Predicted Crack Length Research Articles

Predicting actual crack size through crack signal obtained by advanced Flexible Eddy Current Sensor using ResNet integrated with CBAM and Huber loss function

This study presents an advanced FEC sensor, engineered by arranging coils in a co-directional current configuration. Moreover, boasting a compact design, the FEC sensor showcases significantly enhanced spatial resolution, enabling robust detection of small cracks even at low excitation frequencies and mitigating issues of overlapping in adjacent crack detection. Results indicate successful crack detection through voltage and phase measurements, albeit with phase signals demonstrating variation at specific excitation frequencies, complicating the determination of actual crack sizes. Consequently, a novel model is proposed to forecast actual crack sizes, leveraging experimental data from the FEC sensor system. This model integrates a Residual Neural Network (ResNet) architecture with a Convolutional Block Attention Module (CBAM) and utilizes the Huber loss function to minimize errors during model training. Comparative analysis underscores the superior performance of the proposed model in predicting crack length and depth compared to the standalone ResNet, particularly when utilizing the Huber loss function with a δ value of 1.0. Evaluation metrics, encompassing Mean Squared Error (MSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE), illustrate an average accuracy surpassing 95 % for crack size predictions. Consequently, the proposed model demonstrates remarkable performance, significantly reducing the time required to ascertain actual crack sizes by leveraging voltage and phase measurements.

Dislocation-based entropy as a criterion for fracture

Griffith’s 1920 fracture criteria is well known in the engineering community. Griffith produces a simple formula for the fracture stress of a material using the first law of thermodynamics by relating the decreased elastic energy of an applied load to the increased surface energy of a crack. However, evidence in fatigue research, most notably the concept of fracture fatigue entropy (FFE), suggests that the fracture mechanism is more intimately related to irreversibility and can be treated via the second law of thermodynamics. In this paper, Griffith’s model is approached from the perspective of the second law of thermodynamics, producing a new equation for fracture stress centered on entropy. Fracture tests are performed on 304 stainless steel (SS) and 110 copper specimens. Experimental crack lengths at fracture determined via digital image correlation (DIC) are compared to predicted crack lengths at fracture determined via the entropic fracture stress relation to assess accuracy. Predicted crack lengths at fracture are determined to be accurate to within 2.88% for 304 SS specimens and 7.62% for copper specimens, both of which are comparable to the corresponding accuracy of Griffith criteria predictions. Further, it is shown that the developed entropy model is capable of predicting the entropy-based debonding strength of a material, matching experimental debonding strength values evaluated via DIC to within 25%.

Fatigue Crack Growth on Several Materials under Single-Spike Overloads and Aircraft Spectra during Constraint-Loss Behavior

Abstract The phenomenon of flat-to-slant crack growth has been studied by many in the fracture mechanics community. At low stress-intensity factors, a fatigue-crack surface is flat (tensile mode) and the crack-front region is under plane-strain conditions (high constraint). As the crack grows with higher stress-intensity factors, a 45° shear lip occurs through the thickness of the sheet or plate. This behavior is the shear mode, which is under low constraint or plane-stress conditions. In 1966, Schijve found that the transition from flat-to-slant crack growth on a 2024-T3 Alclad aluminum alloy over a wide range in stress ratios (R) occurred at a “constant” crack-growth rate. Also, Newman and Hudson showed the same behavior on 7075-Temper-6 and Ti–8Al–1Mo–1V alloys, validating Schijve’s observation that crack-growth rate was the key parameter for flat-to-slant crack-growth behavior. The materials considered herein are 2024-T3, 7075-T6, and 9310 steel. Crack-growth behavior during single-spike overloads and simulated aircraft spectrum loading are presented. The fatigue structural analysis (FASTRAN) crack-closure based life-prediction code was used to correlate the constant-amplitude (CA) crack-growth-rate data over a wide range in stress ratios (R = Smin/Smax) and rates from threshold to near fracture, and to calculate or predict the crack-growth behavior on single-spike overload tests. Crack-closure behavior is strongly dependent upon the level of constraint. The main objective was to see if the constraint-loss region is the primary reason for crack-growth delays after single-spike overloads. Also, crack-growth analyses are presented on tests that were conducted by Wanhill on 2024-T3 Alclad aluminum alloy under the transport wing standard (TWIST) spectrum. Crack-growth analyses using crack-closure theory without constraint loss was “unable” to predict crack growth under spike overloads or simulated aircraft spectra. However, predicted crack length against cycles with constraint-loss behavior compared reasonably well with all tests.

