Acoustic Emission During Failure of a Composite Under the von Mises Criterion with Local Structural Defects

Abstract

This study investigates the effect of local structural defects on the acoustic emission (AE) response during composite failure under the von Mises criterion. A fiber bundle model (FBM) is used to simulate failure under transverse shear while varying the initiation time of fracture, which corresponds to changes in defect size or heterogeneity. The results show that increasing the failure initiation time leads to a decrease in AE signal amplitude and a simultaneous increase in its duration, reflecting a slower energy release during fracture. These relationships were confirmed experimentally on fine-grained composite specimens. The obtained findings demonstrate that amplitude–time AE parameters can serve as sensitive indicators of defectiveness and local heterogeneity in composite materials, offering potential for improved nondestructive evaluation and structural health monitoring.

1. Introduction

Composite materials (CMs) offer high mechanical performance and resistance to aggressive environments, temperature fluctuations, cyclic loading, and other demanding conditions. These properties make CMs widely applicable across a broad range of industries and products [1]. However, the complexity of their internal structure, variability in properties, and the occurrence of defects during manufacturing lead to intricate failure mechanisms and avalanche-like damage progression. To detect and assess defects formed during both manufacturing and operation of composite-based structures, various conventional and advanced non-destructive testing (NDT) methods are used [2,3]. At the same time, to ensure the reliability of CM-based components, continuous research efforts—both experimental [4,5,6] and theoretical [7,8,9,10]—are carried out to study the failure processes of composites. These investigations aim to identify criteria for optimizing the internal structure, predicting the physical and mechanical properties of composites, evaluating damage progression stages, and forecasting load-bearing capacity.

One of the widely used methods for studying CM failure is acoustic emission (AE) [11,12,13,14]. AE is characterized by low inertia, and its signals reflect the dynamics of evolving processes within a material under load—plastic deformation, development of submicro-, micro-, and macrocracks, damage accumulation, and more. The method’s sensitivity to processes at all structural levels leads to challenges in interpreting AE data and identifying the mechanisms involved, especially in the case of CMs [13,15,16,17]. Research results show that AE data interpretation and process identification in composites are significantly complicated by the influence of various factors—strain rate, composition and structure of the CM, property uniformity, structural defects, and others. Such factors introduce instability into AE signal patterns and necessitate the collection of large volumes of statistical data.

To investigate failure processes in composites, a variety of models and conceptual frameworks are employed, including the phase-field damage model, smeared damage model, and discrete damage model. The phase-field model represents damage zones as a continuous diffusive field and is used to describe and analyze progressive degradation and failure in composites [18,19]. The smeared damage model focuses on the degree of material degradation and describes the gradual accumulation of microscopic defects (damage) that eventually lead to macroscopic failure [20,21]. The discrete damage model considers localized damage and analyzes the progressive fracture process within specific regions of the material [22,23]. Other approaches include modeling CMs as networks of particles connected by Hookean springs [24,25], allowing analysis of stress redistribution and avalanche behavior during fracture events.

One widely adopted model for analyzing failure processes in composites is the fiber bundle model (FBM) [26,27]. In the classical FBM [28], the composite is represented as a discrete set of elements (fibers), each failing instantaneously when its individual strength limit is reached. All elements are assumed to have identical Young’s modulus, and each fiber exhibits linear elastic behavior up to the point of failure. The failure of elements occurs sequentially. The threshold stress levels at which fibers fail are considered independent random variables with a given probability density and distribution function, reflecting the inherent heterogeneity of the composite. Upon failure of an element, the resulting load is redistributed either uniformly to all remaining elements—equal load sharing (ELS)—or locally to adjacent elements—local load sharing (LLS).

In describing stress variations for a given probability density of threshold failure values and in analyzing the process of composite element failure, studies are conducted on the evolution of stress, the number of surviving elements over time, the distribution of failure avalanches as global failure is approached, the critical failure time, and other parameters. When investigating composite failure processes with a prescribed probability distribution of threshold stresses, additional parameters are introduced to characterize material heterogeneity.

