Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading

Dmytro Babich; Volodymyr Bastun

doi:doi:10.11648/j.ajmp.20170606.11

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Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading

Dmytro Babich, Volodymyr Bastun

Published in American Journal of Modern Physics (Volume 6, Issue 6)

Received: 2 August 2017 Accepted: 23 August 2017 Published: 19 September 2017

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Abstract

A statistical strength criterion for brittle materials under static and repeated loadings is proposed. The criterion relates beginning of a macrofracture in the form of origination of microcracks to the moment at which the microcrack density in the material becomes critical. The idea of the criterion consists in identification of the values of microdefect concentration under static and repeated loadings with the value of microdefect concentration which is held in the case of fracture under uniaxial static loading. It is assumed that the microcrack concentration defines the life of structures made of brittle materials. The numerical example of practical use of the criterion under consideration is presented.

Published in	American Journal of Modern Physics (Volume 6, Issue 6)
DOI	10.11648/j.ajmp.20170606.11
Page(s)	117-121
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Statistical Strength Criterion, Brittle Materials, Static and Repeated Loadings, Microcrack Concentration

References

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[2]	V. V. Bolotin, Machine and Structure Life Prediction. Mashinostroenie, Moscow, 1984, (in Russian).
[3]	V. T. Troshchenko and L. A. Sosnovskii, Fatigue Strength of Metals and Alloys. Handbook in two parts. Part 1. Naukova Dumka, Kyiv, 1987 (in Russian).
[4]	W. Schutz and P. Heuler, A review of fatigue life prediction models for the crack initiation and propagation phases, in: Advances in Fatigue Science and Technology (ed. by C. Moura Branco and L. Cuerra Rosa), 1989, pp. 177-219.
[5]	L. Pook, Metal Fatigue, 2009, Springer.
[6]	J. Luo and P. Bowen, A probabilistic methodology for fatigue life prediction, Acta Materiala, vol. 51 (12). 2003, pp. 3537-3550.
[7]	T. D. Righiniotis and M. K. Chryssanthopoulos, Probabilistic fatigue analysis under constant amplitude loading, J. of Constructional Steel Research, vol. 59 (7), 2003, pp. 867-886.
[8]	K. Ortiz and A. S. Kiremidjian, Stochastic modeling of fatigue crack growth, Engineering Fracture Mechanics, vol. 29 (3), 1988, pp. 317-334.
[9]	W. Schutz and P. Heuler, A review of fatigue life prediction models for the crack initiation and propagation phases, in: Advances in Fatigue Science and Technology (ed. by C. Moura Branco and L. Cuerra Rosa), 1989, pp. 177-219.
[10]	G. Maymon, The problematic nature of the application of stochastic crack growth models in engineering design, Engineering Fracture Mechanics, vol. 53, (6), 1996, pp. 911-916.
[11]	W. Cui, A state-of-the-art review on fatigue life prediction methods for metal structures, J. of Marine Science and Technology, vol. 7 (1), 2002, pp. 43-56.
[12]	W. F. Wu and C. C. Ni, Probabilistic models of fatigue crack propagation, Probabilistic Engineering Mechanics, 18 (3), 2004, pp. 247-257.
[13]	D. V. Babich, O. I. Bezverkhyi, T. I. Dorodnykh, Continuum model of deformation of piezoelectric materials with cracks, Applied Mechanics and Materials, vol. 784, 2015, pp. 161-172.
[14]	D. V. Babich, V. N. Bastun, and T. I. Dorodnykh, Structural-probabilistic approach to determining the durability for structures of brittle materials, Acta Mechanics, vol. 228, 207, pp. 269-274.
[15]	D. V. Babich D. V., T. I. Dorodnykh. Determining cyclic durability of piezoceramic structures using probabilistic approach, Key Engineering Materials, vol. 713, 2016, pp. 216-219.
[16]	Y. C. Xiao, S. Li. Z., K. Gao, A continuum damage mechanics model for high cycle fatigue, International Journal of Fatigue, vol. 20, (7), 1998, pp. 503-508.
[17]	Y. S. Upadhyaya, B. K. Sridhara, Fatigue life prediction. A continuum damage mechanics and fracture mechanics approach, Materials & Design 35, 2012, pp. 220-224.
[18]	A. Eklind, T. Walander, T. Carlberger, U. Stigh, High cycle fatigue crack growth in mode I of adhesive layers: modeling, simulation and experiments, Int. J. of Fracture, vol. 190 (1-2), 2014, pp. 125-146.
[19]	D. V. Babich and V. N. Bastun, On dispersed microdamageability of elastic-brittle materials under deformation, J. of Strain Analysis, vol. 45 (1), 2010, pp. 57-66.
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APA Style

Dmytro Babich, Volodymyr Bastun. (2017). Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading. American Journal of Modern Physics, 6(6), 117-121. https://doi.org/10.11648/j.ajmp.20170606.11

