Attachment Lug Research Articles

Hole-edge crack monitoring in attachment lug with large bolt hole based on guided wave and circular piezoelectric sensor array

The crack damage monitoring of aircraft structures is very significant for ensuring aircraft safety, reducing maintenance costs and extending service life. Due to the extreme service environment, the attachment lug is prone to initiate crack damage at the hole edge, which leads to crack propagation and fracture failure. Structural health monitoring technology based on piezoelectric guided wave has been widely studied, promoting the development of crack monitoring. However, at present, research on hole-edge crack damage monitoring of attachment lugs still needs to be further carried out. It is difficult to monitor small cracks at the initial stage of crack propagation, and the accuracy of crack monitoring needs to be improved. By focusing on the accuracy of the crack monitoring in the attachment lug, a crack damage monitoring method based on the circular piezoelectric sensor array is proposed in this paper. Combined with damage alarming and localization imaging, this method comprehensively evaluates the hole-edge crack damage monitoring situation and improves the monitoring effect. The method is verified by an experiment in attachment lug, and this verification includes small crack monitoring and crack propagation monitoring. The experimental results demonstrate that this method can achieve correct damage alarming results, and the maximum localization error of crack damage is only 3.02 mm, which provides a research idea for the accurate monitoring of crack damage at the hole edge.

Fatigue life of damaged wing-fuselage fitting

Experimental analysis of full-scale wing was carried out for the purpose of numerical model verification. Comparisons of deformations measured and deformations calculated in FE simulations of aircraft wing deflection under load showed very good agreement, also confirming that loads acting on the wing-fuselage attachment lug were accurately evaluated in the analytical step. The detailed analysis has shown that the total maximum axial force transferred to lug by pin would be Pax,max = 208.83 kN, whereas the maximum transverse force would be Ptr,max = 20.17 kN.

Weight function analyses and stress intensity factors for corner/surface crack in straight and tapered lugs

AbstractLug is one of the most important lap joints in many engineering structures, especially airframes. Through‐thickness and part‐through cracks emanating from pin‐loaded lug hole are frequently encountered due to stress concentration. Stress intensity factors for various crack geometries are the prerequisite for damage tolerance design of attachment lug. In this paper, analytical 2D weight functions for through‐thickness crack in lug are derived considering the contact condition between the pin and lug. With the derived 2D weight function, a highly efficient 3D slice synthesis weight function method (SSWFM) is then developed to determine 3D SIFs of hole‐edge corner/surface crack in straight and tapered lugs under various pin loadings. The resulting 3D SIFs are verified by comparisons with the numerical FEM/Franc3D solutions and literature data. The SSWFM is about 1800 times faster than the numerical FEM/Franc3D and therefore will significantly enhance damage tolerance analysis capability for attachment lugs.

A multi-layer ML model evolutionary paradigm for high-accuracy individual aircraft SHM

Evolutionary Machine Learning (EML) has emerged as a novel direction for providing robust methodologies for effectively tackling complex problems. However, most current research focuses on multi-objective optimization problems in machine learning (ML). There is limited research on the EML mechanism along the temporal application process, where a fixed machine learning model trained with the prior dataset will inevitably be not representative of the target problem with time. Taking the Structural Health Monitoring (SHM)-ML damage diagnosis model as an example, this paper proposes a novel multi-layer ML model evolutionary paradigm with multi-source data for high-accuracy individual aircraft SHM. The proposed paradigm considers three interconnected layers for the SHM-ML damage diagnosis model, including the dataset to establish the diagnosis model, the model structure and its parameter training, and mapping relationship used in the model to give the damage size. Besides, for a specific model of aircraft, there exist multiple stages from design to service, where multi-source of data is fused for the multi-layer evolution, enabling continuous improvement of damage diagnosis accuracy. Experimental validation is conducted on critical connection structures of aircraft, specifically the attachment lug structure, using the active guided wave SHM method. The results demonstrate the effectiveness of the proposed multi-layer ML model evolutionary paradigm.