Characterisation of fatigue delamination growth in plain woven hybrid laminated composites subjected to Mode-I loading

Effect of similar and dissimilar crack plane interface configuration on fatigue delamination growth in plain woven hybrid composite laminates under Mode-I has been investigated. Constant displacement amplitude fatigue testing with displacement ratio of 0.1 was carried out on 3 configurations of plain woven glass/carbon epoxy composite laminates. A power law like fit between recorded delamination length and corresponding cycle was used to predict crack length for each of the cycle. Delamination growth rate,da/dN is computed by differentiating the expression of power-law like fit.The obtained crack growth rate for each of the specimens were plotted with respect to two normalised functions, G^Imax=GImax(a)/GIR(a) where GImax is maximum mode-I energy release rate and GIR(a) is the interlaminar fracture toughness resistance and ΔG^Ieff=G^Imax-G^Imin2 as crack driving parameters computed on the basis of Modified Beam Theory (MBT) and Valvo’s mode partition method (MPV) are used in Paris relation to quantify delamination propagation. It is observed that the exponent values predicted by MBT method for G^Imax is lower as compared to ΔG^Ieff. Whereas, exponent values predicted for G^Imax is higher as compared to ΔG^Ieff predicted by MPV method. The higher the exponent value, the higher is the sensitivity of the model leading to uncertainties in the crack growth prediction. Also, it is to be noted that cyclic loading effect is when both GImax and GImin is considered, the use of ΔG^Ieff as crack driving parameter to quantify delamination propagation is justified. Secondly, MBT method does not account for the mode-mixity arising due to hybrid material configuration as in the case of Local Symmetry Fatigue (LSF) and Asymmetry Fatigue (ASF) specimens. Hence, results in higher exponent as compared to MPV method. On the other side, the G^Imax and ΔG^Ieff computed on the basis of MPV method is the pure Mode-I component deduced from the total energy release rate of mode-mixity.The equations of curve fitting is very much the same for Simple Symmetry Fatigue (SSF) specimens indicating that MBT and MPV methods predict pure Mode-I behaviour for symmetric configuration for delamination growth under fatigue Mode-I loading. From the composite laminate configuration point of view, LSF specimens have higher exponents as compared to ASF and SSF specimens indicating, local symmetry configuration laminates are highly sensitive to the small uncertainties and results in unstable crack growth.Comparison of results of all hybrid composite laminates shows that the normalised functions of G^Imax and ΔG^Ieff as crack driving parameters computed on the basis of MPV method is able to capture the effect of interlayers and stacking effect on the delamination growth in hybrid plain woven composites in fatigue loading and MPV method is found to be not sensitive to G^Imax and ΔG^Ieff for displacement ratio of 0.1.

Predicting fatigue crack growth metrics from fractographs: Towards fractography by computer vision

This work utilized computer vision and machine learning techniques to predict both qualitative characteristics and quantitative values, from SEM images of Ti–6Al–4V fracture surfaces from compact tension specimen fatigue crack growth tests. This work found that Convolutional Neural Networks (CNNs) focused on different features in images based on the length scale of the image. This study determined a lower limit field of view related to the number of grains imaged, and confirmed that transfer learning of a pre-trained CNN can distinguish between two forging direction and two different load ratios, and predict crack length, a, and repurposed for ΔK, and dadN.

On predicting crack length and orientation in twill-woven CFRP based on limited data availability using a physics-based, high fidelity machine learning approach

Predicting crack length and orientation in twill woven CFRP plates is notoriously non-trivial due to the interplay of complex physics over multiple length scales. Furthermore, on an industrial scale, a timely yet accurate non-destructive prediction based on a limited amount of data is critical for successful industrial adoption. This paper proposes a physics-assisted surrogate approach, by first measuring electrical conductivities using the Electrical Resistance Charge (ERC) and then developing high-fidelity through-thickness crack models resulting in 42 datasets, and processing the resulting data with a polynomial regression coupled with the leave one out cross validation using physics-based engineered features. The proposed method achieved averaged error of 0.09% and 0.48% for crack length and orientation, respectively, exhibits advantages over the Artificial Neural Network (ANN) in terms of both accuracy and tendency to overfit. This proposed approach paves the way for the maturing of the sought-after real-time Structural Health Monitoring (SHM) of crack length and orientation.

