Structural concepts for metallic LH2 tank designs life enhancement

Curso: 2024-2025 Director/Directora: Herrero Villalibre, Saioa Estudiante: Arana Aretxaga, Andrea STRUCTURAL CONCEPTS FOR METALLIC LH2 TANK DESIGNS LIFE ENHANCEMENT MÁSTER UNIVERSITARIO EN INGENIERÍA MECÁNICA TRABAJO FIN DE MÁSTER Fecha: Bilbao, 24, septiembre, 2025 Supervisado y dirigido en destino por: Ioannis Giannopoulos CRANFIELD UNIVERSITY SCHOOL OF AEROSPACE, TRANSPORT AND MANUFACTURING TRABAJO FIN DE MÁSTER REALIZADO EN MOVILIDAD Resumen El hidrógeno se está posicionando como una solución clave para descarbonizar la aviación, ofreciendo una alternativa limpia y sostenible para reducir las emisiones contaminantes en un sector que contribuye significativamente al cambio climático. Esta tesis presenta un análisis de fatiga de diseños preliminares para tanques de almacenamiento de hidrógeno líquido (LH2) fabricados con aleación de aluminio AA2219-T87 y soldadura por fricción-agitación (FSW). Se ha desarrollado un modelo global de elementos finitos (MEF) para capturar las distribuciones de esfuerzo bajo condiciones criogénicas, apoyado por un submodelo refinado para un análisis preciso de la propagación de grietas. Se han examinado dos enfoques: la estimación clásica de vida a fatiga basada en la iniciación de grietas usando datos S–N y la evaluación de tolerancia al daño mediante mecánica de fractura de crecimiento de grietas a temperaturas criogénicas. Los resultados indican una sobreestimación de la vida a fatiga durante la iniciación, principalmente debido a suposiciones y la limitada evidencia experimental, mientras que la propagación de la grieta es significativamente más rápida y fuertemente influenciada por las condiciones ambientales y el espesor reducido de las paredes del tanque. Estos hallazgos resaltan la importancia de complementar los análisis a escala estructural con evaluaciones localizadas de fractura. El trabajo futuro se centrará en la validación experimental y técnicas avanzadas de monitorización para mejorar la seguridad y fiabilidad de los tanques de hidrógeno líquido. Palabras clave: MEF, Grieta, Fatiga, FSW, KI, Aluminio Abstract Hydrogen is positioning itself as a key solution to decarbonise aviation, offering a clean and sustainable alternative to reduce pollutant emissions in a sector that significantly contributes to climate change. This thesis presents a fatigue analysis of preliminary designs for liquid hydrogen (LH2) storage tanks manufactured from AA2219-T87 aluminium alloy with friction stir welding (FSW). A global finite element method (FEM) model has been developed to capture stress distributions under cryogenic conditions, supported by a refined submodel for precise crack propagation analysis. Two approaches have been examined: classical fatigue life estimation based on crack initiation using S–N data, and damage tolerance assessment through fracture mechanics of crack growth at cryogenic temperatures. The results indicate an overestimation of fatigue life during initiation, mainly due to assumptions and limited experimental evidence, while crack propagation is significantly faster and strongly influenced by environmental conditions and the reduced thickness of the tank walls. These findings highlight the importance of complementing structural-scale analyses with localised fracture assessments. Future work will focus on experimental validation and advanced monitoring techniques to improve the safety and reliability of liquid hydrogen tanks. Keywords: FEM, Crack, Fatigue, FSW, KI, Aluminium Laburpena Hidrogenoa iristen ari da hegazkinaren deskarbonizaziorako soluzio gako bezala, kutsaduraren emisioak murrizteko alternatiba garbia eta jasangarria eskainiz, klima aldaketaren eragile nagusietako bat den sektorea. Tesi honek hidrogenozko tanke baten neke analisia aurkezten du. AA2219-T87 aluminio aleazioko eta marruskadura-agitazioko (FSW) soldadurarekin fabrikatutako hidrogeno likidoko (LH2) biltegiratze-tanken diseinu aldaketa hasiberriak aztertuz. Elementu finitoen metodo orokor (EFM) eredua garatu da krio-tenperaturako baldintzetan tentsio banaketak jasotzeko, eta azpisistema batekin haustura-propagazioaren azterketa zehatza egiteko lagundu da. Bi ikuspegi aztertu dira: haustura hasierako eta nekearen iraupenaren estimazio klasikoa S-N datuetatik abiatuta, eta haustura-propagazioaren kalte-tolerantzia azterketa krio-tenperaturan. Emaitzek neke iraupenaren gehiegizko estimazioa erakusten dute, batez ere hipotesiak eta frogagintza mugatuaren ondorioz; hausturaren propagazioa askoz azkarragoa da eta inguruneko baldintzak eta tankearen hormaren lodiera txikia direla eta eragin handia du. Aurkikuntzak egitura-mailako azterketak haustura lokalizatuarekin osatzea garrantzitsua dela azpimarratzen dute. Etorkizuneko lana izango da frogak egiteko esperimentuak eta aurreratutako jarraipen-teknikak erabiliz hidrogeno likidoko tankeak segurtasun eta fidagarritasunez hobetzera bideratzea. Gako-hitzak: EFM, Haustura, Nekea, FSW, KI, Aluminioa Andrea Arana Structural concepts for metallic LH2 tank designs life enhancement Faculty of Engineering and Applied Science Aerospace Vehicle Design MSc in Aerospace Vehicle Design Academic Year: 2024-2025 Supervisor: Ioannis Giannopoulos Date 25/08/2025 Faculty of Engineering and Applied Science Aerospace Vehicle Design MSc in Aerospace Vehicle Design Academic Year: 2024-2025 Andrea Arana Structural concepts for metallic LH2 tank designs life enhancement Supervisor: Ioannis Giannopoulos August 2025 This thesis is submitted in partial fulfilment of the requirements for the degree of MSc. ©Cranfield University 2025. All rights reserved. No part of this publication may be reproduced without permission. Academic Integrity Declaration I declare that: •The thesis submitted has been written by me alone. •The thesis submitted has not been previously submitted to this university or any other. •All content, including primary and/or secondary data, is true to the best of my knowledge. •All quotations and references have been duly acknowledged according to the requirements of academic research. I understand that to knowingly submit work in violation of the above statement will be considered by examiners as academic misconduct. Structural concepts for metallic LH2 tank designs life enhancement Andrea Arana Abstract This thesis presents a fatigue analysis of preliminary designs for liquid hydrogen (LH2) storage tanks manufactured from AA2219-T87 aluminium alloy with friction stir welded joints. A global finite element model (FEM) was developed to capture stress distributions under cryogenic conditions, supported by a refined submodel for accurate crack propagation analysis. Two approaches are examined: classical fatigue life estimation based on crack initiation using S–N data, and damage tolerance assessment through fracture mechanics of crack growth at cryogenic temperatures. Results indicate an overestimation of fatigue life during initiation, mainly due to assumptions and limited experimental evidence, while crack propagation is significantly faster and strongly influenced by environmental conditions and the thin tank walls. These findings highlight the importance of complementing structural-scale analyses with localised fracture assessments. Future work will focus on experimental validation and advanced monitoring techniques to improve the safety and reliability of LH2tanks. Keywords: FEM, Crack, Fatigue, FSW, KI, Aluminium 8 2.1.4 Insulation Technologies and Thermal Management Effective thermal insulation is critical for minimising boil-offlosses and maintaining operational efficiency. Multi-layer insulation (MLI) systems provide the highest thermal performance, achieving effective thermal conductivities as low as 0.135mW/m−Kunder high vacuum conditions(23). However, MLI systems require complex double-wall construction with vacuum maintenance systems, adding significant weight and complexity to the overall storage system.(24,25). Boil-offoccurs not only during ground storage but also continuously during flight and refueling operations, necessitating careful management to prevent fuel loss and maintain tank pressure within safe limits(12). Spray-on foam insulation (SOFI) offers a simpler, lighter alternative but has lower thermal performance and degrades under thermal cycling. Advanced closed-cell polyurethane foams have shown promise in aerospace, though long-term durability under repeated cryogenic cycles is still being studied(25,26). 