Assessment of fracture process of engineered cementitious composite (ECC) by time-frequency analysis of acoustic emission signals

Engineered cementitious composite (ECC), also known as strain-hardening cementitious composite, exhibits high ductility and high toughness. The high ductility and high toughness of ECC are associated with finely-tuned matrix cracking, fiber rupture, and fiber-matrix debonding. This study investigates the fracture process of ECC through a time-frequency analysis of acoustic emission (AE) signals. The frequency characteristics of individual AE hits were used to evaluate different types of damage throughout the fracture process. The evolution of damage was assessed, and the AE energy was calculated. The effects of matrix flaw and fiber content on the fracture process were investigated. The test results revealed that different damage stages featured different AE frequency characteristics, which were used to classify damage types. ECC showed high energy absorption along with the high toughness. This research enhances the understanding of the fracture process of ECC and advances the capability of assessing the damages.


Introduction
Engineered cementitious composite (ECC), also known as strain-hardening cementitious composite, is a family of * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. cementitious composite that exhibit high ductility and high toughness [1][2][3]. After the cementitious matrix is cracked under tensile stresses, ECC is capable of carrying higher loads with controlled crack widths [4]. The ultimate strain capacity of ECC is often larger than 4%, which is more than 400 times the strain capacity of normal concrete. The crack width is usually less than 60 µm [5]. Due to tight crack widths, ECC has desired self-healing performance [6]. Fine cracks in ECC are automatically healed in the presence of water. Prior studies showed that solid wastes such as fly ash [7] and recycled concrete particles [8] served as supplementary cementitious materials in ECC, largely reducing the material cost and the carbon footprint [8]. ECC provides a unique composite platform to impart multifunctionality such as selfcleaning property [9]. In short, ECC is a sustainable, resilient, durable, and intelligent material.
ECC is reinforced with chopped fibers randomly dispersed in its cementitious matrix [1]. The fibers restrain cracks from widening during crack propagation, thus limiting the crack width and promoting dense microcracks. The design of ECC is different from the conventional tension-softening fiberreinforced cementitious composites. ECC is finely engineered to strategically tune the micromechanical properties of the matrix, fibers, and fiber-matrix interface [1]. The crack stress of the matrix matches the tensile strength of the fibers and the bond strength of the fiber-matrix interface. In other words, it is possible to achieve high tensile properties by adopting a matrix with low crack resistance, as long as the cracking stress of the matrix is kept below the bridging capacity of the fibers. The unique design philosophy leads to significant damage tolerance in ECC that delays fracture failure. The suppression of fracture in favor of volumetric spreading of damage in the presence of a notch was experimentally investigated [10].
The fracture process of ECC was studied through experiments [1] and micromechanics [3]. The fracture process involves alternating or simultaneous damage in matrix, fiber, and fiber-matrix interface. Under uniaxial direct tension, matrix cracks are initiated at defect sites with increasing tensile stress. The propagating matrix cracks are intercepted by bridging fibers. Increased crack opening is accompanied by fiber-matrix interfacial debonding, fiber rupture, and matrix spalling. ECC with high ductility often has dense microcracks and combination of fiber pullout and rupture at the crack faces. High toughness was also promoted by the synergistic energy dissipation from damage in matrix, fibers, and fibermatrix interface. The fracture process was assessed through visual inspection of specimens in tensile or flexural tests. It is difficult to assess the inside damages during the loading tests. The specific contribution and evolution of the different types of damage for energy dissipation in the strain-hardening deformation stage of ECC remain unexplored.
This study aims to assess the fracture process of ECC through time-frequency analysis of AE signals. This research attempts to establish fundamental understandings on three issues: (1) What are the frequency characteristics of AE hits generated in the loading of ECC specimens? (2) How do the frequency characteristics evolve in the loading process of ECC specimens? (3) What are the effects of matrix flaw and fiber content on the frequency characteristics and damage evolution? To address these issues, four types of mixtures were tested under uniaxial direct tension. AE signals were measured using piezoelectric (PZT) sensors. The mechanical properties and AE signals of different mixtures were compared to evaluate the effects of matrix flaw and fiber content. The frequency characteristics of the AE events were analyzed through a continuous wavelet analysis. The evolution of the frequency characteristics was assessed by ternary charts of different frequency components and discussed based on the fracture process of ECC.
