© The Author(s) 2021.In this article, the structural behavior of co-cured composite joint (CC), co-bonded composite joint (CB), and secondary-bonded composite joint (SB) under Mode II fatigue loading was evaluated. Fatigue performance was evaluated in sub-critical strain energy release rate (SERR) associated with Mode II fatigue induced delamination growth onset. Fatigue tests were carried out using the three-point bending End Notched Flexure test setup for different energy ratios. The experimental results are presented in terms of SERR versus number of cycles, and the SERR threshold for no growth is determined (Gth). Fractographic analyses were performed in order to identify the main failure mechanisms related to each joining technology under Mode II. The results indicated an initial cohesive failure followed by an adhesive failure promoted by crack propagation at the interface between the adhesive and the composite adherend on SB and CB samples, through the coalescence of microcracks that promote the adhesive failure process, leading to fiber pull-out from the matrix and cusps formation in the fracture surface. These results explain the low performance behavior observed on SB and CB bonded techniques. It is worth mentioning that the results and behavior observed in this work are valid only for the laminates, adhesives, surface treatment, and environmental conditions tested herein.

© 2021 Elsevier LtdMode I delamination fatigue crack growth behavior was investigated in a carbon-epoxy prepreg fabric laminate by evaluating the mean load effects. The fatigue crack growth rate was determined as a function of the maximum Mode I strain energy release rate considering an exponential fitting function according to the Compliance Based Beam Method (CBBM). Classical data reduction techniques were combined with the proposed method, indicating less scatter on results and satisfying basic assumptions of smoothness and continuity for the fatigue crack growth process. The delamination growth rate curve proved to be strongly affected by the applied mean load as the fatigue onset delamination. The number of cycles to onset is higher for lower load levels and, considering the stable propagation region, a higher delamination growth rate was reported for higher load levels. The fractographic analysis has confirmed the effects of cyclic loading and the mean load levels on fracture surfaces. For a higher mean load, failure mechanisms expose static aspects and substantial presence of microcracks at fiber imprints, while, under lower mean load were noticed significant wear and plasticity and featureless fiber tracks.

© 2020Aeronautic structures are exposed to a great variety of temperatures and humid environments during service. Nowadays, it is known that the combined influence of moisture and temperature induces further detrimental effects on the fatigue behavior of bonded joints when compared to the influence of each isolated condition. The effect of hygrothermal pre-conditioning on the fatigue delamination growth onset of different bonded technologies was investigated. This paper provides a material database for composite-joints tested under different environments and gives important insights on the failure mechanisms observed under cyclic loadings. This information can be latter used to validate analytical and numerical models.

© 2020 Elsevier LtdAdhesively bonded composite structures, if designed properly, have proven to be stiffer and to possess a higher specific strength than their mechanically fastened counterparts. To increase the applicability of these bonded joints in the aircraft industry, a study was performed to investigate the influence of hygrothermal aging on co-bonded composite stiffened panels with an initial disbond under cyclic compression loading. Experiments showed that hygrothermal aging led to a decrease in disbond growth throughout cyclic loading. The decreased disbond growth was likely caused by the increased ductility of the bond due to the presence of moisture. A higher ductility can lead to crack blunting and stress relaxation, resulting in higher fracture toughness of the bond. Furthermore, it was shown that hygrothermal aging did not influence the residual strength and stiffness of the panels after cyclic loading. The experiments were simulated numerically to gain a better understanding of the crack growth behavior and to aid future numerical crack growth predictions.

© 2020, The Brazilian Society of Mechanical Sciences and Engineering.A constitutive damage model is proposed in order to investigate the crushing response of 0 ∘ plies composite laminates, using a VUMAT subroutine implemented in ABAQUS/Explicit. This damage model predicts five failure mechanisms commonly observed in unidirectional carbon fibre-reinforced composite structures: fibre failure in tension, fibre failure in compression, matrix cracking in tension, matrix cracking in compression and in-plane shear failure. Its formulation is based on an energy framework which combines stress-based fracture mechanics and damage mechanics approaches within a unified way, enabling the prediction of the five failure mechanisms aforementioned in terms of damage initiation and damage propagation. In this work, a new strategy is also implemented to remove fully damage elements in order to ensure numerical stability and avoid element distortion problems. An experimental test campaign is proposed for verification of the numerical models. Preliminary results have shown a fairly good correlation between numerical predictions and experimental results for wedge-shaped tip composite laminates.

© 2020, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Glare reinforcements have been adopted in the aeronautics industry to improve fatigue performance of structural components. Glare can be applied on early stages of the project’s design or used as temporary repairs, bonded on monolithic aluminum panels to improve crack retardation. In this work, experimental tests and verified numerical models are used to analyze the crack propagation in hybrid aeronautical structures. A Glare panel bonded to a monolithic aluminum plate with an initial crack, both with the same thickness, is tested under Mode I cyclic loading and fatigue crack propagation is measured. In order to optimize the reinforcement effect of Glare on monolithic aluminum structures, a parametric analysis is performed using verified numerical models, with different monolithic aluminum and Glare thicknesses ratio. The numerical results indicate that, for short cracks, a thinner Glare reinforcement results in a greater fatigue life. On the other hand, thicker Glare reinforcement leads to better results for long cracks. It is concluded that the damage tolerance requirements shall guide the definition of the ratio between plate and Glare thicknesses.