2.1.5 Manufacturing Technologies and Processes The fabrication process involves metal forming techniques to create fine-grained or nanocrystalline aluminum alloys that improve hydrogen trapping and resist embrittlement. Controlled milling optimises particle and grain sizes for better hydrogen absorption and release, while microstructural advances such as dual-precipitate alloys enhance strength and durability(27). For the cylindrical parts of the tanks, backward extrusion is a common method due to its ability to produce seamless, high-integrity structures with excellent mechanical properties(28). In contrast, the domes are typically formed using hydroforming or spinning processes, which allow for precise shaping and thinning of the material while preserving strength and ductility(29,30). These combined manufacturing approaches ensure the structural reliability and performance necessary for demanding cryogenic hydrogen storage applications. The joint between the domes and the cylindrical section in aluminum hydrogen storage tanks is typically achieved using friction stir welding (FSW), a solid-state joining process that has demonstrated superior performance compared to traditional fusion welding methods. FSW employs a rotating tool that generates frictional heat to soften, but not melt, the material, allowing plastic deformation and mixing of the metal at the joint interface. This process yields welds with mechanical efficiencies ranging from 70% to nearly 100%, while effectively eliminating common defects such as porosity, cracking, and heat-affected zone degradation. The resulting welds are fully sealed, structurally robust, and capable of maintaining integrity under the demanding pressure and temperature conditions characteristic of hydrogen storage(28,31). Figure 5: Schematic Diagram of Friction Stir Welding Process(32) 9 2.1.6 Safety Analysis and Load Case Considerations Liquid hydrogen storage systems must withstand a complex array of operational and emergency loading conditions while maintaining structural integrity and performance. Primary load cases include internal pressurisation (typically 1-1.5 bar operational pressure), hydrostatic loads from fuel sloshing during flight manoeuvers, and thermal stresses from cryogenic temperature differentials(33,34). Aircraft-level loading conditions, including ultimate loads of 9g and crash scenarios, must be accommodated without compromising tank integrity(35,3). Hydrogen-specific hazards present unique challenges requiring specialised safety measures. Hydrogen’s wide flammability range (4-75% in air) and extremely low ignition energy create significant fire and explosion risks that must be addressed through comprehensive leak detection, ventilation, and ignition source control. Hydrogen embrittlement effects on structural materials require careful material selection and long-term surveillance programs to ensure continued structural integrity. Pressure relief systems must be designed for the specific characteristics of hydrogen service, including rapid pressure rise rates and the potential for invisible hydrogen flames(36,37). 2.2 Fatigue in Cryogenic Environment 2.2.1 Classical Fatigue and Damage Tolerance Approaches Fatigue damage in metallic structures is traditionally understood as a progressive process that ultimately leads to failure under cyclic loading. The classical fatigue approach divides the fatigue life into two distinct phases: crack initiation and crack propagation. The crack initiation phase refers to the period during which microstructural damage accumulates without the presence of a macroscopically detectable crack. This phase can represent a significant portion of the total fatigue life, often estimated to range between 70% and 90% for various metallic alloys and welded joints(38). Classical fatigue analysis relies heavily on stress-life (S-N) curves, which correlate cyclic stress amplitude to the number of cycles leading to failure. The Miner’s linear damage rule is commonly applied to account for variable amplitude loading, enabling a cumulative damage calculation from different stress levels(39). Within this traditional framework, the integrity of the structure is assumed intact during the initiation phase, with no pre-existing flaws that compromise its load-carrying capacity. This assumption is valid for many engineering applications where careful manufacturing and inspection processes minimise initial defects. However, the microstructural nature of fatigue damage means that crack initiation can be difficult to detect and predict precisely, especially in complex welded joints and harsh environments. In contrast, the damage tolerance methodology adopts a more conservative and realistic premise. Damage tolerance assumes the presence of small cracks or manufacturing defects from the outset and focuses on predicting the rate of crack growth under cyclic stresses. This approach utilises fracture mechanics principles and experimentally derived crack growth laws, such as Paris’ law, to estimate the remaining service life based on the propagation of these flaws to a critical size. Damage tolerance thus emphasises inspection, monitoring, and maintenance to detect and manage cracks before they reach a critical length that could cause catastrophic failure(39). 10 At the academic level, integrating classical fatigue approaches with damage tolerance methodology is essential for a more comprehensive and profound understanding of structural behaviour under cyclic loading. While classical fatigue studies focus on the time to crack initiation, damage tolerance provides the perspective of crack growth and propagation, emphasising structural integrity in the presence of defects. Therefore, this complementary approach strengthens learning, supports applied research, and provides a better understanding of fatigue life. 2.2.2 Crack initiation and propagation under Cryogenic Temperatures When considering fatigue crack initiation mechanisms at cryogenic temperatures near 20 K, materials such as the 2219-T87 aluminum alloy exhibit altered mechanical responses that influence fatigue behaviour. Specifically, tensile testing reveals a significant increase in yield strength and ultimate tensile strength at cryogenic temperatures compared to room temperature (Fig. 6), while the material retains adequate toughness. This increase in strength may affect the initiation and early propagation stages of fatigue cracks by modifying the local stress and strain fields around defects, underscoring the importance of understanding fatigue mechanisms in cryogenic environments for aerospace structural applications(19,40). Figure 6: Low Temperature Yield Strength of A2219-T87(40) Importantly, the fatigue crack growth threshold (∆Kth) increases by approximately 20–30% at 20 K relative to ambient conditions, reflecting enhanced resistance to crack initiation under cyclic loading at cryogenic temperatures. This improvement in the threshold intensity factor significantly contributes to the alloy’s durability in low-temperature service environments(19,41). In conventional service environments, the Paris Law parameters Cand mare regarded as material-dependent constants that remain relatively stable within a given microstructure. These parameters facilitate the prediction of fatigue crack growth rates as a power-law function of the stress intensity factor range (∆K), thus forming a cornerstone of structural life prediction models(39). However, under cryogenic conditions, shifts in microstructural behaviour and fracture mechanics induce significant variations in these parameters. Changes in dislocation mobility, crack tip plasticity, and other low-temperature-specific mechanical phenomena alter both Cand m, as well as the threshold ∆Kth (19,42). 11 Specifically for aluminium alloys, the Paris exponent mtypically falls between 3.5 and 4 and remains relatively stable despite temperature variations. Conversely, the Paris constant Cdemonstrates appreciable sensitivity to temperature, decreasing at cryogenic temperatures around 28% for 6061-T62(43), which corresponds to reduced fatigue crack growth rates for a given ∆K. The accompanying increase in fatigue thresholds reinforces resistance to both crack initiation and propagation at low temperatures. This behaviour aligns with analogous observations in a variety of metallic systems, where lower temperatures elevate threshold stress intensity ranges and suppress crack growth rates, thereby reducing Cwithout markedly affecting m(39,19). Overall, these temperature-dependent variations in Paris Law parameters underscore the critical need for fatigue life models to incorporate environmental and temperature influences, particularly when predicting the performance of aerospace structural materials such as 2219T87 aluminum alloy operating in cryogenic settings. 