This study has three novelties: (1) Time-frequency analysis of each AE event was performed through continuous wavelet analysis to analyze the evolution of the frequency characteristics. This is different from the existing studies that assessed the tensile and shear cracks using the statistics such as the average frequency of AE events [13,[25][26][27][28][29][30][31][32][33][34][35][36]. Since ECC involves different types of damage that take place simultaneously, consideration of individual AE events is essential to supplement the statistics of AE events. (2) Evolution of the types and the severity of damage were investigated using the frequency characteristics of AE signals throughout the fracture process of ECC, and the effects of matrix flaw and fiber content on the evolution were considered. (3) Direct tensile tests were performed to prevent potential interference with compressive and shear damages. This is different from the previous tests that were subjected to the combined effects of tensile, compressive, and shear damages. This research enhances the understanding of the damage process and advances the assessment of fiberreinforced cementitious composites.

Working principle
The AE approaches utilize the acoustic waves that are generated when a material undergoes damage accompanied with energy dissipation. Transient acoustic waves are generated by the rapid release of energy from the damage, propagate in the material, and can be captured by AE sensors attached on or embedded in the material. This research adopted PZT sensors that feature low cost, easy installation, high efficiency, sensitivity, and accuracy. When PZT materials are deformed by acoustic waves, a dynamic voltage waveform will be generated and measured. The waveforms are described by various parameters such as the count, hits, event, risetime, duration, peak amplitude, energy, and principal frequency, as shown in figure 1.
Since AE signals propagate in the host material from the origin of damage to other locations, the AE approach is  available for global monitoring without having to predict the originating location before sensor installation, and does not require any other energy sources as power supply. Other general advantages of the AE approach include the capabilities of detecting damages at an early stage, monitoring the damage development throughout the damage process, and assessing the damage evolution. In previous research, AE signals were utilized to classify tensile and shear cracks by analyzing the parameters of the AE waveforms [31,32]. The traditional AE parameters include the signal amplitudes, number of hits, and cumulative signal strength. Other parameters include the average frequency, risetime-to-amplitude ratio (RA), b-value, and so on [13,[25][26][27][28][29][30][31][32]. The average frequency was the ratio of the number of counts to the duration. The correlation of the average frequency and RA has been utilized to classify tensile and shear cracks, as depicted in figure 2 [32]. The correlation is qualitative because there is no consensus on the separation line between tensile and shear cracks. The use of the average frequency and RA did not consider the possibility of simultaneous occurrence of multiple types of damages.
Given the complexity of the fracture process of ECC, the average frequency in previous research is insufficient to reflect the damage process of ECC since multiple types of damage are involved during the inelastic deformation of ECC [29,38,39]. To solve this problem, this research proposed to analyze the frequency spectrum of individual AE hits using a time-frequency analysis approach based on continuous wavelet transform (CWT). The Gabor wavelet was adopted as the mother wavelet for CWT [40], as described in equation (1): where Ψ (t) is the mother wavelet; WT x is the wavelet coefficients of the signal x (t) ∈ L 2 (R) obtained by CWT; a is the scale parameter; b is the location parameter; Ψ a,b (t) is the basic wavelet function Ψ (t); and the superscript * denotes complex conjugation.
The cumulative AE energy is calculated using the integral of the two-norm of the wavelet coefficients of the AE signals [41,42], as shown in equation (2): where E (t) is the cumulative AE energy; ω is the frequency; ω 1 and ω 2 are the selected minimum and maximum frequencies in the expected frequency band, respectively. An energy ratio is defined in equation (3) to describe the ratio of AE energy to the total work done by the external tensile loads: where E L (t) is the total work done by the external loads; F (τ ) and s (τ ) are the tensile force and the elongation of the tested specimen in the gauge length, respectively; and C is a constant number (in this paper, C = 10). According to the first law of thermodynamics, the work done by the external loads is converted into AE energy, potential energy, and heat. The potential energy and heat represent the absorbed energy. A high AE energy ratio indicates low energy absorption.

