrate, and used a diamond conical indenter geometry equivalent to a Berkovich tip, with a semi-apex angle of 70.3°. The multilayer system was modeled assuming perfect adhesion at the film–substrate interface, meaning that no sliding or interfacial debonding was allowed and displacements remained continu ous across the interface. This assumption, often adopted in similar studies, is justified by the absence of experimental evidence of delamination and contributes to the numerical stability of the simulations. The formulation was based on the hypothesis of large displacements, which is particu larly relevant for accurately capturing the evolution of the contact area and the local deformation field beneath the indenter tip, especially in the post-yield regime. Inverse analysis was implemented in two stages. First, a deterministic approach based on a trust-region optimization algorithm was used to calibrate the elastic modulus and yield strength of the coating. Then, a Bayesian framework was applied to quantify the un certainty of the identified parameters and to evaluate the robustness of the identification with respect to input noise and prior assumptions. The study combined deterministic and Bayesian inverse analyses, balancing computational efficiency and uncertainty quantifica tion. From acomputational perspective, the inverse analyses required repeated evaluation of the model sensitivity via forward finite differences. Each iteration involved three finite element simulations to estimate the Jacobian matrix, resulting in a moderate but manageable computational burden. The results highlight the robustness and reliability of the proposed identification strate gies. The deterministic analysis yields parameter estimates in good agreement with exper imental trends, while the Bayesian approach demonstrates stability under various noise levels and prior assumptions. Final results are compared with literature data, showing consistency with reported yield strengths for amorphous alumina coatings and slightly lower elastic modulus, likely due to the doping effect and structural morphology of the PLD-deposited layer. The methodology developed in this study represents a first step toward the robust me chanical characterization of ceramic coatings for extreme environments. Future work should aim to extend the numerical framework to full three-dimensional models, which would provide a more realistic representation of the actual indentation process, albeit at a higher computational cost. To manage this complexity, model reduction techniques such as Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF) or Arti f icial Neural Networks (ANN) could be integrated. Furthermore, incorporating additional experimental data,such as the residual imprint geometry, into the inverse analysis could improve parameter accuracy and offer a more comprehensive validation of the results.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/239982