In this paper, a comparison between six finite element models of a representative wing structural component performed in the context of Optimised Design for Inspection (ODIN) project of the European Cooperation in Science and Technology (COST) is presented. Six partners from six different countries involved in the project received the drawing of the structure, the material properties, the loading and boundary conditions. Each partner, based on their background and experience in numerical analyses, developed a finite element model with different levels of details and accuracy and performed a blind prediction of the structural behaviour of the wing component. The numerical results are presented and compared with the experimental test data conducted at Cardiff University.@en

This study aims at better understanding the damage tolerance of stiffened composite panels subjected to fatigue loads in the post-buckling regime. Ten single-stringer hat-stiffened specimens with an initial delamination between the skin and the stringer foot were manufactured, and then tested under quasi-static and fatigue loads in post-buckling conditions, with different load levels and load ratios. The tests were monitored with digital image correlation and an ultrasonic system, providing data on the displacements, strains, and extension of the delamination length. The quasi-static results showed that the delamination onset, when the initial delamination begins propagating, occurred at loads over twice the buckling load, while collapse occurred for values almost 20% higher than the delamination onset. During fatigue testing at load levels below the delamination onset, the specimens were able to sustain 150000 cycles and then, when tested statically after fatigue, the average load at collapse was reduced by less than 10% with respect to the quasi-static benchmark. When the maximum load during fatigue was increased to 5% over the delamination onset load, the specimens still withstood between 8000 and 16500 cycles before collapse, depending on the load ratio. It was also seen that for tests at the same load level, the specimens with high load ratio had a slower damage propagation.@en

The standard experimental procedures for determining the interlaminar fracture toughness are designed for delamination propagation in unidirectional specimens. However, in aerospace structural components, delamination usually occurs between plies at different orientations resulting in different damage mechanisms which can increase the value of the fracture toughness as the delamination propagates. Generally, numerical analyses employ the value measured at the delamination onset, leading to conservative results since the increase resistance of the delamination is neglected. In this paper, the fracture toughness and the R-curves of carbon/epoxy IM7/8552 are experimentally evaluated in coupons with delamination positioned at 0°/0° and 45°/−45° interfaces using Double Cantilever Beam (DCB) and Mixed-Mode Bending (MMB) tests. A simplified numerical approach based on the Virtual Crack Closure Technique (VCCT) is developed to simulate variable fracture toughness with the delamination length within a Finite Element code using a predefined field variable. The results of the numerical analyses compared with the experimental data in terms of load-displacement curves demonstrate the effectiveness of the proposed technique in simulating the increase resistance in delamination positioned between plies at 45°/−45° interface.@en

This paper evaluates the capabilities of the recently developed CF20 cohesive fatigue model, which can predict crack initiation as well as the rates of crack propagation by relying on intrinsic relationships between a stress-life diagram and its corresponding Paris law. The model is validated here using a partially reinforced double cantilever beam (R-DCB) benchmark proposed in literature. The two parameters needed for the CF20 cohesive fatigue model were obtained by performing preliminary analyses of a conventional DCB. The analysis results indicate that the CF20 cohesive fatigue model can accurately reproduce the complex evolution of the delamination observed in the R-DCB.@en

This paper focuses on a novel numerical formulation based on cohesive elements and S-N diagram to simulate fatigue-driven delamination in composite laminates. The constitutive model adopts a two-parameters heuristic equation, which coefficients are evaluated using an idealization of the S-N diagram rather than the more commonly used Paris law. The approach is implemented in the finite element code ABAQUS and validated with analysis on Double Cantilever Beam specimen. The numerical outcomes are compared with experimental data taken from literature showing the capability of the model in predicting the crack growth rate. The model is then applied to evaluate the fatigue delamination growth in a specimen similar to the Double Cantilever Beam but with reinforcement plates which force the delamination front to change its shape during the propagation. The results compared with experimental data taken from literature show the effectiveness of the approach in predicting the load-displacement curve and the delamination front shape and position at different load cycles. @en

In this work, an approach based on the Virtual Crack Closure Technique, included in the commercial finite element code ABAQUS, is adopted to study the propagation of delamination in composite structures under quasi-static and fatigue loads. The methodology, originally capable of simulating only delamination under quasi-static loads, has recently been extended introducing the possibility to analyze damage progression under fatigue load condition. The approach is assessed on simple specimens, Double Cantilever Beam and Mixed Mode Bending test, comparing the results with literature data. Afterwards, the behavior of a single-stringer specimen with an initial delamination is numerically investigated considering compressive loading conditions. At first, the single-stringer specimen is analyzed under quasi-static compressive load showing a clear correlation between local buckling phenomena and delamination growth. Then, a cyclic compressive load is applied such that the specimen switches between pre- and post-buckling conditions in a single load cycle. The outcomes of the numerical analyses are compared with the experimental data obtained from an experimental test campaign previously performed, showing the advantages of the adopted numerical technique but also the limitations that need to be addressed to properly analyze this phenomenon.@en

The fatigue life prediction of post-buckled composite structures represents still an unresolved issue due to the complexity of the phenomenon and the high costs of experimental testing. In this paper, a novel numerical approach, called “Min-Max Load Approach”, is used to analyze the behavior of a composite single-stringer specimen with an initial skin-stringer delamination subjected to post-buckling fatigue compressive load. The proposed approach, based on cohesive zone model technique, is able to evaluate the local stress ratio during the delamination growth, performing, in a single Finite Element analysis, the simulation of the structure at the maximum and minimum load of the fatigue cycle. The knowledge of the actual value of the local stress ratio is crucial to correctly calculate the crack growth rate. At first, the specimen is analyzed under quasi-static loading conditions, then the fatigue simulation is performed. The results of the numerical analysis are compared with the data of an experimental campaign previously conducted, showing the capabilities of the proposed approach.@en