Raw materials and mixtures
The raw materials used to prepare the tested mixtures included Type I Portland cement, fly ash, finely ground quartz sand, PVA fiber, and water. The cement and fly ash were used as the binder, and their manufacturer-specified chemical and physical properties are listed in table 1. The cement has a specific surface area of 376 m 2 kg −1 . The finely ground quartz sand with a mean particle size of 75 µm was adopted as the fine aggregate. The PVA fiber (Kuraray Co. Ltd.) has a surface oil coating of 1.2% by weight. The detailed properties are shown in table 2. Table 3 lists the formulation of four mixtures, which are designated as M0, M1, M2, and M3. M3 is a representative ECC mixture developed in previous research [43] and used as the control mixture in this study. A polycarboxylate-based superplasticizer (SP) was used to improve the flowability, and the SP content was determined by flow table tests to achieve a slump spread of 165 mm ± 5 mm, ensuring an adequate flowability of the ECC mixtures and uniform dispersion of the chopped PVA fibers. M0 did not have any PVA fiber. M1 had a PVA fiber content of 1% by volume of the mixture. The PVA fiber content in mixtures M2 and M3 was 2% by volume of the mixture. Mixtures M0 and M1 were used to evaluate the effect of fiber content on the fracture process. Polypropylene beads, 5 mm in diameter, served as artificial flaws in the M2 matrix. The use of artificial flaws is expected to generate more saturated microcrack damage [44].

Specimen fabrication
Cement, fly ash, and sand were added to a mortar mixer (model: HL800, capacity: 19 L) and mixed at a rate of 1 rps for 5 min. Water and SP were mixed, then added to the mixer, and mixed at a rate of 2 rps for 5 min to achieve homogeneous mortar. Finally, the PVA fibers were manually added to the mixer and mixed at 2 rps for 5 min. After mixing, the mixture was visually inspected and examined by hand. No fiber agglomeration was found. The mixture was poured into molds to cast the dog-bone specimens for tensile tests in compliance with JSCE recommendations [45]. The same casting scheme and curing condition were applied to all specimens. The specimens were cast on the same day using the same method. After casting, the specimens were cured in air in an indoor laboratory. The temperature and relative humidity of the curing room were controlled at 20 • C± 1 • C and 55% ± 5%, respectively. All specimens were de-molded after 1 d and then cured under the same condition for 28 d.

Test set-up and instrumentation
Figure 3(a) shows the uniaxial tensile test performed using a load frame (model: Instron 5969) at a constant displacement rate of 0.5 mm min −1 [45]. Two linear variable displacement transducers were deployed at the two sides of the dog-bone specimen to measure the length change within its gauge length. The exact gauge length was measured using a caliber. The applied tensile force was measured by a load cell (capacity: 10 kN) embedded in the load frame. Since the number of piezoelectric sensors (lead zirconate titanate) is limited, four PZT sensors were attached to the specimens of mixture M1, eight PZT sensors were attached to the specimens of mixture M2, and eight PZT sensors were attached to the specimens of mixture M3, as shown in figure 3(b). The dimensions of the PZT sensor are 12 mm × 4 mm × 0.5 mm (length × width × thickness). Each PZT sensor was composed of a copper foil tape (0.1 mm in thickness), a PZT wafer (0.5 mm in thickness), and two copper wires. The PZT wafer was cut by an ADT 7100 dicing saw from a PZT sheet manufactured by the Piezo System (type: PSI-5A4E). After the PZT wafer was calibrated, it was attached to a patch of copper foil tape whose top surface is covered with conductive adhesive, as shown in figure 3(c).