In [29], for an FBM model with a probability distribution of threshold stresses in the interval [0, 1], a damage variable was introduced to account for fiber aging, where failure could occur either upon reaching the threshold stress or the threshold damage level. The process of damage accumulation in composites was analytically described for cases of fiber failure with one damaged neighbor and with an undamaged neighbor. The occurrence of early rupture jumps associated with structural defects (damaged CM elements) was demonstrated.

In [30], composite heterogeneity was introduced through temperature, incorporated into fiber displacement during deformation via applied force and thermal noise. It was determined that the failure time under an applied load follows a power law, while the failure dynamics exhibit avalanche-like behavior with two characteristic rates, governed by the Boltzmann distribution. Similarly, in [31], additional heterogeneity was introduced by local thermal expansion, as well as by fiber orientation—fibers of equal size having a constant inclination angle but being randomly distributed in all directions according to a specified probability density function. An analysis of the temporal evolution of the number of surviving fibers and elastic energy was conducted.

In [32], heterogeneity of the composite was represented as a random fiber bundle structure (random displacement or sagging of fibers with respect to a base length), with each fiber assigned a random displacement under loading. The results revealed the presence of two power-law regimes in the avalanche size distribution depending on the base fiber length. In [33], structural heterogeneity was introduced by assuming correlated fiber strength, where fibers elongate according to an exponential gradient. This creates a transition of stress fields from the fracture zone to an intermediate (active) zone with potential fiber failure, and further to a zone of intact fibers. The study showed that the avalanche distribution is sensitive to the heterogeneity zone length if the stress field shape exceeds the heterogeneity size.

In [34], composite failure modeling considered heterogeneity regulated by increasing the ultimate threshold stress and by raising the exponent of the power-law distribution of threshold stresses. It was shown that decreasing threshold stress values and increasing the distribution exponent accelerate the failure process. Moreover, greater heterogeneity results in larger avalanches.

To investigate the influence of defects on failure under tension, ref. [35] developed a fiber bundle model with a defect based on the classical FBM, where the key parameters are average defect size and defect density. It was demonstrated that for both uniform and Weibull distributions of threshold stresses, an increase in defect size reduces the critical stress. At the same time, defect size has little effect on the probability distribution of avalanches but significantly influences the maximum avalanche size: larger defects lead to larger avalanches.

In [36], the FBM model was applied to the study of composite failure under transverse shear, where failure of CM elements could occur either by tension or shear. Structural heterogeneity was described by the probability distribution of threshold stresses. A relationship was obtained for stress variation during composite failure according to the von Mises criterion

$${\sigma }_m\left(t\right)=\alpha t·0.5\left[\left(2-2\sqrt{\alpha t}+\alpha t^{\frac{3}{2}}log\left({\displaystyle \frac{1+\alpha t}{1-\alpha t}}\right)\right)-\alpha t^{\frac{3}{2}}\left(2\sqrt{{\displaystyle \frac{1-\sqrt{\alpha t}}{\alpha t}}}+log\left({\displaystyle \frac{1+\sqrt{1-\sqrt{\alpha t}}}{1-\sqrt{1-\sqrt{\alpha t}}}}\right)\right)\right],$$

(1)

where $\alpha$ is the composite material loading rate under linear strain input, defined as $ϵ=\alpha t$ (with $\alpha$ being the strain rate).

The study demonstrated the regularities of stress variation during CM deformation, the evolution of the number of surviving elements over time, and the distribution of failure avalanches. In [37,38], the FBM model was applied to the investigation of snow failure. In [37], the potential effect of sintering on stress evolution under loading was shown. In [38], material heterogeneity was defined by the exponent of the threshold stress distribution. It was demonstrated that the greater the degree of heterogeneity, the lower the critical failure stress. Stress variation in granular materials under shear, using the FBM model for different parameters of threshold stress distributions, was analyzed in [39].

