The increasing use of ultrasonic guided waves (GWs) has been shown to have great potential for the detection of fatigue cracks and non-fatigue type damages in metallic structures. This paper reports on a study demonstrating an energy-based damage imaging approach in which signal characteristics identified through relative time differences by fatigue crack (RTD/f) through different sensor paths are used to estimate the location of fatigue crack in steel plates based on GWs generated by an active piezoceramic transducer (PZT) network. The propagation of GWs in the original 10 mm-thick plate was complicated due to its thick geometry, wave dispersion, boundary reflection and the existing boundary notch used to initiate the fatigue crack, resulting in diverse forms of interference with fatigue crack identification. Hence, RTD/fs were extracted from the wave energy spectrum with the aid of a wavelet transform (WT) and a correlation function. The series of tests carried out in this study include a fatigue test in which a fatigue crack was introduced to the steel plate, in addition to subsequent tensile and compressive tests designed to investigate the effect of loading on wave signals. Simultaneously, the proposed method was verified by finite element analysis and good agreement was obtained between the numerical and experimental results using the developed fatigue crack model. The results show that fatigue cracks can scatter GWs via discontinuous contact between crack surfaces under cyclic fatigue loadings, thus demonstrating the effectiveness of the proposed method for the real-time monitoring of fatigue cracks in metallic structures.

The degradation of engineering materials due to the initiation of fatigue cracks is known to be one of the main reasons for the widespread failure of older engineering structures [

The traditional GW method based on PZT transducers has some unique advantages over LBT. First, PZT-based monitoring strategies that employ the GW method rely solely on a series of actuator/sensor transducers for the generation and collection of GWs. Laser vibrometry systems involved in data acquisition also requires a PZT to generate GWs in order to obtain adequate results. Second, although LBT has been adopted and shown to be effective in a large number of applications, it seems more suitable for metallic or composite plate-like structures than for complex structures, due to the conditions in which it is applied [

Fatigue crack detection is a subject that has received increasing attention in recent years. An ultrasonic GW technique has been used to inspect both metallic and composite structures subject to fatigue loadings [

The aim of the study reported in this paper was to demonstrate the application of a probability-based imaging approach based on GWs for detecting fatigue cracks and load effects, while eliminating the effect of adjacent notches. The rest of this paper is organized as follows. The next section describes how a fatigue crack was introduced into a thick steel plate with multiple boundaries due to two supporting holes and a notch. GWs generated by an active PZT transducer network were then combined with an imaging approach with the aid of the RTD/fs concepts to estimate the presence and location of the fatigue crack. The following section of the paper then describes a series of tensile tests and compressive tests employed to assess the different load effects of the fatigue crack. The paper concludes with a brief summary of the findings made and a discussion of their implications.

As shown in

Density | 7.85 g/cm^{3} |
---|---|

Poisson’s ratio | 0.28 |

Elastic constant, E | 210 GPa |

Seven circular PZT transducers with the same dimensions of 6.9 mm in diameter and 0.5 mm in thickness were surface-mounted to the plate to function as an active sensor network. Each PZT transducer with the properties shown in ^{®} and downloaded to an arbitrary waveform generator (HIOKI^{®} 7075) in which D/A conversion was performed. An amplifier (PiezoSys^{®} EPA-104) was then used to amplify the analog signal to 80 Vp-p, which was then applied to each PZT wafer in turn to activate the GWs. When one of the PZT transducers was activated, the rest of them served as sensors to monitor the propagation of GWs in the steel plate using an oscilloscope (HP^{®} Infinium 54810A) at a sampling rate of 10 MHz.

Geometry | φ: 6.9 mm, thickness: 0.5 mm |
---|---|

Density | 7.80 g/cm^{3} |

Poisson’s ratio | 0.31 |

Charge constant, d_{31} |
−170 × 10^{−12} m/V |

Charge constant, d_{33} |
450 × 10^{−12} m/V |

Relative dielectric constant, K_{3} |
1280 |

Dielectric permittivity, P_{0} |
8.85 × 10^{−12} F/m |

Elastic constant, E | 72.5 GPa |

Although it is clear that multiple wave modes cannot be avoided in captured signals, the excitation frequency was strictly restricted to 150 kHz due to the multiple boundaries of the plate. Moreover, the wave packages scattered by the fatigue crack were likely to overlap with those reflected from boundaries because the crack was located particularly close to the physical edges of the plate and to the notch. Based on these conditions, the key points in defining the location of the fatigue crack were a suitable sensor network, an outstanding dominant wave component and a useful set of signal post-processing methods.

