Experimental materials

In order to study the AE characteristics of different tree species under load, common hardwood (Z. schneideriana) and softwood (P. sylvestris var. mongolica) samples were selected as test materials and used to make specimens with dimensions of 800 by 60 by 30 mm (axial by tangential by radial), and the number of specimens for each species was two, numbered as ZS1, ZS2, PSM1, and PSM2, respectively. The density and absolute moisture content of the specimens of Pinus sylvestris var. mongolica and Zelkova schneideriana in the air-dry state were 0.458 g/cm³ and 11.1 percent and 0.705 g/cm³ and 14.3 percent, respectively.

The three-point bending tests for the test piece were carried out using a UTM5105 mechanical testing machine (Jinan Kason Testing Equipment Co., Ltd.) at a loading speed of 2 mm/min and a span of 200 mm. Based on the NI USB-6336 high-speed data acquisition card (National Instruments) and LabVIEW software, a three-channel AE signal acquisition platform was built with a maximum sampling frequency of 2 MHz for each channel. The sensor was an SR-150N single resonant AE sensor (Beijing Soundwel Technology Co., Ltd.) with a bandwidth of 22 kHz to 220 kHz, and a power amplifier interface (PAI) front-end amplifier (Soundwel) with a gain of 40 dB was used to amplify the signal detected by the AE sensor for long-distance transmission of the AE signal. The study showed that the maximum frequency of the AE signal of the wood was about 200 kHz. According to the Shannon sampling theorem, in order to restore the analog signal without distortion, the sampling frequency f_s and the maximum frequency f_max of the signal must satisfy f_s ≥ 2 f_max. Therefore, in the experimental process, the sampling frequency of each channel of the system was set to 500 kHz, and the output voltage range was set to (−5 V, 5 V).

Experimental methods

As shown in Figure 1, the sensors S_AE1, S_AE2, and S_AE3 were equally spaced at 300-mm intervals on the upper surface of the specimen, in which the sensor S_AE1 was placed 100 mm away from the left-end face of the specimen, and the load was applied in the middle position between sensor S_AE1 and sensor S_AE2 by the universal mechanical testing machine for three-point bending tests. In order to ensure sufficient coupling between the sensor and the specimen, high-temperature vacuum insulating grease was filled between the specimen and the sensor to reduce the influence of the air medium on the test results. In addition, the sensor was fixed on the surface of the specimen with a rubber band.

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Due to the influence of environmental noise, the original signal collected was mixed with ambient random noise. The discrete wavelet transform method has excellent denoising effect and time–frequency localization analysis capability, which can realize signal denoising and reconstruct the AE signal waveform at the same time. The principle of wavelet denoising is to decompose the collected original AE signal into different frequency bands to obtain a series of low-frequency approximate signals and high-frequency detail signals and then filter out the noise according to the difference between the noise and the effective signal under the wavelet transform. This study used the Daubechies wavelet as the discrete wavelet transform basis function for the five-layer wavelet decomposition. In the original signal acquisition process, each channel sampling frequency f_s = 500 kHz. According to the Shannon sampling theorem, the AE signal analysis frequency f_h = f_s/2 = 250 kHz; that is, theoretically, the signal components can effectively be identified in the range of 0 to 250 kHz. According to the wavelet multiresolution analysis principle, the frequency bands of each layer of high-frequency detail signals after wavelet decomposition were (125 kHz, 250 kHz), (62.5 kHz, 125 kHz), (31.25 kHz, 62.5 kHz), (15.625 kHz, 31.25 kHz), (7.8125 kHz, 15.625 kHz) … . This means that only five layers of decomposition were needed to cover the full measurement range of the SR-150N single resonant AE sensor.

In order to define AE events more objectively in the frequency domain and identify AE characteristics in the process of material damage, an empirical mode decomposition (EMD) algorithm was used to decompose the AE signal decomposed and reconstructed by the discrete wavelet transform into a series of intrinsic mode functions (IMFs). The IMF with the highest correlation with the reconstructed signal was used as the final AE signal, and the instantaneous frequency of this AE signal was obtained by the Hilbert transform. The basic process is shown in Figure 2.

