Quasi-static axially symmetric viscoplastic flows near very rough walls. (English) Zbl 1443.74154

Summary: The paper deals with asymptotic behavior of viscous and viscoplastic solutions in the vicinity of very rough walls under conditions of axial symmetry. The constitutive equations adopted include a saturation stress. A distinguished feature of this model is that the regime of sticking at the wall may be incompatible with other boundary conditions. In this case the regime of sliding must occur and solutions are singular in the vicinity of such surfaces. The exact asymptotic representation of the singular solutions is controlled by the dependence of the equivalent stress on the equivalent strain rate as the latter approaches infinity. There exist such dependences that the viscoplastic model possesses a smooth transition of qualitative behavior between rigid perfectly plastic and viscoplastic solutions, and this may prove to be advantageous for some applications.


74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
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[1] Alexandrov, S.; Richmond, O., Singular plastic flow fields near surfaces of maximum friction stress, Int. J. Non-Linear Mech., 36, 1-11 (2001) · Zbl 1342.74118
[2] Alexandrov, S.; Lyamina, E., Singular solutions for plane plastic flow of pressure-dependent materials, Dokl. Phys., 47, 308-311 (2002)
[3] Alexandrov, S.; Jeng, Y.-R., Singular rigid/plastic solutions in anisotropic plasticity under plane strain conditions, Cont. Mech. Therm., 25, 685-689 (2013) · Zbl 1341.74028
[4] Spencer, A. J.M., A theory of the kinematics of ideal soils under plane strain conditions, J. Mech. Phys. Solids, 12, 337-351 (1964) · Zbl 0125.15208
[5] Rice, J. R., Plane strain slip line theory for anisotropic rigid/plastic materials, J. Mech. Phys. Solids, 21, 63-74 (1973) · Zbl 0251.73028
[6] Hill, R., The Mathematical Theory of Plasticity (1950), Oxford University Press: Oxford University Press London · Zbl 0041.10802
[7] Shield, R. T., Plastic flow in a converging conical channel, J. Mech. Phys. Solids, 3, 246-258 (1955)
[8] Spencer, A. J.M., A theory of the failure of ductile materials reinforced by elastic fibres, Int. J. Mech. Sci., 7, 197-209 (1965)
[9] Collins, I. F.; Meguid, S. A., On the influence of hardening and anisotropy on the plane-strain compression of thin metal strip, Trans. ASME J. Appl. Mech., 44, 271-278 (1977) · Zbl 0378.73031
[10] Durban, D., Friction and singularities in steady penetration, (Durban, D.; Pearson, J. R.A., IUTAM Symposium on Non-Linear Singularities in Deformation and Flow (1999), Kluwer), 141-154 · Zbl 1073.74599
[11] Alexandrov, S., Comparison of double-shearing and coaxial models of pressure-dependent plastic flow at frictional boundaries, Trans. ASME J. Appl. Mech., 70, 212-219 (2003) · Zbl 1110.74312
[12] Spencer, A. J.M., Compression and shear of a layer of granular material, J. Eng. Math., 52, 251-264 (2005) · Zbl 1079.74018
[13] Alexandrov, S.; Harris, D., Comparison of solution behaviour for three models of pressure-dependent plasticity: a simple analytical example, Int. J. Mech. Sci., 48, 750-762 (2006) · Zbl 1192.74038
[14] Alexandrov, S.; Lyamina, E., Flow of pressure-dependent plastic material between two rough conical walls, Acta Mech \(., 187, 37-53 (2006)\) · Zbl 1103.74014
[15] Alexandrov, S.; Alexandrova, N., On the maximum friction law in viscoplasticity, Mech. Time-Depend. Mater., 4, 99-104 (2000) · Zbl 1022.74030
[16] Fleck, N. A.; Durban, D., Steady penetration of a rigid cone with a rough wall into a power-law viscous solid, Trans. ASME J. Appl. Mech., 58, 872-880 (1991)
[17] Sherwood, J. D.; Durban, D., Squeeze flow of a power-law viscoplastic solid, J. Non-Newtonian Fluid Mech., 62, 35-54 (1996)
[18] Adams, M. J.; Briscoe, B. J.; Corfield, G. M.; Lawrence, C. J.; Papathanasiou, T. D., An analysis of the plane-strain compression of viscous materials, Trans. ASME J. Appl. Mech., 64, 420-424 (1997) · Zbl 0900.73180
[19] Alexandrov, S.; Jeng, Y.-R., A generalization of Prandtl’s and Spencer’s solutions on axisymmetric viscous flow, Arch. Appl. Mech., 81, 437-449 (2011) · Zbl 1271.74050