The steel plate described above was clamped in a 100 kN MTS fatigue-testing machine in the force-controlled mode via an MTS load unit controller (as shown in

In comparison with other GW transducers, PZT transducers can serve as both actuators and sensors, and their portability enables them to be permanently mounted onto the structure to facilitate automated online structural health monitoring through an appropriate sensor network. However, PZTs generally excite multi-mode GWs simultaneously, after which the waves reflected, transmitted or converted at the boundaries cause damage, thus producing complicated wave signals. In addition to the diverse forms of interference caused by materials and natural vibration, fatigue cracks make it more difficult to detect damage due to the characteristics of fatigue failure. In light of the above complications, appropriate high-grade signal processing methods must be applied to discriminate between wave signals and extract wave characteristics. Using advanced signal processing algorithms that have now become prevalent, wavelet transform (WT) technology including a discrete wavelet transform (DWT) and a continuous wavelet transform (CWT) was applied to process the signals obtained in this study. Wavelet analysis can be used to transfer guided-wave signals from the time domain to the time-frequency domain. In numerical analysis and functional analysis, a DWT is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, one of its key advantages over Fourier transforms lies in temporal resolution: it captures both frequency and location information (location in time). In this study, the DWT defined by

where _{k} are the dyadic time-scale integers and wavelet amplitudes. The aims of the DWT procedure were to decompose and rebuild the signals using the Mallat algorithm at different levels of frequency for multi-resolution analysis and to reduce the number of redundant coefficients of equal magnitude.

A CWT has the ability to construct a time-frequency representation of a signal that offers very good time and frequency localization, which is then used to divide a continuous-time function into wavelets. In mathematical terms, the CWT of a continuous, square-integrable function

where

where the wavelet coefficients stand for the energy density of the relevant signal in the time-frequency domain [

According to the principles of WT, the scale representative in the WT is proportional to its reciprocal as a substitute for frequency. Thus, after transformation, each previous scale in terms of the time domain bears an equivalence to homologous frequencies in the time-frequency domain. As a result, signal differences due to reflections from a fatigue crack pertaining to an induced notch can be isolated in a specific sub-domain. The fatigue crack can be separated from the signal rebuilt in the sub-domain corresponding to the excitation frequency via the DWT with a combination of wave energy spectrums based on the CWT by extracting the RTD/fs.

A typical signal obtained in the course of the experiment by the actuator-sensor path _{12} (No. 1 as the actuator and No. 2 as the sensor) in the time domain before and after initiating the fatigue crack is illustrated in

Identifying the fatigue crack in the plate purely on the basis of these original signals would have been extremely difficult. Thus, to obtain information that would be useful for detecting the fatigue crack, the raw signals were decomposed into multiple frequency segments using the DWT procedure, and the corresponding level including the excited frequency of 150 kHz was selected, with outside noises from other frequency bands being filtered out. The purified signals were then transformed into wavelet coefficients in the time-scale domain using the CWT procedure. To obtain and extract signal characteristics for fatigue crack detection, it is better to enhance the signals of waves scattering from the fatigue crack and concentrate the information they convey into a narrow band of the excited frequency. Thus, the energy spectrum based on the wavelet coefficients was integrated along the scale axis. In comparison with the raw signals shown in

A similar phenomenon can also be seen from the wavelet coefficient distribution in the time-scale domain constructed through the CWT analysis as shown in

The changes in wave energy represent the early waves scattered by the fatigue crack rather than those scattered by the initial notch. As shown in

In this study, the key point in detecting the fatigue crack was to identify the difference caused by GW interactions with the fatigue crack when incidental GWs propagated through it. According to the wave scattering rule, the signal collected from the sensor network must include a wave component that differs from the baseline and represents the signal scattering from the fatigue crack. The arrival time of the wave component can also be used to locate the fatigue crack. The direct transmission, reflection and possible mode conversion of the dominant mode are monitored to identify the fatigue crack due to its high level of wave energy [

where _{n} and _{n} are correlated time series. There will be a peak in the correlation coefficient curve, and the corresponding time lag represents the difference in the arrival time of these two peak values when the peak values in the two signals are correlated with each other. In this study, _{n} and _{n} served as the time responses of the purified energy envelope obtained from the wavelet analysis in the autocorrelation function. They were used to establish the correlation coefficient curves of the intact plate and the fatigued plate shown in