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For any continuous time signal Y(t), its Hilbert transform H[Y(t)] is: (1) $$H[Y\left(t\right)]=\frac{1}{\pi }P\underset{-\infty }{\overset{+\infty }{{\displaystyle \int }}}\frac{Y(\tau )}{t-\tau }d\tau$$where P is the Cauchy principal value integral and τ is the time variable. Construction of an analytical signal Z(t) from the real signal Y(t) and its Hilbert transform H[Y(t)] is done by: (2) $$Z(t)=Y(t)+iH[Y(t)]=a(t)e^{i\theta (t)}$$where a(t) is the instantaneous amplitude, and θ(t) is the phase: $$a\left(t\right)=\sqrt{Y^2\left(t\right)+H^2\left[Y\left(t\right)\right]}$$ (3) $$\theta (t)=\arctan \left(\frac{H\left[Y(t)\right]}{Y(t)}\right)$$

The instantaneous frequency is calculated as follows: (4) $$f(t)=\frac{1}{2\pi }\omega (t)=\frac{1}{2\pi }\times \frac{d\theta (t)}{dt}$$

The instantaneous frequency f(t) is a single-valued function of time t, and there is only one definite frequency value at any moment. According to the degree of material damage, AE events with different frequency bands are defined in the frequency domain, and then, at a certain moment, we only need to determine if the corresponding instantaneous frequency value falls within the range of that type of AE event. If so, the corresponding AE event is considered to have occurred.

Results and analysis of the three-point bending test

In the tests, we took the test data from ZS1 and PSM1 for analysis because of the large amount of AE signal data and the highly similar pattern of the damage process of specimens of the same tree species. The destruction process of wood under bending loads can be roughly divided into three typical stages: linear deformation stage, nonlinear deformation stage, and macroscopic fracture stage. The force–time variation curves of Z. schneideriana and P. sylvestris var. mongolica in the damage fracture process are shown in Figures 3a and 3b, respectively. The AE signal waveforms collected by the three sensors are basically similar during the bending damage process. So, only the signal waveform of sensor S_AE2 was taken for analysis. The original AE signal waveforms corresponding to the two specimens are shown in Figure 4.

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According to Figure 3a and Figure 4a, Z. schneideriana is in a linear deformation stage within 0 to 131 seconds, with elastic deformation occurring predominantly. The original AE waveform detected by the sensor also shows a high-amplitude AE phenomenon at the moment when there are several small fluctuations in the force–time curve, indicating that microcracking is occurring within the material at that stage. Within 131 to 208 seconds, the material is in the nonlinear deformation stage, Z. schneideriana begins to undergo significant plastic deformation, and the original AE signal waveform mainly shows many low-amplitude burst-type signals. At the same time, with the expansion of internal microcracks, some high-amplitude AE phenomena occur at this stage. At about 205 seconds, the load decreases significantly for the first time, which indicates that macroscopical damage of Z. schneideriana begins to appear at that time. At about 208 seconds, when the strength limit of the Z. schneideriana specimen is reached, the specimen starts to fracture macroscopically, while new microcracks appear inside the specimen and continue to nucleate and expand. Therefore, the AE signal waveform alternates between high-amplitude and low-amplitude burst signals.

According to Figures 3b and 4b, it can be seen that in comparison with Z. schneideriana, P. sylvestris var. mongolica undergoes a shorter linear deformation phase (0 to 40 seconds), which is characterized by the absence of any significant AE phenomenon in the early part of the phase, and then the material starts to undergo microcracking in the later part of the phase, which gradually results in the emergence of some AE signals with low-amplitude values. The original AE signals of the P. sylvestris var. mongolica specimen during the nonlinear deformation stage (40 to 340 seconds) are quite different from those of the Z. schneideriana specimen: In addition to low-amplitude signals, there are also many significant high-amplitude AE signals.

Compared to Z. schneideriana, P. sylvestris var. mongolica has longer fibers, which are affected by fiber bridging and have more pronounced nonlinear properties. According to the existing research (Lai et al. 2022), it is known that in the early stage of this phase, the difference between the tensile and compressive strengths of the wood leads to a shift in the neutral layer, which results in a small amount of AE. As the load continues to act, the shear gliding between the molecular chains of the stretched lignocellulose is intensified, and microfractures appear between the intercellular or cell-wall layers, resulting in a more intense AE phenomenon. Large numbers of fibers inside the material pull each other, while deformation and microscopic fractures occur, which leads to the phenomenon where large numbers of low-amplitude and high-amplitude AE signals coexist in the original AE waveform. At the macroscopic fracture stage (340 to 420 seconds), accompanied by the extension of a large number of microcracks and the formation of new cracks, significant brittle fracture occurred in the P. sylvestris var. mongolica specimen, and the AE signal characteristics were similar to those when macroscopic fracture occurred in the Z. schneideriana specimen.

