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applied sciences Article The Influence of Sensor Size on Acoustic Emission Waveforms—A Numerical Study ID ID Eleni Tsangouri and Dimitrios G. Aggelis * Department Mechanics of Materials and Constructions (MeMC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium; eleni.tsangouri@vub.be * Correspondence: dimitrios.aggelis@vub.be; Tel.: +32-2629-3541 Received: 24 December 2017; Accepted: 23 January 2018; Published: 25 January 2018 Abstract: The performance of Acoustic Emission technique is governed by the measuring efficiency of the piezoelectric sensors usually mounted on the structure surface. In the case of damage of bulk materials or plates, the sensors receive the acoustic waveforms of which the frequency and shape are correlated to the damage mode. This numerical study measures the waveforms received by point, medium and large size sensors and evaluates the effect of sensor size on the acoustic emission signals. Simulations are the only way to quantify the effect of sensor size ensuring that the frequency response of the different sensors is uniform. The cases of horizontal (on the same surface), vertical and diagonal excitation are numerically simulated, and the corresponding elastic wave displacement is measured for different sizes of sensors. It is shown that large size sensors significantly affect the wave magnitude and content in both time and frequency domains and especially in the case of surface wave excitation. The coherence between the original and received waveform is quantified and the numerical findings are experimentally supported. It is concluded that sensors with a size larger than half the size of the excitation wavelength start to seriously influence the accuracy of the AE waveform. Keywords: acoustic emission; concrete; sensor size effect; source orientation; excitation frequency; coherence 1. Introduction Acoustic Emission (AE) technique is commonly applied for the health monitoring of materials and structures. When the fracture process is of interest, AE offers great sensitivity allowing to detect damage events down to the nano-scale. The number and rate of registered acoustic signals is well related to the damage intensity in different material fields [1–3]. Source localization can accurately detect in 3D space the AE events emitted in small or large size structures [4–6]. Traditionally, the focus in AE has mostly been on the sensitivity or the ability to detect low energy signals and not as much on the accurate interpretation of the waveform in terms of the displacement or pressure field, (as in the case of ultrasound). However, the need for control of the structural performance necessitates more information about the failure type or damage mode. For this purpose, the time-domain parameters extracted from the waveform are investigated, as well as the waveform shape that offers valuable and direct information regarding the source’s nature. In general, the frequency and the gravity of the waveforms (energy distributed between the early or later part) are well correlated to the corresponding fracture modes in bulk media like concrete or composite plates [7–9]. Since damage characterization is based on the received waveforms, the performance of the sensors is of utmost importance. Their performance is governed by their piezoelectric element that transforms the disturbance on the surface of the transducer to an electric signal. The piezoelectric elements have certain physical characteristics (stiffness, thickness) that Appl. Sci. 2018, 8, 168; doi:10.3390/app8020168 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 168 2 of 16 define their frequency response, allowing either resonant or broadband behavior. Although the sensor ’s response is taken into account in several cases for accurate identification of the source through deconvolution [1,10–13], its physical dimensions play a very important role as well. Performance of different sensors can be compared based on calibration curves that are provided by the manufacturer. However, these curves describe mainly the response to elastic waves impinging vertically to the sensor ’s contact surface [10,14] with few exceptions dealing with parallel propagation in plates or bars [15–17]. In the latter studies, it is shown that sensors used for waves propagating on plates or bars (parallel to the sensor ’s contact surface) exhibit a certain decrease in sensitivity at high frequencies. Still, in the case of different size sensors, it remains difficult to decouple the effect of the sensor ’s frequency response from the effect of piezoelectric element physical dimension, namely “aperture” effect. The latter effect is well masked since the voltage output is derived from the average excitation over the whole surface of the element. Any distortions compared to “point” receiver is treated as an error that causes the response to deviate from the ideal behavior [10]. The importance of the aperture effect has been included in numerical studies in plates, coupled with the sensor response function [17]. It was acknowledged that the smaller tip diameter resulted in better match with the reference signal (signal without the presence of the sensor). In a more recent study, it was seen that the sensor sensitivity curves corresponding to bulk, Rayleigh, bar and Lamb waves differ substantially, especially for resonant sensors due to the aperture effect [18]. The present paper is a numerical study that intends to isolate and highlight the effect of sensor physical size on AE measurements, decoupling it from the sensor frequency response. A numeric approach appears to be the only way to evaluate the sensor size effect since experimentally, they exhibit differences in response and that does not allow to individually study the sensor size. Although, sensors with different sizes are commonly available. The numerically simulated sensor measures the average displacement on its length without any resonance effect. Therefore, in all cases the effect of sensor size, source orientation and frequency can be studied with a uniform frequency response of the sensor. Results show that in the case of surface waves and waves impinging under an angle to the surface, both the sensor size and the excitation frequency are parameters that crucially affect the waveform shape. 2. Numerical Simulation Numerical simulations are conducted with commercially available software (Wave 2000) [19]. It computes displacement vectors by solving 2D elastic wave equations using a method of finite differences. The specific acoustic equation that is simulated is: ¶ u ¶ ¶ h ¶ r = m + h r u + l + m + j + r(ru) (1) ¶ t ¶t ¶t 3 ¶t where: u is the displacement vector (consisting of two vertical u and u components), r is the density x y (kg/m ), l and m are the first and second Lamè constants (Pa), h and j are the “shear” and “bulk” viscosity (Pas) and t is time (s) [19]. The simulated two-dimensional geometry is given in Figure 1. The physical properties were chosen close to concrete: longitudinal wave velocity 4300 m/s, shear velocity 2350 m/s and density 2300 kg/m . Concrete was chosen as the most representative example of widely applied structural material used in bulk geometries, as metals and composites are usually formed in plates and the propagation conditions differ. Three receivers with different size were used, namely 20 mm (called “long” sensor), 5 mm (“medium” sensor) and 1 mm (“point” sensor). The receiver sizes are chosen to simulate the commonly used sensors in AE field, while the smallest sensor of 1 mm was used as a reference. The receivers are set at the top side of the geometry shown in grey color in Figure 1. Appl. Sci. 2018, 8, 168 3 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 17 Figure 1. Simulation model geometry. Figure 1. Simulation model geometry. The acoustic source was placed 50 mm away from the receivers at three different positions: on the The acoustic source was placed 50 mm away from the receivers at three different positions: on surface, vertically beneath the receiver and diagonally (Figure 1). Under this configuration, the effect of the surface, vertically beneath the receiver and diagonally (Figure 1). Under this configuration, the the directionality of the source can also be assessed. The source was 1 mm long and produced a vertical effect of the directionality of the source can also be assessed. The source was 1 mm long and produced displacement along its length. An actual source of AE is considered as a step function, thus very short a vertical displacement along its length. An actual source of AE is considered as a step function, thus in time, governed by the movement of the crack front (and the related oscillation around the new very short in time, governed by the movement of the crack front (and the related oscillation around equilibrium position) [20]. The basic excitation was selected as two cycles of five different frequencies, the new equilibrium position) [20]. The basic excitation was selected as two cycles of five different namely 1 MHz, 500 kHz, 200 kHz, 100 kHz and 50 kHz aiming to cover large range of wavelengths. frequencies, namely 1 MHz, 500 kHz, 200 kHz, 100 kHz and 50 kHz aiming to cover large range of A discussion on the influence of the excitation duration is also included later. The simulated time was wavelengths. A discussion on the influence of the excitation duration is also included later. The up to 100 s resulting in a waveform length of 5194 samples and a sampling interval of 0.01925 s or simulated time was up to 100 µs resulting in a waveform length of 5194 samples and a sampling inversely sampling rate of 52 MHz. The space resolution was 0.1 mm, which was quite dense even for interval of 0.01925 µs or inversely sampling rate of 52 MHz. The space resolution was 0.1 mm, which the