Theoretical studies of acoustic emission (AE) during the development of failure processes are carried out in accordance with the general concept of AE—as the generation of elastic displacement waves resulting from the rapid release of energy during instantaneous changes in local stress concentration in the material, such as deformation and fracture [40]. Based on this general definition of AE during the failure of CM elements, and assuming proportionality between the emitted energy and the accumulated elastic energy, ref. [41] investigates the distribution of AE energy for various threshold failure stresses. In [42], the evolution of AE energy over time and its distribution during CM deformation are examined, employing a mathematical representation of the AE signal.

In [43], the AE energy corresponding to critical failure avalanches is studied under the assumption of a power-law distribution of threshold failure stresses. In [44], the AE signal is modeled as a stochastic decaying process, with parameters determined by the type of developing defect. The entire stochastic emission process is considered as the sum of stochastic signals. In this case, AE signal accumulation is analyzed along with the probability density functions of their amplitude and energy distributions.

In [45], an expression for the AE energy release rate during CM failure was derived, showing the variation of accumulated AE energy as complete failure approaches. A similar result for AE energy release rate was obtained in [46]. The distribution of emitted energy during the failure process was considered in [47], where an expression was derived for the energy density distribution of AE. In [39], the AE energy release rate was analyzed for different parameters of threshold stress distributions, demonstrating that increasing load results in a continuous rise in energy release rate.

Assuming proportionality between emitted and accumulated energy, ref. [48] shows how the energy distribution varies with avalanche size for different parameters of threshold stress distributions, and analyzes the correlation function between failure avalanches and emitted energy. In [49], the relationship between emitted energy and avalanche size was established, showing how energy distribution changes with avalanche size under the [0, 1] threshold stress distribution.

An analytical description of AE signals generated during composite failure under transverse shear according to the von Mises criterion, using the FBM model and considering the evolution of surviving elements over time, is presented in [50]. It was shown that an increase in the strain rate of the CM leads to higher maximum amplitudes of AE signals and shorter signal durations. Further studies of AE behavior under various factors—such as CM properties, fracture surface area, variability of CM properties, and non-uniformity in the rate of failure development—were reported in [51,52,53]. These investigations made it possible to identify and describe regularities in the variation of AE signal parameters under the influence of the studied factors. The identified regularities serve as a foundation for developing methods of CM condition monitoring, structural assessment, and load-bearing capacity prediction. However, to improve the reliability of AE data interpretation and the identification of processes evolving in composites during deformation, it is crucial to analyze AE parameter variation in the presence of local defects or local structural heterogeneity during CM failure according to the von Mises criterion. This study investigates the influence of the onset time of CM failure under the von Mises criterion (threshold stress for failure initiation) on the parameters of the generated AE signal.

Although the von Mises criterion was originally developed for ductile metals, in this study it is adopted as a practical approximation for composite materials under transverse shear. Under conditions of dominant shear loading, the local stress state in the fracture zone becomes quasi-isotropic, and the anisotropic influence of fiber orientation is significantly reduced. As a result, the matrix-dominated shear failure mechanism can be effectively represented by the von Mises equivalent stress. This approach enables a direct analytical connection between the evolution of stress concentration and the acoustic emission parameters within the fibre bundle model framework, which would be considerably more complex for multi-parameter criteria such as Tsai–Wu, Hashin, or Puck.

2. Analysis

2.1. Simulation Conditions

The simulation of CM failure according to the von Mises criterion, aimed at determining the regularities in stress variation, the number of surviving elements, and the AE signal evolution over time, is carried out under the following conditions: For the CM, we adopt the FBM model, as in [50]. The composite is deformed under transverse shear with a constant strain rate. The CM is assumed to possess given properties. At the same time, within a certain region of the CM, a local defect or a local zone of structural heterogeneity is present. As shown in [54], with an increase in defect size and density, the critical failure stresses decrease. In the model, we assume that the magnitude of the local defect or heterogeneous region decreases (here we refer not to the quantitative reduction in defect size, but rather to the conceptual fact of a smaller defect). This assumption leads to an increase in the threshold failure stress and, accordingly, to a longer time before the onset of CM failure.