Micromechanical modeling and experimental analysis of yarn separation type sewing damage on continuous filament fabrics

Fabrics with weaves of low interlacing density and smooth yarns such as continuous cuprammonium filaments are often susceptible to sewing damage of cracks perpendicular to the sewing line, seriously influencing the aesthetics of the finished garment. To understand how the important factors such as yarn modulus, yarn bending stiffness, sewing needle radius, yarn-on yarn-friction, fabric counts and fabric weaves act on the crack length of such a fabric, a micromechanical model is proposed, and the experimental results are compared with the theoretical prediction. Single yarn pull-out tests and single yarn axial compression tests are performed to estimate yarn-on-yarn friction and yarn bending stiffness, respectively. The model indicates that the sewing crack length is positively proportional to the yarn tensile modulus, yarn bending stiffness and the needle radius and is negatively proportional to the fabric count and the inter-yarn friction. The model predicted crack lengths are within the range of the experimental results in warp direction while the predicted value is substantially larger than the observed crack lengths in weft direction due to the high compressibility of the weft yarn, which decreased yarn tension, bending stiffness and increased yarn cover power. For a given fabric, increasing yarn-on-yarn friction and raising yarn compressibility is an effective way to control the crack lengths.

PVC failure modelling through experimental and digital image correlation measurements

This paper analyses industrial PVC sheets structural integrity assessment widely used for different ranges of industrial applications. We investigated combined approaches focused on fracture toughness assessment to predict PVC mechanical behavior against failure. We ran a series of tests on tensile and single-edge notched samples at various crosshead speeds on a tensile test machine. PVC sheets' stress intensity factors were evaluated using both theoretical and experimental approaches to model crack growth. In the experimental procedure, we used the digital image correlation (DIC) method. We also developed a semi-empirical model to predict crack length over time. Furthermore, we proposed that the crack growth rate and stress intensity factor were satisfactorily correlated at all crosshead speeds and that the crack growth rate could be represented using a power-law model. In pre-cracked PVC specimens, the results showed that crack growth appears to be influenced by crosshead speed.

Temperature‐dependent interlaminar behavior of unidirectional composite laminates: Property determination and mechanism analysis

AbstractDelamination damage is a critical concern for composites—especially for aircraft structures—considering their complex service conditions, which include extreme temperatures and impact threats. This study considers the effect of temperature (−20°C to 110°C) on the mode‐I interlaminar failure behavior for unidirectional carbon/epoxy composite laminates, through a series of experiments. A simple double compliances method (DCM) without the measurement of crack length was employed to determine mode I interlaminar fracture toughness, and the accuracy of DCM at different temperatures was validated by comparing the results obtained from DCM with those calculated using ASTM methods. The comparison indicates that fracture toughness values determined from DCM are consistent with those from ASTM methods, and the predicted crack lengths from DCM show little difference with experimentally measured crack lengths. The experimental results reveal the significant sensitivity of mode I interlaminar failure behavior with the environmental temperature. Both the peak load and initial interlaminar fracture toughness increases with the increase of test temperature. It is found that propagation fracture toughness shows different temperature sensitivity at high temperatures (50°C to 110°C) than that under low temperatures (−20°C to 25°C). The crack propagation speed tends to be a constant value during the tests and decreases with the increase of test temperature. The fractography analysis illustrates a transition of the mode of failure from fiber–matrix interface debonding at lower temperatures to matrix cleavage at higher temperatures.