© Springer Nature Switzerland AG 2020.This paper presents a novel damage mechanics based failure model enabling the prediction of low cycle fatigue life and residual strength of isotropic structures under multiaxial loading. The approach herein proposed does not discretize every load cycle but instead takes an envelope loading whereby the numerical load remains constant at a maximum load level and the number of cycles is obtained from a given elapsed time defined within a pseudo-time framework. The proposed formulation is based on the smeared cracking approach accounting for damage propagation due to static and fatigue loadings, where the static component is based on the Von-Mises yield criterion and Prandtl-Reuss stress flow rule; whereas the crack propagation in cyclic loading component is based on the Paris-law. Furthermore, the formulation combines damage mechanics and fracture mechanics within a unified approach enabling the control of the energy dissipated in each loading cycle.

© 2019 Society of Plastics EngineersAn experimental investigation of mode-I translaminar fracture toughness and fatigue crack growth behavior of a carbon fiber-epoxy plain weave laminate manufactured by resin infusion under flexible tooling (RIFT) is presented in this article. Pre-cracked compact tension (CT) specimens were used to perform both quasi-static and fatigue tests. Different data reduction techniques for fracture toughness calculation were used and compared with each other. The ASTM E399 test method was modified to account for the material orthotropy and specimen geometry effects using a correction function based on a numerical evaluation of the strain energy release rate. The proposed modification shows good agreement against other experimental methods found in the literature and its application was validated for fatigue tests. Fatigue testing shows that failure in undesired modes is likely to occur prior to translaminar fracture, which was attributed to a higher tensile fatigue threshold than compression or shear fatigue threshold presented by the composite in analysis. Increasing the specimens’ initial notch length was a solution for avoiding these types of failure. The experimental results were compiled in the form of a Paris curve, and their particularities were discussed. A fractographic analysis was carried out to define damage patterns and its evolution process in both types of tests. POLYM. COMPOS., 40:3791–3804, 2019. © 2019 Society of Plastics Engineers.

© 2019 Elsevier LtdConsidering the design of aerospace structures, an experimental campaign is essential for validating the sizing methodology and margins of safety. Particularly for buckling-critical cylindrical shells, the traditional buckling test could lead the specimen to permanent damage. Therefore, the validation of nondestructive experimental procedures for estimating the buckling load of imperfection-sensitive structures from the prebuckling stage is receiving more attention from the industry. In this context, this paper proposes an experimental verification of the robustness of a vibration correlation technique developed for imperfection-sensitive structures. The study comprises three nominally identical unstiffened composite laminated cylindrical shells. Each specimen is tested 10 times for buckling at DLR and, the reproducible results — within a small range of deviation between them — corroborate the equivalence of the cylinders. For the robustness assessment of the vibration correlation technique, two different buckling test facilities are considered. Furthermore, the material properties are recalculated through composite composition rules and the influence of enhanced theoretical buckling loads on the VCT predictions is verified. The experimental campaigns corroborate that the vibration correlation technique provides appropriate estimations representing the influence of the different test facilities; moreover, enhanced theoretical buckling loads can improve the predictions for some of the test cases.

© 2018 Society of Plastics EngineersAdhesive joints are being more extensively applied in the aeronautical industry, allowing for better integration between the structural parts and overall lower weight if compared with joints made with fasteners and rivets. However, a further evaluation of these new technologies is needed, once their critical fracture toughness under different environmental conditions is still unknown and this value is essential for design and certification of aircraft manufactured with these materials. Thus, this work focuses on the mode II fracture toughness characterization of carbon fiber composite laminates joined by co-bonded (CB) and secondarily bonded (SB) techniques, using EA 9695 epoxy adhesive aged at different environmental conditions (room temperature ambient—RTA and elevated temperature wet—ETW). Dynamic mechanical analysis (DMA) was used to understand the effect of moisture absorption on the glass transition of materials and on the decreasing of Mode II fracture toughness after aging. The DMA results showed a reduction of 11% in Tg values for the GIIc values of ETW samples in comparison with specimens tested at RTA condition. Reductions about 92 and 94% in Mode II fracture toughnesses were obtained for CB and SB aged specimens, respectively when compared with the toughness values obtained for specimens tested at RTA. Further inspection of the fracture surfaces using scanning electron microscope proved that light fiber-tear fracture occurred at both RTA and ETW conditions for CB joints, while fracture was mainly light-fiber-tear at RTA condition, becoming mostly cohesive after aging for SB joints. POLYM. COMPOS., 40:3220–3232, 2019. © 2018 Society of Plastics Engineers.