The simulation of stress variation under the von Mises criterion is performed in accordance with Equation (1). The variation in the number of surviving CM elements and the corresponding AE signal are described by expressions of the form given in [50]

$$N\left(t\right)=N_0·e^{-v_0{\int }_{t_0}^t{e}^{r\left[{\sigma }_m\left(t\right)\right]-\sigma \left(t_0\right)}dt},$$

(2)

$$U\left(t\right)=U_0{v}_0[{\sigma }_m\left(t\right)-\sigma \left(t_0\right)]·e^{r[{\sigma }_m\left(t\right)-\sigma \left(t_0\right)]}·e^{-v_0{\int }_{t_0}^t{e}^{r[{\sigma }_m\left(t\right)-\sigma \left(t_0\right)]}dt},$$

(3)

where ${\sigma }_m\left(t\right)$ and $\sigma \left(t_0\right)$ are the equivalent stress on CM elements as a function of time, according to (1), and the threshold stress corresponding to the time $t_0$ at which CM failure begins, respectively; $U_0$ is the maximum possible displacement during instantaneous failure of the CM consisting of $N_0$ elements; $v_0$ and r are constants determined by the physical and mechanical properties of the CM.

The threshold stress $\sigma \left(t_0\right)$, corresponding to the time $t_0$ of failure initiation in the CM, is described by the following expression:

$$\sigma \left(t_0\right)=\alpha t_0·0.5\left[\left(2-2\sqrt{\alpha t_0}+\alpha t_0^{\frac{3}{2}}log\left({\displaystyle \frac{1+\alpha t_0}{1-\alpha t_0}}\right)\right)-\alpha t_0^{\frac{3}{2}}\left(2\sqrt{{\displaystyle \frac{1-\sqrt{\alpha t_0}}{\alpha t_0}}}+log\left({\displaystyle \frac{1+\sqrt{1-\sqrt{\alpha t_0}}}{1-\sqrt{1-\sqrt{\alpha t_0}}}}\right)\right)\right].$$

(4)

The simulation, according to (1), (2), (3), and (5), is carried out in relative units. For the modeling, the strain rate $\alpha$ is taken as $\tilde{\alpha }=10$. The parameter $v_0$, characterizing the CM properties, is assigned the value ${\tilde{v}}_0=\mathrm{100,000}$. The parameter r, which reflects the dispersion of CM properties, is taken as $\tilde{r}=\mathrm{10,000}$.

During the calculations, the time interval $\Delta t_k$ between successive computed values, according to (2) and (3), is set as $\Delta {\tilde{t}}_k=1$ × ${10}^{-7}$. The failure initiation times $t_0$, corresponding to decreasing levels of structural defectiveness, are taken as: ${\tilde{t}}_{01}=0.001$, ${\tilde{t}}_{02}=0.002$, ${\tilde{t}}_{03}=0.003$, ${\tilde{t}}_{04}=0.004$, ${\tilde{t}}_{05}=0.005$.

For these failure initiation times, the corresponding threshold failure stresses ${\tilde{\sigma }}_0$ are calculated.

2.2. Simulation Results

Figure 1 shows the simulation results for the variation of equivalent stresses during composite material deformation, according to (1), at a strain rate of $\tilde{\alpha }=10$. From Figure 1 it can be observed that the dependence of equivalent stress variation under constant strain rate loading is nonlinear.

