The authors regret to inform that an error has been identified in the numerical dataset presented in the original paper (Appendix C.1) for square tubular structures. The mean force values were taken for the entire range (including the peak) instead of the plateau phase of the crushing due to a scripting error. This has an effect on some of the coefficient of determination values, error ranges in Table 2 and causes a change in the generalized equation. However, the coefficient of determination of the generalized model remains unchanged. This corrigendum presents the changes in text and the updated figures and tables. The authors would like to apologise for any inconvenience caused.

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To design crash structures for disruptive aircraft designs, it is required to have fast and accurate methods that can predict crashworthiness of aircraft structures early in the design phase. Axial crushing is one of the key energy absorbing mechanisms during a crash event. In this study, various analytical models proposed for calculation of mean crushing force for thin-walled tubular structures are compared with a database of numerical and experimental values to ascertain their accuracy. Improvements to some of the models have also been proposed. Finally a generalized model based on the studied and improved analytical models for prediction of mean crushing force for closed section thin-walled tubular structures is introduced. The generalized model demonstrates high accuracy when compared against experimental/numerical dataset as evidenced by a high coefficient of determination (R²) value of 0.97 and can therefore be used to estimate the mean crushing force for closed-section thin-walled metallic tubular structures with various cross-sectional shapes and crushing modes early in the design phase.

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Synthetic fibre-reinforced polymer composites (FRPs) have long been favored in structural engineering for their exceptional mechanical properties. However, their environmental impact due to energy intensive manufacturing, and disposal has prompted exploration into sustainable biobased alternatives such as flax FRP composites (FFRPs). While using flax fibres as composite reinforcement has lightness and damping benefits from a structural point of view, it also introduces design challenges as the complex microstructure of flax fibres and flax FRPs induces a more viscoelastic fatigue response. Therefore, prestraining and pre-creeping are proposed in this study as simple methods to improve fatigue performance by taking advantage of alignment mechanisms intrinsic to flax fibre and yarn microstructure. An experimental campaign was conducted on [0/90/0]S flax FRP laminates (hence, predominantly UD) to compare the tension-tension fatigue performance of reference specimens to pre-strained and pre-creeped specimens. It was observed that pre-straining and especially pre-creeping are effective at improving FFRPs fatigue performance with significant increase in fatigue life, increase in dynamic modulus, and decrease in accumulation of deformation (ratcheting).@en

Ageing is known to have significantly detrimental effect on mode I fatigue delamination growth (FDG) in unidirectional (UD) composite laminates. However, composite structures are usually designed with multidirectional (MD) layups, which raises the question that is it enough to only conducted fatigue delamination experiments on specimens with a UD layup. The aim of this study is therefore to explore mode I FDG in MD composite laminates with 45//45 interface after different ageing, i.e. at 70 °C 85 % relative humidity (RH) and immersion in 70 °C water bath. Fatigue delamination experiments were conducted at stress ratios R = 0.1 and 0.5. The fatigue data, interpreted via Paris-type fatigue laws, demonstrated that: (1) the change of ageing severity has no influence on mode I FDG in MD composite laminates; (2) FDG remains the same in composite laminates after different ageing, regardless of layups. In all cases, the same master resistance curves can be obtained to determine the intrinsic mode I fatigue delamination resistance of UD and MD composite laminates after different ageing. The physical reasons for these findings were discussed based on the moisture content analysis, Fourier transform infrared (FTIR) analysis, dynamic mechanical thermal analysis (DMTA), and fractographic examinations. It was found that material degradation and delamination mechanisms remain the same for UD and MD layups, as well as for 85 %RH and water bath conditioning.