© 2019 Elsevier LtdThis paper presents an analytical and numerical investigation of the relationship between the compressive load level and the natural frequency variation toward a vibration correlation technique for the buckling load calculation of imperfection-sensitive isotropic cylindrical shell structures. Firstly, a back-to-basic s study is proposed and the linear equation between the applied load and the square of the loaded natural frequency is revisited. Such review considers the Flügge-Lur'e-Byrne's linear shell theory for the free vibrations of an isotropic unstiffened cylindrical shell under uniform axial loading. The demonstrated linear equation is rearranged for expressing the square of the applied load as a quadratic function of the square of the loaded natural frequency. The suggested formulation provides the analytical support to a novel vibration correlation technique that has been empirically proposed and experimentally validated for unstiffened cylindrical shells. Aiming a numerical verification based on finite element models, two cylindrical shells are defined. At first, the critical buckling load and the fundamental natural frequency for different load levels are determined and compared to the analytical results for validation of the numerical models. The finite element models are extended considering geometric nonlinearities, more realistic boundary conditions and three magnitudes of a benchmark measured initial geometric imperfection. The numerical results are considered for analyzing the variation of the natural frequency in the surroundings of buckling and for verifying the vibration correlation technique.

© 2019 Elsevier LtdTraditional buckling experiments of imperfection-sensitive structures like cylindrical shells can cause the permanent failure of the specimen. Nevertheless, an experimental campaign is crucial for validation of the design and numerical models. There is, therefore, interest in nondestructive methods to estimate the buckling load of such structures from the prebuckling stage. The vibration correlation technique allows determining the buckling load without reaching the instability point. Recently, a novel empirical vibration correlation technique based on the effects of initial imperfections on the first vibration mode demonstrated interesting results when applied to composite and metallic unstiffened cylindrical shells. In this context, this paper explores this novel approach for determining the axial buckling load of a metallic orthotropic skin-dominated cylindrical shell under internal pressure, which represents a simplified downscaled model of a launcher propellant tank. An experimental campaign consisting of buckling tests and noncontact vibration measurements for different axial load levels is conducted considering the specimen without and with three different internal pressure levels. The experimental results validate the above-mentioned vibration correlation technique for determining the axial buckling load of pressurized cylindrical shells. Moreover, finite element models are calibrated in order to evaluate the frequency variation within a broader and dense range of the axial loading leading to an assessment of the considered maximum load level and number of load steps as related to the deviation of the estimation. The results corroborate the applicability of the vibration correlation technique as a nondestructive experimental procedure to assess the axial buckling load of imperfection-sensitive orthotropic skin-dominated cylindrical shells under internal pressure.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.Static line parachuting is an important technique for deploying large amounts of troops on the battlefield. The static line ties the parachute deployment bag to the aircraft; when the paratrooper jumps, the static line tightens, removing the parachute deployment bag and releasing the canopy. One of the failure modes for static line parachuting is the towed paratrooper scenario, which consists in the paratrooper being pulled by the aircraft through its static line and consequently experiencing high force levels. It is necessary to check if the paratrooper’s physical integrity is guaranteed for the entire static line parachuting operational envelope in case of a towed paratrooper incident. A numerical analysis of the towed paratrooper scenario is elaborated to meet that end, providing the means to check how the static line material and length, the paratrooper weight and the aircraft speed affect the maximum load experienced by the paratrooper. Simulation results show that there are mass values inside the operation envelope leading to impact loads surpassing the human body injury threshold and the estimated tensile strength of type VIII webbing static lines. In conclusion, one should be cautious when raising the payload for static line paratroopers, and the force transmission from the paratrooper harness to the paratrooper body should be evaluated.

© 2018 Elsevier LtdThis work focuses on Mode I fatigue induced delamination growth onset characterization of co-cured (CC), co-bonded (CB) and secondary bonded (SB) composite joints with an epoxy interleaf. The CC joints used in this work comprise only fibers and resin, while, CB and SB joints contain an adhesive film. Experimental tests were carried out at room temperature using double cantilever beam (DCB) specimens. The delamination behavior was evaluated in terms of the strain energy release rate (SERR) considering a no-growth criterion based on 106 cycles without crack propagation. For Mode I cyclic loading, the threshold values of the CB and SB joints were about 2.5 times higher than the one achieved by the CC joints, presenting a better performance in terms of fatigue delamination growth-onset. A fractographic study was conducted using scanning electron microscopy in order to relate the SERR results with the joint′s failure mechanisms. It was observed that there is a good mechanical compatibility between the substrate and adhesive in the CB and SB joints studied herein. The results found in this paper indicated that the Mode I SERR threshold values were not significantly affected by the interleaf.