[20] Lyamina, E.; Alexandrov, S., Application of the strain rate intensity factor to modeling material behaviour in the vicinity of frictional interfaces, (Zavarise, G.; Wriggers, P., Trends in Computational Contact Mechanics. Trends in Computational Contact Mechanics, Lecture Notes in Applied and Computational Mechanics, 58 (2011), Springer), 291-320 · Zbl 1273.74360
[21] Dutton, R. E.; Goetz, R. L.; Shamasundar, S.; Semiatin, S. L., The ring test for P/M materials, Trans. ASME J. Manuf. Sci. Eng., 120, 764-769 (1998)
[22] Moylan, S. P.; Kompella, S.; Chandrasekar, S.; Farris, T. N., A new approach for studying mechanical properties of thin surface layers affected by manufacturing processes, Trans. ASME J. Manuf. Sci. Eng., 125, 310-315 (2003)
[23] Trunina, T. A.; Kokovkhin, E. A., Formation of a finely dispersed structure in steel surface layers under combined processing using hydraulic pressing, J. Mach. Manuf. Reliab., 37, 160-162 (2008)
[24] Alexandrov, S.; Grabko, D.; Shikimaka, O., The determination of the thickness of a layer of intensive deformations in the vicinity of the friction surface in metal forming processes, J. Mach. Manuf. Reliab., 38, 277-282 (2009)
[25] Alexandrov, S.; Vilotich, D.; Lyamina, E. A.; Shidzhanin, L., Thickness of the layer of intensive plastic deformation in the vicinity of the friction surface during upsetting of a cylinder with flat dies, J. Appl. Mech. Tech. Phys., 52, 491-495 (2011) · Zbl 1272.74056
[26] Rebelo, N.; Kobayashi, S., A coupled analysis of viscoplastic deformation and heat transfer - II: applications, Int. J. Mech. Sci., 22, 708-718 (1980) · Zbl 0455.73005
[27] Appleby, E. J.; Lu, C. Y.; Rao, R. S.; Devenpeck, M. L.; Wright, P. K.; Richmond, O., Strip drawing: a theoretical-experimental comparison, Int. J. Mech. Sci., 26, 351-362 (1984)
[28] Fries, T.-P.; Belytschko, T., The extended/generalized finite element method: an overview of the method and its applications, Int. J. Numer. Methods Eng., 84, 253-304 (2010) · Zbl 1202.74169
[29] Alexandrov, S.; Mishuris, G., Viscoplasticity with a saturation stress: distinguished features of the model, Arch. Appl. Mech., 77, 35-47 (2007) · Zbl 1161.76433
[30] Alexandrov, S.; Mishuris, G., Qualitative behaviour of viscoplastic solutions in the vicinity of maximum-friction surfaces, J. Eng. Math., 65, 143-156 (2009) · Zbl 1176.74031
[31] Oldroyd, J. G., Non-Newtonian flow of liquids and solids, (Eirich, F. R., Rheology: Theory and Applications, vol. 1 (1956), Academic Press: Academic Press New York), 653-682
[32] Alexandrov, S.; Richmond, O., Couette flows of rigid/plastic solids: analytical examples of the interaction of constitutive and frictional laws, Int. J. Mech. Sci., 43, 653-665 (2001) · Zbl 1010.74009
[33] Sanabria, V.; Mueller, S.; Reimers, W., Microstructure evolution of friction boundary layer during extrusion of AA 6060, Proc. Eng., 81, 586-591 (2014)
[34] Murai, T.; Matsuoka, S.; Miyamoto, S.; Oki, Y., Effects of extrusion conditions on microstructure and mechanical properties of AZ31B magnesium alloy extrusions, J. Mater. Process. Technol., 141, 207-212 (2003)
[35] Kajino, S.; Asakawa, M., Effect of “additional shear strain layer” on tensile strength and microstructure of fine drawn wire, J. Mater. Process. Technol., 177, 704-708 (2006)
[36] Sasaki, T. T.; Morris, R. A.; Thompson, G. B.; Syarif, Y.; Fox, D., Formation of ultra-fine copper grains in copper-clad aluminum wire, Scr. Mater., 63, 488-491 (2010)
[37] Thirumurugan, M.; Rao, S. A.; Kumaran, S.; Rao, T. S., Improved ductility in ZM21 magnesium-aluminium macro composite produced by co-extrusion, J. Mater. Process. Technol., 211, 1637-1642 (2011)
[38] Mitsoulis, E.; Hatzikiriakos, S. G., Capillary extrusion flow of a fluropolymer melt, Int. J. Mater. Form., 6, 29-40 (2013)
[39] Chen, J.-C.; Pan, C.; Rogue, C. M.O. L.; Wang, H.-P., A Lagrangian reproducing kernel particle method for metal forming analysis, Comput. Mech., 22, 289-307 (1998) · Zbl 0928.74115
[40] Dealy, J. M.; Wissbrun, K. F., Melt rheology and its Role in Plastic Processing (1990), Van Nostrand Reinhold: Van Nostrand Reinhold New York
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