Hole-edge Crack Research Articles

Research on the stress intensity factor calculation of multi-elliptical hole-edge crack

Research on the stress intensity factor calculation of multi-elliptical hole-edge crack

Analytical solution to stress intensity factors of cracks on both sides of a triangular hole in an infinite plate

This paper presents an analytical solution for determining the stress intensity factors (SIFs) of double-sided cracks emanating from a triangular hole in an infinite plate. A conformal function is introduced, which can be applied to these cracks, and the SIFs are analytically derived using the Muskhelishvili method. By combining the Schwarz-Christoffel integral with the conformal transformation for cracks originating from circular holes, a mapping function for the cracked triangular hole is presented. The accuracy of the SIF at the single right-sided crack of the triangular hole is validated using finite element method (FEM) and compared with existing references. This study investigates the influence of biaxial loading factors and lengths of cracks on SIFs. The SIF of the hole-edge crack is related to the structure from which the crack emanates. This analytical approach provides a reliable solution for calculating SIFs of double-sided cracks emanating from a triangular hole.

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.

Quantitative diagnosis of fatigue hole-edge crack in composite laminates using guided wave and optical fiber feature fusion

In this paper, a quantitative method for fatigue crack diagnosis of composites is proposed, which combines guided wave and strain multi-source heterogeneous feature fusion with deep learning. Two types of sensors, i.e. piezoelectric sensor and fiber Bragg grating sensor, are used to measure the global and local response of composites under fatigue loading. The one-dimensional signal of the guide wave is encoded into an image by the Gram angular field transform method. The deep features of the image are further extracted by the AlexNet deep learning model. Furthermore, a heterogeneous feature fusion based on image square array of the guided wave and strain is presented. Finally, the CNN models with different input features are constructed. The results show that the quantitative diagnosis of the hole-edge crack based on the heterogeneous fusion of the guided wave and FBG is more accurate and reliable than that based on the single feature of guided wave.

An improved probabilistic diagnosis imaging algorithm for quantifying Hole-edge crack growth

Probabilistic damage imaging (PDI) algorithm based on Lamb wave is one of the most promising structural health monitoring technologies for quantifying the hole-edge crack. However, it is still a challenge how to use a limited number of sensors to quantify the hole-edge crack. This paper proposed an improved probabilistic damage imaging algorithm (IPDI) to track the hole-edge crack growth. A simulation has been conducted to deeply study the interaction of cracks and Lamb waves. A damage index calculated by the frequency-domain energy has been found to have a good capacity for monotonically characterizing crack propagation. The further study derives a unifying relationship between damage index and the ellipse size control factor from the crack to transmitter–receiver paths with different lengths and angles. The unifying relation is used to define a new dynamic elliptical control parameter in PDI algorithm to improve the capacity of crack quantification. The improved PDI algorithm is verified by both of simulation and experiments with different exciting frequencies, whose results show that the crack imaging error of the IPDI algorithm is below 1 mm, and the accuracy is much higher than that of the traditional PDI algorithm. The proposed IPDI algorithm can effectively quantify the hole-edge crack growth.

A Novel Pentagonal EC Sensing Array Film for Quantifying Hole-Edge Crack of Bolted Joints

Hole-edge crack in bolted joints is one of the most critical damages that seriously affect aircraft structural safety. In this article, a novel pentagonal eddy current (EC) sensing array film is proposed to quantify the hole-edge crack parameters. The proposed new sensing film may identify the hole-edge crack angle, depth, and length with fewer layers and eliminate the blind area problem of crack monitoring for the existing sensors at some angles. Finite-element simulation is employed to study the EC distribution around the bolt hole and the interaction between the EC and the crack, which can be used to determine the configuration of the EC array. Both the simulation and the experimental test are conducted to verify the feasibility and effectiveness of the proposed sensing film for quantifying the hole-edge crack angle, depth, and length.

Damage tolerance analysis of wading structures of amphibious aircraft based on Franc3D

Aiming at the combined action effect of the corrosive environment of amphibious aircraft wading structures and random loads including water surface take-off and landing impact, based on the standard load spectrum TWIST of transport aircraft, considering the load level and frequency corresponding to the hydrodynamic load, the simulated random load spectrum of the wading structure was first compiled; the Willenborg/Chang high-load hysteresis model was used to consider the hysteretic effect of hydrodynamic high-amplitude overload on structural crack propagation, and an engineering method for damage tolerance analysis of amphibious aircraft wading structures was established. Taking the common hole edge crack of a typical wading structure of a certain type of aircraft as an example, based on the Franc3D crack propagation analysis software, the crack propagation life under the combined action of corrosive environment and random load spectrum was analyzed, and the inspection threshold value and check interval for maintaining the airworthiness of the structure were determined by residual strength analysis. The method proposed in this study is simple and feasible, and provides a theoretical basis for the damage tolerance analysis and maintenance plan formulation of amphibious aircraft wading structures.