From this analysis, it is obvious that it is not sufficient to identify material damage only by force–time curves or the original time-domain waveform of the AE signal. For example, in the nonlinear deformation phase of the P. sylvestris var. mongolica specimen, damage has actually occurred within the wood, but the load curve has not fluctuated significantly. In addition, the time-domain waveforms of the AE signals of the P. sylvestris var. mongolica specimen show a very high similarity between the nonlinear deformation stage and the macroscopic fracture stage, but the actual damage conditions of the material differ significantly.

Frequency domain characteristics of AE signals at different damage stages

Due to the high sampling frequency, the data sets generated by the experiment were large, so we selected data with a length of 10⁴ (20 ms) from three different damage stages of the specimens for discrete wavelet transform processing, and we reconstructed the AE signals on the basis of wavelet processing and then studied the frequency domain characteristics of the AE signals in different damage stages. The sensors S_AE1 and S_AE3 were close to the boundary of the specimens, and there were a large number of reflected waves in the original AE signals collected, which would affect the signal analysis. In addition, influenced by the viscoelastic property of wood, there would be a high-frequency attenuation of the AE signals in the propagation process (Wang et al. 2020); sensor S_AE3 was farther away from the AE source, and the high-frequency attenuation phenomenon was significant, which had a greater impact on the analysis of signal characteristics. Therefore, in this article, the original signals acquired by sensor S_AE2 were selected for analysis. The AE signal characteristics of the Z. schneideriana specimen and the P. sylvestris var. mongolica specimen at three different damage stages are shown in Figures 5 and 6, respectively.

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In order to investigate the differences in the damage patterns of the two materials in the fracture process, the damage region of the specimen was individually selected to observe the damage on the compression and tension sides. Meanwhile, in order to further observe the internal damage of the material, the selected specimens were cut and their microscopic cracks were observed by XTL-100 electron microscope (Shanghai Yanfeng Precision Instrument Co., Ltd.; Figs. 7c and 7f). The details are shown in Figure 7.

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According to Figure 5, in the linear deformation stage (Fig. 5a), the Z. schneideriana specimen is subjected to an external load, and the wood fibers in the compression zone are pressed into the interior of the specimen. However, due to the high flexural strength of Z. schneideriana, the squeezed wood fibers do not break significantly, but more linear deformation of the wood fibers occurs, and there is some extremely weak microscopic pulling. Upon continued loading, the wood cells in the compression zone are crushed and destroyed, and the surface of the specimen eventually forms the surface indentation shown in Figure 7b. The AE signals generated at this time are concentrated in the 30- to 45-kHz range, and the main frequency signal component is 40.1 kHz, which is a relatively low frequency signal component. In the early stage of the nonlinear deformation stage, the AE signal still mainly comes from the deformation of the material and the microscopic tensile fracture inside the material, and thus the AE signals are not only distributed in the low-frequency band centered at 42.2 kHz and 54.1 kHz, but also in the middle- and high-frequency band caused by the microscopic fracture (102.1 kHz). At the later stage of the nonlinear deformation stage (Fig. 5c), the microscopic cracks inside the specimen have been formed and gradually evolve to macroscopic cracks (Fig. 7c). At this time, microscopic ductile fractures replace material deformation as the main source of the AE phenomenon, and thus the AE signals are concentrated in the high-frequency band with 93.5 kHz as the center of distribution, while the signals in the low-frequency band are very few. During the macroscopic fracture stage (Fig. 5d), significant macroscopic ductile fracture of the Z. schneideriana specimen occurs under external loading, which eventually results in the formation of a pulling fracture wound as shown in Figure 7a. The AE signals produced are mainly characterized by high frequency and high energy, with a signal distribution frequency band of 117.6 to 132.8 kHz.