This paper presents a numerical approach for investigating fatigue delamination propagation in composite stiffened panels loaded in compression in the post-buckling field. These components are widely utilized in aerospace structures due to their lightweight and high-strength properties. However, fatigue-induced damage, particularly delamination at the skin–stringer interface, poses a significant challenge. The proposed numerical approach, called the “Min–Max Load Approach”, allows for the calculation of the local stress ratio in a single finite element analysis. It represents the ratio between the minimum and maximum values of the stress along the delamination front, enabling accurate evaluation of the crack growth rate. The methodology is applied here in conjunction with the cohesive zone model technique to evaluate the post-buckling fatigue behavior of a composite single-stringer specimen with an initial delamination. Comparisons with experimental data validate the predictive capabilities of the proposed approach.@en

In this research, conduction welded C-struts, part of a thermoplastic composite fuselage designed and manufactured in the framework of the Clean Sky 2 STUNNING project, are investigated. Five specimens made of two C-section profiles are manufactured and welded using conduction welding in three different configurations with variations in the direction and distance of the two welded joints. Preliminary numerical analysis using the virtual crack closure technique are conducted to obtain an initial evaluation of the specimens behavior, in preparation of the tests. Experiments are performed under quasi-static loading conditions to measure the strength of the welds. Comparisons with the preliminary numerical analyses show a good agreement in terms of the predicted maximum load, while a clear difference is observed in the initial stiffness, due to the compliance of the support structure. The numerical model is updated, leading to results that closely match the experimental behavior. For all the analyzed specimens, the separation occurs suddenly and no signs of propagation are observed. Experimental and numerical data show no relevant difference in the joint strength among the different conduction welding configurations.@en

In this research, conduction welded C-struts, part of a thermoplastic composite fuselage designed and manufactured in the framework of the Clean Sky 2 STUNNING project, are investigated. Five specimens made of two C-section profiles are manufactured and welded using conduction welding in three different configurations with variations in the direction and distance of the two welded joints. Preliminary numerical analysis using the virtual crack closure technique are conducted to obtain an initial evaluation of the specimens behavior, in preparation of the tests. Experiments are performed under quasi-static loading conditions to measure the strength of the welds. Comparisons with the preliminary numerical analyses show a good agreement in terms of the predicted maximum load, while a clear difference is observed in the initial stiffness, due to the compliance of the support structure. The numerical model is updated, leading to results that closely match the experimental behavior. For all the analyzed specimens, the separation occurs suddenly and no signs of propagation are observed. Experimental and numerical data show no relevant difference in the joint strength among the different conduction welding configurations.@en

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.@en

The fatigue damage tolerance of a composite stiffened structure in post-buckling conditions is experimentally investigated in this work. Single-stringer specimens with an initial delamination, artificially created during the manufacturing process, are tested under cyclic compressive load. Six nominally identical specimens are manufactured: two tested under quasi-static load to understand the compressive behavior of the structure and four under fatigue load cycling between pre- and post-buckling conditions at two different maximum loads. During the tests, digital image correlation system and ultrasonic C-scan are adopted to follow the evolution of the out-of-plane displacements and the propagation of the delamination. Depending on the load level, the delamination starts to grow already in the first cycle or after a few thousand cycles, but in both cases the propagation is fast at the beginning, then slows down gradually. The fatigue tests are interrupted after 150,000 cycles and the specimens are subjected to quasi-static compressive load to evaluate the residual strength of the structure. @en

An approach based on the cohesive zone model for analyzing delamination in composite laminates under cyclic fatigue loading is presented. The proposed technique, called “min-max load approach,” is able to dynamically capture the local stress ratio during the progression of delamination. The possibility to know the local stress ratio is relevant in all the situations where its value is different from the applied load ratio and cannot be determined a priori. The methodology analyzes in a single finite element analysis two identical models with two different constant loads, the minimum and the maximum load of the fatigue cycle. The two models interact with each other, exchanging information to calculate the crack growth rate. At first, the approach has been validated in simulations of mode I and mixed-mode propagation using double cantilever beam and mixed-mode bending tests. Then, to prove the effectiveness of the developed methodology, a modified version of the mixed-mode bending test has been analyzed. Mode I and mode II components of the load are decoupled and applied independently, resulting in a local stress ratio different from the applied load ratio. The results obtained from the simulations, compared with the analytical model obtained using the corrected beam theory, show that the proposed approach is able to predict the local stress ratio and thereby to correctly evaluate the crack growth rate during the propagation of the damage. @en

An approach based on the cohesive zone model for analyzing fatigue-driven delamination in composite structures under cyclic loading is presented. The proposed technique, called “Min-Max Load Approach”, is able to dynamically capture the local stress ratio during the evolution of damage. The possibility to know the local stress ratio is relevant in all the situations where its value is different from the applied load ratio and cannot be determined a priori. In a single Finite Element analysis, two identical models are analyzed with two different constant loads, the minimum and the maximum load during the fatigue cycle. The implemented methodology allows the two models to interact with each other, by exchanging information to correctly calculate the crack growth rate. At first, the approach has been validated in simulations of mode I and mixed-mode propagation by using Double Cantilever Beam and Mixed-Mode Bending. Then, to prove the effectiveness of the developed methodology, a modified version of the Mixed-Mode Bending test has been numerically investigated. In this test, the mode I and mode II components of the load are decoupled and applied independently, resulting in a local stress ratio different from the applied load ratio. @en