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IssuesArchive of Issues2007-6pp.925-934

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Total articles in the database: 9179
In Russian (. . ): 6485
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I. A. Glagolev and Yu. G. Markin, "Determining the thermomechanical characteristics of the separation process," Mech. Solids. 42 (6), 925-934 (2007)
Year 2007 Volume 42 Number 6 Pages 925-934
Title Determining the thermomechanical characteristics of the separation process
Author(s) I. A. Glagolev (Tula State Universit, pr-t Lenina 92, Tula, 300600, Russia, vadim@tsu.tula.ru)
Yu. G. Markin (Tula State Universit, pr-t Lenina 92, Tula, 300600, Russia, markin@uic.tula.ru)
Abstract The crack growth condition was obtained in [1, 2] from energy considerations and holds for arbitrary nonlinearly elastic materials. This condition is reduced to determining the trajectory-independent transition from one of the shores of the mathematical cut to the other shore in the J-integral. The time when the J-integral attains the critical value corresponds to the initiation of crack motion. In the present paper, we consider the steady-state strip separation process starting from the fundamental thermodynamic relation. The strip material behavior is determined both at the stage of stable (in general, elastoplastic) loading and at the stage of Drucker unsdtable strain until the time at which the interaction between particles ceases. We single out a domain of unstable material strain, i.e., an interaction layer whose initial width is assumed to be a universal constant of the material [3]. The proposed approach permits expressing the material surface energy via the critical thermomechanical parameters (determined from the complete strain diagram) and the interaction layer thickness. We obtain expressions for the critical values of J-integrals. The critical values of J-integrals [46] corresponding to nonlinearly elastic and ideally plastic materials follow from general considerations. We have shown that the possibility of using J-integrals as elastoplastic separation criteria depends on the layer thickness of an irreversibly strained material. If the corresponding thickness is independent of the boundary conditions and the body geometry, then it is possible to use the value of the J-integral as a separation criterion; this corresponds to the Irwin-Orowan quasibrittle fracture approach.
References
1.  G. P. Cherepanov, "Crack Propagation in Continuous Media," Prikl. Mat. Mekh. 31 (3), 476-488 (1967) [J. Appl. Math. Mech. (Engl. Transl.) 31 (3), 503-512 (1967)].
2.  J. Reiss, "Path-Independent Integral and Approximate Analysis of Strain Concentrations near Cuts and Cracks," Prikl. Mekhanika, Ser. E 35 (4), 340-350 (1968).
3.  V. V. Glagolev, K. A. Kuznetsov, and A. A. Markin, "A Model of Splitting of Solids," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 61-68 (2003) [Mech. Solids (Engl. Transl.) 38 (6), 49-54 (2003)].
4.  G. P. Cherepanov, Mechanics of Brittle Fracture (Nauka, Moscow, 1974) [in Russian].
5.  N. F. Morozov, Mathematical Problems of Crack Theory (Nauka, Moscow, 1984) [in Russian].
6.  V. V. Panasyuk, Mechanics of Material Quasibrittle Fracture (Naukova Dumka, Kiev, 1991) [in Russian].
7.  A. A. Markin, "On the Variation of Elastic and Plastic Properties under Finite Strains," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 120-126 (1990) [Mech. Solids (Engl. Transl.)].
8.  G. P. Cherepanov, "On Supercritical Strains," Probl. Prochn., No. 8, 3-8 (1985).
9.  A. A. Il'yushin, Mechanics of Continuum (Izd-vo MGU, Moscow, 1990) [in Russian].
10.  G. I. Barenblatt, "On Equilibrium Cracks, Formed in Brittle Fracture," Dokl. Akad. Nauk SSSR 127 (1), 47-50 (1959) [Soviet Math. Dokl. (Engl. Transl.)].
11.  V. Z. Parton and E. M. Morozov, Mechanics of Elastoplastic Fracture (Nauka, Moscow, 1985) [in Russian].
12.  D. D. Ivlev, Theory of Ideal Plasticity (Nauka, Moscow, 1966) [in Russian].
Received 22 April 2004
Link to Fulltext http://www.springerlink.com/content/k115j77513724165
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