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Fiber metal laminates (FMLs) have mainly been used in aerospace applications with synthetic fibers. To improve their environmental credentials and address issues regarding the end-of-life of these materials, a shift to FMLs based on natural fibers can be a promising course of action. However, regarding them as conventional FMLs overlook some of the unique benefits of natural fibers. Therefore, this study pioneers the examination of FLAx-REinforced aluminum (FLARE) for its combined impact resistance and vibration damping. Dynamic mechanical analysis and vibration beam tests demonstrate that the metallic layer predominantly influences the damping behavior of FLARE. The loss factor notably decreases with aluminum addition (by 80% compared to the flax composite), approximated via an inverse mixture rule. Low-velocity impact tests highlight the role of aluminum layers in energy absorption and the composite strength as a critical factor in impact resistance. FLARE exhibits 25% less specific energy absorption compared to its glass fiber counterpart. A quasi-static analytical model suggests the potential of FLARE for practical applications. With its balance of properties and considering its potential advantages at end-of-life, allowing recycling of aluminum, and its expected lower carbon footprint, FLARE renders potential beyond the aerospace sector, e.g., in other forms of transportation.@en

This paper aims to illustrate the effect of the impact damage on fatigue behavior of CF/PEEK-titanium hybrid laminates. To achieve this end, a fatigue life model was proposed to predict the S–N curves of the laminates at various initial impact energy levels and stress ratios based on the energy dissipation approach. The energy dissipation behavior of the laminates during fatigue loading under different experimental conditions was analyzed through a large amount of post-impact fatigue tests, and the correlation between the initial impact damage and the total fatigue dissipation energy was determined. The full-field axial strain distribution of the titanium layer on the impacted side of the laminate was characterized in terms of initial impact energy level and maximum stress using digital image correlation, and then the post-impact fatigue failure mechanism of CF/PEEK-Ti hybrid laminates was summarized. Finally, the validity of the proposed model was verified by fatigue tests under other conditions of stress ratio and impact energy level. It is worth mentioning that the proposed model is also applicable to other types of FMLs, and can accurately predict the residual fatigue life of laminates after impact with only one set of S–N curve data.

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Methods based on fracture mechanics have been widely used in fatigue delamination growth (FDG) characterization of composite laminates. These methods are based on the similitude hypothesis. It is therefore important to have appropriate parameters to well represent the similitude, which is useful for fatigue delamination test standard development aimed by Technical Committee 4 of the European Structural Integrity Society (ESIS TC4) and the ISO/TC61/SC13. In the present study, discussions on similitude parameters for fibre-bridged fatigue delamination interpretation have been conducted via fatigue data with fibre bridging at different R-ratios. The results clearly demonstrate that the strain energy release rate (SERR) indeed applied around the crack front, rather than the total applied SERR, should be employed to represent the similitude for FDG interpretation with large-scale fibre bridging. Particularly, the use of Δ√G_tip can well determine fibre-bridged delamination behavior of a given R-ratio, but it is not valid for FDG at different R-ratios in accordance with the similitude principles. A new similitude parameter, in terms of both Δ√G_tip and the maximum SERR G_{max_tip}, was therefore proposed to appropriately represent FDG behavior with fibre bridging at different R-ratios. This study can not only provide database, but also give important insights for the development of mode I fatigue delamination test standard of composite laminates.

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The development of bio-based fibre-reinforced polymer composites (FPRs) has accelerated in recent years aiming at replacing synthetic FRPs in primary structures. Comparative case studies on biobased fibres (such as flax and hemp) indicate their potential to replace synthetic glass and carbon fibres in certain FRP structures as more sustainable and environmentally friendly alternatives. In those studies, the effects of in-situ hygrothermal conditions on the physical and mechanical performance of the natural fibre composites were generally overlooked, however, due to hygroscopicity of lignocellulosic natural fibres, flax fibre composites mechanical response is sensitive to its environmental temperature and relative humidity. To quantify and understand the effects of in-situ hygrothermal conditions on flax FRP composite, a quasi-static tensile testing campaign was conducted at various temperatures and relative humidities. Glass and flax FRP laminates were tested in cross-ply and angle-ply configurations. It was observed that the strength and stiffness of cross-ply and angle-ply FFRP laminates were significantly affected by relative humidity contrary to GFRP counterparts. All laminates exhibited strength and/or stiffness variation with temperature that can be attributed to the sensitivity of the common epoxy matrix. However, a distinct difference was observed between the flax and glass cross-ply laminates with the modulus of the flax FRP being highly affected by temperature and relative humidity while the glass FRP modulus was unaffected.@en