case of highest frequency of 1 MHz with Rayleigh wavelength 2.35 mm. was quite dense even for the case of highest frequency of 1 MHz with Rayleigh wavelength 2.35 mm. 3. Results 3. Results 3.1. Surface Excitation 3.1. Surface Excitation Results analysis begins with the waveforms received due to surface excitation since it exhibits Results analysis begins with the waveforms received due to surface excitation since it exhibits the highest interest in the sense that the response of the different sensors exhibits strong variations. the highest interest in the sense that the response of the different sensors exhibits strong variations. Figure 2 shows the excited signal (two cycles sinusoid in yellow color at the start of the time axis) and Figure 2 shows the excited signal (two cycles sinusoid in yellow color at the start of the time axis) and the respective waveforms received by each sensor in the case of 1 MHz excitation frequency. The units the respective waveforms received by each sensor in the case of 1 MHz excitation frequency. The of amplitude are arbitrary as they concern the linear regime. If the displacement source waveform units of amplitude are arbitrary as they concern the linear regime. If the displacement source peaks at 1, it can be considered that the maximum source displacement is 1 m. After the initial waveform peaks at 1, it can be considered that the maximum source displacement is 1 µm. After the longitudinal wave arrivals noticed just after 15 s, the considerably stronger Rayleigh wave arrives. initial longitudinal wave arrivals noticed just after 15 µs, the considerably stronger Rayleigh wave The higher Rayleigh amplitude is expected as this wave mode occupies the highest amount of energy arrives. The higher Rayleigh amplitude is expected as this wave mode occupies the highest amount after a surface excitation (approximately 67%, while only around 7% forms the longitudinal) [21]. of energy after a surface excitation (approximately 67%, while only around 7% forms the longitudinal) [21]. Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 17 Appl. Sci. 2018, 8, 168 4 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 17 Figure 2. Waveforms received by different size sensors for the case of surface source and excitation Figure 2. Waveforms received by different size sensors for the case of surface source and excitation frequency of 1 MHz. The excitation wave (yellow starting at time 0) was reduced to the graph axes Figure 2. Waveforms received by different size sensors for the case of surface source and excitation frequency of 1 MHz. The excitation wave (yellow starting at time 0) was reduced to the graph axes for clarity (nominal amplitude of 1). frequency of 1 MHz. The excitation wave (yellow starting at time 0) was reduced to the graph axes for for clarity (nominal amplitude of 1). clarity (nominal amplitude of 1). The “point” sensor (1 mm) registers quite clearly two strong cycles similar to the excited signal. The “point” sensor (1 mm) registers quite clearly two strong cycles similar to the excited signal. The “point” sensor (1 mm) registers quite clearly two strong cycles similar to the excited signal. However, the long sensor (20 mm) records a significantly distorted waveform: it consists of four small However, the long sensor (20 mm) records a significantly distorted waveform: it consists of four small However, the long sensor (20 mm) records a significantly distorted waveform: it consists of four small cycles interrupted by a plateau of nearly zero displacement. Looking at the displacement field of cycles interrupted by a plateau of nearly zero displacement. Looking at the displacement field of cycles interrupted by a plateau of nearly zero displacement. Looking at the displacement field of Figure 3a, corresponding to 22 µs after excitation, the Rayleigh wave packet is entirely on the sensor Figure 3a, corresponding to 22 µs after excitation, the Rayleigh wave packet is entirely on the sensor Figure 3a, corresponding to 22 s after excitation, the Rayleigh wave packet is entirely on the sensor line, line, creating a cancellation effect due to positive and negative peaks acting simultaneously. The line, creating a cancellation effect due to positive and negative peaks acting simultaneously. The creating a cancellation effect due to positive and negative peaks acting simultaneously. The Rayleigh Rayleigh wavelength of 1 MHz is 2.35 mm, while the length of two cycles is 4.70 mm, which is much Rayleigh wavelength of 1 MHz is 2.35 mm, while the length of two cycles is 4.70 mm, which is much wavelength of 1 MHz is 2.35 mm, while the length of two cycles is 4.70 mm, which is much smaller smaller than the sensor size (20 mm). It is seen that if the entire wave packet is within the physical smaller than the sensor size (20 mm). It is seen that if the entire wave packet is within the physical than the sensor size (20 mm). It is seen that if the entire wave packet is within the physical limits of limits of the sensor, cancellation effect of the total output occurs. In contrast, this is not the case for limits of the sensor, cancellation effect of the total output occurs. In contrast, this is not the case for the sensor, cancellation effect of the total output occurs. In contrast, this is not the case for the point the point sensor (1 mm) as a single wavelength cannot fit into the sensor size. The received waveform the point sensor (1 mm) as a single wavelength cannot fit into the sensor size. The received waveform sensor (1 mm) as a single wavelength cannot fit into the sensor size. The received waveform shape shape follows the peaks and valleys of the excited wave packet reaching higher amplitudes than the shape follows the peaks and valleys of the excited wave packet reaching higher amplitudes than the follows the peaks and valleys of the excited wave packet reaching higher amplitudes than the long long sensor case. The waveform received by the medium sensor (5 mm) has mixed characteristics long sensor case. The waveform received by the medium sensor (5 mm) has mixed characteristics sensor case. The waveform received by the medium sensor (5 mm) has mixed characteristics consisting consisting of approximately 5 cycles of amplitude in between the other two cases. From a general consisting of approximately 5 cycles of amplitude in between the other two cases. From a general of approximately 5 cycles of amplitude in between the other two cases. From a general assessment, assessment, it is obvious that the smaller the physical dimension of the sensor (respectively the line assessment, it is obvious that the smaller the physical dimension of the sensor (respectively the line it is obvious that the smaller the physical dimension of the sensor (respectively the line along which along which averaging is conducted), the higher the similarity between the excited and received along which averaging is conducted), the higher the similarity between the excited and received averaging is conducted), the higher the similarity between the excited and received waveform. waveform. waveform. Excitation Excitation 1mm 1mm 5 mm 20 mm 5 mm 20 mm 0 500 1000 1500 2000 0 500 1000 1500 2000 Frequency (kHz) Frequency (kHz) (a) (b) (a) (b) Figure 3. (a) Snapshot of displacement field corresponding to 22 µs after excitation (frequency at 1 Figure 3. (a) Snapshot of displacement field corresponding to 22 s after excitation (frequency at Figure 3. (a) Snapshot of displacement field corresponding to 22 µs after excitation (frequency at 1 MHz). The source is set on the surface; (b) Fast Fourier Transforms (FFT) functions of the waveforms 1 MHz). The source is set on the surface; (b) Fast Fourier Transforms (FFT) functions of the waveforms MHz). The source is set on the surface; (b) Fast Fourier Transforms (FFT) functions of the waveforms received by different size sensors. received by different size sensors. received by different size sensors. Differences are strong in the frequency domain as well, as seen in Figure 3b where the Fast Differences are strong in the frequency domain as well, as seen in Figure 3b where the Fast Fourier Transforms (FFT) of the waveforms of Figure 2 are shown. Only the response of point sensor Fourier Transforms (FFT) of the waveforms of Figure 2 are shown. Only the response of point sensor Magnitude Magnitude Appl. Sci. 2018, 8, 168 5 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 17 Differences are strong in the frequency domain as well, as seen in Figure 3b where the Fast Fourier Transforms (FFT) of the waveforms of Figure 2 are shown. Only the response of point sensor (1 mm) (1 mm) exhibits similarities to the actual FFT of the excited signal, with a clear higher peak at around exhibits similarities to the actual FFT of the excited signal, with a clear higher peak at around 1 MHz. 1 MHz. The responses of medium (5 mm) and long (20 mm) sensors neither have resemblance to the The responses of medium (5 mm) and long (20 mm) sensors neither have resemblance to the excited excited signal nor show strong content around 1 MHz. It is characteristic that the initial excited signal nor show strong content around 1 MHz. It is characteristic that the initial excited content content centered around 1 MHz is distributed approximately evenly to the whole range of the first centered around 1 MHz is distributed approximately evenly to the whole range of the first MHz for MHz for the long sensor. the long sensor. For AE damage characterization purposes, the latter observations are of utmost importance since For AE damage characterization purposes, the latter observations are of utmost importance since the source excitation may be sensed by a severely distorted waveform on the receiver. The effect of the source excitation may be sensed by a severely distorted waveform on the receiver. The effect of sensor