As described in the definitions, the time lag corresponding to each peak in the correlation coefficient curve measures the time difference between the highest amplitude of the incipient wave packet and that of the following wave components. The difference represented by the local wave package can be enhanced when the correlation coefficient curve for the damaged plate is divided by the baseline curve. The first discrepancies between the fatigued and pre-fatigued plates derived from the peaks represent signals directly transmit from one actuator to one sensor. If take this peak value as threshold, the discrepancies derived from the first peaks excess the threshold represent differences induced by the fatigue crack. The fatigue-induced peak highlighted in

In this part of the study, effort was focused on determining the fatigue crack presence probabilities (^{2} each in what follows), the distance from a certain grid _{j} (_{m} can be expressed as, where and are the location vectors of _{m} and _{j} in the global coordinate system, as shown in _{m}_{j}_{n} can then be defined as

The coordinates of the damage center are two unknown variables. The solution of

In principle, the grids correctly located on this locus, i.e., those with coordinates that satisfy _{j} and the sensing path pair _{m,n}

where _{j} when RTD/f_{m,n} is given, denoting the distance between grid _{j} and the ellipse locus in the time domain, _{j} regarding _{m,n} becomes

The _{m,n}. To illustrate, suppose the plate is virtually meshed into _{j}, _{m,n}

In this image, the _{m,n} are available for use in conjunctive fusion schemes, as stated in following expressions:

where _{p} is the number of elements in _{L,P} is so-called fusion result for all

After generating the fatigue crack, both a tensile load and a compressive load were applied to the steel plate to identify the effect of these loads on the fatigue crack. _{67} via the experiments. The envelopes of the amplitudes of this family of periodic curves can be seen in zoom view figure of

The results show that the _{0} waves transmitted were marginally smaller if the fatigue crack was under tension, as represented by a smaller wave amplitude. In contrast, the _{0} waves transmitted were somewhat larger if the fatigue crack was under compression, as represented by a much larger wave amplitude. Apart from amplitude, _{0} wave transmitted when the fatigue crack was under compression. The reason for this is that for a partially open fatigue crack under compression, some of the open area will be closed due to the load being applied and the wave can be transmitted through the closed area instead of scattering from the open area. In cases of GWs transmitted when the fatigue crack was under a fatigue load and a tensile load, there was very little difference in either amplitude or time of flight (

The fatigue crack was simulated by the Seam Assigned Model (SAM) in finite element method (FEM) software ABAQUS^{®}/CAE combined with contact effect to ensure part of the pressure pass through the intersurfaces of the fatigue crack. All the simulation procedures and parameters adopted were same with previous simulation work in this thesis except the model part and mesh part, which were suitable for SAM analysis. Simulation model is shown in

In order to establish the fatigue crack model, the model of steel plate was firstly partitioned with a specific length, i.e., the fatigue crack length, 15 mm in this case, which originated from the notch tip and then the seam and contact effect were assigned on the partitioned surfaces. At the same time, a model of a intact steel plate with the same dimensions and properties was established for obtain a baseline data.

Using the same analytical method and procedure as amentioned in experiments, simulation results obtained from _{12} and processed by data compression and interpretation are shown in

We can see that simulation results and experimental results agree well with each other no matter from the difference of ToFs or amplitudes between the baseline data and signals from fatigued sample. By all the _{s} extracted from FEM results, locations with highest probability of fatigue crack occurrence was picked out and detailed in

In order to differentiate the developed fatigue crack modal with traditional crack modal, which was established by deleting element, three different models for one was an intact plate without crack, one was a plate with a fatigue crack model and one was a plate with deleted elements in the fatigue zone. Except the establishment of crack, the other properties and parameters about the models were the same. _{67} via the simulations.

The envelopes of the amplitude and _{0} wave mode which was transmitted through the crack zone. Results indicate that the _{0} wave modes transmitted were marginally smaller for model with fatigue crack and model with deleted elements compared with that of model for intact plate as the crack reflected most of the wave energy. And for the amplitude obtained from fatigue crack model, wave amplitude is a little larger than that obtained from model with deleting elements because this developed fatigue crack model can transmit part of wave energy through the fatigue crack. Apart from amplitude, _{0} wave transmitted for the intact plate model. And

This paper reports on a study in which an active PZT sensor network was successfully used to identify the location of a 15 mm fatigue crack in a thick steel plate by experiments and FEM analysis with a satisfactory degree of precision.

(1) WT technology and the correlation function on the energy distribution envelope were employed to determine the

(2) The outcome of the study indicates that this method combining a GW propagation-based imaging approach with estimation of the load effect on waves guided through the fatigue crack delivers an acceptable visual estimate of the location of fatigue cracks in steel plates. The proposed approach thus represents an effective method of evaluating the presence and location of such damage in steel structures and has great potential for their real-time SHM.