Copyright © 2018 by the International Astronautical Federation (IAF). All rights reserved.The critical failure criterion for the design of primary launch vehicle's structures, which can be regarded as orthotropic shells, is predominantly buckling. As consequence, there is interest for a proper nondestructive method to estimate the buckling load from the prebuckling state of such structures. The vibration correlation technique allows determining the actual buckling load of the structure without reaching the instability point by loading the specimen at different axial load steps. At each load step, a vibration test is made and the natural frequencies are measured. A relationship between a natural frequency of the loaded structure and the axial load level can be identified and extrapolated to estimate the actual buckling load of the structure. This paper exploits and validates an analytical formulation for the free vibration of pressurized axially loaded orthotropic cylindrical shells towards an analytically verified vibration correlation technique. The effects of the axial loading can be split into contributions due to constant pressure level (1) and due to axial compression (2). This procedure allows expressing the square of the applied load as a quadratic function of the squared loaded natural frequency. The proposed study considers an orthotropic metallic cylindrical shell structure, which represents a simplified downscaled model of a launch vehicle's propellant tank. A detailed numerical model accounting for geometrical nonlinearities effects associated with measured initial imperfections verifies both the analytical equations and the vibration correlation technique. The results are validated with experimental measurements and corroborate the applicability of the vibration correlation technique as a non-destructive experimental procedure to assess the buckling load of imperfection sensitive orthotropic cylindrical shells with or without internal pressure.

Copyright © 2017 Eduards Skukis et al.Applicability of the vibration correlation technique (VCT) for nondestructive evaluation of the axial buckling load is considered. Thin-walled cylindrical shells with and without circular cutouts have been produced by adhesive overlap bonding from a sheet of aluminium alloy. Both mid-surface and bond-line imperfections of initial shell geometry have been characterized by a laser scanner. Vibration response of shells under axial compression has been monitored to experimentally determine the variation of the first eigenfrequency as a function of applied load. It is demonstrated that VCT provides reliable estimate of buckling load when structure has been loaded up to at least 60% of the critical load. This applies to uncut structures where global failure mode is governing collapse of the structure. By contrast, a local buckling in the vicinity of a cutout could not be predicted by VCT means. Nevertheless, it has been demonstrated that certain reinforcement around cutout may enable the global failure mode and corresponding reliability of VCT estimation.

© 2017 World Scientific Publishing Company.The present paper describes a numerical modeling approach to predict impact resistance and residual Shear Strength After Impact (SSAI) of fiber reinforced polymer composites subjected to bird strike loading. An improved damage mechanics based on material model, previously developed by the authors, is combined with an equation of state to simulate the progressive failure in composite aerostructures subjected to bird strike loading. A series of bird strike impacts on flat panels fabricated from low cost woven glass composite materials are used to validate the material model for practical composite component applications. A numerical study on the residual SSAI of a typical composite shear web is also presented. The panels are modelled with shell elements only. The proposed material model formulation accounts for the strain rate enhancement to strength and shear nonlinearities observed in composite materials. A hydrodynamic model for the bird, based on 90% water and 10% air, is derived to represent the behavior of the bird for all impact scenarios considered. The bird is heterogeneous in nature. However, a uniform material behavior is assumed with a geometry based on a 2:1 length to diameter ratio with a cylindrical body and spherical end caps using Lagrangian mesh. Appropriate contact definitions are used between the bird and the composite panel. The simulations results are compared to experimental results and conclusions drawn.

© 2017 Universidade Federal de Sao Carlos. All rights reserved.Aiming to reduce aircraft weight, aeronautic industry seeks alternative materials and processes used to join its different structural parts. An option to traditional methods are high performance adhesive joints, which reduce weight, number of parts and component final cost, also resulting in higher strength structures. Although, the lack of experimental data to provide a detailed structural characterization of these joining techniques had limited their commercial application. The proposal of this work is to investigate the Mode I interlaminar fracture toughness under quasi-static loading using DCB specimens of carbon composite joints made by co-bonding and secondary bonding techniques, the latter giving more reliable results. For a better understanding on the failure in the systems, DSC and microscopy techniques were applied, from which three stages of delamination process during testing were observed: 1st Stage) Cohesive failure represented by an unstable crack propagation from a high energy level; 2nd Stage) transition from cohesive to adhesive and final intralaminar failure mode with lower energy levels than Stage 1; and 3rd Stage) completely stable propagation at low energy levels (delamination migrates from intralaminar to interlaminar, entirely in the substrate).

© 2017 The Authors.Non-destructive methods to estimate the actual buckling load in particularly for imperfection sensitive thin-walled structures, are of severe interest among many fields. Particular techniques for validation of structural limit state and numerical model predictions for large scale structures are getting momentum. The vibration correlation technique (VCT) allows to correlate the ultimate load our instability point with rapid decrement of self-frequency response. Nevertheless this technique is still under development for thin-walled shells and plates. The current research discusses an experimental verification of extended approach, using vibration correlation technique, for the prediction of actual buckling loads on unstiffened cylindrical shells loaded in axial compression. Validation study include two laminated composite cylinders which were manufactured and repeatedly loaded up to instability point. In order to characterize a correlation with the applied load, several initial natural frequencies and mode shapes were measured during tests by 3D laser scanner. Results demonstrate that proposed vibration correlation technique allows one to predict the experimental buckling load with high reliability, without actually reaching the instability point. Additional experimental tests and numerical models are currently under development to further validate the proposed approach to extended composite and metallic structures.