Structure Fatigue Crack Length Estimation and Prediction Using Ultrasonic Wave Data Based on Ensemble Linear Regression and Paris’s Law

This paper presents methods for the 2019 PHM Conference Data Challenge developed by the team named "Angler". This Challenge aims to estimate the fatigue crack length of a type of aluminum structure using ultrasonic signals at the current load cycle and to predict the crack length at multiple future load cycles (multiple-step-ahead prediction) as accurately as possible. For estimating crack length, four crack-sensitive features are extracted from ultrasonic signals, namely, the first peak value, root mean square value, logarithm of kurtosis, and correlation coefficient. An ensemble linear regression model is presented to map these features and their second-order interactions with the crack length. The Best Subset Selection method is employed to select the optimal features. For predicting crack length, variations of the Paris’ law are derived to describe the relationships between the crack length and the number of load cycles. The material parameters and stress range of Paris’ law are learned using the Genetic Algorithm. These parameters will be updated based on the previous-step predicted crack length. After that, the crack length corresponding to a future load cycle number for either the constant amplitude load case or variable amplitude load case is predicted. The presented methods achieved a score of 16.14 based on the score-calculation rule provided by the Data Challenge committees, and was ranked third best among all participating teams.

Damage assessment of carbon fibre reinforced plastic using acoustic emission technique: experimental and numerical approach

In this research work, the acoustic emission results obtained from testing double cantilever beam specimens with carbon fibre reinforced plastic laminates are analysed. The acoustic emission descriptors such as amplitude, frequency centroid, counts, duration and risetime are clustered using k-means++ algorithm. An unconventional and innovative way of using the acoustic emission descriptors, after the clustering, is introduced. This method can favourably be used for relating the different damage progression modes in fibre reinforced plastics. Apart from this, the cumulative acoustic energy is used for predicting the crack length of the specimens. The predicted crack length is almost identical to the actual crack length opening recorded in each specimen. Finally, analytical and finite element models are used for validating the experimental results under the mode I delamination. The finite element studies are carried out using cohesive zone modelling in Comsol Multiphysics® platform.

Rheological and fatigue characterisation of bitumen modified by anti-ageing compounds

When exposed to the ambient environment for an extended period, bitumen ages and causes the failure of asphalt pavement, the addition of anti-ageing compounds (AACs) to bitumen binders can prolong the service life of the pavement. This study investigates the effects of anti-ageing compounds on the fatigue performance of bitumen when subjected to different ageing conditions. The AAC-modified bitumen binders were tested by dynamic shear rheometer (DSR) and Fourier transform infrared spectroscopy test (FTIR) at different ageing conditions including unaged, short-term ageing by thin film oven test (TFOT) and long-term ageing by pressure ageing vessel (PAV). The fatigue performance of the AAC-modified bitumen was characterised by the dissipated energy ratio (DER), SHRP fatigue parameter and the DSR-cracking (DSR-C) approach developed by the authors. Linear amplitude sweep (LAS) tests were firstly run at 20 °C, 10 Hz and 0.1–15% controlled shear strain conditions, to obtain the phase angles and shear moduli at the undamaged conditions. Time sweep (TS) tests were then conducted at 5% shear strain, also at 20 °C and 10 Hz, and up to 24,000 loading cycles to obtain phase angles, shear moduli and DER at damaged conditions. The crack lengths in the TS tests were calculated by DSR-C model and then validated by the image analysis method. The results suggest that, compared to the DER or SHRP fatigue parameter, DSR-C predicted crack lengths show a more consistent and reliable agreement with laboratory measurements. DSR-C test can differentiate fatigue cracking performance among binders modified with AACs, and the normalised carbonyl index may be a reliable parameter to reflect the impact of ageing products on the fatigue resistance of AAC-modified binders. Bitumen samples modified with 12% (1 furfural: 5 Irganox 1076), 15% Irganox 1076 and 3.5% (3 DLTDP: 4 furfural) demonstrated the best anti-ageing behaviour by retarding carbonyl content growth and decreasing the fatigue damage among selected AACs without sacrificing the stiffness of binder. However, rutting susceptibility at earlier stages of service life needs further investigations.

