Experimental study on wire breakage detection by acoustic emission

Abstract

This paper experimentally investigated wire breakage detection in a steel cable by acoustic emission (AE) waveform. In the experiments, the attenuation laws of waveform amplitudes were discussed based on stress wave propagation in the wire, which was generated by kNocking and wire breakage. Then the wave velocity was calculated based on the reach time of the stress wave from each sensor. Finally, based on the waveform attenuation laws and the linear position method, the amplitude and energy of the source were confirmed through the measured waveform to identify the source category. The experimental results illustrated that the stress wave from different sources has a different frequency spectrum, and the amplitude attenuation factor varied with the stress wave frequency; high frequency waves had a greater attenuation factor. Compared with the other source, the wire breakage source contained a much higher energy, and thus, the wire breakage signal can be distinguished from the other source by comparing the non-attenuation energy at the source position.

Keywords

acoustic emission (AE) / waveform / wire breakage / attenuation factor / wave velocity

Introduction

Acoustic emission (AE) is the phenomenon whereby transient elastic waves are generated by the rapid release of energy from a material fracture, which is also called stress wave emission [1]. As a real-time, dynamic, passive non-destructive monitoring method, the AE technique can analyze measured data that comes directly from the damage source, and thus, the type and severity of the structural damage can be identified in real-time.

At present, AE has been widely used in aerospace, machine manufacturing, chemical and civil engineering and many other fields. In bridge engineering, it is primarily used to monitor concrete cracks [2], pre-stressed reinforced defects [3] and cable conditions. Early studies using AE analysis focused on parameter methodology, which is where several characteristics of the full-waveform are extracted. AE analysis is better suited for trend analysis of continuous damage, but accuracy is lost with unexpected damage identification. Casey [4,5] has discussed in detail the AE monitoring results on the impacts of cable structure, size and number of broken wires. Drummond et al. [6] used AE monitoring in the cable fatigue process and established a relationship between the characteristic parameters distribution and the fatigue process. Nair and Cai [7] used AE parameters’ statistical analysis for damage warning. In a study on boom damage in bridges, Li and Ou et al [8] used an AE characteristic parameters relationship map to identify broken wires and non-broken wire signals and used fractal dimensions of the AE characteristic parameters to discriminate whether a wire was healthy. Waveform analysis is based on the full-waveform collected by AE and used to identify damage, and unlike parametric analysis, waveform analysis has more complete information and obtains precise characteristics of the injury; however, the data used in the analysis is large and requires a complex analysis process.

High-strength steel is the basic unit of cables in a load-bearing bridge. Studies on its wave propagation characteristics and damage of the wire are the basis of health monitoring of the cable body. Jin et al. [9,10] performed experiments on wire cable destruction and simulated the propagation of elastic waves using the finite element method. They argues that in noisy environments, accuracy is hampered when signals are identified based only on the characteristic parameters of AE, which is easy to misjudge, and more information should be required, such as the waveform in the time domain and frequency spectrum distribution. Prior to this study, waveform analysis was used for lead break-off, knock, friction and wire breakage of high-strength steel wire. The results showed that in the time domain, the wire breakage signal amplitude and duration were much greater than the other signals; in the frequency domain, the frequency of the wire breakage signal was also greater than the other signals. The signal spectrum of knock and friction had a single peak in which the frequency did not exceed 50 kHz (~30 kHz or so was the most), and the signal spectrum of the wire breakage contained several obvious peaks, where the main peak was typically at 150 kHz. Although these test results could clearly distinguish between non-broken wires and broken wire signals, these waveform characteristics only indicated waveform characteristics at the wave source. If there was only slight damage near the sensor but serious damage far away from the sensor, the differences in the AE signal collected from the sensor might be vague in the waveform and frequency spectrum. To identify the categories of damage, a diverse array of characteristics should be compared at the damage source rather than at the sensor. In this paper, the attenuation factor for impact and wire breakage in wires was fitted based on test data. Then the wave propagation speed was measured. Finally, the energy values of the acoustic wave from various damage sources were compared to illustrate that wire breakage can be identified by comparing the non-attenuation energy at the damage source.

Experiments

Equipments

The PCI-2 acquisition system made by PAC in the US served as the AE collection device in the experiment with a waveform sampling frequency of 1 MHz. The high-strength galvanized steel wire in the experiment was 5 mm in diameter, which is a commonly used size for a bridge cable, and the theoretical yield stress of the high-strength steel wire was 1860 MPa. Tension was provided by a hydraulic jack rated at 50 kN, and the yield strength for the steel wire was 36 kN. The experiment was divided into two stages: impact stage and tensile stage. The device layout of the impact test is shown in Fig. 1, and the tensile test device is shown in Fig. 2.

Methods

The experiment consisted of two parts. In the first part, the impact test was performed for a 25-m-long wire, where the wire was impacted by a piece of iron free-falling from a fixed height. Similar impact energy was guaranteed for each impact so as to have comparable tests. The stress wave from the impact source attenuated after arriving at the sensors based the amplitude and time of the waveform received from different sensors; the attenuation ratio and wave propagation velocity were then measured.