2.2.3 Hydrogen Embrittlement Hydrogen embrittlement (HE) is a degradation process in which metals lose ductility and fracture toughness due to the absorption of atomic hydrogen, potentially leading to catastrophic failure often without visible warning(44). Atomic hydrogen permeates metallic structures through several pathways, including corrosion reactions, direct exposure to high-pressure hydrogen atmospheres in storage tanks and pipelines, and manufacturing processes such as welding or forging(45). Once absorbed, hydrogen atoms diffuse through the metal’s crystal lattice and preferentially accumulate at microstructural trapping sites such as dislocations, grain boundaries, and precipitates. This diffusion is accelerated by stress gradients, especially in regions with high triaxial stress, which concentrate hydrogen at vulnerable sites and promote embrittlement mechanisms. The severity of HE depends on factors including material composition, hydrogen concentration, applied stress, and environmental conditions(46). In hydrogen storage and transport systems, these processes lead to subcritical crack growth and mechanical weakening, posing a significant reliability risk(45,47). Hydrogen embrittlement significantly degrades mechanical properties, especially ductility, causing commercial aluminum alloys to lose up to 40% of elongation and reduction in area, with a shift from ductile to brittle fracture modes(48). Although aluminum alloys generally resist embrittlement better than steels, some high-strength variants remain vulnerable(49). The AA2219 alloy in T87 temper shows relatively low susceptibility due to its moderate strength compared to more embrittlement-prone 7xxx-series alloys(50,51). Yield strength is mostly unaffected, but sudden failures below yield stress can occur due to localised mechanisms(44), posing critical risks for hydrogen-exposed components like storage tanks(47). Hydrogen penetrates metallic structures in both gaseous and aqueous forms, diffusing through microstructural defects such as dislocations, vacancies, inclusions, and grain boundaries. Once absorbed, hydrogen exists in atomic, molecular, or mixed states, promoting localised stress concentration that leads to crack nucleation and propagation. These fracture processes can initiate even under stresses below the material’s yield strength, as hydrogeninduced defects serve as critical weakening sites, causing catastrophic brittle failures(44). 12 2.2.4 Crack propagation in FSW joints FSW is widely regarded as one of the most reliable solid-state joining technologies, enabling the fabrication of joints with excellent mechanical performance in alloys traditionally considered difficult to weld by fusion techniques(52). For this reason, it has been broadly applied in critical sectors such as aerospace, automotive, and hydrogen storage. Despite these advantages, maintaining structural integrity remains a key challenge, since even microscopic flaws can act as precursors of failure through crack initiation and propagation(53). The weld microstructure generated by FSW is highly heterogeneous, shaped by the complex thermal and mechanical cycles of the process. The nucleation zone (NZ) undergoes substantial plastic deformation at elevated but sub-solidus temperatures, leading to dynamic recrystallisation and the formation of fine grains. This grain refinement enhances ductility and fracture toughness but may reduce hardness due to precipitate dissolution, especially in precipitation-strengthened alloys(54). Adjacent to it, the thermomechanically affected zone (TMAZ) experiences both strain and temperature but lacks complete recrystallisation, resulting in elongated grains and reduced hardness due to precipitate coarsening. Finally, heat affected zone (HAZ) is influenced solely by the thermal cycle, where over-aging and precipitate coarsening lead to the lowest hardness and strength within the weld(55). These differences explain why fracture and fatigue failures often localise in the TMAZ and HAZ, which consistently act as the weakest links in the welded joint. The fatigue and fracture behavior of FSW joints is therefore controlled by this microstructural heterogeneity. Cracks frequently initiate in the softened HAZ or TMAZ, although they may also nucleate at local stress concentrators such as voids, inclusions, or surface irregularities left by the tool shoulder(56,57). After initiation, propagation follows the path of least resistance. The highly refined and ductile SZ may facilitate relatively fast crack growth under cyclic loading, while propagation through the TMAZ and HAZ can be slower and more tortuous due to plastic incompatibility and residual stress effects(58,59). Experimental studies have shown that the threshold stress intensity and crack growth constants vary significantly among the SZ, TMAZ, and base material, indicating that microstructural zones alter both initiation resistance and growth kinetics (Fig. 7). Figure 7: Fatigue crack growth data for base material, TMAZ, and stir zone samples(59) 13 3.0 Methodology This study adopted a sequential engineering design and analysis methodology, beginning with a comprehensive literature review to establish the theoretical framework and guide the preliminary configuration of the tank. The initial phase encompassed decisions regarding geometry, integration with and attachment to the fuselage, material selection, and thermal insulation. Structural performance was subsequently assessed through a two-stage FEM approach: first, a global model was developed to evaluate overall structural behaviour, followed by a detailed submodel focusing on critical regions. Stress data obtained from the submodel was then used in a fracture mechanics analysis to estimate crack propagation cycles and predict fatigue life. The resulting findings enabled the identification of fatigue-critical areas, provided an evaluation of structural durability, and supported the proposal of design improvements aimed at future optimisation. Figure 8: Flowchart illustrating the key phases of the project methodology 3.1 Preliminary design During the preliminary design phase, a comprehensive comparative assessment was conducted, encompassing material selection, manufacturing feasibility, integration strategies, and insulation concepts, grounded in findings from relevant aerospace literature. To this end, several decision matrices were developed to evaluate the possible alternatives, the details of which are provided in Appendix B, thereby enabling a systematic comparison of design options. The outcome of this multi-criteria evaluation, as summarised in Table 1, facilitated the identification of the optimal configuration for the intended application. Table 1: Overview of Preliminary Design Selections Feature Design Decision Tank Material Aluminum Alloy AA2219-T87 Integration Non-integral, bolted frames Insulation MLI Manufacturing Cylindrical: Deep drawing, Domes: Hydroforming, Joints: Friction Stir Welding (FSW) Based on these design decisions, the tank dimensions were established according to constraints imposed by the fuselage envelope and informed by the selected parameters. For the design, it will be assumed that the tank is integrated into an A320 fuselage, which sets the constraints for design parameters and informs other requirements. The maximum tank diameter is limited to 3 meters, constrained by the A320 fuselage diameter to ensure proper clearance and structural compatibility(60). Following the literature, a diameter-to-length ratio of approximately 0.66(61) was adopted to define the tank length accordingly. 14 Furthermore, an analysis of the impacts on aircraft range and passenger capacity was conducted, as detailed in Appendix C, comparing hydrogen tank integration with conventional kerosene-fueled configurations. The results of this analysis are presented in Table 2. Table 2: Key Dimensions and Capacities of the Hydrogen Tank Feature Value Units Length 5000 mm Volume 28.27 (60% of A320) m3 Range 1879 km Passengers 126 u 3.1.1 Minimum Thickness Calculation Based on internal pressurisation as the governing load case, the minimum required thickness of the tank wall is calculated following the formulation prescribed by pressure vessel design codes(62). This approach refines the classical thin-walled pressure vessel equation by incorporating factors such as the material allowable stress, joint efficiency, and an accounting term for pressure correction, ensuring compliance with safety and operational standards. The governing equation for minimum thickness is: tmin =P·r S·E−0.6·P (62) (1) Where: •Pis the design internal pressure, accounting for safety factors, •ris the internal radius of the tank, •Sis the allowable tensile working stress of the material at operating temperature, •Eis the joint efficiency factor related to the quality of welds and inspections. For liquid hydrogen tanks in aircraft, typical operational pressures range between 1 and 1.5 bar absolute. However, transient scenarios such as venting or rapid temperature fluctuations can temporarily increase this pressure beyond nominal levels. To conservatively account for these eventualities and ensure structural safety, an ultimate safety factor of 3 is applied in accordance with CS25 standards(3) for low-pressure vessels. This results in a design pressure given by: Pdesign =1.5 bar ×3=4.5 bar =0.45 MPa (2) The material selected for the tank (A2219-T87) exhibits a yield strength of approximately 393 MPa (57 ksi) at room temperature (27◦C) (Fig. 6). To address uncertainties such as hydrogen embrittlement, a reduction factor of 0.8 is applied to the allowable material strength, as recommended in the literature regarding hydrogen service and material performance factors(19). 