Adaptive Gaussian mixture model based structural damage monitoring method under time-varying conditions

Abstract The low reliability of damage monitoring under Time-Varying Conditions (TVCs) is a key challenge for the practical application of Structural Health Monitoring (SHM) technology to aircraft structures. Among the existing SHM methods, Guided Wave (GW) and piezoelectric sensor based SHM technique is a promising method due to its high damage sensitivity and long monitoring range. Nevertheless the reliability problem still should be addressed. To deal with this problem, an adaptive Gaussian Mixture Model (GMM) based structural damage monitoring method is proposed. The probability distribution of GW features under TVCs is represented by the GMM. The center of each Gaussian component in a GMM is determined adaptively first. Then a global optimal GMM which could change with TVCs is constructed by the expectation maximization algorithm. Finally, along with damage monitoring process, the variation of GMMs is measured by a probabilistic similarity based damage index which allows normalized detection of structural damage. The utility of the proposed method is validated in the hole-edge crack monitoring of an aluminum tension sample under varying loading condition.

Monitoring cracks of metal structure based on grating thin-film sensor

The hole edge of a metal structure is the most likely crack position in an aircraft structure. The quantitative monitoring of a hole-edge crack is important for structural health monitoring. Therefore, this paper presented a grating thin-film sensor based on the potentiometric method. Firstly, the anodic oxidation process was used to prepare thin film on 2A12-T4 aluminum alloy matrix to prevent the aluminum alloy matrix from interfering with the monitoring signal of the sensor. Then the DC superimposed pulsed bias arc ion plating technique was used to prepare the grating thin-film sensor on the surface of the specimen. The output characteristics of the grating thin-film sensor are obtained with its finite element model, and the factors affecting the sensitivity of the sensor are analyzed. Finally, the fatigue crack monitoring tests were carried out to verify the quantitative monitoring capability of the grating thin film sensor. The experimental results show that it is feasible for the grating thin-film sensor to quantitatively monitor the fatigue crack at the hole edge of an aircraft metal structure.

Weighted adaptive Kalman filtering-based diverse information fusion for hole edge crack monitoring

The information fusion of different sensors is an effective means of improving the damage quantification of aircraft structures operating in a complex environment. A weighted adaptive Kalman filtering-based information fusion method (WAKFIFM) is proposed to achieve the feature-level fusion of diverse signals of the hybrid piezoelectric-fiber optic sensor network. The damage identification results obtained from guided wave signals and strain signals are described by the quantification curves of damage index (DI) and crack length. A new fusion curve is obtained by fitting the above two quantification curves using the quadratic polynomial method. The mean square error and the root mean square error of the fusion curve and the actual curve are used as the error and the covariance of the proposed WAKFIFM, respectively. The weighted value in WAKFIFM is the reciprocal of the square of the actual measured maximum DI. The hole edge crack propagation experiments are conducted on both an aluminum plate and a carbon fiber reinforced polymer plate in a load-temperature changing environment.A new damage location method integrated with DI information is developed to obtain a more accurate result. The feature-level fusion results show that the proposed WAKFIFM can improve the accuracy of damage quantification, compared against that obtained from the single guided wave signals or fiber optic sensor signals.

Residual fatigue lives assessment of riveted lap joints based on a crack growth model

Many riveted joints bear the action of out-of-plane bending moments in steel truss bridges. The fatigue resistance of these joints isn’t stipulated in the current design criteria. Ensuring the safety of structures necessitates analysing the fatigue process of such riveted joints. This paper attempts to evaluate the fatigue life of riveted lap joints from the perspective of engineering applications. The study first found through fatigue tests with two types of fatigue details in riveted lap joints: plate surface cracking and rivet hole edge cracking. Then, the fatigue progression is divided into three stages: the microstructure short crack (MSC) stage, the physical short crack (PSC) stage and the long crack stage. The crack propagation model in the short crack stage is established by combining a scanning electron microscope test of the material and an empirical formula. The crack propagation model of the long crack stage is established by the crack propagation test and considering the crack closure effect. Results show that the fatigue life corresponding to the hole edge crack fatigue detail category is shorter than that to the plate surface crack. In each crack propagation stage, the crack propagation life decreases with increasing load and decreasing load ratio RL. For the two fatigue detail categories, the proportion of the long crack stage to the whole fatigue life is small, and the effect of the crack closure on the overall fatigue life is limited; therefore the effect of the load ratio RL on the fatigue life can be ignored.

