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S.E. Aleksandrov and R.V. Goldstein, "Study of Compression Settlement of a Three-Layer Rigid-Plastic Strip between Parallel Plates," Mech. Solids. 49 (6), 703-712 (2014)
Year 2014 Volume 49 Number 6 Pages 703-712
DOI 10.3103/S0025654414060120
Title Study of Compression Settlement of a Three-Layer Rigid-Plastic Strip between Parallel Plates
Author(s) S.E. Aleksandrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr.†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.†Vernadskogo†101, str.†1, Moscow, 119526 Russia, goldst@ipmnet.ru)
Abstract The process of compression settlement of a three-layer strip between parallel plates is investigated under the plane strain conditions. The inner layer of the strip is assumed to be made of a rigid-plastic hardening material, and the two outer layers are assumed to be ideally rigid-plastic. The boundary value problem has two symmetry axes. It is assumed that the strip thickness is much less than its width. The boundary conditions at the strip edge and at the center are satisfied in integral form. Two friction regimes, i.e., sliding and adhesion, are possible on the surface of contact between the strip and the plates and on the interface between the layers. It is shown that the general structure of the solution depends on the regimes realized at the moment. In particular, one of the layers can remain rigid at a certain stage of the deformation process. The differential equations are stated which permit exactly determining the conditions of the friction regime change and the state of each layer (rigid or plastic); these equations must be solved numerically. For some values of parameters of the boundary value problem, the velocity field is singular near one or both surfaces of friction. In these cases, it is necessary to calculate the strain rate intensity coefficient whose value probably controls the process of formation of a narrow layer with strongly changed properties near the corresponding surface of friction.
Keywords three-layer strip, compression settlement, friction regime, rigid-plastic body, strain rate intensity coefficient
References
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8.  T. T. Sasaki, R. A. Morris, G. B. Thompson, et al., "Formation of Ultra-Fine Copper Grains in Copper-Clad Aluminum Wire," Scripta Mater. 63, 488-491 (2010).
9.  M. Thirumurugan, S. A. Rao, S. Kumaran, T. S. Rao, "Improved Ductility in ZM21 Magnesium-Aluminum Macrocomposite Produced by Co-Extrusion," J. Mater. Process. Technol. 211, 1637-1642 (2011).
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11.  T. A. Trunina and E. A. Kokovikhin, "Formation of Highly Dispersed Structure in Surface Layers of Steel under Combined Treatment with Hydraulic Forging," Probl. Mashinostr. Nadezhn. Mashin, No. 2, 71-78 (2008).
12.  S. E. Aleksandrov, D. Z. Grabko, and O. A. Shikimaka, "o the Determination of Intensive Strain Layer Thickness near the Friction Surface in Metal Forming Processes," Probl. Mashinostr. Nadezhn. Mashin, No. 3, 72-78 (2009).
13.  S. Aleksandrov and O. Richmond, "Singular Plastic Flow Fields near Surfaces of Maximum Friction Stress," Int. J. Non-Lin. Mech. 36 (1), 1-11 (2001).
14.  S. Alexandrov, "Strain Rate Intensity Factor and Its Applications: A Review," Mater. Sci. Forum 623, 1-20 (2009).
15.  R. E. Sliwa, "A Test Determining the Ability of Different Materials to Undergo Simultaneous Plastic Deformation to Produce Metal Composites," Mater. Sci. Engng 135A, 259-265 (1991).
Received 01 August 2014
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