© 2016, Springer Science+Business Media Dordrecht.Buckling is a critical failure phenomenon for structures, and represents a threat for thin shells subjected to compressive forces. The global buckling load, for a conical structure, depends on the geometry and material properties of the shell, on the stacking sequence, on the type of applied load and on the initial geometric imperfections. Geometric imperfections, occurring inevitably during manufacturing and assembly of thin-walled composite structures, produce a reduction in the carrying load capability with respect to the design value. This is the reason why investigating these defects is of major concern in order to avoid over-conservative design structures. In this paper, the buckling behavior a conical structure with 45° semi-vertical angle is numerically investigated. The initial imperfections are taken into account by using different strategies. At first, the Single Perturbation Load Approach (SPLA), which accounts for defects in the form of a lateral load, normal to the surface, has been adopted. Then, the actual measured defects have been applied to the structure by using the Real Measured Mid-Surface Imperfections (MSI) approach. Investigations on cylindrical shells using the first strategy have already shown the occurrence of a particular phenomenon called “local snap-through”, which represents a preliminary loss of stiffness. In order to better understand this phenomenon for conical shells, both the aforementioned techniques have been used to provide an exhaustive overview of the imperfections sensitiveness in conical composite shells. This study is related to part of the work performed in the frame of the European Union (EU) project DESICOS.

© 2014, Springer Science+Business Media Dordrecht.Thin-walled cylindrical composite shell structures can be applied in space applications, looking for lighter and cheaper launcher transport system. These structures are prone to buckling under axial compression and may exhibit sensitivity to geometrical imperfections. Today the design of such structures is based on NASA guidelines from the 1960’s using a conservative lower bound curve generated from a database of experimental results. In this guideline the structural behavior of composite materials may not be appropriately considered since the imperfection sensitivity and the buckling load of shells made of such materials depend on the lay-up design. It is clear that with the evolution of the composite materials and fabrication processes this guideline must be updated and / or new design guidelines investigated. This need becomes even more relevant when cutouts are introduced to the structure, which are commonly necessary to account for access points and to provide clearance and attachment points for hydraulic and electric systems. Therefore, it is necessary to understand how a cutout with different dimensions affects the buckling load of a thin-walled cylindrical shell structure in combination with other initial geometric imperfections. In this context, this paper present some observations regarding the buckling load behavior vs. cutout size and radius over thickness ratio, of laminated composite curved panels and cylindrical shells, that could be applied in further recommendations, to allow identifying when the buckling of the structure is dominated by the presence of the cutout or by other initial imperfections.

© 2015 Elsevier Ltd. All rights reserved.Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells. This paper presents and discusses an experimental and numerical validation of a novel approach, using the vibration correlation technique, for the prediction of realistic buckling loads on unstiffened cylindrical shells loaded in compression. From the experimental point of view, a batch of three composite laminated cylindrical shells are fabricated and loaded in compression up to buckling. An unsymmetric laminate is adopted in order to increase the sensitivity of the test structure to initial geometric imperfections. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation, without actually reaching the instability point. Furthermore, a series of numerical models, including non-linear effects such as initial geometric and thickness imperfection, are carried-out in order to characterize the variation of the natural frequencies of vibration with the applied load and compare the results with the experiment findings. Additional experimental tests are currently under development to further validate the proposed approach for metallic and balanced composite structures.

© 2014, Springer Science+Business Media Dordrecht.Since the development of the first theories to predict the buckling induced by axial compression in shells sensitive to imperfections, a significant discrepancy between theoretical and experimental results has been observed. Donnell and Koiter are among the first authors demonstrating, for these structures, the relevant influence of the geometrical imperfections on the reduction of the buckling load. Currently, the preliminary design of imperfections sensitive shell structures used in space applications is carried out according to the NASA SP-8007guideline. However, several studies have proven that this guideline leads to over-conservative design configurations when considering the geometrical and material imperfections existing in real cones. Since the pioneer work of Arbocz, alternative methods have been investigated to overcome this issue. Among the different approaches, in this paper, the Single Perturbation Load Approach (SPLA), originally developed byHühne as a deterministic way to calculate the knock-down factor of imperfection sensitive shells, is further studied. Indeed, a numerical investigation about the application of the SPLA to the simulation of the mechanical behavior of imperfection sensitive composite conical structures under axial compression is presented. This study is related to part of the work performed in the frame of the European Union (EU) project DESICOS.

© 2015 Elsevier Masson SAS. All rights reserved.This paper presents a detailed investigation on the post-buckling behaviour of adhesively bonded stiffened panels subjected to in-plane shear loading. An experimental programme was carried to determine the buckling load, buckling shape, collapse load and failure modes of two bonded stiffened panels. A nonlinear finite element based modelling approach, accounting for geometrical and material nonlinearities as well as progressive failure in the adhesively bonded interface between the skin and the stiffener is proposed to predict the structural behaviour of the panels up to failure. This approach consists in modelling the bonded interfaces using a newly developed cohesive zone based constitutive damage model. In order to account for damage in the stiffener and the skin a Von Mises based constitutive damage model is also formulated and presented in the paper. Both constitutive models were implemented into ABAQUS/Explicit finite element code as user-defined material models. A very good agreement between experimental results and numerical predictions is obtained using the proposed modelling approach, with deviations smaller than 8% in buckling load and bonded interface failure load onset.