size modifies the output and influences the accuracy of the AE signal features and waveform sensor size modifies the output and influences the accuracy of the AE signal features and waveform shape in general. For lower frequencies, the differences in all aspects (waveform shape, FFTs) on shape in general. For lower frequencies, the differences in all aspects (waveform shape, FFTs) on sensors’ response to horizontal surface source diminish and are minimized for the excitation sensors’ response to horizontal surface source diminish and are minimized for the excitation frequency frequency of 50 kHz (respective wavelength equal to 48 mm). Indicative waveforms are shown in of 50 kHz (respective wavelength equal to 48 mm). Indicative waveforms are shown in Figure 4a. Figure 4a. The longest sensor (20 mm) still registers the lowest amplitude, but the difference is much The longest sensor (20 mm) still registers the lowest amplitude, but the difference is much smaller smaller in this case while the waveform shape is very close to the one of point sensor. The FFTs show in this case while the waveform shape is very close to the one of point sensor. The FFTs show closer closer results as revealed in Figure 4b. results as revealed in Figure 4b. 0.3 50 kHz, surface propagation 20 mm 0.2 5 mm 0.1 1 mm -0.1 -0.2 10 30 50 70 90 Time (μs) (a) (b) Figure 4. (a) Waveforms received by different size sensors for the case of surface source and excitation Figure 4. (a) Waveforms received by different size sensors for the case of surface source and excitation frequency of 50 kHz; (b) FFT functions of waveforms received by different size sensors (exc. frequency frequency of 50 kHz; (b) FFT functions of waveforms received by different size sensors (exc. frequency at 50 kHz and surface source). The corresponding waveforms are depicted in Figure 4a. at 50 kHz and surface source). The corresponding waveforms are depicted in Figure 4a. 3.2. Vertical Excitation Beneath the Sensor 3.2. Vertical Excitation Beneath the Sensor In the case of vertical excitation beneath the sensor, the study concerns the longitudinal wave In the case of vertical excitation beneath the sensor, the study concerns the longitudinal wave since since Rayleigh is not directly created from the excitation within the material. The simulation Rayleigh is not directly created from the excitation within the material. The simulation waveforms are waveforms are shown in Figure 5a. The differences at the waveforms received by different size shown in Figure 5a. The differences at the waveforms received by different size sensors are almost sensors are almost negligible. It should be noted that the amplitude of the signal received by long negligible. It should be noted that the amplitude of the signal received by long sensor (20 mm) is sensor (20 mm) is slightly lower than the waveforms of the other two cases. Additionally, the point slightly lower than the waveforms of the other two cases. Additionally, the point and medium sensors’ and medium sensors’ waveforms begin slightly sharper than the corresponding of long sensor. This waveforms begin slightly sharper than the corresponding of long sensor. This is due to the circular is due to the circular shape of the wave front that affects the wave arrival. More specifically, wave shape of the wave front that affects the wave arrival. More specifically, wave energy arrives vertically energy arrives vertically to the long sensor only in its center, but part of the energy arrives in slightly to the long sensor only in its center, but part of the energy arrives in slightly different angles at the different angles at the sensors edges due to spreading. The above agrees with recent literature, stating sensors edges due to spreading. The above agrees with recent literature, stating that when the sensor that when the sensor diameter increases, the displacement distribution along the diameter becomes diameter increases, the displacement distribution along the diameter becomes non-uniform [22]. This is non-uniform [22]. This is not the case for smaller size sensors at which the whole energy arrives not the case for smaller size sensors at which the whole energy arrives vertically and the wave front vertically and the wave front shape effect is negligible. The differences are minimized for lower shape effect is negligible. The differences are minimized for lower frequencies with the example of frequencies with the example of 50 kHz in Figure 5b being indicative. 50 kHz in Figure 5b being indicative. Amplitude Appl. Sci. 2018, 8, 168 6 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 17 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 17 0.2 0.2 1 MHz vertical propagation 50 kHz vertical propagation 20 mm 0.2 0.15 50 kHz vertical propagation 1 MHz vertical propagation 0.2 20 mm 20 mm 0.15 5 mm 20 mm 0.1 5 mm 0.1 5 mm 0.1 1 mm 0.1 5 mm 0.05 1 mm 1 mm 0.05 1 mm -0.05 -0.1 -0.05 -0.1 -0.1 -0.1 -0.2 -0.15 -0.2 -0.15 -0.2 -0.3 -0.2 -0.3 10 11 12 13 14 15 16 0 20 406080 100 10 11 12 Time 1 ( 3μs) 14 15 16 0 20 4Ti06 me (μs)080 100 Time (μs) Time (μs) (a) (b) (a) (b) Figure 5. (a) Waveforms received by different size sensors for the case of vertical source and excitation Figure 5. (a) Waveforms received by different size sensors for the case of vertical source and excitation Figure 5. (a) Waveforms received by different size sensors for the case of vertical source and excitation frequency of 1 MHz; (b) Waveforms received by different size sensors for the case of vertical source frequency of 1 MHz; (b) Waveforms received by different size sensors for the case of vertical source frequency of 1 MHz; (b) Waveforms received by different size sensors for the case of vertical source and excitation frequency of 50 kHz. and excitation frequency of 50 kHz. and excitation frequency of 50 kHz. 3.3. Diagonal Excitation 3.3. Diagonal Excitation 3.3. Diagonal Excitation Diagonal wave propagation provides an intermediate response between the vertical and the Diagonal wave propagation provides an intermediate response between the vertical and the Diagonal wave propagation provides an intermediate response between the vertical and the surface cases, but strong differences can still be observed. Figure 6a shows the waveforms received surface cases, but strong differences can still be observed. Figure 6a shows the waveforms received surface cases, but strong differences can still be observed. Figure 6a shows the waveforms received by each sensor in the case of 1 MHz excitation frequency. The early strong burst originates from the by each sensor in the case of 1 MHz excitation frequency. The early strong burst originates from the by each sensor in the case of 1 MHz excitation frequency. The early strong burst originates from longitudinal wave impinging on the sensors at an angle of 45°. This angle is also the reason of the longitudinal wave impinging on the sensors at an angle of 45°. This angle is also the reason of the the longitudinal wave impinging on the sensors at an angle of 45 . This angle is also the reason of lower amplitude (up to 0.2 peak to peak for the point sensor) compared to longitudinal waves of lower amplitude (up to 0.2 peak to peak for the point sensor) compared to longitudinal waves of the lower amplitude (up to 0.2 peak to peak for the point sensor) compared to longitudinal waves vertical source excitation (amplitude higher than 0.5, Figure 2). Once again, the waveform of the long vertical source excitation (amplitude higher than 0.5, Figure 2). Once again, the waveform of the long of vertical source excitation (amplitude higher than 0.5, Figure 2). Once again, the waveform of the sensor (20 mm) significantly differs from the excited signal (sinusoid of two cycles) due to the sensor (20 mm) significantly differs from the excited signal (sinusoid of two cycles) due to the long sensor (20 mm) significantly differs from the excited signal (sinusoid of two cycles) due to the aforementioned cancellation effect. As shown in Figure 6a, at approximately 20 µs, a second wave aforementioned cancellation effect. As shown in Figure 6a, at approximately 20 µs, a second wave aforementioned cancellation effect. As shown in Figure 6a, at approximately 20 s, a second wave packet arrives attributed to the slower shear wave front which is detected due to the angle of packet arrives attributed to the slower shear wave front which is detected due to the angle of packet arrives attributed to the slower shear wave front which is detected due to the angle of incidence. incidence. incidence. 0.1 0.1 0.08 20 mm 0.08 20 mm 0.06 5 mm 0.06 0.04 5 mm 1 mm 0.04 0.02 1 mm 0.02 -0.02 -0.02 1 MHz, diagonal -0.04 1 MHz, diagonal propagation -0.04 -0.06 propagation -0.06 -0.08 -0.08 -0.1 -0.1 5 1015 2025 5 101 Time (5μs) 2025 Time (μs) (a) (b) (a) (b) Figure 6. (a) Waveforms received by different size sensors for the case of diagonal source and Figure 6. (a) Waveforms received by different size sensors for the case of diagonal source and frequency Figure 6. (a) Waveforms received by different size sensors for the case of diagonal source and frequency excitation of 1 MHz; (b) Snapshot of displacement field corresponding to 10 µs after excitation of 1 MHz; (b) Snapshot of displacement field corresponding to 10 s after excitation (exc. frequency excitation of 1 MHz; (b) Snapshot of displacement field corresponding to 10 µs after excitation (exc. frequency at 1 MHz). frequency at 1 MHz). excitation (exc. frequency at 1 MHz). Respectively, in Figure 7a,b the FFTs of waveforms received by different size sensors in the Respectively Respectively ,, in in Figur Figure e 7a,b 7a,b the the FFTFFTs o s of waveforms f waveforrms eceived received by dif by fer ent different size se size nsors sen in the sors in extreme the extreme cases of 1 MHz and 50 kHz are shown. Strong differences from the original FFT envelope cases extreme case of 1 MHz s of and 1 M 50H kHz z and 50 kH are shown. z ar Str e shown. Stro ong differences ng d fri om fference the original s from the or FFT envelope iginal Far FT en e observed velope are observed in the case of 1 MHz excitation, especially by long and medium sensors attributed to are observed in the case of 1 MHz excitation, especially by long and medium sensors attributed to in the case of 1 MHz excitation, especially by long and medium sensors attributed to the cancellation the cancellation effect (Figure 7a). On the contrary, in the case of 50 kHz excitation frequency (Figure ef the cance fect (Figur llation effect (Fig e 7a). On the ure contrary 7a). On th , in the e contrar case of y, 50 in kHz the case excitation of 50 kHz excit frequency atio (Figur n freqe uency 7b), the (Fig FFT ure 7b), the FFT functions of three size sensors are almost identical converging to the same curve. 