Structural Engineering and Mechanics

Techno-Press (테크노프레스)
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Planar plastic flow of polymers near very rough walls

  • Lyamina, Elena A. (Laboratory for Strength and Fracture of Materials and Structures, Institute for Problems in Mechanics) ;
  • Date, Prashant P. (Metal Forming Laboratory, Department of Mechanical Engineering)
  • Received : 2015.10.18
  • Accepted : 2016.03.26
  • Published : 2016.05.25
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Abstract

The main objective of the present paper is to investigate, by means of a boundary value problem permitting a semi-analytic solution, qualitative behaviour of solutions for two pressure-dependent yield criteria used for plastically incompressible polymers. The study mainly focuses on the regime of friction (sticking and sliding). It is shown that the existence of the solution satisfying the regime of sticking depends on other boundary conditions. In particular, there is such a class of boundary conditions depending on the yield criterion adopted that the regime of sliding is required for the existence of the solution independently of the friction law.

Keywords

References

  1. Alexandrov, S. and Harris, D. (2006), "Comparison of solution behaviour for three models of pressuredependent plasticity: a simple analytical example", Int. J. Mech. Sci., 48(7), 750-762. https://doi.org/10.1016/j.ijmecsci.2006.01.009
  2. Alexandrov, S. and Mishuris, G. (2009), "Qualitative behaviour of viscoplastic solutions in the vicinity of maximum-friction surfaces", J. Eng. Math., 65(2), 143-156. https://doi.org/10.1007/s10665-009-9277-z
  3. Deshpande, V.S. and Fleck, N.A. (2001), "Multi-axial yield behaviour of polymer foams", Acta Materialia, 49, 1859-1866. https://doi.org/10.1016/S1359-6454(01)00058-1
  4. Harren, S.V. (1995), "Toward a new phenomenological flow rule for orientationally hardening glassy polymers", J. Mech. Phys. Solid., 43(7), 1151-1171. https://doi.org/10.1016/0022-5096(95)00025-E
  5. Harren, S.V. (1997), "A yield surface and flow rule for orientationally hardening polymers subjected to arbitrary deformations", J. Mech. Phys. Solid., 45(1), 1-20. https://doi.org/10.1016/S0022-5096(96)00077-4
  6. Heise, R. (2016), "Friction between a temperature dependent viscoelastic body and a rough surface", Friction, 4(1), 50-64. https://doi.org/10.1007/s40544-016-0103-0
  7. Mills, N.J. (2010), "Deformation mechanisms and the yield surface of low-density, closed-cell polymer foams", J. Mater. Sci., 45, 5831-5843. https://doi.org/10.1007/s10853-010-4659-1
  8. Pantani, R., Coccorullo, I., Speranza, V. and Titomanlio, G. (2005), "Modeling of morphology evolution in the injection molding process of thermoplastic polymers", Prog. Polym. Sci., 30, 1185-1222. https://doi.org/10.1016/j.progpolymsci.2005.09.001
  9. Raghava, R., Caddell, R.M. and Yeh, G.S.Y. (1973), "The macroscopic yield behaviour of polymers", J. Mater. Sci., 8, 225-232. https://doi.org/10.1007/BF00550671
  10. Spitzig, W.A. and Richmond, O. (1979), "Effect of hydrostatic pressure on the deformation behavior of polyethylene and polycarbonate in tension and in compression", Polym. Eng. Sci., 19(16), 1129-1139. https://doi.org/10.1002/pen.760191602
  11. Viana, J.C. (2004), "Development of the skin layer in injection moulding: phenomenological model", Polym., 45, 993-1005. https://doi.org/10.1016/j.polymer.2003.12.001

Cited by

  1. Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers vol.12, pp.17, 2016, https://doi.org/10.3390/ma12172725