© 2015 International Committee on Composite Materials. All rights reserved.With the evolution of composite materials and moreover of the manufacturing process of large composite structures, a new window of possibilities is opened from the optimization point of view. Currently, one has great materials and reliable manufacturing processes than can be used for extremely optimized structures. The problem is that even nowadays some calculation processes make use of design guidelines based on data from 50 years ago, which limits the optimization process due to outdated allowables and process tolerances, increasing the final cost of the structure and putting on the edge the reliability of the entire design process. Currently, imperfection sensitive shell structures prone to buckling are designed according to the NASA SP-8007 guideline, dating from 1968, using its conservative lower bound curve. In this guideline the structural behaviour of composite materials is not appropriately considered, since the imperfection sensitivity and the buckling load of shells made of such materials depend among other things on the layup design as well. In this context, a numerical investigation about the different methodologies to characterize the behaviour of imperfection sensitive composite structures subjected to compressive loads up to buckling is presented. A benchmark test is developed using a 500 mm diameter unstiffened composite cylindrical shell. A series of non-linear analyses considering geometric and thickness imperfection, obtained from real measurements, are carried-out to characterize the knock-down factor of the benchmark test. The effect of each type of imperfection on the knock-down factor is compared against the experimental results.

© 2015 Kaspars Kalnins et al.Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, such as large-scale aerospace structures, are one of the most important techniques for the evaluation of new structures and validation of numerical models. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells. This paper presents and discusses an experimental verification of a novel approach using vibration correlation technique for the prediction of realistic buckling loads of unstiffened cylindrical shells loaded under axial compression. Four different test structures were manufactured and loaded up to buckling: two composite laminated cylindrical shells and two stainless steel cylinders. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation without actually reaching the instability point. Additional experimental tests and numerical models are currently under development to further validate the proposed approach for composite and metallic conical structures.

© 2015 Elsevier Ltd All rights reserved.A semi-analytical model for the non-linear analysis of simply supported, unstiffened laminated composite cylinders and cones using the Ritz method and the Classical Laminated Plate Theory is proposed. A matrix notation is used to formulate the problem using Donnell's and Sanders' non-linear equations. The approximation functions proposed are capable to simulate the elephant's foot effect, a common phenomenon and a common failure mode for cylindrical and conical structures under axial compression. Axial, torsion and pressure loads can be applied individually or combined, and solutions for linear static, linear buckling and non-linear buckling analyses are presented and verified using a commercial finite element software. The presented non-linear buckling analyses used perturbation loads to create the initial geometric imperfections, showing the capability of the method for arbitrary imperfection patterns. The linear stiffness matrices are integrated analytically and for the conical structures an approximation is proposed to overcome the non-integrable expressions.

Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein. © 2014 Elsevier Ltd.

© 2014 Elsevier Ltd.Semi-analytical models for the linear buckling analysis of unstiffened laminated composite cylinders and cones with flexible boundary conditions are presented. The Classical Laminated Plate Theory and the First-order Shear Deformation Theory are used in conjunction with the Donnell's non-linear equations to derive the buckling equations. Axial, torsion and pressure loads can be applied individually or combined in the proposed models. The stiffness matrices are integrated analytically and for the conical shells an approximation is proposed to overcome non-integrable expressions. Comparisons with the literature show that the classical base functions available for axial compression cannot capture the buckling modes for non-orthotropic laminates. For torsion loads these classical shape functions do not catch the buckling modes even when applying the assumption of pure orthotropy, and it is shown how the proposed models correlate well with experimental data from the literature and finite element results. The use of elastic constraints at the boundaries allows the simulation of different boundary conditions in a versatile way and it is shown how those constants can be adjusted in order to change from one type of boundary condition to another.

The importance of taking into account geometric imperfections for cylindrical and conical thin-walled structures prone to buckling had been already recognized by the first authors dealing with new formulations. Nowadays, the analysts still use empirically based lower-bound methods such as the NASA SP-8007 guideline to calculate the required knock-down factors (KDFs), which does include important mechanical properties of laminated composite materials, such as the stacking sequence. New design approaches that allow taking full advantage of composite materials are required. The single perturbation load approach (SPLA), a new deterministic approach first proposed by Hühne, will be investigated with unstiffened composite conical structures varying the geometry, lamina and layup. The SPLA's capability for predicting KDF is compared with the NASA approach. The SPLA was applied to the geometrically perfect structures and to the structure with geometric imperfections of two types, mid-surface imperfections and thickness imperfections. The study contributes to the European Union (EU) project DESICOS, whose aim is to develop less conservative design guidelines for imperfection sensitive thin-walled structures. © 2014 Elsevier Ltd. All rights reserved.

The Vibration Correlation Technique (VCT) is a nondestructive experimental method that can be used for the estimation of realistic boundary conditions and to improve the correlation of numerical models used to estimate the buckling load of shell structures. This paper presents initial experimental results of vibration frequencies and modes shapes of a cylindrical shell loaded in compression, up to buckling. The experimental results are used to point out the influence of the boundary conditions and material properties on the correlation with a finite element model. The results show that the application of calibrated boundary conditions and material properties are not enough to guarantee a good numerical-experimental correlation, requiring further studies suggested herein.