The copper adhesive tape was used as an electrode for the wire connection. One of the copper wires was connected to the copper electrode made using a copper foil tape with single-side conductive adhere facing the PZT wafer, and the other copper wire was directly soldered to the top surface of the PZT wafer. The copper foil tape was used at the bottom side to create a flat surface attached to the ECC specimen, and the flat surface was used to control the location of the PZT sensor with high precision. In addition, the copper foil tape was flexible and can deform to comply with the surface of the specimen. To improve the contact surface between the copper foil tape and the ECC specimen, a layer of epoxy was applied before the AE sensor was attached to the ECC specimen. After the epoxy was hardened, the bottom of copper foil tape was in direct contact with the ECC specimen and attached to the specimen surface using a fast-curing super glue. After drying for 10 min, the sensor was covered using a two-part epoxy and then cured in air at room temperature (22 • C) for 6 h before testing. When acoustic waves passed the PZT sensor, the voltages at the top and the bottom surfaces of the PZT wafer changed, and the change was measured.
The two wires of the AE sensor were connected to a data acquisition (DAQ) system. A PXIe-6361 DAQ card (National Instruments) was used to measure the voltage change in the PZT sensor in real time. One 16-bit analog-to-digital converter  M0  578  693  460  330  6  0  0  M1  578  693  460  330  6  13  0  M2  578  693  460  330  6  26  63  M3  578  693  460  330  6 26 0 channels of the DAQ card was used to sample the AE signals with a sampling rate of 1 MHz. A user interface was created to save the measured data in a computer. The AE monitoring system was synchronized with the tensile test to record the AE signals generated by damages in the ECC specimen.
To minimize the environmental noise in the received signals, a Chebyshev I bandpass filter with a passing frequency from 1 kHz to 600 kHz was applied in the data post-processing using MATLAB.  The results of the M0 specimens were not plotted because they showed brittle failure, similar to normal concrete. Each M0 specimen showed a single crack, broke into two, and lost load-carrying capacity. Figure 4 shows the tensile stress-strain curves of four M1 specimens. The curves are representative for conventional strain-softening fiber-reinforced concrete. The tensile stress linearly increased with the tensile strain until the matrix was cracked. Immediately after the matrix was cracked, the stress rapidly dropped. The tensile strength of the specimen was equal to the cracking stress of the matrix, which was comparable with the tensile strength of normal concrete. The difference from the normal concrete is that mixture M1 had residual load-carrying capability, although the residual load was low. After the matrix was cracked, the specimen did not fail abruptly, while normal concrete is brittle and usually fails immediately after the matrix is cracked. Figure 5 shows the tensile stress-strain curves of eight M2 specimens that show sustained tensile stresses after the first crack of the matrix. The post-cracking behavior of mixture M2 was different from that of mixture M1. After the matrix of M2 was cracked, the tensile stress slightly increased as the tensile strain was further increased. The sustained tensile stress significantly increased the toughness, which was represented by the energy dissipation in the damage process. Figure 6 shows the tensile stress-strain curves of eight M3 specimens that are typical for ECC, which are also known as strain-hardening cementitious composites. After the matrix was cracked, the composite continued carrying higher tensile stresses as the tensile strain was further increased. The strainhardening behavior further increased the ductility, toughness, and tensile strength. The results of the acoustic signals are discussed in section 4.3.  were in a range of 0.036%-0.152% with an average value of 0.055% (550 µε). The ultimate strains of the M2 specimens were in a range of 1.098%-2.794% with an average value of 1.988% (19 880 µε). The ultimate strains of the M3 specimens were in a range of 3.406%-5.164% with an average value of 4.096% (40 960 µε). The total number of AE events of the M1 specimens were in a range of 10-74, the total number of AE events of the M2 specimens were in a range of 196-833, and the total number of AE events of the M3 specimens were in a range of 110-187. In general, the amplitude/intensity and the number of the AE signals are often used to reveal the energy released by the damage of material. The specimens of the mixture M2 released the highest number of AE events compared with those of the mixtures M1 and M3.

Crack patterns
After tensile testing, the fracture sections of the tested specimens were examined under an optical microscope with a magnification factor of ×25. Three different scenarios, according to the three mixtures, are selected as examples to demonstrate the relationship between the AE signals and the optically observed surface damages, as shown in figure 7.
