PROBABILITY DISTRIBUTION OF CRITICAL TENSIONS OF SAMPLE BREAK OF POROUS MATERIAL

DOI:

https://doi.org/10.52575/2687-0959-2021-53-4-312-316

Keywords:

Griffith’ law, concentration, microcrack, ultimate strength, pores distribution, fragile destruction, statistical independence

Abstract

Porous materials are studied in frameworks of phenomenological representations of general physics. The statistical model for theoretical description of origin conditions of such microcracks in volume samples which leads to their transverse break is proposed. The break occurs due to the cracks growth when the external directed ultimate elastic power is applied which exceeds the material ultimate strength. On the basis of the model the probability of fragile destruction of the sample is calculated as the function of pores concentration.

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References

Batdorf S. B. 1973. A statistical theory for failure of brittle materials under combined stresses. AIAA Paper. 381: 1-5.

Batdorf S. B. 1975. Fracture statistics of brittle materials with intergranular cracks. Nucl. Eng. and Des. 35(3): 349-360.

Chechulin B. B. 1963. Scale factor and statistical nature of metal strengh. Moscow, Metallurizdat, 120.

Epstein B. 1948. Application of the theory of extreme values in fracture problems. Amer. Stat. Assoc. J. 13(9): 403-412.

Fisher J. C., Hollomon J. M. 1947. A statistical theory of fracture. Metals Technol. 14(5): 1-16.

Frenkel Ya. I., Kontorova T. A. 1943. A statistical theory of the brittle strength of real crystals. J. Phys. Moscow. 7: 108- 120.

Gardiner C. W. 1985. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2d ed. Berlin-Heidelberg-New York, Springer-Verlag, 436.

Gilbert E. N. 1962. The Poisson random medium in statistical physics. Ann. Math. Statistics. 33(3): 958-968.

Griffith A. A. 1921. The Phenomenon of Rupture and Flow in Solids. Phil. Trans. Roy. Soc. of London. A221: 163-198.

Gumbel E. 1962. Statistics of Extremes. New York, Columbia University Press, 540.

Matthes K., Kerstan J., Mecke J. 1978. Infinitely Divisible Point Processes. New York, Chichester, 360.

Minlos R. A. 2002. Inroduction into mathematical statistical physics. Moscow, MCNMO, 112.

Virchenko Yu. P., Sheremet O. I. 2000. To the Statistical Theory of Brittle Destruction of Solid Media. Dopovidi NANU. 7: 92-95.

Weibull W. 1949. A statistical representation of fatigue failure in solids. Trans. Roy. Inst. Tech. (Stocholm): 27-43.

Ziman J.M. 1979. Models of disorder. The theoretical physics of homogeneously disordered systems. New York, Cambridge University Press, 420.


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Published

2021-12-28

How to Cite

PROBABILITY DISTRIBUTION OF CRITICAL TENSIONS OF SAMPLE BREAK OF POROUS MATERIAL. (2021). Applied Mathematics & Physics, 53(4), 312-316. https://doi.org/10.52575/2687-0959-2021-53-4-312-316

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Section

Physics. Mathematical modeling