PSI - Issue 41

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

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(b)

(a)

Fig. 7 - Multifractal spectra built for cluster 1 (red) and for cluster 2 (blue) dependencies ε(t) for composites under conditions of uniaxial quasi static (a) and cyclic (b) loading

The phase portraits observed at different stages of composite failure are similar to the phase portraits obtained during dynamic crack propagation in PMMA [12-14] and reflect the strain localization determined by the stress field in the vicinity of the fracture region and strain field fluctuations due to the localization of damage. Time distributions of strain at the point where the most intense strain occurs, representing compact sets of points, reflect the hyperbolicity of the stress field in the vicinity of the crack tip in accordance with Irwin's self-similar (singular) solution. "Random" point clouds correspond to the second self-similar solution, which determines the singular temporal kinetics of the formation of fracture centers (child cracks). The distributions in the coordinates "strain - strain gradient" reflect the role of collective phenomena in the development of damage, taking into account the peculiarities of the stress state. The results obtained on the kinetics of damage development in the presence of two types of self-similar solutions are in agreement with the concepts reflected in the two-parameter failure criteria. The values of cohesive strength and cohesive length are related to the patterns of damage localization kinetics and are determined by parameters reflecting the nonlinearity of free energy release during the nucleation and growth of defects under conditions of their interaction at different structural scales. Justification of the relationship between structural parameters and fracture mechanics criteria for composite materials involves the use of tomography data on the development of defects at various scale levels. 4. Conclusion The phase portraits observed at different stages of composite failure are similar to those observed during dynamic crack propagation in PMMA obtained earlier by the authors and reflect the strain localization determined by the stress field in the vicinity of the concentrator and strain field fluctuations due to damage localization. Time phase portraits for deformation, representing compact sets of points, reflect the hyperbolicity of the stress field in the vicinity of the crack tip in accordance with Irwin's self-similar (singular) solution. The division of the energy of acoustic emission phenomena into clusters under cyclic loading makes it possible to determine the staging of the transition from damage accumulation to destruction. And also, to conclude that there are two self-similar solutions that determine the singular temporal kinetics of the formation of fracture centers (child cracks). Phase portraits in the coordinates "deformation - strain gradient" reflect the role of collective phenomena in the development of damage, taking into account the peculiarities of the stress state. The results obtained on the kinetics of damage development in the presence of two types of self-similar solutions are in agreement with the concepts reflected in the two-parameter failure criteria. Justification of the relationship between structural parameters and fracture mechanics criteria for composite materials involves the use of tomography data on the development of defects at various scale levels.