Scaled fatigue cracks under service loads

Scaled experimentation is a powerful engineering tool yet its application to fatigue is limited by significant changes in behaviour with scale. The recent discovery of new similitude rules however opens new possibilities that are explored in this work through numerical experimentation for industrially representative fatigue-crack growth scenarios. It is shown for the first time, how the geometric size effects present in mixed mode fatigue tests are eliminated by performing two appropriately designed scaled experiments. The first order finite similitude theory is applied to mixed mode (modes I and II) fatigue crack growth in three case studies, viz., compact tension shear (CTS) specimen, wing fuselage attachment lug, and a T-joint with an inclined semi elliptical crack. Both planar and non-planar crack growth feature, along with surface and through thickness cracks. Low and high cycle fatigue (up to circa 60,000 cycles) is examined for three different materials (Al-6061 T6 alloy, structural steel, and AISI 316 stainless steel) under a variety of load ratios. The new rules return near exact crack-path predictions whereas lifecycle predictions have errors ranging between 1 % and 9 %. Paris law constants C and m are predicted with up to 99.9 % accuracy supporting the theory that Paris law is a first order similitude rule. Geometric size effects afflicting industrial type scaled-fatigue studies employing a damage tolerant design approach are confirmed to be eliminated on combination of information from two appropriately designed scaled models.

Adaptive GMM and OTWD-based structural crack quantification under random load

A challenge for online guided wave-based structural health monitoring is the reliable crack quantitative evaluation under time varying conditions (TVCs). This paper proposed an adaptive guided wave (GW)-Gaussian mixture model (GMM) and optimal transport Wasserstein distance (OTWD)-based structural crack quantification method. Firstly, adaptive GMM tracking the probability distribution of GW signal features obtained under different structural healthy states is utilized to suppress the uncertain influence caused by TVCs. Then, OTWD is proposed to measure the GMM difference with improved linearity by finding the optimal transport between two GMMs. The OTWD between GMMs established under structural healthy state and monitoring state respectively is utilized as the damage indicator, where the data discrepancy caused by TVCs is further reduced. Finally, the quantitative relationship between OTWD and crack length is established to estimate the crack length. The overall method is demonstrated on the aircraft attachment lug specimens under random load. The generalization and necessity of the method is verified by cross validation and comparison with existing methods. The results illustrate the improved reliability and accuracy of the proposed method in crack quantitative evaluation under the uncertain influence of random load.

A new GW-based heteroscedastic Gaussian process method for online crack evaluation

Accurate evaluation of fatigue crack by using structural health monitoring (SHM) methods is very important to the life management of aircraft structures. However, fatigue crack propagation is always a complicated process for individual aircraft structures during their long-term service. And the monitoring has to be performed under different environmental and operational conditions. These factors result in the uncertain distribution of the damage index obtained by SHM. The distribution usually changes along with the service time, which can be defined as heteroscedasticity. The heteroscedasticity characteristic of the uncertain distribution of damage index has an important negative impact on the SHM based diagnostics algorithms if not considered during the evaluation. However, till now, few researchers have considered this important aspect. To improve the evaluation accuracy under different environmental and operational conditions for individual aircraft, this paper proposes a new guided wave-based heteroscedastic Gaussian process method. Gaussian process quantile regression is adopted to estimate the conditional quantiles of the damage index distribution during the service to deal with the heteroscedasticity. The method is validated on an attachment lug fatigue test, an important aircraft structural component. The experimental results demonstrate that the proposed method can quantify the heteroscedastic uncertainty associated and obviously improve the quality of crack evaluation. For the serious heteroscedastic specimen, the maximum evaluation is only 0.7 mm reduced from the original 7.4 mm, which is an order of magnitude.

XFEM based analysis of fatigue crack growth in damaged wing-fuselage attachment lug

The research presented in this paper is based on the use of extended finite element method (XFEM) for stress intensity factors (SIFs) determination in the case of fatigue crack presented in the wing-fuselage attachment lug used in light aerobatic aircraft. The presence of the through crack at the attachment lug hole is not allowed since its growth due to high dynamic loads is usually fast and can lead to catastrophic consequences. To demonstrate how dangerous the appearance of the crack could be, as well as to estimate the residual strength and fatigue life of cracked component, finite element model of attachment lug was made, and analyses were carried out using the maximum load that can occur during the flight (load factor n = 6). The predicted number of cycles to complete failure was – as expected – low, confirming the fact that attachment lugs must be designed using safe-life approach.