For mixture M1, all the specimens failed with a major crack and a few microcracks in vicinity of the major crack. The major crack is indicated by the abrupt peak of the stress-strain curve in figure 4. Matrix cracking is the main failure pattern. A few ruptured PVA fibers were found from the fracture surface. Such a failure mode is typical to tension-softening fiberreinforced concrete with a low fiber content.
For mixture M2, the specimens showed saturated microcracks and high ductility. The fracture section showed numerous ruptured PVA fibers, as indicated by many short fibers at the fracture section, meaning that fiber rupture played important roles in M2. For mixture M3, numerous fibers were pulled out from the concrete as indicated by the long fibers at the fracture section, meaning that fiber pullout played important roles in M3.
In this testing, mixture M2 showed fewer cracks than mixture M3. This is different from the previous testing that observed more cracks by the addition of PP beads, as elaborated in [44]. The discrepancy is attributed to the different rheological properties of the mixtures since the viscosity was not kept the same, as indicated by the same SP content in M2 and M2 in table 3. The addition of PP beads increased the viscosity, and the change of viscosity affected the dispersion of the PP beads and PVA fibers in the matrix, in turn affecting the crack patterns.

AE signals
The AE signal was recorded in time domain throughout the tensile tests. With the constant loading rate, the AE signals were correlated to the tensile stress-strain curves, as shown in figure 4. The voltage amplitude represents the intensity of acoustic waves caused by the damage processes in the ECC specimens. Figure 4 shows that a high amplitude (420 mV) of voltage was measured as the first crack was generated in mixture M1, indicating that a significant amount of energy was stored in the stressed specimen and released during cracking. As the tensile stress was increased, more AE events were detected, but the corresponding amplitudes of voltage were low (about 3 mV). In the M0 specimens, only a single voltage peak was measured from each specimen when the specimen cracked because the specimens were brittle. Figure 5 shows that the amplitude of voltage corresponding to the first crack of mixture M2 was much lower than that of mixture M1, indicating that mixture M2 had a lower cracking stress. More AE events were detected as the strain was increased, and the voltage amplitudes (6 mV-20 mV) were higher than those of mixture M1 in the post-cracking stage. More frequent AE events were measured as the tensile stress started to decrease.  Figure 6 shows that the voltage amplitude corresponding to the first crack of mixture M3 was also lower than that of mixture M1. Fewer AE events were detected as the strain increased, except for the moment shortly before the specimen failed. As the averaged tensile strain increased from 0.05% to 4.09%, few AE events were detected, indicating that M3  had high energy absorption in the fracture process. After the strain exceeded approximately 3.0%, frequent AE events were detected, and the corresponding amplitudes of voltage were higher than those from M1 and M2, indicating that more AE energy was released from the specimen at the high strain levels.

Frequency characteristics
Different types of damage showed different characteristics regarding the AE signals. Previous research on AE signals  emitted from cracked concrete qualitatively indicated that high-frequency AE signals were related to tensile cracks and low-frequency AE signals were related to shear cracks. The frequencies of AE hits were associated with the material properties such as the toughness and the elastic modulus. The AE waveforms were associated with the material and damage type. Figure 8 shows the time-frequency plots of two representative types of AE signals respectively obtained from the M0 and M1specimens. It should be noted that each plot represents an individual AE hit at a particular time instant, rather than the cumulative AE hits of the entire testing of a specimen. The AE signals were analyzed using the CWT approach elaborated in section 2. Figure 8(a) shows the time-frequency plot of a signal at the first crack of a specimen made using mixture M0. In the frequency domain, an energy peak is observed. The energy peak was generated by the single crack in the brittle matrix of mixture M0 without any PVA fiber. Figure 8(b) shows the time-frequency plot of a signal generated shortly after the first crack of a specimen made using mixture M1. The two energy peaks are attributed to two types of damages. In other words, the AE hit contained the information of two types of damage that occurred at the same time. This finding motivated the time-frequency analysis of individual AE hits in this research. The proposed analysis approach is different from the analysis approach of the previous research that analyzed the average frequency, which did not consider simultaneous occurrence of different damages.

