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The singular integral equations method makes it possible to determine a general analytical solution to the problem of a crack subjected to any stresses, including singular ones. The singularity of stresses means that they tend to infinity in the concentration point. In exponential functions describing this relationship, the exponent characterizes the stress curvature growth. Also the energy released by crack opening can be described by a simple analytical formula. The problem is solvable for an exponent greater than –1. The class of all the cracks subject to stresses that exponentially grow to one of the crack ends is divided into three sub-classes. One of these embraces most of crack types, also Griffith’s. The remaining two are a source of microcracks in an elastic medium. The onset of such a stress concentration gives rise to a microcrack which cancels the stress singularity up to that with the exponent of –1/2, ensuring a strong stability of the medium. An analysis of the nucleation of such cracks brought about a concept of elastic field rupture without destruction of interatomic bonds, which has implications relating to the conductivity of metals. A general formula for the crack energy singles out a special crack of unit length, whose energy is constant and independent of stress concentration.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
174--194
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland, bogdan@igf.edu.pl
Bibliografia
- Czechowski, Z. (1995), Dynamics of fracturing and cracks. In: R. Teisseyre (ed.),Theory of Earthquake Premonitory and Fracture Processes, Polish Scientific, Publishers, Warszawa, 447-468.
- Domański, B.M. (1990), Analysis of energy stability of stress singularities in an elastic medium, Acta Geophys. Pol. 4, 407-415.
- Domański, B., S.J. Gibowicz, and P. Wiejacz (2001), Source time functions of seismic events induced at a copper mine in Poland: Empirical Green’s function approach in the frequency and time domains. In: G. van Aswegen, R.J. Durrheim, and W.D. Ortlepp (eds.), Dynamic Rock Mass Response to Mining, South African Institute of Mining and Metallurgy, Johannesburg, 99-108.
- Domański, B., S.J. Gibowicz, and P. Wiejacz (2002), Source time function of seismic events at Rudna copper mine, Poland, Pure Appl. Geophys. 159, 131-144,
- Freund, F.T., A. Takeuchi, and B.W. Lau (2006), Electric currents streaming out of stressed igneous rocks. – A step towards understanding pre-earthquake low frequency EM emission, Phys. Chem. Earth 31, 389-396,
- Griffith, A.A. (1920), The phenomena of rupture and flow in solids, Phil. Trans.Roy. Soc. Ser. A 221, 163-198.
- Matczyński, M. (1970), The static problem of a crack in elastic medium, Arch.Mech. Stos. 22, 439-478.
- McGarr, A., S.M. Spottiswoode, N.C. Gay, and W.D. Ortlepp (1979), Observations relevant to seismic driving stress, stress drop, and efficiency, J. Geophys.Res. 84, 2251-2261,
- Nabarro, F.R.N. (1967), Theory of Crystal Dislocations, Oxford University Press, Oxford.
- Stroh, A.N. (1954), The formation of cracks as a result of plastic flow, Proc. Roy. Soc. London A 223, 404-414.
- Tricomi, F. (1957), Integral Equations, Int. Publ. New York Ltd., New York. Yamashita, T. (1995), Multiple interaction of cracks and models of seismicity. In: R. Teisseyre (ed.), Theory of Earthquake Premonitory and Fracture Processes, Polish Scientific Publishers, Warszawa, 447-468.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSL7-0037-0009