As shown in Figure 6, in the linear deformation stage (Fig. 6a), the AE signals collected from the P. sylvestris var. mongolica specimen are mainly distributed in the low-frequency band, as in the Z. schneideriana specimen, and the difference is that there are high-frequency signals centered at 102.1 kHz in the P. sylvestris var. mongolica specimen at this stage. This is mainly due to the fact that compared to Z. schneideriana, the P. sylvestris var. mongolica specimen is brittle and has many internal cavities, which means that the material bearing capacity is relatively low and sensitive to external loads. In the linear deformation stage, the wood fibers are pressed against each other by the load, resulting in deformation of the material, while some of the fibers that are pressed into the material by the extrusion of the surface fibers reach their strength limit, and microscopic brittle fracture occurs, resulting in the formation of a more obvious fracture phenomenon on the surface of the material, as shown in Figure 7e, thus producing both high-frequency and low-frequency signals. At the early stage of nonlinear deformation (Fig. 6b), as the degree of deformation intensifies, the microscopic brittle fracture of the P. sylvestris var. mongolica specimen becomes more and more obvious, and the proportion of high-frequency signal components increases, gradually replacing the low-frequency signal generated by deformation as the main signal component at this stage. At the later stage of nonlinear deformation (Fig. 6c), microscopic brittle fracture damage mainly occurs in the material, with the center of the main frequency signal distribution at 103.7 kHz. At the same time, some of the microscopic cracks that accumulated in the early stages (as shown in Fig. 7f) gradually become macroscopic cracks that are recognizable to the naked eye, so there are also a large number of high-frequency signals in the range of 120 to 130 kHz. After entering the macroscopic fracture stage (Fig. 6d), under the continuous action of the load, the cracks on the tensile side of the specimen gradually spread to the interior of the material, and a significant macroscopic brittle fracture occurs, and finally a brittle fracture-type wound is formed on the surface of the material, as shown in Figure 7d. At the same time, the internal microcracks (Fig. 7f) continue to expand, so there are two frequency distribution centers of AE signals, 101.2 kHz and 119.7 kHz, and the frequency band of 119 to 130 kHz is the main component of the AE signals.

According to this analysis, the AE signals generated during the damage process of the two specimens can be divided into three categories by the frequency domain characteristics: the deformation AE signals generated during the linear deformation stage, the microfracture AE signals generated during the nonlinear deformation stage, and the fracture AE signals generated during the macroscopic fracture stage. In this article, these three signals were defined as deformation AE (DAE), microfracture AE (MAE), and fracture AE (FAE), respectively.

Statistics of AE events

The previous analysis shows that the method of identifying damage in wood in the frequency domain is more effective and objective than that in the time domain. In this article, the frequency bands of DAE, MAE, and FAE events were defined as [30 kHz, 60 kHz], [90 kHz, 115 kHz], and [115 kHz, 135 kHz], respectively, according to Figures 5 and 6. In order to determine the instantaneous frequency of the AE signals at a certain time, the reconstructed AE signals were first decomposed by EMD after wavelet transform, and the Hilbert transform was used to obtain the instantaneous frequency. In order to objectively reflect the AE event level of the specimen during the damage process, the occurrence density of the three types of AE events was calculated at intervals of 50 ms according to the frequency range of the FAE, MAE, and DAE determined in advance. Figures 8 and 9 respectively show the density curves of the three types of AE events during the whole loading process for the Z. schneideriana and P. sylvestris var. mongolica specimens.

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According to Figure 8, in the early stage of linear deformation and nonlinear deformation, the density of DAE and MAE events is stable at a high level of 160 times/ms and 150 times/ms, respectively, while the density of FAE events is much lower than that of DAE and MAE events, being roughly distributed at 60 times/ms. This suggests that the deformation of Z. schneideriana under loading is accompanied by a high level of strain energy release due to microtoughness fracture of the wood fibers as the fibers within the material pull against each other. However, the material still has a strong ability to resist damage, and the deformation and microscopic fractures that accumulate during loading are not sufficient to cause a macroscopic fracture recognizable to the naked eye. At the later stage of nonlinear deformation, the frequency of abrupt changes in the density of the three types of AE events shows a decreasing trend, which indicates that the material has yielded at this stage and has a strong ability to resist the external load, which coincides with the results that the load level rises at a slower rate in the range of 170 to 205 seconds in Figure 3a. At around 208 seconds, the density curve of DAE events undergoes a significant abrupt change, and the simultaneous abrupt change in the density levels of MAE and FAE events reaches a high value. This indicates that the cumulative deformation and microcrack extension (Fig. 7c) reach the maximum limit that the Z. schneideriana specimen can withstand, which leads to macroscopic fracture of the material, as shown in Figure 7a. There is also a large number of new microscopic cracks nucleating and expanding at this stage, as shown in Figure 7c, which is consistent with the result of Figure 3a, where the Z. schneideriana specimen loses its ability to resist the load and appears to fracture macroscopically at 208 seconds.