On-line updating Gaussian process measurement model for crack prognosis using the particle filter

The particle filter (PF) has shown great potential for on-line fatigue crack growth prognosis by combining crack measurements from structural health monitoring (SHM) techniques. In this method, a key problem is to construct the mapping between the feature extracted from SHM signals and the crack size. However, this mapping may be inaccurate since the data used for establishing the mapping is affected by uncertainties from sources like damage geometries, sensor placements, and boundary conditions. To deal with this problem, this paper proposes an on-line updating Gaussian process (GP) measurement model within the PF based crack prognosis framework. The GP measurement model outputs the mean and variance of the crack length corresponding to the feature of SHM signals, which are input into the PF for evaluating the posterior estimation of the crack length for crack prognosis. Then, this posterior estimation is sequentially appended to the GP dataset for updating the measurement model. Moreover, once crack inspection data is obtained, it is combined with existing SHM data for additional updating of the GP measurement model. Validations are performed on the fatigue test of attachment lug structures, in which the guided wave based SHM technique is applied for crack monitoring. As the cyclic load may cause intricate influences on the guided wave propagation, it is more difficult to quantify the crack length. The validation result shows that the on-line updating GP measurement model can effectively map the feature of SHM signals to the crack length, and result in accurate crack growth prognosis with the PF based method.

Lamb Wave-Minimum Sampling Variance Particle Filter-Based Fatigue Crack Prognosis.

Fatigue cracks are one of the common failure types of key aircraft components, and they are the focus of prognostics and health management (PHM) systems. Monitoring and prediction of fatigue cracks show great application potential and economic benefit in shortening aircraft downtime, prolonging service life, and enhancing maintenance. However, the fatigue crack growth process is a non-linear non-Gaussian dynamic stochastic process, which involves a variety of uncertainties. Actual crack initiation and growth sometimes deviate from the results of fracture mechanics analysis. The Lamb wave-particle filter (LW-PF) fatigue-crack-life prediction based on piezoelectric transducer (PZT) sensors has the advantages of simple modeling and on-line prediction, making it suitable for engineering applications. Although the resampling algorithm of the standard particle filter (PF) can solve the degradation problem, the discretization error still exists. To alleviate the accuracy decrease caused by the discretization error, a Lamb wave-minimum sampling variance particle filter (LW-MSVPF)-based fatigue crack life prediction method is proposed and validated by fatigue test of the attachment lug in this paper. Sampling variance (SV) is used as a quantitative index to analyze the difference of particle distribution before and after resampling. Compared with the LW-PF method, LW-MSVPF can increase the prediction accuracy with the same computational cost. By using the minimum sampling variance (MSV) resampling method, the original particle distribution is retained to a maximum degree, and the discretization error is significantly reduced. Furthermore, LW-MSVPF maintains the characteristic of dimensional freedom, which means a broader application in on-line prognosis for more complex structures.

On particle filter improvements for on-line crack growth prognosis with guided wave monitoring

Accurate prognosis of fatigue crack growth is of great importance to ensure structural integrity, which is a challenging task due to various uncertainties affecting crack growth. To deal with this problem, the particle filter (PF) based prognostics that incorporates on-line structural health monitoring (SHM) becomes a new trend. However, most existing studies adopt the basic PF algorithm, which needs improvements to meet the requirement for on-line prognosis. It refers to the choice of the importance density and the resampling strategy, as well as the definition of the measurement equation that correlates SHM data to crack states. Till now, no literature addresses this topic in-depth. Aiming at on-line crack growth prognosis, this paper combines four improved PFs with the guided wave based SHM. The study is carried out under two cases respectively, which involve whether or not the measurement equation is accurately trained based on fatigue test data of a kind of aircraft attachment lug. Not only prognostic accuracy and consistency, but also effects of the particle number on the performance and computational cost are analyzed. The result shows advantages and disadvantages of each improved PF for on-line crack growth prognosis, giving instructions to choose appropriate PFs for different application scenarios.