15 Additionally, a conservative safety factor of 1.15 is applied to the material strength, leading to a design allowable tensile stress of approximately: σp=0.8×393 MPa 1.15 ≈341.8 MPa (3) As studies have shown, Friction Stir Welding of aluminum alloys such as AA2219 yields welds with mechanical efficiencies ranging from approximately 70% to nearly 100% depending on welding parameters and process control(28). The microstructural refinement and reduced defects compared to fusion welding translate into joint efficiencies typically in the range of 0.85 to 0.95(63). Considering the rigorous inspection and qualification standards in aerospace manufacturing, an initial joint efficiency value of E=0.85 is assumed for this study as a conservative yet realistic parameter for structural calculations. Applying the calculated values to Equation (1): tmin =0.45 MPa ×1500 mm 341.8 MPa ×0.85 −0.6×0.45 MPa ≈675 290.53 −0.27 =675 290.26 ≈2.33 mm (4) This theoretical minimum thickness is increased to a conservative initial wall thickness of 3.5 mm. This choice accounts for uncertainties in manufacturing tolerances, extended operational loads, and the inactive safety margins commonly adopted in aerospace cryogenic storage designs. Additionally, the decision was informed by comparisons with similar designs in previous projects(35,64,65), which support the selected thickness as both safe and practical. With a wall thickness of 3.5 mm, the hoop stress under internal pressurisation is approximately 192 MPa, which aligns with standard aerospace practice for cryogenic hydrogen storage and provides an additional safety margin to manage material behaviour uncertainties and load variations. Since experimental validation lies outside the scope of this thesis, this conservative thickness serves as a robust initial baseline for the subsequent detailed structural verification via finite element analysis. 16 3.2 Load Cases Definition The structural verification of the liquid hydrogen (LH2) storage tank requires consideration of the full spectrum of mechanical solicitations expected during a 25-year service life. In accordance with the methodology(66), a representative envelope of load types has been defined, encompassing both operational cycles and certification-driven extremes. Table 3 summarises these load categories in terms of cycle frequency, stress variation, and stress ratio. Table 3: Loading Types for LH2Storage Tanks in Regional Aviation(66) Loading Type Cycle Frequency Stress Variation Stress Ratio (R) Storage pressurisation Low Large 0 Pressure control system High Small 0.9 Ground manoeuvring and gusts High Small–medium 0.2 Extreme manoeuvring Very low Very large 0 Cycle Quantification within the Operational Envelope In all cases, to ensure the structural integrity of the component throughout its service life, a conservative approach is adopted by considering the most critical scenario within the operational envelope. This means that the maximum number of cycles and the most severe stress ratio Rare assumed for each load case, ensuring that the design accounts for the highest possible fatigue demand. Pressurisation cycles (R=0) correspond to refills from ambient pressure to 1.5 bar prior to flight. For a regional aircraft operating three sectors daily without fuel tankering, two full refills per day are assumed, leading to: 2×365 ×25 =18,250 cycles . Valve venting due to thermal boil-offand ambient pressure variations occurs intermittently during flight. Literature reports a typical frequency of one to two events per day(67,68), yielding: 2×3×365 ×25 ≈54,750 cycles , with R≈0.9 given the narrow stress fluctuation. Gust and manoeuvre responses contribute additional stress variations in the range R= 0.2–0.3. Assuming 3–5 significant events per sector(69), one obtains: 5×3×365 ×25 ≈136,875 cycles . Finally, extreme manoeuvres under combined inertial loads (R=0) are rare, expected once or twice over the lifetime of the airframe(70). These scenarios, although exceptional, are prescribed by certification frameworks such as CS-25(3) and must be considered for ultimate load verification. 17 Selection of Load Cases for Analysis Although three principal load cases were modelled in detail using finite element methods, additional operational loads were accounted for using simplified analytical calculations, literature data, and conservative scaling based on FEM results. This hybrid approach allowed the incorporation of service condition variability while remaining computationally manageable. Using Miner’s rule to accumulate fatigue damage, both detailed and estimated stress cycles were integrated to provide a comprehensive prediction of the component’s fatigue life. Baseline pressurisation The reference load case consists of steady internal tank pressurisation, representing the nominal operating condition across all flight altitudes. Variations due to the pressure control system are conservatively modelled as 1.1 times the nominal stress. Pressurisation with severe inertial loads These cases assess the interaction of internal pressure with inertial accelerations representative of realistic manoeuvres. The loads examined correspond to 2.5gvertical, 1.5glongitudinal, and 3glateral, combined individually with nominal pressurisation. This approach parallels CS-25 certification practice(3), where pressurisation and inertia may be applied in combination. Pressurisation with extreme inertial envelopes Selected ultimate load scenarios are included to verify robustness under rarely experienced, exceptionally severe conditions. The combinations analysed are: •Pressurisation +9glongitudinal +3glateral: simulates an extreme deceleration event like a hard emergency landing or sudden stop with lateral gusts, representing a rare but severe inertial load the tank must withstand. •Pressurisation +6gvertical downward +3glateral: replicates severe downward vertical acceleration combined with lateral loading, simulating turbulence or rapid descent and imposing compressive and shear stresses. •Pressurisation +2.5gvertical upward +1.5glongitudinal: represents significant upward and forward acceleration during steep climbs or pull-ups under pressurised conditions, testing structural integrity during dynamic ascent. Summary of Load Cases Analysed The selected load cases addressed in the numerical work are summarised in Table 4: Table 4: Summary of Load Cases Considered in the Analysis Case Description Loads Applied 1 Storage pressurisation Pressurisation only 2a Severe manoeuvre (vertical) Press. +2.5 g vertical 2b Severe manoeuvre (longitudinal) Press. +1.5 g longitudinal 2c Severe manoeuvre (lateral) Press. +3 g lateral 3a Extreme man. (long. +lat.) Press. +9 g long. +3 g lat. 3b Extreme man. (vert. down +lat.) Press. +6 g vert. down +3 g lat. 3c Extreme man. (vert. up +long.) Press. +2.5 g vert. up +1.5 g long. 24 a) Weld Zones b) Crack Front Figure 16: 3D Submodel Partitioning: The crack itself was modelled with a semi-elliptical geometry. The Mode I stress intensity factor, KI, was calculated using the contour integral method, commonly known as the J-integral, applied along several contours closely surrounding the crack tip. This approach provides a path-independent and reliable evaluation of KI, which is critical for fracture analysis. A meticulous meshing strategy was employed, involving progressively finer mesh elements concentrated around the crack tip to achieve numerical convergence while managing computational costs. Near the crack front, special singular or focused elements were likely used to capture stress gradients with high accuracy. Service loads consistent with the global FEM results were applied. At the interface between the submodel and the global model, boundary conditions were imposed to constrain displacements as necessary, ensuring continuity between the refined region and the overall structure. Along the crack surface, movement perpendicular to the crack plane was restricted to realistically simulate crack face behaviour under loading. Figure 17: Submodel: Boundary Contidions Finally, multiple extraction points were placed along the crack front to record the spatial distribution of KI. For each crack size, all computed KIvalues were collected and documented (with full datasets available in Appendix E). The maximum KIvalue along the crack front was selected as the representative parameter for fracture assessment, typically occurring near the intersection of the crack with the free surface. 