After that, as the load continues to act, the original microscopic cracks continue to expand, leading to further macroscopic fracture. Some internal areas of the material have not yet occurred damage, but with the continuous action of the external load, deformation accumulation gradually appears, thus generating new microscopic cracks, and the new cracks continue to expand, further aggravating the macroscopic fracture of the specimen. Therefore, the density curves of MAE events and FAE events remain synchronized to increase or decrease at a certain level, and where there is an abrupt change in the density of corresponding DAE events, there is a synchronized increase in the density of MAE events.

As shown in Figure 9, the density curves of the three types of AE events are maintained at a low level during the linear deformation stage of the P. sylvestris var. mongolica specimen, and there is almost no abrupt change in signal generation except around 20 seconds. By the early stage of nonlinear deformation, the DAE event density as a whole remains stable at the level of 60 times/ms, whereas the MAE and FAE event density curves are increasing, which is different from the changes in the three types of AE event density curves in the Z. schneideriana specimen. The main reason for this is that, compared to Z. schneideriana, the internal structure of P. sylvestris var. mongolica is more porous and brittle, which make it less resistant to loads. Therefore, a lower load level at the beginning of loading can trigger the fracture of the wood fibers on the surface of the material (as shown in Fig. 7e), which leads to microscopic brittle fracture (as shown in Fig. 7f) of the wood fibers near the loading point without the need for a long time of deformation accumulation.

At the late stage of nonlinear deformation, the crushed but unbroken wood fiber groups had a strong resistance to the load effect, which mainly caused the accumulation of plastic deformation. At the same time, the undamaged areas under the crushed layer were loaded to form a new crushed region, which led to the microscopic brittle fracture of a large number of wood fibers, so there were multiple abrupt changes in the density of DAE and MAE events.

Before the macroscopic fracture stage, with the continuous action of external loads, a large number of the ductile fibers without brittle fracture formed an extrusion effect on the adjacent xylem vessel, and the xylem vessel wall was forced to collapse into the internal cavity. The originally relatively dispersed fibers were gathered together to form a new bonding structure, and the energy exerted by the external load was constrained by the new bonding mechanism of the wood, which made the material less sensitive to the load, and therefore the specimen underwent a longer period of nonlinear deformation accumulation. Therefore, before the macroscopic fracture, the density of FAE events remained stable and was maintained at a certain level. The abrupt change of MAE and FAE event density at 340 seconds indicates that the material lost its ability to resist load damage and began to undergo macroscopic fracture, which is consistent with the sudden downward change in the stress level and macroscopic brittle fracture of the P. sylvestris var. mongolica specimen at 340 seconds in Figure 3b. After that point, the cracks within the material continued to develop, and the density curves of all three AE events show varying degrees of fluctuation.

Figures 8 and 9 show that defining and counting AE events in the frequency domain by instantaneous frequency not only can better distinguish different types of AE signals, but also the frequency of abrupt changes in the density can effectively characterize the damage of the material and the degree of intensity of the event, and even characterize the material properties to a certain extent. Zelkova schneideriana has high toughness and compact arrangement of internal wood fibers. Before the occurrence of macroscopic ductile fracture, the material properties showed that the levels of DAE, MAE, and FAE event densities were stabilized at a high level, and the three AE event densities had a high frequency of abrupt changes, which indicated that the damage to the Z. schneideriana specimen was characterized by a significant accumulation of strain with an extremely intense stress-release process. In the fracture stage, the frequency of abrupt changes in the density of DAE events was significantly reduced, while MAE and FAE events changed abruptly and significantly, indicating that the type of material damage in this stage was mainly high-strength microfracture and macroscopic ductile fracture.

Pinus sylvestris var. mongolica has a brittle texture and a more dispersed arrangement of wood fibers. At the beginning of loading, there was no obvious abrupt change in DAE event density, and there was a certain increase in MAE and FAE event density levels. The material properties were characterized by macroscopic fracture with higher intensity and extremely weak deformation accumulation. In the middle stage of loading, the dispersed fibers were gathered together, and the material showed strong resistance to damage. In the process of strain accumulation, the stress was released rapidly, so the DAE events showed obvious abrupt change with large amplitude, and the MAE and FAE events increased in the frequency of abrupt change, but the amplitude was small. Loading continued until macroscopic fracture occurred, and abrupt changes in the density of MAE and FAE events were evident, indicating that the stress release in the material became intense.