Identification of Crack Length and Angle at the Center Weld Seam of Offshore Platforms Using a Neural Network Approach

The reconstruction algorithm for the probabilistic inspection of damage (RAPID) is aimed at localizing structural damage via the signal difference coefficient (SDC) between the signals of the present and reference conditions. However, tomography is only capable of presenting the approximate location and not the length and angle of defects. Therefore, a new quantitative evaluation method called the multiple back propagation neural network (Multi-BPNN) is proposed in this work. The Multi-BPNN employs SDC values as input variables and outputs the predicted length and angle, with each output node depending on an individual hidden layer. The cracks of different lengths and angles at the center weld seam of offshore platforms are simulated numerically. The SDC values of the simulations and experiments were normalized for each sample to eliminate external interference in the experiments. Then, the normalized simulation data were employed to train the proposed neural network. The results of the simulations and experimental verification indicated that the Multi-BPNN can effectively predict crack length and angle, and has better stability and generalization capacity than the multi-input to multi-output back propagation neural network.

Ensemble Linear Regression and Paris’ Law Based Methods for Structure Fatigue Crack Length Estimation and Prediction Using Ultrasonic Wave Data

This paper presents the methods developed for the 2019 PHM Conference Data Challenge. The PHM Data Challenge aims to estimate the fatigue crack length of a type of aluminum structure using ultrasonic signals at the current loading cycle, and to predict the crack length at multiple future loading cycles (multiple-step ahead prediction) as accurate as possible. For the crack length estimation, four crack sensitive features are extracted from ultrasonic signals, namely, the first peak value, root mean squared value, log of kurtosis and correlation coefficient. These features and their 2nd order interactions are used as inputs for an ensemble linear regression model which is built to map the features to crack length. The Best Subset Selection method is employed to select optimal features. For the crack length prediction, variations of the Paris’ law are derived to describe the mutual relationships between crack length and the number of loading cycles. The specimen material parameters and stress range of the Paris’ law are learned using the Genetic Algorithm, and updated with the next-step predicted crack length. The crack length corresponding to a future loading cycle number under constant amplitude cyclic loading and under variable amplitude cyclic loading is predicted respectively. The presented overall methodology achieves a score of 16.14 with the score calculation rule provided by the Data Challenge organization team, and ranks 3rd among all teams.

Fracture Properties of Multirecycled Asphalt Mixes from Four-Point Bending Test Using Digital Image Correlation and Back Calculation

Abstract Six different asphalt mixes were subjected to the four-point bending fracture tests designed at the University of Lyon/École Nationale des Travaux Publics de l’État (ENTPE). Among the six tested mixes, three were hot mixes and three were produced according to a warm process with foamed binder. For each of the two processes, the first mix contained 0 % reclaimed asphalt pavement (RAP). The second mix contained 40 % RAP from a milling process. The third mixes contained 40 % of the second mix, aged artificially in the lab and recycled. Two methods were applied to determine the crack propagation during fracture testing. The first one, called the displacement ratio method for predicting crack length, is based on displacements measurements. The second one used digital image correlation and strain field analysis. The two methods gave similar results for crack length values during the tests. The stress intensity factor (KIC) as a function of crack length was calculated. Results showed rather close fracture properties for the six mix types.

Predicting crack growth in viscoelastic bitumen under a rotational shear fatigue load

This study develops a damage mechanics-based crack growth model to predict crack length in a typical viscoelastic material (i.e. bitumen) under a rotational shear fatigue load. This crack growth model was derived using torque and dissipated strain energy equilibrium principles. The crack length was predicted using bitumen’s shear moduli and phase angles in the undamaged and damaged conditions, measured by linear amplitude sweep (LAS) tests and time sweep (TS) tests, respectively. The two tests were both performed using Dynamic Shear Rheometer (DSR), thus the crack growth model was named as a DSR-C model. To validate the DSR-C model, the crack lengths after the TS tests were measured using digital visualisation of cracking surfaces for one virgin bitumen and one polymer-modified bitumen at two temperatures (15, 20°C), two frequencies (10, 20 Hz) and two strain levels (5%, 7%) under unaged and aged conditions. Results show that the DSR-C model can accurately predict the crack length in the viscoelastic bitumen under the rotational shear fatigue load at different loading and material conditions. The crack growth includes initial transition period, steady growth period and rapid growth period under a controlled strain loading mode. The degradation of the material property results from the crack growth that initiates from the outer edge toward the centre of the sample under the rotational shear load.