A uniform initialization Gaussian mixture model–based guided wave–hidden Markov model with stable damage evaluation performance

During practical applications, the time-varying service conditions usually lead to difficulties in properly interpreting structural health monitoring signals. The guided wave–hidden Markov model–based damage evaluation method is a promising approach to address the uncertainties caused by the time-varying service condition. However, researches that have been performed to date are not comprehensive. Most of these research studies did not introduce serious time-varying factors, such as those that exist in reality, and hidden Markov model was applied directly without deep consideration of the performance improvement of hidden Markov model itself. In this article, the training stability problem when constructing the guided wave–hidden Markov model initialized by usually adopted k-means clustering method and its influence to damage evaluation were researched first by applying it to fatigue crack propagation evaluation of an attachment lug. After illustrating the problem of stability induced by k-means clustering, a novel uniform initialization Gaussian mixture model–based guided wave–hidden Markov model was proposed that provides steady and reliable construction of the guided wave–hidden Markov model. The advantage of the proposed method is demonstrated by lug fatigue crack propagation evaluation experiments.

On-line crack prognosis in attachment lug using Lamb wave-deterministic resampling particle filter-based method

Fatigue crack growth prognosis is important for prolonging service time, improving safety, and reducing maintenance cost in many safety-critical systems, such as in aircraft, wind turbines, bridges, and nuclear plants. Combining fatigue crack growth models with the particle filter (PF) method has proved promising to deal with the uncertainties during fatigue crack growth and reach a more accurate prognosis. However, research on prognosis methods integrating on-line crack monitoring with the PF method is still lacking, as well as experimental verifications. Besides, the PF methods adopted so far are almost all sequential importance resampling-based PFs, which usually encounter sample impoverishment problems, and hence performs poorly. To solve these problems, in this paper, the piezoelectric transducers (PZTs)-based active Lamb wave method is adopted for on-line crack monitoring. The deterministic resampling PF (DRPF) is proposed to be used in fatigue crack growth prognosis, which can overcome the sample impoverishment problem. The proposed method is verified through fatigue tests of attachment lugs, which are a kind of important joint component in aerospace systems.

Prognostic analysis of fastener joints in straight attachment lugs

PurposeMany failures of aircraft structural components in the past were attributed to cracks emanating from joints, which are identified as the most critical locations. In cases using the recently emerging structural health monitoring (SHM) systems, continuous monitoring needs be carried out at many major joint locations. The purpose of this paper is to develop computational techniques for fastener joints, including the possible change in contact conditions and change in boundary values at the pin-hole interface. These techniques are used for the prognostic analysis of pin-loaded lug joints with rigid/elastic pin subjected to fatigue loading by estimating the residual life of the component at any given instance to assist the SHM systems.Design/methodology/approachStraight attachment lug joints with rigid/elastic push-fit pin and smooth pin-hole interface are modelled in commercial software MSC PATRAN. In each case, the joint is subjected to various types of fatigue load cycles, and for each type of cycles, the critical locations and the stress concentrations are identified from the stress analysis. Later, for each type of fatigue cycle, the number of cycles required for crack initiation is estimated. A small crack is located at these points, and the number of cycles required to reach the critical length when unstable crack growth occurs is also computed. The novelty in the analysis of life estimations is that it takes into account possible changes in contact conditions at the pin-hole interface during load reversals in fatigue loading.FindingsThe current work on fastener joints brings out the way the load reversals leading to change in contact conditions (consequently changing boundary conditions) are handled during fatigue loading on a push-fit joint. The novel findings are the effect of the size of the hole/lug width, elasticity of the material and the type of load cycles on the fatigue crack initiation and crack growth life. Given other parameters constant, bigger size hole and stiffer pin lead to lesser life. Under load controlled fatigue cycles, pull load contributes to significant part of fatigue life.Originality/valueThe analysis considers the changing contact conditions at the pin-hole interface during fatigue cycles with positive and negative stress ratios. The results presented in this paper are of value to the life prediction of structural joints for various load cycles (for both pull-pull cases, in which the load ratios are positive, and pull-push cycles, where the load ratios are negative). The prognostic data can be used to effectively monitor the critical locations with joints for SHM applications.