Classification of damages
Motivated by the observations from figure 8, the timefrequency features of AE signals from the different mixtures were analyzed and plotted in figure 9. The evolution of the characteristics of the AE signals is plotted against the increase of the strain to show the change in the different stages of the failure process. Each AE hit is represented by a ball, and the ball diameter is proportional to the intensity of the energy of the AE hit. The color darkness of a ball represents the frequency, and high frequency is represented by a dark red color. Considering that the 3D plot is inconvenient to examine the trends, the data points are projected to the three planes: (1) frequency versus RA (blue dots), (2) frequency versus strain (green dots), and (3) RA versus strain (red dots). In the projection of data points, the energy threshold was set at 40 dB to minimize the effects of noise and prevent the display of too many data points.
The relationship between the frequency and RA of M1, as shown by the blue dots in figure 9(a), is consistent with the relationship between the average frequency and RA in previous research on conventional tension-softening fiberreinforced concrete. The data points with high frequency and low RA represent tensile cracks such as matrix crack, and the data points with low frequency and high RA represent shear cracks such as fiber-matrix interface damage. Two large balls with frequencies 20 kHz and 60 kHz are observed at the instant corresponding to the first crack, indicating that the AE hit involves two types of damage. The two types of damage are likely matrix cracking, corresponding to the energy peak at 60 kHz, and fiber-matrix interfacial damage, corresponding to the energy peak at 20 kHz. Such results revealed that fibermatrix damage occurred simultaneously at the instant when the first crack in the matrix was generated.
Consistent observations were verified by the other AE events generated at higher strain levels in the same specimen. As the applied strain increased, multiple energy peaks were identified from each of the individual AE hits, revealing that  Mixtures M2 and M3 showed different distributions of data points from mixture M1 regarding the frequency versus RA. Figures 9(b) and (c) show a fewer number of balls with low frequency and high RA. This is attributed to the energy threshold (40 dB) in processing of data. AE hits with energy below the threshold are not displayed. Without applying the threshold, many balls with low frequency and high RA were seen, but the plots became too crowded. This is different from the results from mixture M1. The discrepancy is attributed to the different ductility of the mixtures.
The energy ratios of the mixtures are plotted in figure 10. Mixture M1 showed higher energy ratios than mixtures M2 and M3, meaning that a higher proportion of work done by the external loads was released as AE energy by mixture M1. This comparison implies that mixtures M2 and M3 have higher energy absorption capabilities, as indicated by the low AE energy ratios in figure 11. The high energy absorption capabilities are consistent with the high toughness of ECC [1]. More energy is converted into internal energy and mild damages with low AE energy. In the fiber pullout process, there is significant friction at the fiber-matrix interface for energy dissipation. Figure 11 shows representative results of AE events and energy cumulation of mixtures M1, M2, and M3. The AE signals were classified as low-frequency (lower than 20 kHz), middle-frequency (20 kHz-50 kHz), and high-frequency (higher than 50 kHz), which were used to represent the different types of damage in ECC. Previous studies [29][30][31][37][38][39] provide evidence that the frequency of the AE signals generated by concrete cracking remains relatively constant regardless of the loading conditions. Their experiments in normal concrete and ECC specimens shows that the AE signals released by normal concrete and the cement matrix in ECC specimen have the same frequency range. In other words, the frequency ranges of cement matrix in M1, M2, and M3 were verified by previous research. Matrix cracking is associated with low frequency, fiber rupture is associated with middle frequency, and fiber-matrix debonding is associated with high frequency. It is noted that the three frequency ranges were roughly selected according to the tensile test results. Further research is necessary to sophistically evaluate the frequencies and correlation with the damages. With the above assumption, the fracture process is discussed for each mixture as follows:

Damage evolution
For mixture M1, the cumulative energy and the number of low-frequency signals are higher than those from middlefrequency signals, and the cumulative energy and number of high-frequency signals are the lowest. Such results are consistent with the test results and the previous knowledge of the fracture process of tension-softening mixtures. Due to the low fiber content, mixture M1 was brittle, and a very limited number of fibers were pulled out of the matrix. For mixture M2, the cumulative energy and number of events from middlefrequency signals are higher than those from low-frequency and high-frequency signals, meaning that fiber rupture was dominant. This is consistent with the increase of the fiber content in mixture M2, which was twice that of mixture M1, and more ruptured PVA fibers were observed at the fracture section. In mixture M3, the cumulative energy and number of events from high-frequency signals are higher than those from low-frequency and middle-frequency signals, consistent with the more PVA fibers that were pulled out of the matrix. The pullout of fibers promoted dissipation of energy via friction at the fiber-matrix interface, alleviation of AE events, and improvement of the ductility.