Prediction of delamination propagation in polymer composites

Delamination within composite laminates has been typically characterized by the critical strain energy release rate, or fracture toughness, by performing double cantilever beam (DCB) tests. However, significant variations of the fracture toughness can occur across the width of a DCB test article due to the anticlastic curvature of composite laminates in bending. To obtain more accurate fracture toughness values, this study demonstrates a Lagrangian cross-correlation method that uses strain measurements directly from the delamination front in a DCB test to estimate the internal fracture toughness. Unmodified optical fibers were embedded in DCB test articles fabricated from non-crimped carbon fabric using a VARTM process. The variation in the strain energy release rate along the delamination front is obtained using multiple optical fiber passes. Predicted crack lengths, fracture toughness, and flexural moduli are in excellent agreement with those from surface measurements.

Acoustic emission detection and prediction of fatigue crack propagation in composite patch repairs using neural network

This article presents the results of acoustic emission (AE) monitoring of crack propagation in 2024-T3 clad aluminum panels repaired with adhesively bonded octagonal and elliptical boron/epoxy composite patches using FM-73 adhesive under tension–tension fatigue loading. Two crack propagation gages and four broadband AE sensors were used to monitor crack initiation and propagation, respectively. The acquired AE signals were processed in time and frequency domain to identify sensor features correlated with fatigue cycle and crack propagation, which were used to train neural networks for predicting crack length. The results show that AE events are correlated with crack propagation, and crack propagation signals can be differentiated from signals due to matrix cracking, fiber breakage, and shear of the composite patch. Three back-propagation cascade feed-forward networks were trained to predict crack length using number of fatigue cycles, number of AE events, and number of fatigue cycles and number of AE events together as inputs, respectively. It was found that network with fatigue cycles as input gave good results, while the network with just AE events as input gave greater error. However, the network using both fatigue cycles and number of AE events as inputs to predict crack length gave much better results.

Prediction of delamination growth in carbon/epoxy composites using a novel acoustic emission-based approach

Delamination is the most common failure mode in laminated composites and it leads to loss of structural strength and stiffness. In this paper, acoustic emission monitoring was applied on the carbon/epoxy laminated composites when subjected to mode I, mode II, and mixed-mode I and II loading conditions. The main objective is to investigate delamination behavior and to predict propagation curve of the delamination in different GII/GT modal ratio values by the acoustic emission. First, a combination of acoustic emission and mechanical data (sentry function) is used to characterize the propagation stage of the delamination. Next, the crack tip location during propagation of the delamination in the specimens is identified using two methods. In the first method, by determining the velocity of the acoustic emission waves in the specimens, the position of the crack tip can be estimated throughout the tests. In the second method, the cumulative energy of the acoustic emission signals is utilized for localization of the crack tip. Agreement between the predicted crack length and the actual crack length verifies the presented procedures. It can be concluded from the results that the acoustic emission method is a powerful approach to investigate the delamination behavior and to estimate the crack tip position in the composites.

Finite element analysis of crack mouth opening displacement compliance in crack length evaluation for clamped single edge tension specimens

ABSTRACTIn the unloading compliance method developed for clamped single edge tension (SE(T)) specimens, six crack mouth opening displacement (CMOD)‐based compliance equations (i.e. a/W = f(BCE′)) were proposed for the crack length evaluation without clearly clarifying the corresponding predictive accuracies. In addition, the effective elastic modulus (Ee) that reflects the actual state of stress should also be introduced in the crack length evaluation for SE(T) specimens, because the actual state of stress in the remaining ligament of the test specimen is neither plane stress (E) nor plane strain (E′). In this study, two‐dimensional (2D) plane strain and three‐dimensional (3D) finite element analyses (FEAs) are carried out to investigate predictive accuracies of the six compliance equations. In both 2D and 3D FEA, specimens with a wide range of crack lengths and geometric configurations are included. For a given specimen, the value of Ee that presents the equivalent stress state in the remaining ligament is calculated on the basis of 3D FEA data. A set of formulae for the clamped SE(T) specimen is proposed that allows to evaluate Ee from the corresponding CMOD compliance. This approach is verified using numerical data. The observations of the numerical verification suggest that the use of Ee instead of E or E′ in CMOD‐based compliance equations markedly improves the accuracy of the predicted crack length for clamped SE(T) specimens.