Abstract
Acoustic emission before the failure of heterogeneous materials is studied as a function of applied hydrostatic pressure. A formula for the energy release is suggested, which is valid in the whole diapason of pressures, from zero to the critical pressure of rupture. This formula is obtained by employing the extrapolation technique of the self-similar approximation theory. The result is fitted to experiment in order to demonstrate the correct general behaviour of the obtained expression for the energy release.
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References
Anifrani J. C., Le Floch C., Sornette D. and Souillard B., Universal log-periodic correction group scaling for rupture stress prediction from acoustic emission. J Phys. I France 5 (1995) 631-638.
Gluzman S., Andersen J. V. and Somette D., Functional renormalization prediction of rupture. In A. Levshin, G. Molchan and B. Naimark (eds.) Computational Seismology. Moscow, GEOS (2001).
Herrmann H. J. and Roux S., Statistical Models for the Fracture of Disordered Media. North-Holland, Amsterdam (1990).
Johansen A. and Sornette D., Critical ruptures. Eur. Phys. J. B 18 (2000) 163-181.
Lamagnere L., Carmona F. and Sornette D., Experimental realization of critical thermal fuse rupture. Phys. Rev. Lett. 77 (1996) 2738-41.
Nauenberg M. et a1., Scaling representation for critical phenomena. J. Phys. A 8 (1975) 925-928.
Poincare H., New Methods of Celestial Mechanics. Am. Inst. Phys., New York (1993).
Sahimi M. and Arbabi S., Scaling laws for fracture of heterogeneous materials and rocks. Phys. Rev. Lett. 77 (1996) 3689-3692
Sornette D. and Andersen J. V., Scaling with respect to disorder. Eur. Phys. J. B 1 (1998) 353-357
Sornette D., Discrete scale invariance and complex dimensions. Phys. Rep. 297 (1998) 239-270.
Yukalov V.I., Statistical mechanics of strongly nonideal systems. Phys. Rev. A 42 (1990) 3324-3334.
Yukalov V.I., Method of self-similar approximations. J. Math. Phys. 32 (1991) 1235-1239.
Yukalov V.I., Stability conditions for method of self-similar approximations. J Math. Phys. 33 (1992) 3994-4001.
Yukalov V.I. and Gluzman S., Critical indices as limits of control functions. Phys. Rev. Lett. 79 (1997-a) 333-336.
Yukalov V. I. and Gluzman S., Self-similar bootstrap of divergent series. Phys. Rev. E 55 (1997-b) 6552-6565.
Yukalov V.I. ard Gluzman S., Self-similar exponential approximants. Phys. Rev E 58 (1998-a) 1359-1382.
Yukalov V.I., Yukalova E.P. and Gluzman S., Self-similar interpolation in quantum mechanics, Phys. Rev. A 58 (1998-b) 96-115.
Yukalov V. l.and Gluzmaéé S., Weighted fixed points in self-similar analysis of time series. Int. J Mod. Phys. B 13 (1999) 1463-1476.
Yukalov V. I., Self-similar extrapolation of asymptotic series and forecasting for time series. Mod. Phys. Lett. B 14 (2000) 791-800.
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Moura, A., Yukalov, V. Self-similar extrapolation for the law of acoustic emission before failure of heterogeneous materials. International Journal of Fracture 118, 63–68 (2002). https://doi.org/10.1023/A:1022908821917
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DOI: https://doi.org/10.1023/A:1022908821917