Computational Fatigue Analysis of the Pin-Loaded Lug with Quarter-Elliptical Corner Crack

In the present paper, mathematical models based on a new fracture mechanics methodology are developed for the failure analysis of an attachment lug with one/two quarter-elliptical crack(s) emanating from a hole. The strength of lug subjected to cyclic loading is theoretically examined through the following issues: the stress analysis, the estimation of life up to failure and the crack path evolution. The nonlinear stress field along the crack front is simulated by using the [Formula: see text]-integral method together with the finite element method. Furthermore, analytical and numerical methods are employed for the stress intensity factor calculation. The stress-ratio dependence crack growth model is applied in order to evaluate both the life up to failure and the crack growth path. The proposed models are validated through available crack growth data, and the comparison between different results is satisfactory.

Probabilistic fatigue crack growth assessment of Al 7075-T6 aerospace component

In this paper, an engineering approach of fatigue crack growth mechanism of Al 7075-T6 aerospace component is proposed. The proposed approach was implemented by coupling of Extended Finite Element Method (XFEM), Residual Corrected Stress intensity Factor (RC-SIF) and Monte Carlo simulation (MCS) method. Particular focus was put on considering the effect of material dispersions and the residual stress distribution near the crack tip for evaluating FCG life of cracked attachment lug. Lemaitre-Chaboche's model has been used to describe material behavior. The iso-probabilistic a-N curves corresponding to5%, 50% and 95% of reliability are determined. The reliability of the proposed engineering approach is verified through a comparison with experimental FCG life data.

Fatigue damage analysis of wing-fuselage attachment lug

In the present paper, the fatigue behavior of failure critical pin-loaded lug with the through-the-thickness crack at a hole is analyzed. Such an investigation examines the stress analysis and the residual life estimation through a computational model here proposed in which suitable fracture mechanics concepts are employed. Hence, the stress ratio dependence crack growth model is taken into account to assess the fatigue strength of damaged lug. Further, in order to calculate the stress intensity factor, fracture mechanics based analytical and numerical approaches are applied. Finally, to demonstrate the compatibility of developed model, relevant experimental data are used. Such crack growth observations show a fairly good correlation with obtained failure assessments.

Extended Isogeometric Analysis (XIGA) of Fatigue Life in Attachment Lug

In the present paper, extended isogeometric analysis (XIGA) is used to compute the stress intensity factor (SIF) in straight lugs of Aluminum 7075-T6. XIGA uses the non-uniform rational B-spline (NURBS) functions and enrichment functions through the partition of unity. The Heaviside function is enriched to capture jump at the crack faces, while the analytical asymptotic solutions are incorporate with NURBS to perform the crack tip singularity. The XIGA-based SIF of edge-cracked plate and straight attachment lug are compared with analytical solution and extended finite element method capability available in ABAQUS. Also, crack growth and fatigue life of single crack in attachment lug are estimated and then compared with the available experimental data for two different load ratios equal to 0.1 and 0.5. The SIF calculated from XIGA are in reasonable agreement with the available data.

Fatigue life prediction of cracked attachment lugs using XFEM

In the present paper, a three dimensional finite element method (FEM) is used to compute the stress intensity factor (SIF) in straight lugs of Aluminum 7075-T6. Extended finite element method (XFEM) capability available in ABAQUS is used to calculate the stress intensity factor. Crack growth and fatigue life of single through-thickness and single quarter elliptical corner cracks in attachment lug are estimated and then compared with the available experimental data for two different load ratios equal to 0.1 and 0.5. The SIF calculated from XFEM shows that the introduction of different loading boundary conditions significantly affect the estimated fatigue life.

English

Attachment lug joints are commonly used in aerospace and mechanical structures. Lug joints are generally used to connect major structure components for transfer of loads and they often subjected to repeated load spectra. Lug and pin joints have been designed based on theoretical strength of materials models. In this study, geometry was determined and analysed using theoretical Strength of material calculations. The ultimate loads and allowable stresses by using different materials (Inconel718, Waspaloy, Stellite6, 2024T351 plate, 7075T651 plate, Mg Bronze, 4130 steel) in the current lug joint geometry are caliculated by strength of material calculations. From calculations we determined the allowable limiting loads for those different materials in the double shear lug joint. It is suggested the highest allowable limiting load of a double shear lug joint by using different materials in the geometry under allowable stresses.