 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| A. A. Gruzdkov, N. F. Morozov, and Yu. V. Petrov, "Equal power principle in multilevel dynamic fracture of solids," Mech. Solids. 41 (6), 135-139 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
6 |
Pages |
135-139 |
| Title |
Equal power principle in multilevel dynamic fracture of solids |
| Author(s) |
A. A. Gruzdkov (St. Petersburg)
N. F. Morozov (St. Petersburg)
Yu. V. Petrov (St. Petersburg) |
| Abstract |
Dynamic fracture of continuous media is a nonequilibrium process happening
at various structure-scale levels in both space and time. Experiments on
dynamic fracture of solids show numerous effects essentially contradicting
classical models of strength and crack resistance [1-3]. It is assumed in
the corresponding classical criteria that energy and momentum used in the
formation of new fracture surfaces and domains in the course of dynamic
fracture process are spent continuously. It is shown in [1] that the
introduction of physical discreteness (along with the spatially-geometric
discreteness discussed in [4-6]), i.e., discrete consumption of energy and
momentum necessary to maintain the dynamic fracture process, permits one to
resolve a series of inconsistencies in the classical theory. Similar ideas
have been stated a little later in [7]. This approach, essentially
corresponding to taking into account the discreteness of the space-time
metric of dynamic fracture processes in continuous media [8], permits one
to construct a generalization of linear fracture mechanics to dynamic
problems [9, 10]. The main difference of this approach from other
approaches is the explicit introduction of the concept of incubation period
(the characteristic relaxation time of the "prefracture" process [9])
representing a scale parameter on the time scale and also the corresponding
limit condition (criterion) of fracture of a continuous medium at a given
scale level taking into account both the space-time structure and the
physical (energy) discreteness of the fracture process. |
| References |
| 1. | Yu. V. Petrov, "On the 'quantum' nature of dynamic fracture of
brittle media," Doklady AN, Vol. 321, No. 1, pp. 66-68, 1991. |
| 2. | N. F. Morozov and Yu. V. Petrov, "Dynamic fracture viscosity in
crack growth initiation problems," Izv. RAN. MTT [Mechanics of Solids],
No. 6, pp. 108-111, 1990. |
| 3. | N. F. Morozov and Yu. V. Petrov, "On the concept of structural
time in the theory of dynamic fracture of brittle materials," Doklady AN,
Vol. 324, No. 5, pp. 964-967, 1992. |
| 4. | V. V. Novozhilov, "On a necessary and sufficient criterion for
brittle strength," PMM [Applied Mathematics and Mechanics], Vol. 33,
No. 2, pp. 212-222, 1969. |
| 5. | M. A. Sadovskii, V. F. Pisarenko, and V. N. Rodionov, "From
seismology to geomechanics. About a model of geophysical medium," Vestn.
AN, No. 1, pp. 82-88, 1983. |
| 6. | E. I. Shemyakin, Doklady AN SSSR, Vol. 300, No. 5, pp. 1090-1094, 1988. |
| 7. | Yu. A. Hon and V. E. Panin, "Strongly excited states and the
origin of cracks in stress raiser zones," Fizika Tverdogo Tela, Vol. 38,
No. 6, pp. 1767-1774, 1996. |
| 8. | Yu. V. Petrov, "Quantum analogy in fracture mechanics of solids,"
Fizika Tverdogo Tela, Vol. 38, No. 11, pp. 3385-3393, 1996. |
| 9. | Yu. V. Petrov, "Quantum" Macromechanics of Dynamic Fracture of
Solids. Preprint No. 139 [in Russian], IPMash RAN, St. Petersburg, 1996. |
| 10. | N. Morozov and Yu. Petrov, Dynamics of Fracture, Springer,
Berlin-Heidelberg-New York, 2000. |
| 11. | V. N. Bovenko and L. Zh. Gorobets, "Scale effect under rapid
fracture of solids," Problemy Prochnosti, No. 1. pp. 92-94, 1987. |
| 12. | A. G. Ivanov, "Dynamic fracture and scale effects," Zh. Prikl. Mekhaniki
i Tekhn. Fiziki, No. 3, pp. 116-131, 1994. |
| 13. | V. A. Ogorodnikov and A. G. Ivanov, "On the time dependence of
fracture energy for metals under scabbing," Fizika Goreniya i Vzryva,
Vol. 37, No. 1, pp. 133-136, 2001. |
| 14. | N. F. Morozov and Yu. V. Petrov, "The 'quantum' nature and the
dual character of fracture dynamics of solids," Doklady AN, Vol. 382, No. 2,
pp. 206-209, 2002. |
| 15. | V. A. Bratov, A. A. Gruzdkov, S. I. Krivosheev, and Yu. V. Petrov,
"On the energy balance for crack growth initiation under pulse loading
conditions," Doklady AN, Vol. 396, No. 3, pp. 345-348, 2004. |
| 16. | Yu. V. Petrov and E. V. Sitnikova, "The effect of abnormal
melting points under shock-wave loading," Doklady AN, Vol. 400, No. 4, 2005. |
| 17. | G. I. Kannel and S. V. Razorenov, "Abnormalities in the
temperature dependences of bulk and shear strength of aluminum monocrystals
in the submicrosecond range," Fizika Tverdogo Tela, Vol. 43, No. 5,
pp. 839-845, 2001. |
|
| Received |
15 September 2006 |
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