Carbon emissions from commercial aircraft are expected to reach more than twice as much as the current levels by 2050. Unconventional aircraft, such as the Flying-V, are projected to achieve more than 20% fuel savings when compared to conventional configurations. However, these unconventional aircraft configurations pose a unique set of design challenges, being one of them the crashworthiness of wing-fuselage structures, which have an oval-shaped cross section that leads to a significant reduction in space underneath the cabin floor. Evaluating the feasibility of a design early in the design phase is vital to avoid cost overruns and minimize the need for drastic design changes. For assessing crashworthiness early in the design phase, the development of low-fidelity models is an attractive as well as a viable option because these models offer both low computational cost and the capability to conduct parametric studies on the crash structure. To develop and implement such low-fidelity models, we propose to explore the analytical modeling of various energy-absorbing mechanisms, namely axial crushing, plastic bending, and joint failure. In the present study, we present the modelling of plastic bending for beam-like structural members. We also present an envisaged method applying user-defined elements to simulate plastic bending in structural members for cases where the location of plastic hinges cannot be predetermined.@en

In this study, a novel experimental approach was devised to investigate shear dominant and combined opening-shear planar delamination behaviours in composite laminates subjected to quasi-static out-of-plane loading. The patterns of planar delamination growth were depicted through different inspection techniques, including digital image correlation (DIC), C-scan, and microscopic observation. The artificially embedded delamination propagated in the direction parallel to the fibre orientation of the layer above the mid interface, but migrated to an upper interface in the direction transverse to the directing ply. A continuous stiffening process was recognized with increasing delamination area. Furthermore, a numerical analysis based on virtual crack closure technique (VCCT) indicated that the local mode II was dominant for delamination growth, while the local mode III triggered delamination migration.

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Vacuum-insulated, all-composite hydrogen storage vessels are promising for achieving viable gravimetric and volumetric efficiencies in aviation applications. However, stress concentrations arise due to the connections between the composite shells and to the surrounding structure. This study develops analytical models which capture the stress state of composite cylinders subjected to pressure loading and discrete in-plane edge loads. The models allow for easy adjustments in tank geometry, lamination, and load introduction parameters, including the number and width of connection points. This aids in the preliminary structural and thermal analysis of composite hydrogen storage vessels, pushing the implementation of hydrogen as a sustainable fuel for aviation. @en

Biobased fibre-reinforced polymer (FRP) composites, consisting of natural lignocellulosic fibres such as flax or hemp, are great alternatives to synthetic fibres to mitigate the environmental impact of high-performance composites in engineering structures. Natural fibres such as flax have damping and specific mechanical properties suitable to potentially replace glass fibres in FRP composites in engineering structures. However, structural design with flax FRPs can be challenging for engineers due to their rather peculiar mechanical responses thanks to the complex multi-scale microstructure of the flax fibres. In particular, flax FRP composites have shown large ratcheting (accumulation of plastic deformation) and stiffness increase when subjected to tensile fatigue loading. Therefore, this paper proposes a novel yet simple 'pre-straining' method as a promising strategy for improving the fatigue response of flax FRP, to potentially replace synthetic glass FRP in various engineering structures. To this end, cross-ply flax, and glass FRP composite laminates were manufactured and subsequently tensile-tensile fatigue experiments were performed. It was observed that pre-straining of flax FRP composite coupons can improve their mechanical performance by increasing stiffness and reducing ratcheting during fatigue which is attributed to further alignment of the fibres within the twisted yarns, as well as possible microfibril alignment. The pre-straining of glass fibre reinforced composites samples did not lead to any remarkable reduction in ratcheting nor increase in stiffness. @en