Quantifying Hole-Edge Crack of Bolt Joints by Using an Embedding Triangle Eddy Current Sensing Film

Hole-edge crack quantification of bolt joints is critical for monitoring and estimating structural integrity of aircraft. The paper proposes a new triangle eddy current sensor array for the purpose of increasing the level of quantifying hole-edge crack parameters, especially, the crack angle. The new senor array consists of triangular coils instead of planar rectangular coils. The configuration of the novel sensor array, including the excitation current directions and the excitation winding shape, is optimized by simulation. The ability of the proposed sensing film to identify the crack parameters has been verified by finite element simulations and experiments. Results shows that triangular coils with same current directions in circumferentially adjacent coils and opposite current directions in axially adjacent coils achieve better performance in sensor linearity and resolution compared to rectangular coils. In addition, it has also been proved that the sensing film has a good potential to identify the crack depth and length.

A new interleaving eddy current array-based sensing film for fatigue crack quantification of bolted joints

Fatigue crack quantification for bolted joints attracts much attention to determine the structural integrity for aircraft structures. In this paper, a new sensing film with interleaving eddy current array is proposed to evaluate the parameters of the hole-edge crack for single- or multiple-lap bolted joints. In this sensing film, the exciting layer is one coil throughout the hole wall which consists of a one-dimension rectangle coil array in the axial direction connecting in series, while the sensing layer is made up of two interleaving layers with a two-dimensional sensing coil array distributed in the circumferential and axial directions for each layer. Finite element simulation is conducted to study the effect of different crack parameters on the induced voltage of sensing coils. Simulation results reveal that the sensing film has no blind angle of crack detection but a strong capability of quantifying the crack angle, and the arctangent value of the ratio between interleaving coils can be used for estimating the crack angle. After the crack angle is estimated, induced voltages of sensing coils at this angle may be used to track the crack propagation in the axial or radial directions of the bolt hole. Experiments are conducted to verify the feasibility and effectiveness of the new sensing film to monitor the angle, depth, and length of the hole-edge crack of bolted joints.

An Analytical Model for Predicting the Stress Intensity Factor of Single-Hole-Edge Crack in Diffusion Bonding Laminates with Preset Unbonded Area

The diffusion bonding titanium alloy laminates with preset unbonded area (DBTALPUA) compared with other titanium alloy structural forms has good damage tolerance performance and designability. It is important to fast get the damage estimation of the DBTALPUA with crack. The stress intensity factor (SIF) of the crack is an effective indicator to give the damage estimation. In order to get the SIF fast, this paper proposed an analytical model to calculate SIF for single hole-edge crack in DBTALPUA with hole under tension loading. Comparison of the results obtained through this analytical model and numerical simulation illustrated that the analytical model can rapidly predict the SIF with fine precision.

Experimental Study on Crack Detection at Bolt Hole Edge in Rail Joint Using the Third Harmonic

In this paper, a nonlinear ultrasonic detection method for detecting the hole edge crack in rail joint was proposed. The experimental results show that a single frequency sinusoid wave modulated by Hanning window is input to the rail specimen, there are higher order harmonics in the received signals for cracked rail, but there are no any harmonics for the rail with no crack bolt hole. That is to say the higher order harmonics can be used to indicate the presence of a crack. Furthermore, a nonlinear parameter μ is defined by the ratio of the third harmonic frequency peaks to the peak of the fundamental frequency. The relationship between nonlinear parameters and crack size is approximately linear, which means that the third harmonic not only can detect the presence of the hole edge crack, but also can assess the size of the hole edge crack.

Calculation of Stress Intensity Factor on Typical MSD Structure of Aircraft Wing

The research object of this paper is Multiple site damage (MSD) structures which are common in the service of aging aircraft. A complex function modified method is proposed to calculate the stress intensity factor of MSD cracks. On the basis of Muskhelishvili complex function method and its approximate superposition method, the concept of equivalent crack is introduced to solve the accurate stress function of MSD cracks. The stress intensity factor of MSD hole edge crack of infinite plate under far end uniform load is calculated and compared with the finite element method. The method is applied to the typical MSD structure of aircraft wing, and the stress intensity factors of cracks in three modes are compared and analyzed. This method can be used to discuss the damage tolerance of MSD structure, it has certain application value in the reliability evaluation of aircraft.