25 Analysis Procedure and Output Processing The described procedure was applied to all eight modelled crack sizes, maintaining consistent boundary conditions, mesh refinement, and material property assignments to ensure accurate and comparable results. For each configuration, the maximum Mode I stress intensity factor along the crack front was extracted from the numerical output. These maximum KIvalues were then correlated with their respective crack lengths to construct the KIversus a (crack length) relationship. This relationship serves as the fundamental input for fatigue crack growth assessment and is illustrated in Fig. 18. Figure 18: Relation between Mode I stress intensity factor, KI, and crack length, a(mm). Within this context, failure is defined as occurring either when the stress intensity factor KI reaches the material’s fracture toughness KIC, or when the crack length exceeds the material thickness. The latter case is critical because through-thickness crack penetration can cause leakage. For the Heat Affected Zone, the calculated stress intensity factor at the point of full thickness penetration is KI=25.13 MPa √mm, while the fracture toughness of the material is KIC =27.5 MPa √mm. Since KI<KIC, failure in this case is governed by crack penetration through the thickness rather than by exceeding the material’s fracture toughness. 3.4 Classical Fatigue Life Calculation and Damage Tolerance The fatigue life of metallic structures is generally divided into two principal phases: crack initiation and crack propagation. The initiation phase involves the accumulation of microstructural damage under cyclic loading until a crack becomes detectable, whereas the propagation phase describes the growth of this crack until failure(39). For aluminium alloys and welded joints, initiation is often the dominant portion, representing up to 70–90% of total fatigue life(38). 26 In this study, a conservative 50% of the total fatigue life (Nf) is allocated to crack initiation, reflecting both methodological assumptions and the limited relevant experimental data under cryogenic service conditions. A damage tolerance approach assumes an initial microscopic flaw of 0.02 mm within the critical weld region, consistent with engineering standards and typical nondestructive inspection capabilities(78). The adopted fatigue life assessment methodology follows the dual-phase workflow presented in Fig.19, combining classical fatigue life estimation to crack initiation using S-N data, and fracture mechanics-based crack propagation analysis utilising Paris law parameters specific to friction stir welded aluminium alloys at cryogenic temperatures. This complementary approach enables a thorough evaluation of structural durability. Figure 19: Workflow Diagram of Dual-phase Fatigue Life Assessment Methodology 3.4.1 Classical Fatigue Life Calculation Crack initiation modelling for the AA2219-T87 aluminium alloy was undertaken using S-N data sourced from the literature(79) (see Fig. 20), which correlates the applied service stress amplitude to the corresponding fatigue life in cycles,Nf. Figure 20: S-N data for 2219-T87 welded under cryogenic temperature conditions Stress Range (ksi) vs Number of Cycles (N)(79). 27 The available S-N dataset for cryogenic testing was obtained from experiments conducted on TIG welded joints under a load ratio of R=−1, representing fully reversed tension–compression loading. Although the present study focuses on friction stir welded (FSW) joints, the use of TIG-based S-N data introduces a degree of conservatism. FSW joints have been demonstrated to outperform TIG welds in fatigue performance owing to their finer microstructure and absence of solidification defects(31). Therefore, TIG fatigue data provide a safe lower bound for fatigue life estimation in the absence of direct cryogenic test data for FSW joints. Furthermore, the application of S-N data obtained at a load ratio of R=−1 to predict fatigue life under tension–tension loading conditions with Rvalues ranging from 0 to 0.9 is an accepted engineering approximation. For the same maximum stress magnitude, fully reversed loading results in a larger cyclic stress range compared to tension–tension loading, effectively doubling the stress amplitude, thus leading to shorter fatigue lives. Since a positive mean tensile stress (R>0) generally reduces crack opening and delays crack initiation, basing life predictions on R=−1 data provides a conservative estimate(38). This conservative approach considering both the weld type and loading ratio ensures the inclusion of safety margins to account for potential uncertainties. The S-N data were digitised using WebPlotDigitizer (version 5.2) and subsequently plotted on logarithmic scales to linearise the power-law relationship between stress amplitude and fatigue life. A linear regression analysis was performed on the transformed dataset, fitting a straight line of the form: log(N)=−mlog(S)+log(C∗),(6) where Nis the number of cycles to crack initiation, Sis the applied stress amplitude, and C∗=Cmfor convenience in the fitting process. The regression yields the slope and intercept of the best-fit line, from which the fatigue strength exponent mis obtained as the negative of the slope, and the fatigue strength coefficient Cis calculated by: C=10intercept m.(7) These parameters characterise the material’s fatigue behaviour under cyclic loading. The resulting Basquin equation then allows calculation of the fatigue life Nfor any applied stress amplitude Sas: N=C Sm .(8) Table 7: Load cases with corresponding stress levels and number of cycles. Load case Stress [MPa] Number of cycles Pressurisation 172 755,424 Pressurisation over pressure 174 683,353 Severe manoeuvre 195 254,365 Extreme manoeuvre 270 15,125 28 To assess cumulative fatigue damage under variable amplitude loading, Miner’s linear damage rule was applied by considering the characteristic number of in-service cycles niexperienced at each stress level i. The damage fraction Dis calculated as: D=X i ni Ni =n1 N1 +n2 N2 +··· +nk Nk ,(9) where Niis the number of cycles to crack initiation at stress level iobtained from the Basquin equation. Miner’s rule assumes linear damage accumulation and does not account for load sequence effects, interaction between different stress levels, or potential material memory effects. Despite these limitations, it remains widely accepted in engineering practice due to its simplicity and generally conservative nature, especially when combined with adequate safety factors. Using the specific load spectrum and cycle counts detailed in Table 19, the damage fraction was calculated as D=0.64, indicating that approximately 64% of the critical fatigue damage has already accumulated. Considering a total of 1,708,269 applied load cycles in the analysed spectrum, the estimated total fatigue life is obtained by dividing this number by the damage fraction D, yielding: Ntotal =Nspectra D=1,708,269 0,642 ≈2,658,725 cycles.(10) Thus, the structure is expected to endure approximately 2.66 million cycles before reaching the critical fatigue damage threshold. While the classical fatigue life calculation and Miner’s rule provide a useful estimate of accumulated damage and remaining life before crack initiation, they inherently assume that the structure remains free of detectable cracks up to that point. Given the critical nature of hydrogen storage tanks, where small defects may already exist or initiate earlier, it is essential to complement this analysis with a fracture mechanics-based assessment of crack propagation and its impact on structural integrity. 3.4.2 Damage Tolerance Unlike classical fatigue life calculations that focus on crack initiation, the damage tolerance approach directly addresses the growth of existing cracks under cyclic loading, providing essential insights into residual life and structural safety. This section outlines the methodology and key inputs required to model crack propagation. Crack propagation analysis requires the following critical inputs: 1. The variation of the Mode I stress intensity factor KIwith crack size a(the KI–arelationship), previously obtained from a refined finite element submodel. 2. The fatigue crack growth rate parameters of the material, namely Cand m, taken from the literature(59) . These inputs are then used to implement the Paris–Erdogan law: da dN =C·(∆K)m,(11) where da dN is the crack growth rate per cycle and ∆Kis the stress intensity factor range. 