This paper presents the application of the Ritz method for the analysis of laminated composite cylinders and cones using the classical laminated plate theory (CLPT) and the first shear deformation theory (FSDT). The Donnell and Sander kinematic approximations are investigated for the CLPT. It is shown that the equations proposed by Sanders when applied with the CLPT increase the range of applicability of the CLPT in comparison with the Donnell kinematics. The developed models are suitable to obtain linear and non-linear responses of conical and cylindrical shells under displacement or load controlled axial compression and geometric imperfections. This paper brings the investigation of static and buckling responses and the commercial finite element solver Abaqus was used to validate all the linear and non-linear results.

The importance of taking into account geometric imperfections for cylindrical and conical thin-walled structures in buckling had been already recognized a long time ago. Nowadays, the designers still use empirically based lower-bound methods such as the NASA SP-8007 guideline to calculate the required knock-down factors (KDFs). New design approaches that allow taking full advantage of using composite materials are required. The single perturbation load approach (SPLA), a new deterministic approach developed by Hühne for cylindrical shells, will be investigated with unstiffened composite conical structures. The SPLA's capability for predicting KDF is compared with the NASA approach. The SPLA was applied to perfect conical shells with different semi-vertex angles, and three different positions of the perturbation load were considered. The study contributes to the European Union (EU) project DESICOS, whose aim is to develop less conservative design guidelines for imperfection sensitive thin-walled composite structures.

Imperfection sensitive structures such as unstiffened or skin-dominant shell structures are commonly used for aeronautic and aerospace applications. Cylindrical shells are dominating satellite launcher structures and a reliable methodology to calculate their behaviour in the early stages of design is fundamental to achieve optimum results. Launcher design requires fast and precise prediction of structural weight as well its weight distribution already in the early design phase, because in that phase different concepts of the whole launcher system have to be evaluated in order to identify the optimal one. The prediction has to be precise, because less reliable ones might lead to basic changes, later in the detailed design phase, which might also influence the design of the whole system. Such changes in later design phases are extremely costly in terms of time and money; they definitely have to be avoided. The dimensioning criterion with the design of launcher structures is buckling not before ultimate load, thus they do not have an exploitable post-buckling area. The most critical aspect for numerical buckling prediction is the structure's sensitivity to geometric and loading imperfections. Currently, imperfection sensitive shell structures prone to buckling are designed according to the NASA SP-8007 guideline [1], from 1968, using its conservative lower bound curve. In this guideline the structural behaviour of composite materials is not appropriately considered, since the imperfection sensitivity and the buckling load of shells made of such materials depend on the lay-up design. There is no specific design guideline for imperfection sensitive composite structures prone to buckling. NASA performed high investments for the last 5 years with one project called "Shell Buckling Knock-down Factor" (SBKF) in order to develop a new guideline to calculate the knock-down factor of cylindrical shells prone to buckling [2], and also the European project DESICOS [3] (New Robust DESign Guideline for Imperfection Sensitive Composite Launcher Structures) is working on new methodologies to estimate the ultimate load of such structures. An example of applicability of these new design guidelines could be the next generation of the European launchers family "Ariane" in order to maintain the actual position in the satellite launchers market [4].

Space and aircraft industry demands for reduced development and operating costs. Structural weight reduction by exploitation of structural reserves in composite space and aerospace structures contributes to this aim, however, it requires accurate and experimentally validated stability analysis. Currently, the potential of composite light weight structures, which are prone to buckling, is not fully exploited as appropriate guidelines in the field of aerospace and space applications do not exist. This paper deals with the state-of-the-art advances and challenges related to coupled stability analysis of composite structures which show very complex stability behaviour. Two types of thin-walled light weight structures endangered by buckling will be considered; imperfection tolerant and imperfection sensitive structures. For both groups improved design guidelines for composites structures are still under development. This paper gives a short state-of-the-art and presents proposals for future design guidelines. © 2014 Elsevier Ltd.

Currently, imperfection sensitive shell structures prone to buckling are designed according to the NASA SP-8007 guideline, from 1968, using its conservative lower bound curve. In this guideline the structural behavior of composite materials is not appropriately considered, since the imperfection sensitivity and the buckling load of shells made of such materials depend on the lay-up design. In this context a numerical investigation about the different methodologies to characterize the behavior of imperfection sensitive composite structures subjected to compressive loads up to buckling is presented in this paper. A comparative study is addressed between a new methodology, called "Single Perturbation Load Approach", adopted by the European project DESICOS, and some classical approaches such as non-linear analyses considering geometric and thickness imperfection obtained from real measurements. An extension of the Single Perturbation Load Approach called "Multiple Perturbation Load Approach" is also introduced in this paper to investigate if one perturbation load is enough to create the worst geometrical imperfection case.The aim of this work is to validate these numerical methodologies with experimental results and point out their limitation, advantage and disadvantage, to calculate less conservative knock-down factors than the obtained with the NASA SP-8007 guideline for unstiffened composite cylinders. © 2013 Elsevier Ltd.

