PSI - Issue 41

Mikhail Bannikov et al. / Procedia Structural Integrity 41 (2022) 518–526 Author name / Structural Integrity Procedia 00 (2019) 000–000

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To assess the effect of damage on the stages of destruction of composites, the time and space dependences ε ~ ∂ε/∂t and ε ~ ∂ε/∂x ~ ∂ε/∂y were analyzed, shown in Fig. 6. For their calculation, an algorithm for calculating the corresponding derivatives using difference analogs was used. Cluster analysis of dependences ε ~ ∂ε/∂t and ε ~ ∂ε/∂x ~ ∂ε/∂y reflects the temporal dynamics of damage development during the entire loading process and confirms the presence of two clusters.

(а)

(b)

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(d)

Fig. 6 - Dependence’s strain - strain change rate (a, b) and strain - strain gradient (c, d) for composites under conditions of uniaxial quasi-static (a, c) and cyclic (b, d) loading

Multifractal spectra of dependences ε(t) for composites under conditions of uniaxial quasi-static and cyclic loading are shown in Fig. 7 a, b, respectively, dwindle to a point, which characterizes this cluster with monofractal properties. For the experiment on cyclic loading of a unidirectional composite, both spectra are multifractal. In this case, the spectrum of cluster 2 has a large width. These results confirm the correctness of the decision to perform differential processing of clustering data in multifractal analysis algorithms.