7b), the FFT functions of three size sensors are almost identical converging to the same curve. functions of three size sensors are almost identical converging to the same curve. Amplitude Amplitude Amplitude Amplitude Amplitude Amplitude Appl. Sci. 2018, 8, 168 7 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 17 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 17 (a) (b) (a) (b) Figure 7. (a) FFT functions of waveforms received by different size sensors (exc. frequency at 1 MHz Figure 7. (a) FFT functions of waveforms received by different size sensors (exc. frequency at 1 MHz Figure 7. (a) FFT functions of waveforms received by different size sensors (exc. frequency at 1 MHz and diagonal source); (b) FFT functions of waveforms received by different size sensors (exc. and diagonal source); (b) FFT functions of waveforms received by different size sensors (exc. and diagonal source); (b) FFT functions of waveforms received by different size sensors (exc. frequency frequency at 50 kHz and diagonal source). frequency at 50 kHz and diagonal source). at 50 kHz and diagonal source). 4. Discussion 4. Discussion 4. Discussion 4.1. Impact of Sensor Size on Signal Amplitude 4.1. Impact of Sensor Size on Signal Amplitude 4.1. Impact of Sensor Size on Signal Amplitude The effect of sensor size on signal response is quantified considering the amplitude of the signal The effect of sensor size on signal response is quantified considering the amplitude of the signal The effect of sensor size on signal response is quantified considering the amplitude of the signal received by different size sensors normalized over the amplitude of the point sensor which is received by different size sensors normalized over the amplitude of the point sensor which is received by different size sensors normalized over the amplitude of the point sensor which is considered considered as reference. The relative amplitude values are presented in Figure 8 for all three source considered as reference. The relative amplitude values are presented in Figure 8 for all three source as reference. The relative amplitude values are presented in Figure 8 for all three source directions and directions and covering the frequency range from 50 kHz to 1 MHz. directions and covering the frequency range from 50 kHz to 1 MHz. covering the frequency range from 50 kHz to 1 MHz. 1 mm 1 mm 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 200 400 600 800 1000 0 200 400 600 800 1000 Frequency (kHz) Frequency (kHz) (a) (a) 1 1 mm 1 mm 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 200 400 600 800 1000 0 200 400 600 800 1000 Frequency (kHz) Frequency (kHz) (b) (b) Figure 8. Cont. Relative amplitude Relative amplitude Relative amplitude Relative amplitude Appl. Sci. 2018, 8, 168 8 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 17 1 mm 5 mm 0.8 0.6 0.4 0.2 0 200 400 600 800 1000 Frequency (kHz) (c) Figure 8. Relative amplitude of the received signal for point (1 mm, in grey), medium (5 mm, in blue), Figure 8. Relative amplitude of the received signal for point (1 mm, in grey), medium (5 mm, in blue), long (20 mm, in red) along the frequency range, from 50 kHz to 1 MHz, and concerning the three long (20 mm, in red) along the frequency range, from 50 kHz to 1 MHz, and concerning the three source source positions: (a) surface; (b) diagonal; (c) vertical. positions: (a) surface; (b) diagonal; (c) vertical. In the surface wave propagation case (Figure 8a) and for high frequencies (up to 1 MHz), the In the surface wave propagation case (Figure 8a) and for high frequencies (up to 1 MHz), the output of the larger sensors is just a fraction of the response of the point sensor. Specifically, output of the larger sensors is just a fraction of the response of the point sensor. Specifically, considering considering the long sensor (20 mm), the relative amplitude is equal to 3.6% of the reference. Moving the long sensor (20 mm), the relative amplitude is equal to 3.6% of the reference. Moving towards towards lower frequencies, the relative amplitude is gradually restored, earlier for the medium and lower frequencies, the relative amplitude is gradually restored, earlier for the medium and then for the then for the long sensor. At 50 kHz, the relative amplitude of the long sensor is still around 0.65 long sensor. At 50 kHz, the relative amplitude of the long sensor is still around 0.65 indicating that indicating that even at low frequencies the signal remains significantly distorted. even at low frequencies the signal remains significantly distorted. In the diagonal wave propagation case (Figure 8b), the medium sensor seems to approach the In the diagonal wave propagation case (Figure 8b), the medium sensor seems to approach the point sensor response especially at low excitation frequency ranges (from 50 to 200 kHz). This is not point sensor response especially at low excitation frequency ranges (from 50 to 200 kHz). This is not the case for the long sensor that receives a much lower amplitude. Indicatively, at 500 kHz excitation the case for the long sensor that receives a much lower amplitude. Indicatively, at 500 kHz excitation frequency, the amplitude of the long sensor is just 22% of the point sensor, while for 200 kHz it is just frequency, the amplitude of the long sensor is just 22% of the point sensor, while for 200 kHz it is just above 54%. above 54%. Concerning the last case, where the source is placed vertically beneath the receiver (Figure 8c), Concerning the last case, where the source is placed vertically beneath the receiver (Figure 8c), relative amplitude is much closer to unity (difference between point sensor and long sensor at 1 MHz relative amplitude is much closer to unity (difference between point sensor and long sensor at 1 MHz excitation frequency is about 15%). These results indicate that the sensor size effect is minimized for excitation frequency is about 15%). These results indicate that the sensor size effect is minimized for propagation vertical to the sensor surface in contrast to other angles of incidence. propagation vertical to the sensor surface in contrast to other angles of incidence. It is concluded that sensor size effect dominantly influences the received waveform shape in It is concluded that sensor size effect dominantly influences the received waveform shape in almost the whole frequency range and especially when the source does not stand directly beneath almost the whole frequency range and especially when the source does not stand directly beneath the the sensor. As expected, the measurements obtained by AE on bulk materials, such as concrete where sensor. As expected, the measurements obtained by AE on bulk materials, such as concrete where stochastic defects are included, carry an error due to sensor size effect and may provide less accurate stochastic defects are included, carry an error due to sensor size effect and may provide less accurate signal amplitude. In real size structures, wave attenuation eliminates the higher frequencies, but still signal amplitude. In real size structures, wave attenuation eliminates the higher frequencies, but still frequencies up to 200 kHz are commonly measured, therefore the signal amplitude can be affected frequencies up to 200 kHz are commonly measured, therefore the signal amplitude can be affected by by the sensor size. However, in tests done in laboratory, even higher frequencies are measured the sensor size. However, in tests done in laboratory, even higher frequencies are measured meaning meaning that the influence of the sensor effect will be even stronger. that the influence of the sensor effect will be even stronger. 4.2. Effect of Wavelength over Sensor Size 4.2. Effect of Wavelength over Sensor Size The case o The case of f surfac surface e wa waves ves obviously obviously exhibits the st exhibits the ron str gest aperture ongest apertur effect. e ef To fect. quanti To fquantify y the trends, the trends, the amplitude data are presented in terms of the normalized parameter D/l (sensor size over the amplitude data are presented in terms of the normalized parameter D/λ (sensor size over wavelen wavelength) gth) in Fig in Figur ure e 9. 9. The The ind individual ividual cu curves rves fo follow llow a a « «master master curve» curve», , stressi stressing ng tha that t the the crucia crucial l parameter is the ratio of sensor size/wavelength. This curve can be well fitted by an exponential parameter is the ratio of sensor size/wavelength. This curve can be well fitted by an exponential function function.. As As the the sensor size incr sensor size increases eases away away from from the ideal the ide caseaof l c “point” ase of “poi sensor nt,” sensor, the relative the relative amplitude sharply decreases until the point D/l 1 when the sensor size is equal to the wavelength. At that amplitude sharply decreases until the point D/λ ≈ 1 when the sensor size is equal to the wavelength. At tha point, tthe poi rn elative t, the rela ampl tive itude ampl has itude has al already dr rea opped dy dr to op 20% ped to of the 20% refer of the re ence. ferenc For lareger . For sensor larger size, sensor the amplitude decreases further but with a lower rate reaching 4% for D/l > 8. size, the amplitude decreases further but with a lower rate reaching 4% for D/λ > 8. Relative amplitude Appl. Sci. 2018, 8, 168 9 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 17 0.417972832 20 mm 0.8 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 17 0.6 0. 