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Erschienen in: Strength of Materials 5/2019

06.12.2019

Power Law of Crack Length Distribution in the Multiple Damage Process

verfasst von: S. R. Ignatovich, N. I. Bouraou

Erschienen in: Strength of Materials | Ausgabe 5/2019

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Abstract

Multiple fatigue damage, which is characterized by crack initiation and propagation processes, is considered. We proposed two models of multiple damage, which imply random crack initiation and further propagation, with the exponential dependence between their length on the number of loading cycles. Crack initiation is modeled by the stationary Poisson flow with a constant intensity, while crack propagation is characterized by the rate parameter controlling the dependence of crack propagation rate and its length. The first model describes the deterministic case of multiple crack propagation at a fixed value of the above rate parameter, while the second one predicts their propagation by random trajectories according to distribution of the rate parameter. In the former case, crack length distribution is shown to be the Pareto power law with the exponent, which is defined by the ratio of kinetic parameters of initiation and propagation of defects. In the latter case, the rate parameter is uniformly distributed, in accordance with experimental data, so that the power-law distribution of crack length is close to the Pareto distribution. The respective distribution exponent also depends on the ratio of kinetic parameters of multiple damages and tends to drop during damage accumulation to the threshold level (namely, reaches the value of 2). This finding complies with experimental data on multiple damages of various classes of materials, including metals and rock masses. We also substantiated the range of ratios of kinetic parameters of defect initiation and propagation, which ensure the Pareto law of cracks length distribution and can be used to estimate the critical state of cracked bodies.

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Fußnoten
1
The Yule process that models the formation of genus from species is the fundamental law substantiating the nature of power distribution laws [4].
 
Literatur
1.
Zurück zum Zitat L. R. Botvina and G. I. Barenblatt, “Self-similarity of damage cumulation,” Strength Mater., 17, No. 12, 1653–1663 (1985).CrossRef L. R. Botvina and G. I. Barenblatt, “Self-similarity of damage cumulation,” Strength Mater., 17, No. 12, 1653–1663 (1985).CrossRef
2.
Zurück zum Zitat L. R. Botvina, Kinetics of Destruction of Structural Materials [in Russian], Nauka, Moscow (1989). L. R. Botvina, Kinetics of Destruction of Structural Materials [in Russian], Nauka, Moscow (1989).
3.
Zurück zum Zitat N. I. Delas and V. A. Kas’yanov, “Nongauss distribution as a property of complex systems that are organized by type of cenoses,” East.-Eur. J. Enterpr. Technol., 3, No. 4 (57), 27–32 (2012). N. I. Delas and V. A. Kas’yanov, “Nongauss distribution as a property of complex systems that are organized by type of cenoses,” East.-Eur. J. Enterpr. Technol., 3, No. 4 (57), 27–32 (2012).
4.
Zurück zum Zitat M. E. J. Newman, “Power laws, Pareto distributions and Zipf’s law,” Contemp. Phys., 46, No. 5, 323–351 (2005).CrossRef M. E. J. Newman, “Power laws, Pareto distributions and Zipf’s law,” Contemp. Phys., 46, No. 5, 323–351 (2005).CrossRef
5.
Zurück zum Zitat V. A. Vladimirov, Yu. L. Vorob’ev, G. G. Malinetskii, et al., Risk Management. Risk, Sustainable Development, Synergetics [in Russian], Nauka, Moscow (2000). V. A. Vladimirov, Yu. L. Vorob’ev, G. G. Malinetskii, et al., Risk Management. Risk, Sustainable Development, Synergetics [in Russian], Nauka, Moscow (2000).
6.
Zurück zum Zitat L. R. Botvina, Destruction: Kinetics, Mechanisms, General Laws [in Russian], Nauka, Moscow (2008). L. R. Botvina, Destruction: Kinetics, Mechanisms, General Laws [in Russian], Nauka, Moscow (2008).
7.
Zurück zum Zitat A. Carpinteri, G. Lacidogna, and S. Puzzi, “Prediction of cracking evolution in full scale structures by the b-value analysis and Yule statistics,” Phys. Mesomech., 11, Nos. 5–6, 260–271 (2008).CrossRef A. Carpinteri, G. Lacidogna, and S. Puzzi, “Prediction of cracking evolution in full scale structures by the b-value analysis and Yule statistics,” Phys. Mesomech., 11, Nos. 5–6, 260–271 (2008).CrossRef
8.
Zurück zum Zitat S. R. Ignatovich and V. S. Krasnopol’skii, “Probabilistic distribution of crack length in the case of multiple fracture,” Strength Mater., 49, No. 6, 760–768 (2017).CrossRef S. R. Ignatovich and V. S. Krasnopol’skii, “Probabilistic distribution of crack length in the case of multiple fracture,” Strength Mater., 49, No. 6, 760–768 (2017).CrossRef
9.
Zurück zum Zitat V. T. Troshchenko and L. A. Khamaza, “Conditions for the transition from nonlocalized to localized damage in metals and alloys. Part 3. Determination of the transition conditions by the analysis of crack propagation kinetics,” Strength Mater., 46, No. 5, 583–594 (2014).CrossRef V. T. Troshchenko and L. A. Khamaza, “Conditions for the transition from nonlocalized to localized damage in metals and alloys. Part 3. Determination of the transition conditions by the analysis of crack propagation kinetics,” Strength Mater., 46, No. 5, 583–594 (2014).CrossRef
10.
Zurück zum Zitat L. Molent, M. McDonald, S. Barter, and R. Jones, “Evaluation of spectrum fatigue crack growth using variable amplitude data,” Int. J. Fatigue, 30, No. 1, 119–137 (2008).CrossRef L. Molent, M. McDonald, S. Barter, and R. Jones, “Evaluation of spectrum fatigue crack growth using variable amplitude data,” Int. J. Fatigue, 30, No. 1, 119–137 (2008).CrossRef
11.
Zurück zum Zitat E. J. Gumbel, Statistics of Extremes, Columbia University Press, New York (1958).CrossRef E. J. Gumbel, Statistics of Extremes, Columbia University Press, New York (1958).CrossRef
12.
Zurück zum Zitat R. O. Ritchie and J. F. Knott, “Mechanisms of fatigue crack growth in low alloy steel,” Acta Metall., 21, No. 5, 639–648 (1973).CrossRef R. O. Ritchie and J. F. Knott, “Mechanisms of fatigue crack growth in low alloy steel,” Acta Metall., 21, No. 5, 639–648 (1973).CrossRef
13.
Zurück zum Zitat I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products [in Russian], Nauka, Moscow (1971). I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products [in Russian], Nauka, Moscow (1971).
Metadaten
Titel
Power Law of Crack Length Distribution in the Multiple Damage Process
verfasst von
S. R. Ignatovich
N. I. Bouraou
Publikationsdatum
06.12.2019
Verlag
Springer US
Erschienen in
Strength of Materials / Ausgabe 5/2019
Print ISSN: 0039-2316
Elektronische ISSN: 1573-9325
DOI
https://doi.org/10.1007/s11223-019-00122-4

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