According to the simulations, the calculated values of the failure initiation stress ${\sigma }_0=\sigma \left(t_0\right)$ for the assumed failure initiation times ${\tilde{t}}_{01}$, ${\tilde{t}}_{02}$, ${\tilde{t}}_{03}$, ${\tilde{t}}_{04}$, ${\tilde{t}}_{05}$ (marked in Figure 1) are summarized in

Table 1. Calculated threshold stresses ${\tilde{\sigma }}_0$ for different failure initiation times ${\tilde{t}}_0$.

${\tilde{\mathit{t}}}_0$	${\tilde{\mathit{\sigma }}}_0$
0.001	0.008897277688462064
0.002	0.016761288967306002
0.003	0.023884393144868957
0.004	0.03037385029676163
0.005	0.03629375023308743

.

In Figure 2, the simulation results for the variation of the number of surviving elements over time during the failure process of the CM under the von Mises criterion are presented. For comparison of the regularities in the evolution of surviving elements, each failure initiation time in Figure 2 has been normalized to zero, i.e., $\tilde{t}=\tilde{t}-{\tilde{t}}_0$ for $\tilde{t}\ge {\tilde{t}}_0$.

From the graphs in Figure 2 it can be seen that with increasing failure initiation time, and consequently increasing threshold stress of CM failure, the rate of element failure decreases for the chosen modeling parameters. This corresponds to a reduction in the slope of the curves describing the number of surviving elements over time.

The simulation results of the variation of AE signal amplitudes, according to (3), during the CM failure process under the von Mises criterion are presented in Figure 3. Similar to the data in Figure 2, for comparison of regularities in AE amplitude variation, each failure initiation time in Figure 3 has been normalized to zero, i.e., $\tilde{t}=\tilde{t}-{\tilde{t}}_0$ for $\tilde{t}\ge {\tilde{t}}_0$.

From the graphs in Figure 3 it can be observed that as the failure initiation time, and consequently the threshold stress of CM failure, increases, the maximum AE signal amplitude decreases while its duration increases for the chosen modeling parameters.

Analysis of the simulation results with respect to the dependence of the maximum AE signal amplitude on the failure initiation time and on the threshold stress at failure initiation is presented in Figure 4a,b.

The results (Figure 4a,b) show that an increase in failure initiation time, and correspondingly in the threshold stress of CM failure, leads to a decrease in the maximum AE signal amplitude. The dependence of maximum amplitude on failure initiation time exhibits a nonlinear decrease, whereas the dependence of maximum amplitude on threshold failure stress demonstrates a linear decrease.

Analysis of the simulation results for the dependence of AE signal duration on the failure initiation time and on the threshold failure stress is shown in Figure 5.

The results (Figure 5) indicate that increasing failure initiation time, and correspondingly the threshold stress of CM failure, leads to an increase in the AE signal duration. The dependence of AE signal duration on failure initiation time is linear, while the dependence of AE signal duration on threshold failure stress shows a nonlinear increase.

3. Discussion of Research Results

When applying AE to the study of composite material failure processes, the problem arises of interpreting AE signals and identifying the evolving processes within the material structure [12,13]. Experimental studies show that AE is sensitive to a variety of factors—type and magnitude of load [14,15], type of damage and composite composition [16], size of the failing structural elements [17], strain rate [19], among others. Clearly, in order to increase the reliability of monitoring and diagnostic methods for CM condition, as well as the interpretation of AE data and the identification of processes occurring during CM failure under different criteria, it is essential to analyze the influence of local defects or local structural heterogeneities on the parameters of AE signals.

In this study, based on the FBM model, an analysis is performed of CM failure according to the von Mises criterion, considering an increase in the failure initiation time and, accordingly, an increase in the threshold stress for failure initiation. Such an increase in threshold failure stress may result from a reduction in the size of a defect (local heterogeneity) within the composite [54].

