PSI - Issue 47

Mikhail Bannikov et al. / Procedia Structural Integrity 47 (2023) 685–692 Author name / StructuralIntegrity Procedia 00 (2019) 000–000

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In Eq. 1, the indices 1 and 2 represent the numbers of the points between which the distance is determined. As shown in Figure 2, under cyclic loading conditions, the spatiotemporal dynamics of the multiscale development of composite damage is characterized by two clusters (see Fig. 2d, cluster 1 - red markers, cluster 2 - blue markers). However, under quasi-static loading conditions, it is not possible to divide into clusters (Figure 4.1b). For cluster analysis, the amplitude A(t), energy E(t), and time of occurrence R(t) of acoustic emission events were selected as data, which were recorded from two sensors in the form of discrete signals. Figures 3 a and b show typical distributions of amplitude, energy, and time of occurrence of acoustic emission events for a woven composite sample with a hole under uniaxial quasi-static and cyclic loading, respectively. As seen from Fig. 3 a, under quasi-static loading conditions, the dynamics of the multiscale development of composite damage is characterized by a single cluster. However, under cyclic loading conditions, there is a division into clusters (Fig. 3 b).

(a)

(b)

Fig.3 – Typical distributions of amplitude, energy and time of occurrence of acoustic emission events for a woven composite sample with a concentrator in the form of a hole located in the center under conditions of uniaxial quasi-static (a) and cyclic loading (b)

To divide the studied set of points into two clusters, an algorithm for calculating multifractal spectra based on the wavelet leader method [11] was used for each cluster separately. This method is an analogue of the method of the maxima of the wavelet transform modules (wavelet transform maxima modulus - WTMM) and was used in this work since the studied signals were discrete. Figure 4 shows the multifractal spectra constructed for two clusters of experimental data corresponding to 68,500 cycles at a load of 390 MPa. The analyzed signal was a sequence of times of occurrence of acoustic emission events, which were chosen due to the most pronounced division into clusters (see Figure 3 b). The results obtained show that the spectrum of the first cluster, represented in Figure 4.5 by blue markers, has a bell-shaped appearance and is multifractal. In contrast, the spectrum of the second cluster (represented by red markers in Figure 4) shrinks to a point and is monofractal. Comparing the results of the analysis of acoustic emission data obtained under quasi-static and cyclic loading of unidirectional and woven polymer composite samples with a hole, general patterns are visible, including the appearance of two clusters under cyclic loading, while under quasi-static loading, there is no separation into two or more clusters. Additionally, for woven composites with a stress concentrator, two clusters are characterized by different multifractal properties, with one spectrum being monofractal and the second being multifractal. In contrast, for unidirectional composites, both spectra are characterized as monofractal. It is also noteworthy that according to the results of experiments with cyclic loading, the number of clusters of acoustic emission data may vary, which may correlate with the stages of damage development.