29 Experimental studies have shown significant variability in fatigue crack growth rates across friction stir welded aluminum joints due to spatial differences in grain structure, hardness, and residual stresses(72,59). Accordingly, distinct Paris law parameters are applied to each weld zone: NZ, TMAZ, and HAZ. Crack growth data for cryogenic FSW aluminum joints were digitised from Fig. 7 using WebPlotDigitizer (version 5.2). For each weld zone, the data were linearised on logarithmic scales, and the Paris parameters mand Cwere obtained through regression analysis in MATLAB (see Table 8). To account for the cryogenic condition (−253◦C), adjustment factors from previous studies were applied proportionally(64). The modified Paris parameters are hereafter referred to as m′ to distinguish them from the baseline values. Table 8: Paris law parameters for FSW aluminium joints under cryogenic conditions Zone mAdjusted m′ NZ 3.30 3.84 TMAZ 3.08 3.58 HAZ 3.08 3.58 Zone-by-Zone Propagation Simulation Utilising the zone-specific Paris law parameters alongside the FEM-derived KI–acurve, crack growth was simulated incrementally across the weld, sequentially progressing from the NZ through the TMAZ to the HAZ. Due to the absence of direct experimental crack growth data in the HAZ, and considering its typically higher crack propagation rates, the Paris parameters for the TMAZ were conservatively applied to the HAZ. The total number of fatigue cycles Nrequired for crack growth from an initial length ai to a final length afin each weld zone was calculated via numerical integration of Paris’ law. Crack growth in the nugget zone was considered from the minimum detectable crack length up to the transition into the TMAZ. In turn, the TMAZ was modelled from its onset until the beginning of the HAZ, and finally, the HAZ was analysed from its start until the crack reached the full plate thickness. N=Zaf ai 1 C[∆K(a)]mda,(12) where Ndenotes the total number of cycles required for crack growth between the initial length ai(onset of fatigue crack growth) and the final length af(critical crack length at failure). The parameters Cand mare the Paris coefficients corresponding to each weld zone, while ∆K(a) represents the stress intensity factor range as a function of crack length. This integration was implemented in MATLAB, employing the zone-specific Paris parameters, FEM-derived KIdata, and prescribed crack length increments. The total crack propagation life Npwas obtained by summing the calculated cycles for crack growth through each weld zone: Np=NNZ +NTMAZ +NHAZ.(13) The results of this crack propagation simulation are presented and discussed in 3.3 Damage Tolerance Analysis section, providing critical insight into the damage tolerance behaviour. 30 4.0 Results and discusion 4.1 Validation of Finite Element Model The finite element model developed for the LH2tank was validated against hand calculations performed for the pressurisation load case. These hand calculations, based on classical pressure vessel theory, provided analytical estimates of the maximum hoop and longitudinal stresses. The comparison focused on the points of maximum tension identified in the FEM results under the pressurisation load. Good agreement was observed, with a deviation of approximately 11% (see Table 9). This difference is attributed to the FEM’s ability to account for local stress concentrations, which are not captured by the simplified analytical approach. Table 9: Comparison of stress results from hand calculation and FEM analysis Analysis type Stress (MPa) Hand calculation 192.9 FEM analysis 172.1 Deviation 11% Furthermore, the finite element model not only confirmed the analytical stress levels but also provided a detailed picture of the stress distribution across the tank structure, which is essential for predicting potential crack initiation areas. Unlike the uniform stress fields assumed in classical pressure vessel theory , the FEM allowed the identification of local tensile and compressive regions, thereby highlighting critical zones where stress concentrations may favor damage onset(71). 4.2 Classical Fatigue Life Calculation The classical fatigue life estimation, based on the applied load spectrum and Miner’s cumulative damage rule, yielded a total fatigue life of approximately 2.66 million cycles. Figure 21: Damage fraction ( ni NI) accumulated under each load case. 31 Severe manoeuvres, although less frequent than venting pressurization or pressurization cycles, induce higher stress amplitudes that cause greater cumulative damage. Load cases associated with these highest stress amplitudes, such as severe manoeuvres, exert the greatest influence on Miner’s damage accumulation, despite their lower frequency compared to pressures generated during venting. This effect is illustrated in Fig. 21, which displays the contribution of each load case to the overall damage fraction. Overall, the classical fatigue approach suggests that crack initiation under the specified operational spectrum would require a large number of cycles, confirming the inherent durability of the AA2219-T87 alloy under cryogenic conditions and the conservative assumptions employed in this analysis. If crack initiation is assumed to constitute 50% of the total fatigue life, the initiation phase would last approximately 1.33 million cycles. The subsequent crack propagation phase is analysed using a damage tolerance approach in the following section. 4.3 Damage Tolerance Analysis In striking contrast, the damage tolerance approach predicts a fatigue crack propagation life of approximately 12,000 cycles, starting from an initial microscopic flaw of 0.02 mm up to critical failure, assumed when the crack reached the tank thickness, which occurs before the stress intensity factor reaches KIC. A detailed examination of crack propagation lifetimes calculated using the baseline exponent mand its adjusted counterpart m′reveals that incorporating cryogenic effects decreases life estimates by approximately 57%, underlining the crucial need to consider environmental influences in damage tolerance assessments as shown in Fig. 22. Figure 22: Crack growth (a vs N) - Comparison between m and m′ 32 The crack propagates more rapidly in the TMAZ and HAZ despite having a lower Paris law exponent m compared to the NZ. This accelerated propagation occurs because the stress intensity factor KIreaches higher values due to the larger crack size in these zones, which compensates for the reduced material sensitivity to crack growth. This behaviour is clearly illustrated in Fig. 23. Furthermore, an important observation emerges when analysing the blue dotted line, which represents the crack propagation behaviour considering only the NZ parameters throughout the entire specimen. This idealized scenario predicts a lower total number of cycles to failure compared to the realistic case that incorporates the specific Paris law parameters for each zone (TMAZ and HAZ). This comparison underscores the critical importance of implementing zone-specific material parameters that account for microstructural heterogeneity in welded joints. Neglecting these variations would lead to non-conservative predictions that underestimate crack propagation rates and overestimate the fatigue life of the component. Figure 23: Crack growth (a vs N) - Comparison between FSW Different Zones (NZ, TMAZ and HAZ) or Constant NZ These results complement the classical fatigue life estimation presented earlier, which focused on crack initiation. Together, they provide a comprehensive understanding of the total fatigue life of the LH2tank weld joints, bridging the gap between fatigue initiation and growth phases under realistic cryogenic service environments. 33 4.4 Discussion on Fatigue Life Perspectives The results clearly underscore the dual and complementary nature of fatigue life assessment methods. From an academic perspective, these findings align with extensive literature reporting that AA2219-T87 aluminium alloy exhibits a notably low fatigue threshold ∆Kth (41). This low threshold explains why the crack initiation phase can encompass a substantial portion of the total fatigue life, often spanning millions of loading cycles even under demanding service conditions. Conversely, once a crack initiates, crack propagation proceeds rapidly, particularly through the heterogeneous microstructural zones of the weld. This accelerated growth is markedly exacerbated by the combined effects of cryogenic temperatures and exposure to hydrogen environments, both of which are documented to degrade fatigue crack growth resistance significantly(64). Such environmental factors reduce Paris law parameters and shorten propagation life, as evidenced in the adjusted parameters and reduced cycle counts observed in this study. Figure 24: Crack growth (a vs N) - Initiation (99%) and Propagation(1%) From a practical engineering standpoint, given the criticality of the LH2storage tank, fracture control and damage tolerance principles should guide the fatigue life assessment and maintenance strategies. 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Keys, T. F. Kiefer, and F. R. Schwartzberg. Determination of low-temperature fatigue properties of structural metal alloys: Final report, jul. 1964 – aug. 1965. NASA 43 Contractor Report NASA-CR-67818 /CR-65-70, Martin Company, Denver, Colorado, United States, October 1965. Fatigue testing and determination of low-temperature properties of structural metal alloys: aluminum alloy, stainless steel, and nickel alloys. 