5 m 104 m493208 -0.84 0.4 y = 0.227x R² = 0.9528 0.417972832 20 mm 0.8 0.2 0.6 0. 5 m 104 m493208 0123 4567 89 0.4 -0.84 y = 0.227x D/λ R² = 0.9528 0.2 Figure 9. Relative amplitude vs. sensor size over wavelength parameter (D/l). Figure 9. Relative amplitude vs. sensor size over wavelength parameter (D/λ). 0123 4567 89 D/λ 4.3. Impact of Sensors Size Effect on Frequency Content 4.3. Impact of Sensors Size Effect on Frequency Content Figure 9. Relative amplitude vs. sensor size over wavelength parameter (D/λ). The sensor size effect does not only influence the amplitude but also the wave shape in both time The sensor size effect does not only influence the amplitude but also the wave shape in both time and frequency domain. Considering the frequency content, the most crucial measure of the similarity and frequency domain. Considering the frequency content, the most crucial measure of the similarity 4.3. Impact of Sensors Size Effect on Frequency Content between two waveforms (X(t), Y(t)) is the “coherence function, γxy”. This function is given by: between two waveforms (X(t), Y(t)) is the “coherence function, g ”. This function is given by: xy The sensor size effect does not only influence the amplitude but also the wave shape in both time ( ) ( ) = ,0≤ ( )≤1 and frequency domain. Considering the frequency content, the most crucial measure of the similarity (2) ( ) ( ) G ( f ) xy 2 2 between two waveforms (X(t), Y(t)) is the “coherence function, γxy”. This function is given by: g ( f ) = , 0 g ( f ) 1 (2) xy xy where: and ( ), ( ) are the G auto(spectral den f )G ( f ) sity functions of X(t) and Y(t) respectively and xx yy ( ) ( ) is the cross-spectral density function between X(t) and Y(t). Coherence is analogous to the ( ) = ,0≤ ( )≤1 (2) ( ) ( ) where: and G ( f ), G ( f ) are the autospectral density functions of X(t) and Y(t) respectively and squared cor xx relation coe yy fficient of time domain functions underlying the frequency similarities of the G (sign f ) is als [23]. the cross-spectral In case of iddensity entical emitted and re function between ceived wavefo X(t) and rms, coherence Y(t). Coherence gets a un is analogous ity value. to the where: and ( ), ( ) are the autospectral density functions of X(t) and Y(t) respectively and xy Coherence has also been measured to classify AE [24] and acousto-ultrasonics signals [25] based on squar ed(corr ) is the cross-spectra elation coefficient l densi of time ty functi domain on between X( functions t) and Y( underlying t). Coherence the frequency is analogous to the similarities of their similarity to reference waveforms. In this case it was calculated based on a standard Matlab the signals squared cor [23].re In lation case coe offidentical ficient of tim emitted e domain and func received tions underlying the waveforms,fr coher equency si encemil gets aria ties of unity the value. function. The waveforms were zero-padded to the length of 32,768 points while the required overlap signals [23]. In case of identical emitted and received waveforms, coherence gets a unity value. Coherence has also been measured to classify AE [24] and acousto-ultrasonics signals [25] based on window was 1250 points. These settings were constant for all calculations below but are not unique Coherence has also been measured to classify AE [24] and acousto-ultrasonics signals [25] based on their similarity to reference waveforms. In this case it was calculated based on a standard Matlab and could be changed leading to a somehow different final function. their similarity to reference waveforms. In this case it was calculated based on a standard Matlab function. The waveforms were zero-padded to the length of 32,768 points while the required overlap Figure 10a shows indicatively the wave emitted with excitation frequency at 1 MHz (in red), and function. The waveforms were zero-padded to the length of 32,768 points while the required overlap window was 1250 points. These settings were constant for all calculations below but are not unique the waveforms received by the medium sensor (5 mm) for the cases of source set on the surface (in window was 1250 points. These settings were constant for all calculations below but are not unique and could be changed leading to a somehow different final function. black) and vertically beneath the sensor (in blue). It is shown that the similarity to the original wave and could be changed leading to a somehow different final function. Figure 10a shows indicatively the wave emitted with excitation frequency at 1 MHz (in red), and is stronger for the vertically placed source, when two clear cycles are depicted, while for the case of Figure 10a shows indicatively the wave emitted with excitation frequency at 1 MHz (in red), and the w sur avface w eformasve rs, the major eceived by tcontent of the Rayle he medium sensorigh w (5 mam ves show ) for the s four to five c cases of sour yccles e seinste t onatd he of two. surfa ce (in the waveforms received by the medium sensor (5 mm) for the cases of source set on the surface (in Figure 10b shows the corresponding coherence functions between the received waveforms and the black) and vertically beneath the sensor (in blue). It is shown that the similarity to the original wave is black) and vertically beneath the sensor (in blue). It is shown that the similarity to the original wave excitation up to 2 MHz. The level of coherence is much higher for the direct propagation vertical to is stronger for the vertically placed source, when two clear cycles are depicted, while for the case of stronger for the vertically placed source, when two clear cycles are depicted, while for the case of surface the sensor where the function is almost constantly close to unity, indicative of excellent similarity surface waves, the major content of the Rayleigh waves shows four to five cycles instead of two. waves, the major content of the Rayleigh waves shows four to five cycles instead of two. Figure 10b between the excitation and the sensor output. On the other hand, the coherence function of surface Figure 10b shows the corresponding coherence functions between the received waveforms and the shows the corresponding coherence functions between the received waveforms and the excitation up to waves has significantly lower values with an average around 0.6 indicative of strong distortion that excitation up to 2 MHz. The level of coherence is much higher for the direct propagation vertical to 2 MHz. The level of coherence is much higher for the direct propagation vertical to the sensor where the affects the received waveform. the sensor where the function is almost constantly close to unity, indicative of excellent similarity function is almost constantly close to unity, indicative of excellent similarity between the excitation and between the excitation and the sensor output. On the other hand, the coherence function of surface 0.25 the sensor output. On the other hand, the coherence function of surface waves has significantly lower 1.0 waves has significantly lower values with an average around 0.6 indicative of strong distortion that 0.2 Excitation Vertical (90 degrees) values with a 0. n 15average around 0.6 indicative of strong distortion that affects the received waveform. affects the received waveform. 0.8 0.1 Horizontal (0 degrees) 0.05 0.6 0.25 1.0 0.2 Excitation Vertical (90 degrees) -0.05 0.4 0.15 Vertical (90 0.8 -0.1 degrees) 0.1 Horizontal (0 degrees) 0.2 -0.15 Horizontal (0 1 MHz 0.05 0.6 degrees) -0.2 0.0 -0.25 -0.05 0.4 0 102030 0 500 1000 1500 2000 Vertical (90 -0.1 Time (μs) Frequency (kHz) degrees) 0.2 -0.15 Horizontal (0 1 MHz (a) (b) degrees) -0.2 0.0 -0.25 Figure 10. (a) Waveforms received by the 5 mm size sensor emitted from source set on the surface (in 0 500 1000 1500 2000 0 102030 Time (μs) Frequency (kHz) black) and vertically beneath the sensor (in blue) with excitation frequency equal to 1 MHz. Original (a) (b) waveform is added in red color and in reduced scale to fit the graph; (b) Respective coherence functions between received waves and original. Figure 10. (a) Waveforms received by the 5 mm size sensor emitted from source set on the surface Figure 10. (a) Waveforms received by the 5 mm size sensor emitted from source set on the surface (in (in black) black) and and vertically verticallybeneath beneath t the he sensor ( sensor (in in bblue) lue) wi with th excita excitation tion frequency frequency equal to equal 1 MH to 1 MHz. z. Original Original waveform is added in red color and in reduced scale to fit the graph; (b) Respective coherence waveform is added in red color and in reduced scale to fit the graph; (b) Respective coherence functions functions between received waves and original. between received waves and original. Amplitude Amplitude Relative amplitude Relative amplitude Coherence, γ Coherence, γ Appl. Sci. 2018, 8, 168 10 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 17 The average level of coherence between the excitation and the received signal is shown in Figure The average level of coherence between the excitation and the received signal is shown in 11 for the different angles of incidence and the various sensors sizes for two indicative excitation Figure 11 for the different angles of