The results show that, under the von Mises criterion and at a fixed strain rate, the equivalent stress increases nonlinearly with time (Figure 1), consistent with earlier findings [50,52]. With increasing failure initiation time (threshold stress), the continuity of the failure process does not change. However, the rate of failure development decreases, as reflected by the reduced slope of the survival curves of CM elements over time (Figure 2). This reduction in the rate of failure progression influences the parameters of the generated AE signals:

• A decrease in the failure rate with increasing failure initiation time leads to a reduction in the amplitude of the generated AE signals.
• At the same time, the greater the failure initiation time (corresponding to a smaller defect size), the longer the duration of the AE signal.

The effect of failure rate on AE signal parameters has also been reported in [50]. Moreover, as shown in [54], with decreasing defect size (increasing composite strength), the general form of the avalanche distribution law remains largely unchanged, although the overall avalanche size decreases.

Analysis of AE signal amplitudes shows that the dependence of the maximum AE signal amplitude on the failure initiation time ${\tilde{t}}_0$ under the von Mises criterion exhibits a nonlinear decrease (Figure 4a) and follows a power-law relationship ${\tilde{U}}_m\left({\tilde{t}}_0\right)\sim e^{b{\tilde{t}}_0}$, with the exponent $b=-115.77406$. At the same time, the dependence of the maximum AE signal amplitude on the threshold failure stress ${\tilde{\sigma }}_0$ shows a linear decrease (Figure 4b) and is proportional to the threshold stress: ${\tilde{U}}_m\left({\tilde{\sigma }}_0\right)\sim d{\tilde{\sigma }}_0$, where the coefficient $d=-55.74186$.

Processing of the simulation results also revealed that the dependence of AE signal duration on the failure initiation time ${\tilde{t}}_0$ under the von Mises criterion is linear (Figure 5a) and increases proportionally with initiation time: $\tilde{\tau }\left({\tilde{t}}_0\right)\sim q{\tilde{t}}_0$, where the coefficient $q=0.00172$. At the same time, the dependence of AE signal duration on the threshold failure stress ${\tilde{\sigma }}_0$ is nonlinear (Figure 5b) and follows a power-law relationship $\tilde{\tau }\left({\tilde{\sigma }}_0\right)\sim e^{\theta {\tilde{\sigma }}_0}$, with the exponent $\theta =7.70732$.

According to the simulation results (Figure 4 and Figure 5), data processing shows that during CM failure under transverse shear according to the von Mises criterion, when the failure initiation time increases from ${\tilde{t}}_{0}1=0.001$ to ${\tilde{t}}_{0}2=0.002$, and correspondingly the threshold stress increases from ${\tilde{\sigma }}_{0}1$ to ${\tilde{\sigma }}_{0}2$, the maximum AE signal amplitude decreases by 11.69 %, while the signal duration increases by 6.14%. When the failure initiation time increases further to ${\tilde{t}}_{0}5=0.005$ and the threshold stress to ${\tilde{\sigma }}_{0}5$, the maximum AE signal amplitude decreases by 36.97%, while the signal duration increases by 23.54%.

The calculated results indicate that, with increasing failure initiation time and, correspondingly, threshold failure stress, the reduction in maximum AE signal amplitude outpaces the increase in signal duration.

The obtained results (Figure 5) show that an increase in the failure initiation time leads to a decrease in the maximum AE signal amplitude and a simultaneous increase in its duration. This effect is associated with the change in the rate of fracture development: when the local defect is smaller, the formation and propagation of damage occur more gradually, causing a slower redistribution of stresses in the material. As a result, the stored elastic energy is released over a longer time interval rather than in a short impulsive burst, which leads to a lower peak amplitude and an increased signal duration.