44 Appendices 18 June 2025 Dear Andrea Reference: CURES/25628/2025 Project ID: 29195 Title: Structural Concepts for Metallic LH2 Tank Designs Thank you for your application to the Cranfield University Research Ethics System (CURES). We are pleased to inform you your CURES application, reference CURES/25628/2025 has been reviewed. You may now proceed with the research activities you have sought approval for. If you have any queries, please contact CURES Support. We wish you every success with your project. Regards, CURES Team 46 APPENDIX B: Preliminary Design This appendix details the preliminary design considerations for the liquid hydrogen storage tank, emphasising material selection, integration strategies, insulation concepts, and manufacturing feasibility. The content is grounded on authoritative aerospace literature and recent advances, with proposed refinements to enhance clarity, completeness, and scientific rigour. Where appropriate, tables summarise decision criteria to facilitate comprehension and future reference. Tank Material Selecting a suitable material for LH2storage tanks entails balancing extreme cryogenic performance with mechanical, thermal, and manufacturing properties. Among conventional and emerging materials, the leading candidates are austenitic stainless steels, aluminium alloys, and composite materials. Austenitic stainless steels (e.g., AISI 304L, 316L) offer robustness at cryogenic temperatures with excellent ductility and resistance to hydrogen embrittlement. Their lower thermal conductivity aids insulation, but their density imposes a weight penalty detrimental for mobile aerospace applications. Aluminium alloys, notably AA2219T87, combine low density with adequate mechanical strength and cryogenic toughness, maintaining tensile integrity even at 20 K and exhibiting minimal hydrogen-induced degradation. Aluminium’s higher thermal conductivity challenges insulation but can be compensated by advanced multilayer systems. Composite tanks, using CFRP or glass fibre laminates with metallic or polymer liners, promote weight reduction and fatigue resistance, yet introduce concerns over microcracking and permeation under thermal cycling, making their industrial readiness less mature. Table 10: Comparison matrix for material selecction Criterion /Property Steel Aluminum (AA2219-T87) Composites Weight (%) Score Steel Weighted Steel Score Aluminum Weighted Aluminum Score Composites Weighted Composites Strength and Toughness at 20K High Good High 25 4 1.00 4 1.00 5 1.25 Weight Efficiency Low High Very High 25 2 0.50 4 1.00 5 1.25 Resistance to Hydrogen Embrittlement Good Good Moderate 15 4 0.60 5 0.75 3 0.45 Thermal Conductivity Low Higher Low to moderate 10 4 0.40 2 0.20 3 0.30 Manufacturability Moderate High Moderate to Low 15 3 0.45 4 0.60 2 0.30 Cost Low Moderate High 10 4 0.40 3 0.30 1 0.10 Total Score — — — 100 — 3.35 —3.85 —3.65 Based on this evaluation and literature evidence, AA2219-T87 aluminium alloy is selected for the tank to optimise structural integrity, manufacturability, and weight performance in the cryogenic environment. Tank Integration Tank geometry and placement strongly influence aircraft performance and maintenance. LH2tanks are typically classified as integral or non-integral relative to the airframe. Integral tanks serve dual roles as both hydrogen storage and structural members, offering superior mass efficiency and load transfer optimisation, particularly suited for future blended wing body (BWB) aircraft with high internal volume utilisation. However, they pose challenges in access, inspection, and require bespoke design adaptations for each aircraft configuration. 47 Non-integral tanks are modular units isolated from primary structure, offering maintenance ease, retrofit flexibility, and standardised designs. The trade-offincludes increased structural parasitism and reduced volumetric and aerodynamic optimisation, especially for advanced airframes like BWB. Table 11: Comparison matrix for tank integration selection Criterion Integral Tank Non-Integral Tank Weight (%) Score Integral Weighted Integral Score Non-Integral Weighted Non-Integral Maintenance Access and Downtime Challenging Easy; modular and replaceable 25 1 0.25 5 1.25 Load Isolation and Structural Contribution Direct load-bearing; highly efficient Structurally isolated; parasitic weight 25 5 1.25 2 0.50 Mass Efficiency Highest; integrated structure reduces weight Lower; extra supports add weight 15 5 1.00 3 0.60 Integration with Current Aircraft Requires redesign; less versatile Easily retrofitted; flexible 20 2 0.40 5 1.00 Suitability for Future Configurations (BWB) Optimal volumetric and aerodynamic synergy Limited optimization due to modular constraints 15 4 0.60 2 0.30 Total Score — — 100 — 3.00 —3.65 Considering operational flexibility and scope, the tank design adopts a non-integral configuration with bolted attachments to fuselage I-type frames. These attach points will be conceptual only, with frame sizing and bolt configuration based on analogous designs validated via FEM. Insulation Concepts Insulation critically governs boil-offrates and safety. The two main approaches are: Multilayer Insulation (MLI): Vacuum-based, consisting of many reflective foil layers separated by spacers inside a double-wall structure maintaining vacuum below 1 Pa, MLI minimizes conductive/radiative heat transfer, achieving heat leaks as low as 0.9 W/m2and boil-offnear 0.20%. However, vacuum integrity risk necessitates robust structures and backup foam layers to maintain insulation if vacuum is lost. Spray-On Foam Insulation (SOFI): Polyurethane foam applied on surfaces offers ease and weight benefits but is prone to microcracks on thermal cycling, has higher thermal conductivity, and results in about 43 W/m2heat leak and 12% daily boil-off, less suited for aviation LH2storage. Table 12: Comparison matrix for insulation systems Criterion Value MLI Value SOFI Weight (%) Score MLI Weighted MLI Score SOFI Weighted SOFI Thermal Conductivity /Heat Leak (W/m2) 0.9 43 30 5 1.50 2 0.60 Daily Boil-off(%) 0.20 12 30 5 1.50 2 0.60 Vacuum Dependency High None 15 2 0.30 5 0.75 Weight Penalty Moderate (double-wall) Low 10 3 0.30 4 0.40 Operational Safety (Boil-off/Pressure Control) High (minimal boil-off) Medium (higher boil-off) 10 5 0.50 3 0.30 Durability Under Thermal Cycling High; stable with vacuum Low; prone to microcracking 5 4 0.20 2 0.10 Maintenance Complexity Medium; vacuum maintenance Low; easier inspection 5 3 0.15 4 0.20 Total Weighted Score — — 100 — 4.45 — 2.95 48 Given the critical requirement to minimise boil-offand maximise operational safety, MLI is selected as the primary insulation method. Secondary foam layers will be considered for vacuum breach mitigation. Manufacturing Feasibility Manufacturing techniques directly impact tank performance via material properties and structural integrity. Cylindrical Zone: Deep drawing is employed to form seamless cylindrical shells with uniform wall thickness, crucial for fatigue resistance. The process induces strain hardening, enhancing yield strength but requiring post-forming heat treatment to relieve residual stresses and prevent fatigue crack initiation. For very large tanks, rolling plates into cylindrical shells followed by high-integrity welding is an option, though it introduces anisotropy and tensile residual stresses if not controlled. Table 13: Comparison matrix for cylindrical zone manufacturing Criterion Weight (%) Score – Rolling Weighted – Rolling Score – Deep Drawing Weighted – Deep Drawing Residual Stress Control 25 2 0.50 4 1.00 Grain Refinement Quality 20 3 0.60 4 0.80 Fatigue Life Potential 25 3 0.75 4 1.00 Manufacturability 15 3 0.45 5 0.75 Suitability for LH Cylinders 15 3 0.45 5 0.75 Total Score 100 — 2.75 — 4.30 Dome Ends: Spin forming (spinning) allows symmetric, robust dome production, with hot spinning preferred for thicker domes to maximise deformation without cracking. Hydroforming offers superior precision and uniform thickness with lower residual stresses, beneficial for complex dome geometries and specially alloys, enhancing fatigue life. Table 14: Comparison matrix for dome ends manufacturing Criterion Weight (%) Score – Spinning Weighted – Spinning Score – Hydroforming Weighted – Hydroforming Residual Stress Control 25 4 1.00 5 1.25 Grain Refinement Quality 20 4 0.80 5 1.00 Fatigue Life Potential 25 4 1.00 5 1.25 Manufacturability 15 4 0.60 4 0.60 Suitability for LH Domes 15 4 0.60 5 0.75 Total Score 100 — 4.00 — 4.85 Attachment between Sections: Friction Stir Welding (FSW) is selected for joints due to its solid-state nature, resulting in refined microstructure, high tensile strength, and superior fatigue resistance with minimal defects. While Tungsten Inert Gas (TIG) welding is common, it is more prone to defects and induces coarser grain zones and residual stresses, which may limit fatigue performance. 