incidence and the various sensors sizes for two indicative excitation frequencies (a) 1 MHz and (b) 500 kHz. For the case of 1 MHz the coherence is quite high (more than frequencies (a) 1 MHz and (b) 500 kHz. For the case of 1 MHz the coherence is quite high (more 95%) for diagonal and vertical to the sensor surface propagation for all sensors. However, for than 95%) for diagonal and vertical to the sensor surface propagation for all sensors. However, for propagation parallel to the surface (angle 0°), coherence is lower. Still, again the point sensor yields propagation parallel to the surface (angle 0 ), coherence is lower. Still, again the point sensor yields higher values (0.66) compared to the longer sensor (0.49). For the surface propagation of 500 kHz higher values (0.66) compared to the longer sensor (0.49). For the surface propagation of 500 kHz (case b), coherence is very low (below 0.3) showing a huge amount of distortion on the frequency (case b), coherence is very low (below 0.3) showing a huge amount of distortion on the frequency content for all sensors, while it is again close to unity for diagonal and vertical direction of incidence. content for all sensors, while it is again close to unity for diagonal and vertical direction of incidence. The above coherence analysis indicates that the received signal is crucially distorted in spectral The above coherence analysis indicates that the received signal is crucially distorted in spectral content content for surface propagation meaning that sources on or close to the surface will exhibit lower for surface propagation meaning that sources on or close to the surface will exhibit lower spectral spectral similarity to the finally obtained waveform than a source at the same distance beneath the similarity to the finally obtained waveform than a source at the same distance beneath the sensor. sensor. The latter should be considered in studies that use sensors calibrated in face-to-face The latter should be considered in studies that use sensors calibrated in face-to-face configurations to configurations to assess the response of waveforms that travel on the material’s surface. assess the response of waveforms that travel on the material’s surface. (a) (b) Figure 11. Average coherence up to 2 MHz for different sensor size and angles of propagation Figure 11. Average coherence up to 2 MHz for different sensor size and angles of propagation relatively relatively to the sensor surface and excitation frequencies (a) 1 MHz; (b) 500 kHz. to the sensor surface and excitation frequencies (a) 1 MHz; (b) 500 kHz. 4.4. Experimental Evidence 4.4. Experimental Evidence Experimentally, the sensor size effect cannot be directly compared between two different Experimentally, the sensor size effect cannot be directly compared between two different sensors, sensors, since apart from their possible difference in size or surface contact area, they also possess since apart from their possible difference in size or surface contact area, they also possess different different frequency response characteristics. In addition, in the specific case studied herein, results frequency response characteristics. In addition, in the specific case studied herein, results between between simulations and experiments cannot be directly compared for a number of reasons. First, the simulations and experiments cannot be directly compared for a number of reasons. First, the damping damping of the material is not readily known like other parameters (e.g., the elastic modulus) to be of the material is not readily known like other parameters (e.g., the elastic modulus) to be imported in imported in the simulation. In addition, although a numerical source can be excited within the the simulation. In addition, although a numerical source can be excited within the material to introduce material to introduce a pure longitudinal wave, this cannot be realized experimentally as the a pure longitudinal wave, this cannot be realized experimentally as the excitation takes place on the excitation takes place on the surface forming again stronger Rayleigh waves. Therefore, it is surface forming again stronger Rayleigh waves. Therefore, it is reasonable to compare simulated and reasonable to compare simulated and experimental waveforms after excitation on the same surface experimental waveforms after excitation on the same surface (case of horizontal propagation above) (case of horizontal propagation above) but there is no straightforward quantitative comparison for but there is no straightforward quantitative comparison for the case of vertical propagation. the case of vertical propagation. However, there is one point of interest which shows the strength of the sensor size effect. However, there is one point of interest which shows the strength of the sensor size effect. As As mentioned above, when excitation takes place on the surface, 67% of the energy forms the Rayleigh mentioned above, when excitation takes place on the surface, 67% of the energy forms the Rayleigh wave. On the other hand, experimentally, the only amount of energy captured by the sensor standing wave. On the other hand, experimentally, the only amount of energy captured by the sensor standing at the opposite side is the 7% of the longitudinal wave. Therefore, it is expected that the horizontal at the opposite side is the 7% of the longitudinal wave. Therefore, it is expected that the horizontal propagation case will result in stronger waveform than the vertical, also because Rayleigh waves suffer propagation case will result in stronger waveform than the vertical, also because Rayleigh waves less geometric spreading. Numerically, this is shown when comparing the waveform received by the suffer less geometric spreading. Numerically, this is shown when comparing the waveform received point sensor coming from the surface excitation (Figure 2, with peak to peak amplitude higher than 0.5) by the point sensor coming from the surface excitation (Figure 2, with peak to peak amplitude higher and vertical excitation (Figure 5a, respective amplitude range 0.3). The response to surface excitation is than 0.5) and vertical excitation (Figure 5a, respective amplitude range 0.3). The response to surface much higher due to the strength of the Rayleigh wave and the reduced geometric spreading of the beam. excitation is much higher due to the strength of the Rayleigh wave and the reduced geometric In this direction, experimental measurements with pencil lead breakage (Hsu-Nielsen source) spreading of the beam. as acoustic source were conducted (Figure 12). A receiver sensor was positioned at the top surface In this direction, experimental measurements with pencil lead breakage (Hsu-Nielsen source) as acoustic source were conducted (Figure 12). A receiver sensor was positioned at the top surface of a Appl. Sci. 2018, 8, 168 11 of 16 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 17 of a normal strength concrete sample. The sample had 50 mm thickness. Pencil lead breakages were normal strength concrete sample. The sample had 50 mm thickness. Pencil lead breakages were performed at 50 mm far from the receiver at the top surface and at the bottom side of the sample, just performed at 50 mm far from the receiver at the top surface and at the bottom side of the sample, just beneath the receiver, as shown in Figure 12. beneath the receiver, as shown in Figure 12. Figure 12. Experimental setup showing the receiver at the top concrete surface and pencil lead Figure 12. Experimental setup showing the receiver at the top concrete surface and pencil lead breakage breakage applied at the horizontal and vertical direction. applied at the horizontal and vertical direction. The above experimental arrangement was realized using two types of AE sensors. One is the The above experimental arrangement was realized using two types of AE sensors. One is the widely used in practice “R15” of Mistras Group with a sharp resonant peak at 150 kHz and diameter widely used in practice “R15” of Mistras Group with a sharp resonant peak at 150 kHz and diameter of 19 mm. The other is the “Pico” of the same manufacturer with a broader response and much of 19 mm. The other is the “Pico” of the same manufacturer with a broader response and much smaller smaller diameter of 5 mm. A pre-trigger capturing time of 50 µs was used. The sampling rate was 2 diameter of 5 mm. A pre-trigger capturing time of 50 s was used. The sampling rate was 2 MHz and MHz and the pre-amplification gain was 40 dB. the pre-amplification Figure 13 shogain ws sever was al w 40adB. veforms, each one corresponding to an individual pencil lead break, recorded by vertical (a) and surface horizontal (b) propagation recorded by the Pico (5 mm) sensor. Figure 13 shows several waveforms, each one corresponding to an individual pencil lead break, The waveforms are quite repeatable especially at the early part that contains the so-called “ballistic” recorded by vertical (a) and surface horizontal (b) propagation recorded by the Pico (5 mm) sensor. pulse which is not much influenced by scattering [26]. Visually, the waveforms from the surface The waveforms are quite repeatable especially at the early part that contains the so-called “ballistic” excitation (Figure 13b) obtain higher amplitude in average than the ones of vertical excitation (Figure pulse which is not much influenced by scattering [26]. Visually, the waveforms from the surface 13a). Measuring the peak-to-peak absolute voltage of the highest cycle of the waveforms, the average excitation (Figure 13b) obtain higher amplitude in average than the ones of vertical excitation for the horizontal ones is 0.84 V while for the vertical the average amplitude is 0.54 V. This is verified (Figure 13a). Measuring the peak-to-peak absolute voltage of the highest cycle of the waveforms, by