Temperature can significantly affect fatigue delamination growth (FDG) behavior in composites, while fiber bridging has been frequently reported during FDG. The focus of this study was therefore on investigating temperature effects on FDG behavior with fiber bridging. Mode I fatigue delamination experiments were conducted on a thermoset composite laminates M30SC/DT120 at different temperatures. The Paris relation and fatigue resistance curve (i.e. fatigue R-curve) were used to interpret bridging effects on FDG behavior and to explore temperature effects on fiber bridging development. A modified Paris relation was employed to determine the effects of temperature on the intrinsic FDG behavior at the crack front excluding fiber bridging. The Paris interpretations clearly demonstrate that fiber bridging can significantly retard FDG behavior at different temperatures. Temperature can have different effects on fiber bridging development and the intrinsic FDG behavior. Particularly, elevated temperature can promote more bridging fibers, whereas decreased temperature has negligible influence on fiber bridging. When looking at the intrinsic delamination resistance, mode I FDG can accelerate at elevated temperature but decrease at freezing temperature. Fractographic examinations indicate that fiber/matrix interface debonding is the dominant damage mechanism in mode I FDG at different temperatures. Elevated temperature can lead to the weakening of interface adhesion, contributing to faster intrinsic mode I FDG behavior and more fiber bridging development. And a semi-empirical fatigue model based on normalization was finally proposed to determine mode I intrinsic FDG behavior at different temperatures for engineering applications.

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Improvements in current design approaches require further studies of the damage interaction effects of composite materials subjected to repeated out-of-plane concentrated loads. To that end, a combined simulation and experimental investigation on composite laminate under repeated indentations is reported. The repeated indentations consist of seven identical peak-force indentations that are separately applied to the centre of the laminate. The results show that delaminations grow in all seven indentations, which can be interpreted as a continuous degradation of the effective delamination growth threshold with each subsequent indentation. More specifically, the second indentation effective delamination growth threshold is 62.4 MPa, which is about 19 % lower compared to the first one (77.2 MPa). Subsequently, the delamination growth threshold degraded approximately linearly with indentation. This effective delamination growth threshold reduction can be associated with the occurrence and evolution of the crack-rich zone preceding the delamination front.

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Hydrogen is being investigated as aviation fuel, with the objective to achieve an energy transition for the aviation sector. Effective storage solutions are crucial to mitigate the aerodynamic penalty caused by its low volumetric energy density. The focus of this study is the integration of a cryo-compressed vacuum-insulated storage vessel into the primary structure of aircraft, aiming to enhance structural efficiency. This is achieved by implementing analytical methods to analyse the thermo-mechanical loading of the inner and outer walls of the fuel tank. It is envisioned that the inner wall rather than the outer wall is more suitable to sustain additional loads. However, it is unclear how the cryogenic environment affects the stress state of the composite material.

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Fatigue delamination growth (FDG) is an important failure in composite structures during their long-term operations. Hygrothermal aging can have significant effects on interlaminar resistance. It is therefore really necessary to explore FDG behavior in composite laminates with hygrothermal aging. Dynamic mechanical thermal analysis (DMTA), mode I FDG experiments and fractographic examinations were conducted to fully investigate hygrothermal aging effects and the corresponding mechanisms on FDG behavior. The DMTA results indicated that environmental aging can induce obvious T_g decrease. Mode I experimental fatigue data interpreted via different Paris-type correlations demonstrated that: Bridging has obvious retardation effects on FDG behavior via the Paris interpretations; The modified Paris relation can well characterize the intrinsic FDG behavior around the crack front; The use of the two-parameter Paris-type relation can appropriately account for R-ratio effects, contributing to a master resistance curve in determining mode I FDG behavior. According to these interpretations, it can be concluded that hygrothermal aging can have adverse effects on mode I FDG behavior. SEM examinations demonstrated that moisture absorption can cause fibre/matrix debonding and resin matrix pores/voids in the composite. However, no obvious difference in damage mechanisms was identified in mode I fatigue delamination for composite with/without environmental conditioning. Both fibre/matrix debonding and matrix brittle fracture were identified on fatigue fracture surfaces. Accordingly, it was concluded that fibre/matrix interface and matrix degradation induced by water absorption were the main reasons for a faster mode I fatigue crack growth in environmental aged composite.