The important role of geometric imperfections on the decrease of the buckling load for thin-walled cylinders had been recognized already by the first authors investigating the theoretical approaches on this topic. However, there are currently no closed-form solutions to take imperfections into account already during the early design phases, forcing the analysts to use lower-bound methods to calculate the required knock-down factors (KDF). Lower-bound methods such as the empirical NASA SP-8007 guideline are commonly used in the aerospace and space industries, while the approaches based on the Reduced Stiffness Method (RSM) have been used mostly in the civil engineering field. Since 1970s a considerable number of experimental and numerical investigations have been conducted to develop new stochastic and deterministic methods for calculating less conservative KDFs. Among the deterministic approaches, the single perturbation load approach (SPLA), proposed by Hühne, will be further investigated for axially compressed fiber composite cylindrical shells and compared with four other methods commonly used to create geometric imperfections: linear buckling mode-shaped, geometric dimples, axisymmetric imperfections and measured geometric imperfections from test articles. The finite element method using static analysis with artificial damping is used to simulate the displacement controlled compression tests up to the post-buckled range of loading. The implementation of each method is explained in details and the different KDFs obtained are compared. The study is part of the European Union (EU) project DESICOS, whose aim is to combine stochastic and deterministic approaches to develop less conservative guidelines for the design of imperfection sensitive structures. © 2013 Elsevier Ltd.

Some of the knock-down factors applied in design of rocket launcher structures are based on design recommendations which rely on lower-bound curves from experimental data. The best known example is the NASA guideline SP 8007, published in 1965 and revised in 1968, which is applied for cylindrical structures in the space industry. This guideline is based on test data, computational methods and resources from the 1930-1960's. At that time the application of less empirical methods for the design of actual cylindrical shells could not count with the current computational power, and the available methods led to quite large discrepancies between experiments and test observations. Significant improvement on the available analyses approaches and manufacturing techniques since 1960's have not been taken into account in design processes using the NASA SP-8007, and many authors have recognized that for the current standards this guideline is leading to conservative structures. Another aspect for attention regarding application of the NASA SP-8007 for composite shells is that it does not consider the laminate stacking sequence. Moreover, physical observations regarding how does the imperfection sensitivity of unstiffened cylindrical shells change with the presence of an induced geometric imperfection have also suggested that the current applied design rules are too conservative. This conservativeness is confirmed by many tests carried out recently. This study presents an overview of the problem and a detailed description of the physical observations regarding the buckling mechanism of the thin shells under consideration. It is discussed how these observations can be used for less conservative, laminate dependent, knock-down factors accounting for geometric imperfections. The single perturbation load approach is studied in detail and a physically based definition for the minimum perturbation load (P1) is given, paving the way for the development of semi-analytical methods to calculate this minimum perturbation load. © 2013 Published by Elsevier Ltd.

This paper presents a detailed experimental and numerical investigation on the structural behavior of stiffened composite panels subjected to in-plane shear loads. The experimental work includes the development of a test device for post-buckling analyses of laminated panels subjected to shear loads. The panels out-of-plane displacement field in the post-buckling regime was experimentally characterized using a non-contact 3-D optical device. A test procedure was proposed to obtain reliable and reproducible results. The following parameters were established: geometry and instrumentation of the specimens, test mechanisms, data acquisition procedures and analysis procedures for test data.The numerical objective of this work is to implement a modeling methodology for analysis of composite stiffened panels using finite elements. The proposed methodology takes into account large displacements and material nonlinearity effects by using a damage mechanics based progressive failure model.Preliminary results for tested specimens with the proposed configuration indicate that the stiffened composite shear webs have significant post-buckling strength. © 2010 Elsevier Ltd.

This paper presents a detailed numerical investigation of the post-buckling behavior of composite shear webs using the finite element method. The numerical analysis accounts for material and geometric non-linearity effects and has been divided into three steps. The first step consists of computing the critical buckling loads as well as their corresponding buckling modes. Geometric imperfections described approximately in terms of linear combinations of different normal modes are then introduced into the model. Finally a quasi-static analysis is carried out including a progressive failure model. The progressive failure model has been implemented as a user defined material model within shell elements in Abaqus/Explicit finite element code. © Taylor & Francis Group, LLC.

This work presents the results of the modal analysis performed during the ground vibration testing of a testbed originally designed by the Group for Aeronautical Research and Technology in Europe (GARTEUR). The model testing brought challenges in determining modes with very close frequency values, which were detected independently of the excitation signal. A modal validation process was carried out in order to identify these close-spaced modes as well as their dynamic characteristics. The reliability of the experimental modal model was verified by modal assurance criterion calculations between the experimental data and validated by comparison with a finite element model. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

This work deals with a numerical investigation on the structural behaviour of stiffened composite panels subjected to in-plane shear loads in the post-buckling regime. The modelling approach takes into account large deformations and material nonlinearity effects by using a damage mechanics based progressive failure model.