the higher peak of the FFT curve of the surface horizontal wave shown in Figure 13c. The FFT the average for the horizontal ones is 0.84 V while for the vertical the average amplitude is 0.54 V. This is curves presented here are obtained by averaging the individual FFTs of waveforms in Figure 13a,b verified by the higher peak of the FFT curve of the surface horizontal wave shown in Figure 13c. respectively. The FFT curves presented here are obtained by averaging the individual FFTs of waveforms in In contrast, using the longer sensor R15 (19 mm), the waveforms from vertical orientation are higher than surface (Figure 14a,b respectively). Specifically, the peak-to-peak absolute amplitude for Figure 13a,b respectively. vertical averages at 6.88 V while for the horizontal propagation this is 5.81 V. The FFT curves of Figure In contrast, using the longer sensor R15 (19 mm), the waveforms from vertical orientation are 14c confirm this trend, showing higher magnitude for the vertical excitation case compared to the higher than surface (Figure 14a,b respectively). Specifically, the peak-to-peak absolute amplitude horizontal surface excitation. The data imply that the sensor size effect influences the surface for vertical averages at 6.88 V while for the horizontal propagation this is 5.81 V. The FFT curves of propagation leading to a received wave magnitude decrease, even though physically surface waves Figure 14c confirm this trend, showing higher magnitude for the vertical excitation case compared are stronger than longitudinal. to the horizontal surface excitation. The data imply that the sensor size effect influences the surface propagation leading to a received wave magnitude decrease, even though physically surface waves are stronger than longitudinal. The main content of the FFT curve (Figure 14c) is positioned around 150 kHz. Considering this frequency, the Rayleigh wavelength is calculated at around 16 mm, a value similar to the R15 sensor size (19 mm) and three times greater than the Pico size (5 mm). It is shown that considering the same propagation distance and for sensor physical size similar to the wave length (case of R15), the aperture effect diminishes the Rayleigh wave magnitude to levels lower than the corresponding longitudinal of the vertical excitation. However, for a smaller sensor, the Rayleigh wave magnitude remains higher than the corresponding longitudinal impinging vertically. This is confirmed in recent literature, in which the sensitivity of specific AE sensors was measured against both vertically incident and bar waves propagating parallel to the sensor surface. For various sensors, the sensitivity to parallel waves Appl. Sci. 2018, 8, 168 12 of 16 was lower than the sensitivity to vertical waves as the frequency increased [16]. It is characteristic that concerning sensor “R6” of Mistras, the sensitivity curves start to deviate at approximately 300 kHz, corresponding to a diameter over wavelength ratio of approximately 0.5 (element size according to [16] is 12.7 mm and the wavelength on reference aluminum bar for this frequency is approximately 22 mm). This agrees with the presented master curve of Figure 9, where the relative amplitude has high values only for D/l < 0.5. Furthermore, in another study related to surface wave measurements, it is stated that the optimal operation frequency of the sensor is when the aperture size is no longer than half or even a quarter of the wavelength [27]. Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 17 0.6 0.4 0.2 -0.2 -0.4 -0.6 50 70 90 110 130 150 Time (μs) (a) 0.6 0.4 0.2 -0.2 -0.4 -0.6 50 70 90 110 130 150 Time (μs) (b) Vertical Horizontal 0 100 200 300 Frequency (kHz) (c) Figure 13. Individual waveforms received by Pico (5 mm) sensor in the case of (a) horizontal Figure 13. Individual waveforms received by Pico (5 mm) sensor in the case of (a) horizontal excitation; excitation; (b) vertical (c) the average FFT curves of previous waveforms. (b) vertical (c) the average FFT curves of previous waveforms. The main content of the FFT curve (Figure 14c) is positioned around 150 kHz. Considering this frequency, the Rayleigh wavelength is calculated at around 16 mm, a value similar to the R15 sensor size (19 mm) and three times greater than the Pico size (5 mm). It is shown that considering the same propagation distance and for sensor physical size similar to the wave length (case of R15), the aperture effect diminishes the Rayleigh wave magnitude to levels lower than the corresponding longitudinal of the vertical excitation. However, for a smaller sensor, the Rayleigh wave magnitude remains higher than the corresponding longitudinal impinging vertically. This is confirmed in recent literature, in which the sensitivity of specific AE sensors was measured against both vertically incident and bar waves propagating parallel to the sensor surface. For various sensors, the sensitivity Amplitude Amplitude Magnitude Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 17 to parallel waves was lower than the sensitivity to vertical waves as the frequency increased [16]. It is characteristic that concerning sensor “R6” of Mistras, the sensitivity curves start to deviate at approximately 300 kHz, corresponding to a diameter over wavelength ratio of approximately 0.5 (element size according to [16] is 12.7 mm and the wavelength on reference aluminum bar for this frequency is approximately 22 mm). This agrees with the presented master curve of Figure 9, where the relative amplitude has high values only for D/λ < 0.5. Furthermore, in another study related to surface wave measurements, it is stated that the optimal operation frequency of the sensor is when Appl. Sci. 2018, 8, 168 13 of 16 the aperture size is no longer than half or even a quarter of the wavelength [27]. -1 -2 -3 -4 50 70 90 110 130 150 Time (μs) (a) -1 -2 -3 -4 50 70 90 110 130 150 Time (μs) (b) Vertical Horizontal 0 100 200 300 Frequency (kHz) (c) Figure 14. Waveforms received by long size (R15, 20 mm) sensor in the case of (a) horizontal surface; Figure 14. Waveforms received by long size (R15, 20 mm) sensor in the case of (a) horizontal surface; (b) vertical excitation; (c) The average FFT curves of previous waveforms. (b) vertical excitation; (c) The average FFT curves of previous waveforms. 5. Secondary Effects The influence of the pulse length or waveform duration is also of interest as it results in a different physical waveform length acting on the sensor ’s surface. This should not be confused with the wave length which is the wave parameter defined as propagation velocity over frequency. To examine the influence of the waveform duration (i.e., short vs. long signal of the same basic frequency), surface wave simulations were repeated for different number of excitation cycles (from 1 to 20). Two cases of excitation frequencies and sensor sizes were applied, i.e., 1 MHz (wavelength = 2.35 mm) with 5 mm sensor size and 500 kHz ( = 4.7 mm) with 20 mm sensor size. For both cases, one cycle of excitation Amplitude Magnitude Amplitude Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 17 5. Secondary Effects Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 17 The influence of the pulse length or waveform duration is also of interest as it results in a different physi 5. Secondary Effects cal wavef orm length acting on the sensor’s surface. This should not be confused with the wave length which is the wave parameter defined as propagation velocity over frequency. To The influence of the pulse length or waveform duration is also of interest as it results in a examine the influence of the waveform duration (i.e., short vs. long signal of the same basic different physical waveform length acting on the sensor’s surface. This should not be confused with frequency), surface wave simulations were repeated for different number of excitation cycles (from 1 the wave length which is the wave parameter defined as propagation velocity over frequency. To to 20). Two cases of excitation frequencies and sensor sizes were applied, i.e., 1 MHz (wavelength Appl. examine Sci. 2018 the , 8,influence 168 of the waveform duration (i.e., short vs. long signal of the same bas 14 of 16 ic frequency), surface wave simulations were repeated for different number of excitation cycles (from 1 λ = 2.35 mm) with 5 mm sensor size and 500 kHz (λ = 4.7 mm) with 20 mm sensor size. For both cases, to 20). Two cases of excitation frequencies and sensor sizes were applied, i.e., 1 MHz (wavelength one cycle of excitation produces a wavelength smaller than the sensor size, while adding more cycles produces a wavelength smaller than the sensor size, while adding more cycles results eventually in a λ = 2.35 mm) with 5 mm sensor size and 500 kHz (λ = 4.7 mm) with 20 mm sensor size. For both cases, results eventually in a total wave longer than the sensor size. Indicative waveforms for frequency of total wave longer than the sensor size. Indicative waveforms for frequency of 500 kHz received by the one cycle of excitation produces a wavelength smaller than the sensor size, while adding more cycles 500 kHz received by the 20 mm size sensor for 1 and 10 cycles of excitation are shown in Figure 15a. 20 mm size sensor for 1 and 10 cycles of excitation are shown in Figure 15a. results eventually in a total wave longer than the sensor size. Indicative waveforms for frequency of 500 kHz received by the 20 mm size sensor for 1 and 10 cycles of excitation are shown in Figure 15a. 0.04 1 10 cycles 0.03 0.8 20 cycles 20 cycles 0.04 1 cycles 0.02 10 cycles 0.6 0.03 1 cycle 0.8 20 cycles 20 cycles 0.01 1 cycles 0.02 1 cycle 0.4 500 kHz, 20 mm sensor 0.6 1 cycle 0.01 1 cycle 0.4 0.2 500 kHz, 20 mm sensor -0.01 1MHz, 5 mm sensor -0.02 0.2 -0.01 1MHz, 5 mm sensor -0.03 -0.02 01 23456 789 10 0 2040 6080 -0.03 01 23456 789 10 Waveform length/sensor