The Simulated Distortion Spectrum on Aluminum Alloy Structure with the Fatigue Crack Propagation

Fiber Bragg Grating (FBG) is expected to be a means of real-time monitoring of crack damage at the edge of the hole due to the sensitive perception of strain. In this paper, an optical fiber fatigue monitoring test platform is built for real-time monitoring of hole edge crack damage. Experimental results found that the grating could be sensed the strain variation with the crack propagation, caused by crack singularity, and the spectrum is highly correlated with the crack length. Full width at half maximum (FWHM) is a type of damage feature extracted from the simulated distortion spectrum, which has a high correlation with crack propagation. Meanwhile, the signal processing technique is used for the FWHM extraction, and the spectrum simulation, combined transfer matrix method and the finite element method, is investigated in this paper. The results show that the FWHM broadened obviously with the crack length, and the FWHM can be used as an effective index for evaluating fatigue crack growth.

Suitability of constraint and closure models for predicting crack growth in generic configurations

The effective stress intensity factor range ΔKeff is commonly considered to govern the fatigue crack growth and may be estimated through the crack opening stress Sop and the constraint factor α. In the literature closed-form expressions have been developed for estimating both variables in a center-cracked plate with elastic-perfectly plastic behavior subjected to remote uniform stresses. However, such expressions are frequently adopted regardless of geometry, material and loading and, moreover, α is often given a fixed value. The final objective is to assess the suitability of existing constraint and closure models for performing accurate crack-growth predictions in configurations that do not meet the original hypotheses. The region-II growth of a hole-edge crack is predicted in the 42CrMo4 steel by integrating crack growth laws calibrated with data from standard compact tension (CT) specimens. The results show overall better predictions by using the same constraint model for estimating α in both geometries, rather than by treating it as a fitting parameter in CT specimens. Unexpectedly, the predictions obtained at different stress ratios were, in general, more accurate by integrating a non-closure law based on ΔK and independent of Sop and α.

A novel eddy current array sensing film for quantitatively monitoring hole-edge crack growth in bolted joints

Fatigue crack growth in bolted metallic joints is one of the most serious and concerning types of damage in aircraft structures. The problem of how to quantitatively track the size of a crack in order to determine structural integrity has attracted much attention. In this paper, a novel eddy current array sensing film, with one exciting coil covering the entire thickness and several sensing coils distributed along the axial length of the hole, bonded onto the bolt, is proposed to quantitatively monitor a bolt-hole crack in the radial and the axial directions. Finite element simulation is utilized to investigate the eddy current disturbance caused by the crack growth and to optimize the coil configuration of both exciting and sensing coils in order to improve the crack monitoring capability of the sensing film. The simulation results show that the proposed sensing film has very good capability for tracking cracks when the traces of the exciting coil are designed to be similar to the sensing coils’ and have opposite current direction at the boundary of two adjacent sensing coils. An experiment is conducted to verify the feasibility and effectiveness of the proposed eddy current array sensing film to quantitatively track hole-edge crack growth in bolted joints.

Discussions on weight functions and stress intensity factors for radial crack(s) emanating from a circular hole in an infinite plate

A thorough verification is made for two recently developed weight functions (WFs) by Jin et al. for a single crack and two symmetric radial cracks emanating from a circular hole in an infinite plate. Through comparisons with other WFs (or Green’s functions), it is found that the Jin et al.’s WFs are in marked disagreement to those of Shivakumar-Forman, Newman and Wu-Carlsson, especially for the single crack geometry. Significant disagreements in SIFs obtained by using Jin et al.’s WFs are also found for loadings which are much different from the reference load cases used for deriving their WFs. Possible sources for the poor accuracy of Jin et al.’s WFs are discussed and identified, including limitation of the two-reference-load-cases-based WF approach, choice of reference load cases and sensitivity of these WFs to the inaccuracy of the two reference SIF-solutions. By using a the Wu-Carlsson unified WF approach with crack opening displacement as an additional condition, new analytical WFs for the two hole-edge crack geometries are developed and verified, and further used to derive closed form SIF-expressions for several basic crack line stresses. The new analytical WFs will facilitate more accurate fatigue and fracture analyses for arbitrarily loaded hole-edge crack(s) in an infinite plate.