In the second part, the wire tensile test was processed with a 6.5-m-long steel wire and a 50 kN hydraulic jack as the source of tension. Before the tension, the break points were set, which were marked by ring snicks with a notch depth of 0.1 mm. During tension, loading was added step by step, and the duration was maintained at 3 min from the beginning to the break of the wire. According to the fracture waveform collected by the sensors, the waveform amplitude attenuation curve was fitted.

Data analysis

Stress wave attenuation curve

The amplitude and energy will attenuate as the propagation distance increases when a stress wave is traveling along the wire. The magnitude of the attenuation is often described by the attenuation ratio. The attenuation ratio is based on the material properties, cross-section shape, wave frequency, etc., but when the material properties and section shape are given, it is a function of wave frequency. In geophysics, the attenuation ratio is often expressed as a quality factor of the rock found from using various measurement methods, such as the amplitude attenuation method [11], rise time method [12], frequency spectrum peak ratio method [13], and waveform inversion method [14] and so on. In this experiment, the attenuation ratio was calculated using the amplitude attenuation method.

The attenuation of elastic waves is caused by many factors, and it is generally accepted that when an elastic wave is propagating, the attenuation of the amplitude with propagation distance is expressed as:

(1)u(r)=u_{\mathrm{0}}\exp (-ar),

where u(r) is the amplitude of the stress wave r away from the wave source; u₀ is the initial amplitude at the wave source; and \alpha is the attenuation factor.

The wave propagation attenuation factor can be calculated based on two points on the wave propagation path. Assuming that the two points are away from the wave source at a distance of r₁ and r₂, and the amplitude of the two points is u(1) and u(2), then the attenuation factor, \alpha, can be calculated according to Eq. (2):

(2)\alpha =-{\displaystyle \frac{\ln u(\mathrm{1})-\ln u(\mathrm{2})}{r_{\mathrm{1}}-r_{\mathrm{2}}}}.

With the same material and cross-section shape, the calculated attenuation factor is affected by the wave source frequency, and the wave source frequency depends on the energy release speed of the damage. To measure the attenuation factor of the stress waves with different frequencies in steel, two kinds of wave sources were adopted in the tests: impact and tensile sources.

Impact damage attenuation factor

For the impact process, equal altitude free-fall impact is suggested. The layout of the sensors is shown in Fig. 3. It is better to place sensors in the middle section of the steel wire to reduce the impact of reflected waves on the attenuation ratio.

Table 1 lists the testing data from six groups with the waveform amplitude of the sensors.

Because the energy values were similar for each impact process, the mean of the six groups was used to fit the attenuation curve. Equation (1) shows that the amplitude followed an exponential attenuation. The exponential attenuation curve was fitted using the least-squares method, as shown in Fig. 4.

The resulting fitted curvilinear equation was u(r)=u_{\mathrm{0}}\exp (-\mathrm{0.373}r).

Thus, the attenuation factor of the impact stress wave was α = 0.373. The waveform frequency spectrum is shown in Fig. 5 and the peak frequency was 10 kHz.

Fracture damage attenuation factor

The wire tensile test was performed in the Shanghai Pujiang Cable Factory. The layout of the testing sensors is shown in Fig. 6, and the amplitude of the waveform received by the sensors is shown in Table 2.

Because there were large differences in the fracture energy of each group, the least squares method was used on the four data sets to fit the attenuation curve, as shown in Fig. 7 and based on Eq. (1).

The attenuation factors of the four fracture signals were α1= 0.643, α2= 0.562, α3= 0.614, and α4= 0.564. There were small differences between the attenuation factors of each signal, but overall, the factors were larger than the amplitude attenuation factors from the impact signal. The fracture signal waveform frequency spectrum is shown in Fig. 8.

From Fig. 8, it can be seen that the frequency from the fracture signal was no longer confined within a single interval; there were several peaks, where the main peak frequency was 150 kHz and the sub-peak was approximately 80 kHz, which were greater than the wave frequency from the impact test.

By comparing the frequency spectrum and the attenuation factor of the impact source and fracture source, it can be seen that the fracture wave had a greater main spectrum peak value than that of the impact wave. The fracture wave had an average attenuation factor of 0.596 from the four tests, which was much greater than that from the impact signal.

Wave velocity in high-strength steel wire

When using the linear time difference method to locate damage sources, the time difference of the stress wave arriving at different sensors and the propagation velocity of the stress wave in the wire should be measured. There are different modes of stress wave transmission in a steel wire, and the velocity is also different; in general, the longitudinal wave is the fastest, followed by the distorted wave and then the surface wave. When the wave velocity is measured by the time difference of the sensors, only the longitudinal wave velocity that first reaches the sensor can measured. The velocities of the subsequent distorted and surface waves cannot be calculated due to their uncertain starting points.

The velocity of the longitudinal wave is affected by its wavelength when propagating through a wire. According to the Pochhammer dispersion equation [15], when the wire diameter is small, velocity can be calculated as:

(3)C={\left({\displaystyle \frac{E}{\rho }}\right)}^{\frac{\mathrm{1}}{\mathrm{2}}}\left(\mathrm{1}-{\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}{v}^{\mathrm{2}}{k}^{\mathrm{2}}{a}^{\mathrm{2}}\right).