size Time (μs) 0 2040 6080 Waveform length/sensor size Time (μs) (a) (b) (a) (b) Figure 15. (a) Simulated waveforms received by 20 mm size sensor after surface source excitation with Figure 15. (a) Simulated waveforms received by 20 mm size sensor after surface source excitation with Figure 15. (a) Simulated waveforms received by 20 mm size sensor after surface source excitation with frequency of 500 kHz and different number of cycles; (b) Relative amplitude vs. waveform length frequency of 500 kHz and different number of cycles; (b) Relative amplitude vs. waveform length over frequency of 500 kHz and different number of cycles; (b) Relative amplitude vs. waveform length sensor size. over sensor size. over sensor size. As the waveform becomes longer, the received peak amplitude increases (see Figure 15a). There As the waveform becomes longer, the received peak amplitude increases (see Figure 15a). There is As the waveform becomes longer, the received peak amplitude increases (see Figure 15a). There is a ch a is characteristic ar a ch act ar eact rist eri ic point stic point point at at at which a which which a a jump jump jump in in in amplitude amplit amplitud ude e is is ob is ob observed. served. served. This This This is is when when is when the the t t total h oe t tal wav o wave tal wav e lengt length e lengt h h becomes equal to the sensor size, as seen in Figure 15b. In this figure, the amplitude for each curve is becomes equal to the sensor size, as seen in Figure 15b. In this figure, the amplitude for each curve is becomes equal to the sensor size, as seen in Figure 15b. In this figure, the amplitude for each curve is normalized normalized t to o max maximum, imum, while while t the he ho horizontal rizontal ax axis is measur measures the es the total total wa waveform veform l length ength ( (number number of of normalized to maximum, while the horizontal axis measures the total waveform length (number of cycles times the wave length) over the sensor size. Therefore, it is seen that the duration of a waveform cycles times the wave length) over the sensor size. Therefore, it is seen that the duration of a cycles times the wave length) over the sensor size. Therefore, it is seen that the duration of a has waveform an indir ha ect s an eff ind ectirect on the effect measur on thed e meas amplitude ured am since plitude when since its when it length sbecomes length becomes equal or eq longer ual or waveform has an indirect effect on the measured amplitude since when its length becomes equal or than the sensor, it can increase the latter by approximately 35%. This influence of waveform length longer than the sensor, it can increase the latter by approximately 35%. This influence of waveform longer than the sensor, it can increase the latter by approximately 35%. This influence of waveform (pulse length length) (pulse len over gth) ove sensorrsize senis sor noticeable size is notice in the ab simul le in the si ation but mulis atnot ion but as str is not a ong as the s strong wavelength as the length (pulse length) over sensor size is noticeable in the simulation but is not as strong as the over size influence that was presented in Figure 9. In addition, for experimental waveforms which wavelength over size influence that was presented in Figure 9. In addition, for experimental wavelength over size influence that was presented in Figure 9. In addition, for experimental usually waveform do s w not hich usually have constant do not have c amplitude onstant amp cycles thislit ef ude cyc fect would les this e be weaker ffect would be we due to lower aker level due to of waveforms which usually do not have constant amplitude cycles this effect would be weaker due to constructive interference. lower level of constructive interference. lower level of constructive interference. The The minimum sensor siz minimum sensor size e used used in in this st this study udy as as r reference wa eference was s 1 m 1 mm. m. Al Although though thi this s i is s not not exactl exactly y aThe minimum sensor siz “point”, or infinitesimally e small used sensor in this st , the udy as results reference wa do not deviate s 1 m significantly m. Although for the this casual is not AE exactly a “point”, or infinitesimally small sensor, the results do not deviate significantly for the casual AE wavelengths. wavelengths. F Figur igure e 16 sh 16 shows ows the the s simulated imulated rec received eived wa waveforms veforms f for or sensors of sensors of 1 mm, 0.5 1 mm, 0.5 mm mm a and nd a “point”, or infinitesimally small sensor, the results do not deviate significantly for the casual AE 0.1 0.1 m mm m after after a a s surface urface exci excitation tation of of 2 200 00 kHz kHz which which is is typical typical for for A AE E in conc in concrret ete. e. wavelengths. Figure 16 shows the simulated received waveforms for sensors of 1 mm, 0.5 mm and 0.1 mm after a surface excitation of 200 kHz which is typical for AE in concrete. 0.4 1 mm sensor 0.3 0.4 0.5 mm sensor 0.2 1 mm sensor 0.3 0.1 mm sensor 0.1 0.5 mm sensor 0.2 0.1 mm sensor 0.1 -0.1 -0.2 -0. -0 1.3 0 1020304050 -0.2 Time (μs) -0.3 Figure 16. Simulated waveforms received by different size sensors from surface source with excitation Figure 16. Simulated waveforms0 received102 by differ03 ent size sensors 04 fr05 om surface0 source with excitation frequency equal to 500 kHz (curves overlap). Time (μs) frequency equal to 500 kHz (curves overlap). Figure 16. Simulated waveforms received by different size sensors from surface source with excitation frequency equal to The waveforms 500 kHz ( are literally curves overlap) identical . without distortion on the shape or the peak to peak amplitude. Therefore, considering that element sizes smaller than 1 mm are not commonly used in AE practice, the sensor of 1 mm was considered as reference. Amplitude Amplitude Amplitude Amplitude Amplitude (-) Amplitude (-) Appl. Sci. 2018, 8, 168 15 of 16 A further point that should be kept in mind is related to the dispersion phenomenon. This study focuses on a homogeneous bulk material and monochromatic frequency in order to quantify the sensor size effect. Different cases of media can be considered in the future, like the case of heterogeneous bulk material, where scattering dispersion may impose a frequency dependent velocity as well as the case of thin plates where dispersion originates from the geometry (plate wave dispersion). In these cases, the pulse would spread in time domain altering the duration and the contact time with the sensor. Another interesting case is of anisotropic media where velocity (and thus wavelength) changes with direction, typical of composite plates. There the “aperture” effect would change for different directions depending on the orientation of the fibres. 6. Conclusions Although the sensor size effect is acknowledged in wave propagation studies, it is rarely quantified. Herein, the sensor size effect is numerically assessed for AE wave propagation in concrete and different angles of incidence to the surface. Simulations enable the isolation of the size effect without influence from the frequency response of the piezoelectric element. It is shown that the small physical size of sensor enables more precise representation of the actual propagating wave. Concerning Rayleigh waves that present the strongest aperture effect, the results can be expressed in terms of the sensor size over wavelength parameter. As this ratio increases from zero (the ideal case of point sensor) to 0.5, the amplitude has already lost approximately 35% and when the wavelength becomes equal to the sensor, the amplitude has lost 80% of the amplitude of a point sensor. For longer sensors relative to the wavelength, the amplitude continues to decrease with a smoother slope. Coherence analysis conducted between the received and original waves shows that waveforms received from surface propagating waves carry stronger distortion compared to longitudinal waves emitted from a source into the material standing diagonally or vertically beneath the sensor. Experimental evidence was taken using two widely applicable sensors. The smaller size sensor records the Rayleigh wave on the surface with higher amplitude than the longitudinal impinging vertically emitted by source located at the opposite side of a concrete sample and at the same distance. The result is inverse for a larger sensor, being a clear manifestation of the sensor size effect. The latter indicates that the amplitude of sources near the surface are more prone to underestimation errors when a large sensor size is used. Frequency content of the received waves is also distorted due to the sensor size, increasing the possible distortion due to scattering or reflections. Acknowledgments: Financial support of the Research Foundation Flanders (FWO-Vlaanderen, Project No 28976) for this study is gratefully acknowledged. Author Contributions: Dimitrios G. Aggelis conceived, designed and performed the numerical simulations; Eleni Tsangouri performed the experiments and analyzed the data; Dimitrios G. Aggelis and Eleni Tsangouri wrote the paper. Conflicts of Interest: The authors declare no conflict of interest. References 1. Prosser, W.H. Acoustic Emission. In Nondestructive Evaluation, Theory, Techniques and Applications; CRC Press: New York, NY, USA, 2002; pp. 369–446, ISBN 9780824788728. 2. Ishibashi, A.; Matsuyama, K.; Alver, N.; Suzuki, T.; Ohtsu, M. Round-robin tests on damage evaluation of concrete based on the concept of acoustic emission rates. Mater. Struct. 2016, 49, 2627–2635. [CrossRef] 3. Sagasta, F.; Benavent-Climent, A.; Roldán, A.; Gallego, A. 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Applied Sciences – Multidisciplinary Digital Publishing Institute
Published: Jan 25, 2018
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