49 Table 15: Comparison matrix for aluminum joining Criterion Weight (%) Score – FSW Weighted – FSW Score – TIG Weighted – TIG Residual Stress Control 25 5 1.25 2 0.50 Grain Refinement Quality 20 5 1.00 2 0.40 Fatigue Life Potential 25 5 1.25 2 0.50 Manufacturability 15 4 0.60 3 0.45 Suitability for LH Joints 15 5 0.75 3 0.45 Total Score 100 — 4.85 — 2.30 Attachment to the Fuselage As previously discussed, the cylindrical section and the domes will be joined using friction stir welding (FSW) in combination with I-section circular beams. This joint configuration presents some particular considerations. The fuselage frames have a greater thickness than the tank components (both the cylindrical shell and the domes). Since FSW requires consistent thickness at the welding interface to ensure optimal joint quality, the frame geometry will incorporate a gradual thickness reduction in the welding zone to match the tank wall thickness. Furthermore, the edge of the dome is structurally critical due to the presence of geometric discontinuities, which can concentrate stresses and accelerate fatigue damage. Welding the frame directly at the dome’s termination would therefore increase stress concentrations and reduce fatigue life. To mitigate this effect, the frames are positioned slightly inward from the dome edge, closer to the cylindrical mid-section, where stress distribution is more uniform. These frames serve as the attachment interface for the I-section fuselage frames. The connection between the tank frames and fuselage structure will be realised through bolted joints to ensure structural integrity under operational loads. The detailed design of this bolted attachment lies outside the scope of the present thesis but is acknowledged as a critical step in the integration process. Summary of Preliminary Design Decisions: Table 16: Summary of Preliminary Design Decisions Feature Design Decision Tank Material Aluminum Alloy AA2219-T87 Integration Non-integral, bolted frames Insulation Multilayer Insulation (MLI) Manufacturing Cylindrical: Deep drawing Domes: Hydroforming Joints: Friction Stir Welding (FSW) 56 Figure 32: Analytical field defintion for longitudinal 9g intertial load Figure 33: Longitudinal 9g intertial load applied Figure 34: Longitudinal 9g intertial load: pressure load (PDLOAD) 57 The mentioned cases are analysed, and shown in the following pictures: a) Max VM stress: 172.10 MPa b) Max deformation: 3.58 mm Figure 35: Results under 1 load case a) Max VM stress: 191.6 MPa b) Max deformation: 4.08 mm Figure 36: Results under 2a load case a) Max VM stress: 195.5 MPa b) Max deformation: 4.18 mm Figure 37: Results under 2b load case 58 a) Max VM stress: 184.8 MPa b) Max deformation: 3.85 mm Figure 38: Results under 2c load case a) Max VM stress: 270.8 MPa b) Max deformation: 5.72 mm Figure 39: Results under 3a load case a) Max VM stress: 233.8 MPa b) Max deformation: 5.16 mm Figure 40: Results under 3b load case 59 a) Max VM stress: 204.2 MPa b) Max deformation: 4.31 mm Figure 41: Results under 3c load case Results from these analyses are summarised in the table below, showing maximum stress and deformation values per load case, providing clear insights into structural performance and critical loading conditions. Table 19: Global FEM analysis results: Von Mises stress, deformation and safety factor for different load cases Load case Maximum VM stress (MPa) Maximum deformation (mm) SF 1 172.1 3.58 1.98 2a 191.6 4.08 1.78 2b 195.5 4.18 1.74 2c 184.8 3.85 1.84 3a 270.8 5.72 1.26 3b 233.8 5.16 1.45 3c 204.2 4.31 1.67 As can be observed from the results, all calculated safety factors exceed unity, which confirms that the tank structure remains within the allowable design limits. This outcome indicates that, under the applied loading conditions, the stresses experienced by the tank do not surpass the permissible material strength, thereby ensuring structural integrity and compliance with the established safety requirements. 60 APPENDIX E: Detailed FEM This appendix provides a comprehensive description of the detailed finite element analysis conducted to investigate the behaviour of cracks in the welded joint regions of the structure. This analysis builds upon the global model, narrowing focus to critical areas where cracks may initiate and propagate, with particular emphasis on the evaluation of the Stress Intensity Factor (SIF). The detailed model was developed as a submodel extracted from the global Abaqus model, specifically targeting the welded joint area. Submodelling is a technique in Abaqus that allows the extraction of detailed stress and strain information in a localised region using boundary conditions transferred from the global model, ensuring consistency between global and local responses while managing computational cost effectively. This method requires careful alignment of the submodel with the global geometry to ensure accurate information transfer. Figure 42: Submodel from general model The submodel geometry focussed on the welded joint, which was isolated and converted into a three-dimensional solid model with a thickness of 3.5 mm, matching the shell thickness used in the global model. This consistency in thickness between the global shell model and the detailed 3D submodel prevents errors at the interface and ensures compatible boundary conditions. The welded zone was subdivided into distinct microstructural regions known to have different mechanical properties, namely: •Nugget Zone (NZ) •Thermo-Mechanically Affected Zone (TMAZ) •Heat-Affected Zone (HAZ) •Base Material (BM) 61 Figure 43: Model partition for different FSW zones This subdivision reflects the real variations in microstructure and material behaviour observed in friction stir welded joints, allowing a more accurate fracture assessment. To represent cracks, the crack size was initially defined by specifying the crack face within the submodel. The crack tip region was meshed with an increased level of detail by generating contours around the crack tip. The geometry near the crack tip was partitioned and meshed using the sweep tool to facilitate a high-quality, structured mesh that is critical for accurate fracture mechanics calculations. Figure 44: Division of crack to facilitate the meshing Material properties were assigned distinctly for each microstructural zone, reflecting their specific elastic and plastic behaviours documented in the literature for friction stir welded joints. Table 20: Mechanical properties across different weld zones Zone E (GPa) Poisson (–) J (kJ/m2) Max Principal Stress (MPa) Distance from centre (mm) NZ 70 0.33 28 295 2.75 TMAZ 70 0.33 22.5 250 5.25 HAZ 72 0.33 32 292.5 10.25 BM 72 0.33 40 477.5 — 62 In assembling the submodel, a local coordinate system was defined to ensure proper alignment with the global tank model. This alignment was confirmed by placing the submodel within the global assembly, allowing the boundary conditions and load transfer to be correctly applied. Figure 45: Submodel from general model Hexahedral (hex) elements were used for most of the model, while the crack tip and its immediate vicinity were meshed with tetrahedral elements to accurately capture singularity and stress gradients during contour integral evaluations in Abaqus. The surrounding region employed free meshing to balance mesh quality with computational efficiency. a) Detailed mesh of the crack b) Global mesh of the model Figure 46: Submodel meshing The crack definition within Abaqus employed the contour integral method, a robust technique to compute stress intensity factors that leverages a set of integral contours around the crack tip to capture the singular stress field without requiring extrapolation. The crack front and propagation direction were explicitly defined to guide the calculation of KIand facilitate potential crack growth analyses. 63 Figure 47: Contour integral: crack direction definition Boundary conditions were applied to reflect symmetry and continuity. The crack face lying on a symmetry plane was constrained in translation perpendicular to the plane, reflecting realistic structural constraints and reducing the computational domain. At the interfaces connecting the submodel to the tank model (the lateral and parallel faces adjacent to the crack), submodel constraints were imposed to restrict unwanted rigid body motions and ensure displacement compatibility with the global model. The internal surface of the model was subjected to a uniform internal pressure of 0.45 MPa, consistent with the pressurisation load used in the global analysis. Figure 48: Boundary conditions for submodel (yellow) 64 Figure 49: Boundary conditions for submodel: submodel constraints Results from the analysis revealed that the maximum KIvalues coincided spatially with the locations of maximum stress, validating the accuracy of the modelling approach. The variation of KIalong the crack front was examined across different contour layers, demonstrating the expected stability and convergence of the fracture parameter. Figure 50: Submodel results: Stress (VM) Figure 51: KIvalue along the crack contour and crack length 65 The analysis was repeated for several crack lengths, and the resulting KIversus crack length relationship was plotted to provide insight into the fracture behaviour under increasing crack sizes. Figure 52: Collected KIvalues for four different cracks This is the final graph that shows KI vs. crack length along the tank’s thickness. Figure 53: KIvs a (crack length) graph