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ACS Style

Dmytro Babich; Volodymyr Bastun. Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading. Am. J. Mod. Phys. 2017, 6(6), 117-121. doi: 10.11648/j.ajmp.20170606.11

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AMA Style

Dmytro Babich, Volodymyr Bastun. Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading. Am J Mod Phys. 2017;6(6):117-121. doi: 10.11648/j.ajmp.20170606.11

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@article{10.11648/j.ajmp.20170606.11,
  author = {Dmytro Babich and Volodymyr Bastun},
  title = {Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading},
  journal = {American Journal of Modern Physics},
  volume = {6},
  number = {6},
  pages = {117-121},
  doi = {10.11648/j.ajmp.20170606.11},
  url = {https://doi.org/10.11648/j.ajmp.20170606.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20170606.11},
  abstract = {A statistical strength criterion for brittle materials under static and repeated loadings is proposed. The criterion relates beginning of a macrofracture in the form of origination of microcracks to the moment at which the microcrack density in the material becomes critical. The idea of the criterion consists in identification of the values of microdefect concentration under static and repeated loadings with the value of microdefect concentration which is held in the case of fracture under uniaxial static loading. It is assumed that the microcrack concentration defines the life of structures made of brittle materials. The numerical example of practical use of the criterion under consideration is presented.},
 year = {2017}
}

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TY  - JOUR
T1  - Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading
AU  - Dmytro Babich
AU  - Volodymyr Bastun
Y1  - 2017/09/19
PY  - 2017
N1  - https://doi.org/10.11648/j.ajmp.20170606.11
DO  - 10.11648/j.ajmp.20170606.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 117
EP  - 121
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20170606.11
AB  - A statistical strength criterion for brittle materials under static and repeated loadings is proposed. The criterion relates beginning of a macrofracture in the form of origination of microcracks to the moment at which the microcrack density in the material becomes critical. The idea of the criterion consists in identification of the values of microdefect concentration under static and repeated loadings with the value of microdefect concentration which is held in the case of fracture under uniaxial static loading. It is assumed that the microcrack concentration defines the life of structures made of brittle materials. The numerical example of practical use of the criterion under consideration is presented.
VL  - 6
IS  - 6
ER  -

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Author Information

Dmytro Babich

Department of Electroelasticity, Stepan Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
Volodymyr Bastun

Department of Fracture Mechanics of Materials, Stepan Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

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APA Style

Dmytro Babich, Volodymyr Bastun. (2017). Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading. American Journal of Modern Physics, 6(6), 117-121. https://doi.org/10.11648/j.ajmp.20170606.11

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ACS Style

Dmytro Babich; Volodymyr Bastun. Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading. Am. J. Mod. Phys. 2017, 6(6), 117-121. doi: 10.11648/j.ajmp.20170606.11

Copy | Download

AMA Style

Dmytro Babich, Volodymyr Bastun. Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading. Am J Mod Phys. 2017;6(6):117-121. doi: 10.11648/j.ajmp.20170606.11

Copy | Download

@article{10.11648/j.ajmp.20170606.11,
  author = {Dmytro Babich and Volodymyr Bastun},
  title = {Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading},
  journal = {American Journal of Modern Physics},
  volume = {6},
  number = {6},
  pages = {117-121},
  doi = {10.11648/j.ajmp.20170606.11},
  url = {https://doi.org/10.11648/j.ajmp.20170606.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20170606.11},
  abstract = {A statistical strength criterion for brittle materials under static and repeated loadings is proposed. The criterion relates beginning of a macrofracture in the form of origination of microcracks to the moment at which the microcrack density in the material becomes critical. The idea of the criterion consists in identification of the values of microdefect concentration under static and repeated loadings with the value of microdefect concentration which is held in the case of fracture under uniaxial static loading. It is assumed that the microcrack concentration defines the life of structures made of brittle materials. The numerical example of practical use of the criterion under consideration is presented.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Statistical Fracture Criterion of Brittle Materials Under Static and Repeated Loading
AU  - Dmytro Babich
AU  - Volodymyr Bastun
Y1  - 2017/09/19
PY  - 2017
N1  - https://doi.org/10.11648/j.ajmp.20170606.11
DO  - 10.11648/j.ajmp.20170606.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 117
EP  - 121
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20170606.11
AB  - A statistical strength criterion for brittle materials under static and repeated loadings is proposed. The criterion relates beginning of a macrofracture in the form of origination of microcracks to the moment at which the microcrack density in the material becomes critical. The idea of the criterion consists in identification of the values of microdefect concentration under static and repeated loadings with the value of microdefect concentration which is held in the case of fracture under uniaxial static loading. It is assumed that the microcrack concentration defines the life of structures made of brittle materials. The numerical example of practical use of the criterion under consideration is presented.
VL  - 6
IS  - 6
ER  -

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