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IssuesArchive of Issues2012-6pp.654-664

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S.E. Aleksandrov and R.V. Goldstein, "Generalization of the Prandtl Solution to the Case of Axisymmetric Deformation of Materials Obeying the Double Shear Model," Mech. Solids. 47 (6), 654-664 (2012)
Year 2012 Volume 47 Number 6 Pages 654-664
DOI 10.3103/S0025654412060076
Title Generalization of the Prandtl Solution to the Case of Axisymmetric Deformation of Materials Obeying the Double Shear Model
Author(s) S.E. Aleksandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, sergei_alexandrov@yahoo.com)
R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, goldst@ipmnet.ru)
Abstract A semianalytic solution of the problem on the compression of an annular layer of a plastic material obeying the double shear model on a cylindrical mandrel is obtained. The approximate statement of boundary conditions, which cannot be satisfied exactly in the framework of the constructed solution, is based on the same assumptions as the statement of the classical plasticity problem of compression of a material layer between rough plates (Prandtl's problem). It is assumed that the maximum friction law is satisfied on the inner surface of the layer. The solution is singular near this surface. The strain rate intensity factor is calculated, and its dependence on the process and material parameters is shown.
Keywords strain rate intensity factor, singular velocity field, semianalytic solution, double shear model
References
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16.  S. E. Aleksandrov and E. A. Lyamina, "Singular Solutions for Plane Plastic Flow of Pressure-Dependent Materials," Dokl. Ross. Akad. Nauk 383 (4), 492-495 (2002) [Dokl. Phys. (Engl. Transl.) 47 (4), 308-311 (2002)].
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19.  S. E. Aleksandrov, D. Z. Grabko, and O. A. Shikimaka, "To the Determination of Intensive Strain Layer Thickness near the Friction Surface in Metal Forming Processes," Probl. Mashinostr. Nadezh. Mashin, No. 3, 72-78 (2009).
20.  S. E. Aleksandrov and E. A. Lyamina, "Prediction of Fracture in the Vicinity of Friction Surfaces in Metal Forming Processes," Zh. Prikl. Mekh. Tekhn. Fiz. 47 (5), 169-174 (2006) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 47 (5), 757-761 (2006)].
21.  E. A. Lyamina and S. E. Aleksandrov, "Application of the Strain Rate Intensity Factor to Modeling Material Behavior in the Vicinity of Frictional Interfaces," in Lecture Notes in Applied and Computational Mechanics, Vol. 58: Trends in Computational Contact Mechanics, Ed. by Giorgio Zavarise and Peter Wriggers (Springer, 2011), pp. 291-320.
22.  S. E. Aleksandrov and E. A. Lyamina, "On Constructing the Theory of Ductile Fracture near Friction Surfaces," Zh. Prikl. Mekh. Tekhn. Fiz. 52 (4), 183-190 (2011) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 52 (4), 657-663 (2011)].
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26.  R. Z. Valiev, R. K. Islamgaliev, and I. V. Aleksandrov, "Bulk Nanostructured Materials from Severe Plastic Deformation," Prog. Mater. Sci. 45, 103-189 (2000).
27.  S. E. Aleksandrov and R. V. Goldstein, "Kinetic Equation for the Grain Size in Processes of Intense Plastic Deformation," Dokl. Ross. Akad. Nauk 429 (6), 754-757 (2009) [Dokl. Phys. (Engl. Transl.) 54 (12), 553-556 (2009)].
Received 05 August 2012
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