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TECHNICAL PAPERS

Comparison of Double-Shearing and Coaxial Models for Pressure-Dependent Plastic Flow at Frictional Boundaries

[+] Author and Article Information
S. Alexandrov

Center for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, 3810-193 Averio, Portugale-mail: salexandrov@mec.ua.ptInstitute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, 117526 Moscow, Russia

J. Appl. Mech 70(2), 212-219 (Mar 27, 2003) (8 pages) doi:10.1115/1.1532319 History: Received November 30, 1999; Revised August 19, 2002; Online March 27, 2003
Copyright © 2003 by ASME
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References

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Spencer, A. J. M., 1982, “Deformation of Ideal Granular Materials,” Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, H. G. Hopkins and M. J. Sewell, eds., Pergamon Press, Oxford, UK, pp. 607–652.
Spencer, A. J. M., 1983, “Kinematically Determined Axially Symmetric Deformations of Granular Materials,” Mechanics of Granular Materials: New Models and Constitutive Relations, J. T. Jenkins and M. Satake, eds., Elsevier, Amsterdam, pp. 245–253.
Hill,  J. M., and Wu,  Y.-H., 1993, “Plastic Flows of Granular Materials of Shear Index n—I. Yield Functions,” J. Mech. Phys. Solids, 41, pp. 77–93.
Hill,  J. M., and Wu,  Y.-H., 1993, “Plastic Flows of Granular Materials of Shear Index n—II. Plane and Axially Symmetric Problems for n=2,” J. Mech. Phys. Solids, 41, pp. 95–115.
Harris,  D., 1993, “Constitutive Equations for Planar Deformations of Rigid-Plastic Materials,” J. Mech. Phys. Solids, 41, pp. 1515–1531.
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Yoshida,  S., Oguchi,  A., and Nobuki,  M., 1971, “Influence of High Hydrostatic Pressure on the Flow Stress of Copper Polycrystals,” Trans. Jpn. Inst. Met., 12, pp. 238–242.
Spitzig,  W. A., Sober,  R. J., and Richmond,  O., 1976, “The Effect of Hydrostatic Pressure on the Deformation Behavior of Maraging and HY-80 Steels and Its Implications for Plasticity Theory,” Metall. Trans. A, 7A, pp. 1703–1710.
Spitzig,  W. A., 1979, “Effect of Hydrostatic Pressure on Plastic-Flow Properties of Iron Single Crystals,” Acta Metall., 27, pp. 523–534.
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Schey, J. A., 1984, Tribology in Metalforming, ASM International, Materials Park, OH.
Alexandrov,  S., and Richmond,  O., 2001, “Singular Plastic Flow Fields Near Surfaces of Maximum Friction Stress,” Int. J. Non-Linear Mech., 36, pp. 1–11.
Alexandrov,  S., and Richmond,  O., 1998, “Asymptotic Behavior of the Velocity Field in the Case of Axially Symmetric Flow of a Material Obeying the Tresca Condition,” Dokl. Phys., 43(6), pp. 362–364 (translated from Russian).
Alexandrov, S., and Richmond, O., 1999, “Estimation of Thermomechanical Fields Near Maximum Shear Stress Tool/Workpiece in Metalforming Processes,” Proc of 3rd Int. Cong. on Thermal Stress, J. J. Skrzypek and R. B. Hetnarski, eds., Cracow University of Technology, Cracow, pp. 153–156.
Pemberton,  C. S., 1965, “Flow of Imponderable Granular Materials in Wedge-Shaped Channels,” J. Mech. Phys. Solids, 13, pp. 351–360.
Marshall,  E. A., 1967, “The Compression of a Slab of Ideal Soil Between Rough Plates,” Acta Mech., 3, pp. 82–92.
Alexandrov,  S., and Richmond,  O., 2001, “Couette Flows of Rigid/Plastic Solids: Analytical Examples of the Interaction of Constitutive and Frictional Laws,” Int. J. Mech. Sci., 43, pp. 653–665.
Alexandrov,  S., Mishuris,  G., and Miszuris,  W., 2000, “Planar Flow of a Three-Layer Plastic Material Through a Converging Wedge-Shaped Channel: Part 1—Analytical Solution,” Eur. J. Mech. A/Solids, 19, pp. 811–825.
Alexandrov,  S., and Alexandrova,  N., 2000, “On the Maximum Friction Law in Viscoplasticity,” Mech. Time-Depend. Mater., 4, pp. 99–104.
Alexandrov,  S., and Alexandrova,  N., 2000, “On the Maximum Friction Law for Rigid/Plastic, Hardening Materials,” Meccanica, 35, pp. 393–398.
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Collins,  I. F., and Meguid,  S. A., 1977, “On the Influence of Hardening and Anisotropy on the Plane-Strain Compression of Thin Metal Strip,” ASME J. Appl. Mech., 44, pp. 271–278.
Adams,  M. J., Briscoe,  B. J., Corfield,  G. M., Lawrence,  C. J., and Papathanasiou,  T. D., 1997, “An Analysis of the Plane-Strain Compression of Viscoplastic Materials,” ASME J. Appl. Mech., 64, pp. 420–424.
Nepershin,  R. I., 1997, “Non-Isothermal Plane Plastic Flow of a Thin Layer Compressed by Flat Rigid Dies,” Int. J. Mech. Sci., 39, pp. 899–912.

Figures

Grahic Jump Location
Flow in wedge-shaped channel and coordinate systems
Grahic Jump Location
Variation of the parameter c1 with the angle θ0 at ϕ=0.01
Grahic Jump Location
Compression of block between parallel plates and coordinate system
Grahic Jump Location
Variation of the parameter s, which is involved in the condition of zero tangent velocity at the interface, with the friction factor m

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