The experimental validation was carried out on fine-grained VK6 composite specimens with a prefabricated edge notch (0.1 mm wide and 1.5 mm deep, positioned 2 mm from the specimen edge). The specimen was cylindrical, 8 mm in diameter and 4 mm in thickness, and was subjected to transverse shear loading at a constant deformation rate of 1 mm/min. The AE sensor was mounted on the specimen support using an acoustic coupling gel to ensure stable transmission of elastic waves. AE signals were recorded using an AE acquisition system with software-controlled data capture and processing, a passband of 100–2000 kHz (±3 dB), a sensor sensitivity of 5 μV, a dynamic range of 60 dB, a 14-bit analog-to-digital converter with 1.22 mV/LSB resolution, and a sampling interval of 5 μs. A schematic of the measurement chain and sensor placement is shown in Figure 6. Figure 7 presents the recorded AE signals obtained during shear failure of the notched VK6 specimens.

The AE signal in Figure 7a was recorded at a failure load of 2 kN for the first specimen, while the signal in Figure 7b corresponds to a failure load of 2.4 kN for the second specimen (higher strength).

The obtained results show that the signal in Figure 7a has a strongly jagged form with fluctuations and amplitude drops. Such strong irregularity in the trailing edge of the signal is caused by variations in the rate of damage evolution (accelerations and decelerations) due to property dispersion in strength or the presence of structural defects. At the same time, the signal in Figure 7b has a smoother trailing edge with only minor irregularities, indicating a more stable damage evolution process with less variation in its rate, which may be attributed to lower heterogeneity in strength properties or fewer structural defects. Moreover, a decrease in signal amplitude (Figure 7b) and an increase in its duration are observed.

Processing of the obtained data shows that when the failure load increases from 2 kN to 2.4 kN, the AE signal amplitude decreases by 14.5%, while the AE signal duration increases by 9.8%, which is consistent with the simulation results.

Analysis of the amplitude–time parameters of AE signals recorded during CM loading can therefore be used to assess the state of the composite—its defectiveness, structural heterogeneity, and other characteristics. Such an analysis provides a basis for improving the reliability of monitoring, control, and diagnostics methods for composite materials and structures.

4. Conclusions

In this work, the results of modeling composite material failure under transverse shear according to the von Mises criterion were presented, considering variations in failure initiation time and, correspondingly, in threshold failure stress caused by changes in the size of a local defect or a local region of heterogeneity. Regularities were obtained for the evolution of the number of surviving CM elements over time and for AE signals. It was established that with increasing failure initiation time and threshold failure stress (corresponding to a reduction in defect size or heterogeneity), the rate of CM failure decreases. The reduction in failure rate leads to a decrease in AE signal amplitude and an increase in signal duration, consistent with earlier results reported in [51].

The study demonstrated that the dependence of the maximum AE signal amplitude on failure initiation time is nonlinear and is well described by a power-law function, while the dependence of the maximum AE signal amplitude on threshold failure stress is linear. Conversely, the dependence of AE signal duration on failure initiation time is linear, whereas its dependence on threshold failure stress is nonlinear and well described by a power-law function. It was also found that the decrease in maximum AE signal amplitude with increasing failure initiation time or threshold failure stress outpaces the corresponding increase in signal duration.

Quantitative analysis showed that when the failure initiation time increases from ${\tilde{t}}_{01}=0.001$ to ${\tilde{t}}_{05}=0.005$, the maximum AE signal amplitude decreases by 36.97%, while the signal duration increases by 23.54%. At the initial stage, when ${\tilde{t}}_{01}$ changes to ${\tilde{t}}_{02}$, the amplitude decreases by 11.69%, and the duration increases by 6.14%. These results confirm that the reduction in AE amplitude occurs faster than the growth in its duration, which is consistent with the delayed energy release during failure of a less defective composite structure.

Experimental studies of AE signals recorded during shear tests of fine-grained VK6 composite specimens with a notch showed good agreement with the modeling results.

The analysis of amplitude–time parameters of AE signals recorded during CM loading can therefore be used to assess the state of composites—including defectiveness, structural heterogeneity, and other characteristics. Future research should focus on analyzing the sensitivity of AE energy parameters to structural defects and heterogeneities during CM failure. This will improve the reliability of advanced methods for monitoring and evaluating the condition of composite materials during manufacturing and of CM-based components during operation.