Equation (3) can be written as a function of wire diameter and wavelength.

(4){\displaystyle \frac{C}{C_{\mathrm{0}}}}=\mathrm{1}-v^{\mathrm{2}}{\mathrm{\pi }}^{\mathrm{2}}{\left({\displaystyle \frac{\mathit{a}}{\lambda }}\right)}^{\mathrm{2}},

where C is the stress wave velocity, C_{\mathrm{0}}=\sqrt{\mathit{E}/\rho } is the wave velocity without diffusion, v is the Poisson’s ratio, k is the wave number, a is the wire radius, λ is the wavelength, E is the Young's modulus, and ρ is the wire density, where typically, E = 2.05 MPa, \rho =\mathrm{7.8}\times {\mathrm{10}}^{\mathrm{3}}\mathrm{k}\mathrm{g}/{\mathrm{m}}^{\mathrm{3}}, C_{\mathrm{0}}=\sqrt{\mathit{E}/\rho }=\mathrm{5126}\mathrm{m}/\mathrm{s}.

From Eqs. (3) and (4), we can see that with the same wire, the higher the frequency of the wave is, the slower its wavelength and wave velocity; when the wire radius is much smaller than the wavelength, the propagation velocity is close to C₀.

High-strength steel wire with a radius of 2.5 mm was used in the experiment, and the impact damage source had a spectrum main peak at approximately 10 kHz. The initial velocity, C₀, had a wavelength of 0.513 m and {\displaystyle \alpha /\lambda }=\mathrm{0.005}, which were used in Eq. (4). The inversely calculated wave velocity is very similar to C₀, and thus, the effect of frequency dispersion was neglected. When the fracture damage source has a spectrum main peak around 150 KHz and using the same initial velocity with a wavelength of 0.034 m and {\displaystyle {\displaystyle \alpha /\lambda }}=\mathrm{0.074}, using Eq. (4), the calculated velocity was also close to C₀. Through the previous calculation, it can be seen that as a result of the small radius of the high-strength steel wire, the frequency dispersion phenomenon resulting from different frequencies was not clear, and the impact of dispersion on the velocity could be neglected when measuring the wave velocity.

The impact velocity signal was used to measure the wave velocity in the high-strength steel wire. According to the time points when the impact wave reached the sensors, the stress wave velocity was computed based on the time differences and the distance between sensors, where the distance between each sensor was 2.5 m. The times when the waveforms were received are shown in Table 3.

Comparing the results of the wave velocity measured in the different test groups, the mean velocity of the six test groups was 5114 m/s, and the dispersion of the data from each group was very small. The measured velocity was slightly less than the theoretical no-dispersion wave velocity.

Sourse identification

After measuring the velocity of the stress wave in a steel wire, a linear source location method can be used to identify the damage location based on the time difference of the received signals between two sensors. Assuming that the distance between the two sensors is L and the time the two sensors receive the signal is t1 and t2, C is measured wave velocity and

(5)\{\begin{array}{l}t\mathrm{1}-t\mathrm{2}=\mathrm{\Delta }t;\\ t\mathrm{1}+t\mathrm{2}={\displaystyle \raisebox{1ex}{$L$}\!\left/ \!\raisebox{-1ex}{$C$}\right.}\mathrm{.}\end{array}

The distances between the source and sensors are:

L_{\mathrm{A}}={\displaystyle \frac{L+\mathrm{\Delta }tV}{\mathrm{2}}},L_{\mathrm{B}}={\displaystyle \frac{L-\mathrm{\Delta }tV}{\mathrm{2}}}.

Based on the location of the wave source and attenuation factor, the amplitude and energy of the stress wave from the wave source can be inversed by the testing waveform. The measured waveform of the impact source and wire breakage source are shown in Figs. 9 and 10.

It can be seen from the figures that in contrast to the impact signal, the wire breakage signal continues for a longer period of time with high amplitude values and much energy. The non-attenuation energy values of different damage sources varied greatly; in this case, using the wave attenuation factor and source location, the wire breakage damage can be identified by comparing the non-attenuation energy values of different damage sources.

Conclusions

1) After conducting impact and tensile experiments on high-strength steel wire, the frequency spectrum distributions of different damage sources were compared. The wire breakage process released energy faster and with a higher frequency compared with that of the impact source. For the breakage process, the spectrum main peak value was 150 kHz, whereas for the impact source, it was less than 20 kHz.

2) Based on the measured wave amplitude attenuation at different locations of the wire, the wave amplitude attenuation factors at different frequencies were fitted. The high-frequency wave attenuation factor was greater than that of the low-frequency wave.

3) The stress wave speed was calculated according to the start points of the waveforms obtained from sensors at different locations. The results indicated that because the diameter of the wire was very small, the stress wave velocity was less affected by frequency dispersion, where the measured wave velocity was 5114 m/s, which is slightly smaller than the theoretical value.

4) The energy released from the wire breakage process was much greater than that from the impact process. By comparing the non-attenuation energy values from different damage sources, wire breakage can be identified.

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