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Interlaminar crack propagation in layered materials, such as composites, is still a not fully understood phenomenon in fracture mechanics. Experimental observations reveal a broad spectrum of crack propagation velocities during the interlaminar fracture of layered materials under varying loading conditions and rates. While there have been numerous studies examining interlaminar crack propagation under quasi-static, fatigue, and more recently, high-speed loading, there has been a notable lack of endeavors to present and interpret crack growth data within a unified framework. To this direction, we present a new interpretation of interlaminar crack propagation data acquired from a broad test campaign under various mode-I loading conditions (quasi-static, fatigue and high-speed). We connect the crack tip velocity to the rate of change of the SERR to propose a new equation/model that shows potential in presenting and explaining the variety of experimental crack growth data. This correlation arises from a simple mathematical analysis of the rate of change of the SERR using the chain differentiation rule. Subsequently, it is further substantiated by experimental evidence, in an effort to accommodate results from various experiments under a unified description. A robust correlation of the test data is established through a range of slopes which are proven -experimentally- to be characteristic constants of the mode-I interlaminar fracture of a specific material system.

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For the past few decades, research into fatigue delamination behaviour of Carbon Fibre Reinforced Polymer (CFRP) composites has predominantly relied on standard test methods. These methods typically utilize a uniaxial delamination length to quantify the fatigue delamination process. However, this approach is inadequate to describe the nature of delamination growth in a planar manner. In this work, an experimental study was conducted to gain insights into the planar delamination behaviour of CFRP composites under mode II fatigue loading. Delamination growth of two specimen configurations, each containing an embedded initial defect, was monitored through ultrasound scanning (C-scan). During load-control fatigue testing, the growth rate exhibited an initial rise, followed by a subsequent decrease as loading cycles increased. Despite the development of a larger delamination area under fatigue loading, a consistent overall stiffness was observed. Fractography revealed the presence of various fracture mechanisms ocurring at different locations near the initial delamination front. Micro matrix cracking and fibre-matrix debonding emerged as dominant mechanisms in 2D fatigue delamination growth following the fibre direction. Matrix cracking within the laminate ply occurred at the locations where the growth direction deviated from the fibre direction, consequently triggering delamination migration. @en

Hygrothermal ageing has detrimental effect of the fatigue delamination growth (FDG) in carbon fibre reinforced polymer laminates, and may increase the crack growth rate by a factor of ∼5. The paper examines, how this degradation for Mode I fatigue delamination is affected by the severity of the ageing conditions. Fatigue delamination tests for R = 0.1 and R = 0.5 are conducted after ageing (1) at 70 °C 85 % relative humidity (RH) and (2) immersion in 70 °C water bath (WB). Paris-type FDG characterisation is derived, in the form, which accounts for the effect of fibre bridging. It is demonstrated that parameters of FDG degradation do not differ for these two types of hygrothermal ageing. The physical reasons for this are examined using dynamic mechanical thermal analysis (DMTA) and fractographic analysis, which revealed similar irreversible degradation of the material near the fibre/matrix interface and in the matrix itself, and the similar damage mechanisms in fatigue delamination. Furthermore, this study can highlight the importance of obeying similitude principles in FDG characterisation, and provide extra information for the ISO standard development for mode I fatigue delamination in unidirectional carbon fibre reinforced polymer composites.

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