It should be noted that the above discussions are built on the assumption of the three ranges of frequency for the AE signals. Although the deductions of the assumption agree with the results of experimental tests in this study and previous knowledge of the fracture process in general, it is still necessary to perform further tests to justify the assumed frequency ranges. It is likely that the frequencies will be determined if AE signals generated by single types of damage are analyzed.
Because different specimens showed different numbers of AE events and dissipated energy, normalized ternary charts were used to show the evolution of damage, as shown in figure 12. The ternary charts show the percentages of AE signals at the three frequencies. For instance, the circled red point in figure 12(a) represents a specimen of mixture M1 at a particular load level, when the tensile strain was 0.0011%. The corresponding values of the three axes were 32%, 33%, and 35%, respectively. The results indicate that the percentages of the AE signals with the three frequencies were almost the same. The corresponding energy dissipation of the same AE event is shown in figure 12(b). The percentages of energy related to the three frequencies are 41%, 34%, and 25%, respectively, indicating that the low-frequency damage dissipated the highest energy.
The color of the number and the energy of AE events for each specimen gradually change from light to dark. The color change indicates the damage evolution in the loading process. In figures 12(a) and (b), the dark red points gradually move towards the right bottom corner, indicating that the M1 specimens were mainly related to the low-frequency damage as the load level was increased. The dark blue points are mainly located at the top center, meaning that the M2 specimens were mainly related to the middle-frequency damage as the load level was increased.
In figure 12(a), the dark green points are mainly located at the bottom left corner of the ternary chart, meaning that the M3 specimens had high percentages of the middle-frequency and high-frequency AE events. In figure 12(b), the dark green points are mainly located at the left, revealing that the lowfrequency damages were mainly responsible for the energy dissipation.

Conclusions
This paper proposes to assess the damage process of ECC using AE signals based on a time-frequency analysis using CWT. The damages in different mixtures were assessed via tracing the frequency characteristics of the AE signals throughout the fracture process. The frequency components of individual AE hits were evaluated. The AE energy was calculated to reveal the damage evolution process. The following conclusions are drawn: • The time-frequency analysis using wavelet transform is a promising approach to reveal the features of AE signals. The AE signals of ECC under tension contain multiple frequency components. The duration of high-frequency components is shorter than that of the low-frequency components and likely stands for brittle damage. Three frequency ranges were identified: low frequency band (<20 kHz), middle frequency band (20-50 kHz), and high frequency band (>50 kHz). The three frequency ranges were correlated with matrix crack, fiber rupture, and fiber-matrix interface debonding. • The damaged evolution of ECC was revealed by the number and cumulative energy of the three frequency ranges. The cumulative energy was reflected by the wavelet coefficients. The cumulative energy slowly increased at the beginning, and rapidly increased at the latter stage of tensile testing. Different types of damage dominated different mixtures. Overall, matrix cracking dominated the early stage while fiber-matrix interfacial damage and fiber fracture dominated the latter stages. • The addition of the PVA fibers increased the percentages of high-frequency signals. This is consistent with the many PVA fibers that were pulled out of the matrix. The pullout of fibers promoted dissipation of energy via friction at the fibermatrix interface, alleviation of AE events, and improvement of the ductility. The inclusion of artificial flaws in the matrix decreased the percentage of high-frequency signals, consistent with the promotion of fiber rupture. • The discovery of the correlation between frequency characteristics and damages in ECC is promising in development and assessment of ECC with high toughness. The understanding of the evolution of damage and energy dissipation mechanisms is helpful for strategically tuning the mixture design and finely engineering the progressive fracture process of the microstructures of fiber-reinforced cementitious composites.