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IssuesArchive of Issues2005-6pp.69-80

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V. N. Kukudzhanov and A. L. Levitin, "Rheological instability and localization of strains in plane elastoplastic specimens under extension," Mech. Solids. 40 (6), 69-80 (2005)
Year 2005 Volume 40 Number 6 Pages 69-80
Title Rheological instability and localization of strains in plane elastoplastic specimens under extension
Author(s) V. N. Kukudzhanov (Moscow)
A. L. Levitin (Moscow)
Abstract We study buckling of plated specimens under extension for elastoplastic materials with various forms of stress-strain curves and plasticity conditions. Buckling of elastoplastic specimens in a supercritical state for material models taking into account damageability is accompanied by strain localization along shear bands and by necking. If damageability is not taken into account, then localization of extension prevails in specimens. We study the influence of the geometry of specimens and the physical properties of the material on the plastic strain localization process and on the character of fracture of specimens. It is shown that the factors determining the character of strain localization and of the subsequent fracture include, on the one hand, weakening and plastic compressibility of the material, which arise owing to the nucleation and growth of microdefects (primarily, microvoids), and, on the other hand, the geometric constraint condition on the plastic flow.

Our analysis enables a more realistic approach to the construction of medium models adequately describing experimental data on the falling section of the stress-strain curve as well as the character of strain localization and fracture of specimens under extension.
References
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2.  V. Tvergaard, "Influence of Voids on Shear Band Instabilities under Plane Strain Condition," Intern. J. Fracture Mechanics, Vol. 17, pp. 389-407, 1981.
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6.  V. N. Kukudzhanov and V. Yu. Kibardin, "Numerical simulation of plastic strain localization and fracture of viscoelastic materials," Izv. RAN. MTT [Mechanics of Solids], No. 1, pp. 109-119, 2000.
7.  D. A. Kazakov, D. A.`Kapustin, and Yu. G. Korotkikh, Modeling of Deformation and Fracture Processes for Materials and Structures [in Russian], Izd-vo Nizhegorod. Un-ta, Nizhnii Novgorod, 1999.
8.  N. G. Burago and V. N. Kukudzhanov, Numerical Solution of Continual Fracture Problems, Preprint No. 746 [in Russian], In-t Problem Mekhaniki RAN, Moscow, 2004.
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10.  J. Rice, "The localization of plastic deformation," in Theoretical and Applied Mechanics, pp. 207-220, North-Holland, 1997.
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12.  E. I. Ryzhak, "A case of indispencible localized instability in elastic-plastic solid," Int. J. Solids Struct., Vol. 36, pp. 4669-4691, 1999.
13.  V. I. Kondaurov and N. V. Kutlyarova, "Damage and rheological instability of initially porous materials," Izv. RAN. MTT [Mechanics of Solids], No. 4, pp. 99-109, 2000.
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Received 12 May 2005
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