Friction coefficient evaluation using physically based viscoplasticity model at the contact region during high velocity sliding. (English) Zbl 1272.74074
Summary: Many physical systems require the description of mechanical interactions across interfaces if they are to be successfully analyzed. One of the well-known examples of such a system in the engineering world is the metal to metal friction. This is a complex process that needs to be adequately identified by a constitutive relation in order to better facilitate the design components in severe contact stress applications. In this paper, the formulation of A. Molinari et al.’s work [J. Tribology Trans ASME 121, No. 1, 35–41 (1999)] is revisited in order to investigate the coefficient of dry friction for steel on steel in the high velocity range using physically based viscoplastic constitutive relations. First some of the errors in the work are corrected, and their results are regenerated. The phenomenological constitutive relation used in Molinari et al. (loc. cit.) is then replaced by the physically based viscoplastic model used in this paper. This constitutive model is implemented into ABAQUS (Analysis User’s Manual, 2008) as user-defined subroutine as VUMAT in order to obtain the stress-strain curves at different strain rates and various temperatures. It is shown that the material responses obtained from the simulation using the physically based constitutive viscoplastic model agree well with the real behavior of the metals. Comparing this proposed work with that of Molinari et al. (loc. cit.) one observes that the proposed theory and constitutive model are superior to the one presented by Molinari et al. This is specifically the case for the artificial shape of softening in the curve.
MSC:
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
| 74M10 | Friction in solid mechanics |
Software:
ABAQUSReferences:
| [1] | ABAQUS 6.8-1. Analysis Users Manual, Dassault Systèmes Simulia Corp., Providence, RI. (2008) |
| [2] | Abed, F.H., Voyiadjis, G.Z.: Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of bcc and fcc mechanisms of metals. Int. J. Plast., 1618–1639 (2005) · Zbl 1148.74306 |
| [3] | Andrews K.T., Shillor M., Wright S., Klarbring A.: A dynamic thermoviscoelastic contact problem with friction and wear. Int. J. Eng. Sci. 35, 1291–1309 (1997) · Zbl 0903.73065 · doi:10.1016/S0020-7225(97)87426-5 |
| [4] | Blok H.: Fundamental mechanical aspect of boundary lubrication. S.A.E. J. 46(2), 54–68 (1940) |
| [5] | Bowden, F.P., Leben, L.: The nature of sliding and the analysis of friction. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci., 0371–0391 (1939) |
| [6] | Bragov A.M., Konstantinov A.Y., Lomunov A.K.: Determining dynamic friction using a modified Kolsky method. Tech. Phys. Lett. 34, 439–440 (2008) · doi:10.1134/S1063785008050234 |
| [7] | Christensen, P.W., Klarbring, A., Pang, J.S., Stromberg, N. (145-173). Formulation and comparison of algorithms for frictional contact problems. Int. J. Numer. Methods Eng. 42 (1998) · Zbl 0917.73063 |
| [8] | Clifton R.J., Duffy J., Hartley K.A., Shawki T.G.: On critical conditions for shear band formation at high strain rates. Scr. Metall. 18, 443–448 (1984) · doi:10.1016/0036-9748(84)90418-6 |
| [9] | Coleman, B.D., Gurtin, M.E.: Thermodynamics with internal state variables. J. Chem. Phys., 597–613 (1967) |
| [10] | Coleman, B.D., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal., 167–178 (1963) · Zbl 0113.17802 |
| [11] | Coulomb, C.A.: Theorie des mechines simples memorie. Math. Phys. Acad., 161–342 (1785) |
| [12] | Heilmann, P., Rigney, D.A.: An energy-based model of friction and its application to coated systems. Wear, 195–217 (1981) |
| [13] | Ireman P., Klarbring A., Stromberg N.: A model of damage coupled to wear. Int. J. Solids Struct. 40, 2957–2974 (2003) · Zbl 1038.74510 · doi:10.1016/S0020-7683(03)00121-5 |
| [14] | Johansson L., Klarbring A.: Study of frictional impact using a nonsmooth equations solver. J. Appl. Mech. Trans. ASME 67, 267–273 (2000) · Zbl 1110.74500 · doi:10.1115/1.1304825 |
| [15] | Johnson, R.L., Swikert, M.A., Bisson, E.E.: Friction at high sliding velocities; naca-tn-1442 (1947) |
| [16] | Klarbring A.: A mathematical-programming approach to 3-dimensional contact problems with friction. Comput. Methods Appl. Mech. Eng. 58, 175–200 (1986) · Zbl 0595.73125 · doi:10.1016/0045-7825(86)90095-2 |
| [17] | Klarbring, A.: Examples of nonuniqueness and nonexistence of solutions to quasi-static contact problems with friction. Ingenieur Arch., 529–541 (1990) |
| [18] | Kocks, U.F.: Realistic constitutive relations for metal plasticity. Mater. Sci. Eng. A Struct. Mater., 181–187 (2001) |
| [19] | Krieg, R.D., Krieg, D.B.: Accuracies of numerical-solution methods for elastic-perfectly plastic model. J. Press. Vessel Technol. Trans. ASME, 510–515 (1977) |
| [20] | Lim, S.C., Ashby, M.F.: Wear-mechanism maps. Acta Metall., 1–24 (1987) |
| [21] | Lim, S.C., Ashby, M.F., Brunton, J.H.: The effects of sliding conditions on the dry friction of metals. Acta Metall., 767–772 (1989) |
| [22] | Martins, J.A.C., Oden, J.T.: Existence and uniqueness results for dynamic contact problems with nonlinear normal and friction interface laws. Nonlinear Anal. Theory Methods Appl., 407–428 (1987) · Zbl 0672.73079 |
| [23] | Molinari, A., Clifton, R.J.: Analytical characterization of shear localization in thermoviscoplastic materials. J. Appl. Mech. Trans. ASME, 806–812 (1987) · Zbl 0633.73118 |
| [24] | Molinari A.: Shear band analysis. Solid State Phenom. 3(4), 447–468 (1988) · doi:10.4028/www.scientific.net/SSP.3-4.447 |
| [25] | Molinari, A., Estrin, Y., Mercier, S.: Dependence of the coefficient of friction on the sliding conditions in the high velocity range. J. Tribology Trans. ASME, 35–41 (1999) |
| [26] | Montgomery R.S.: Surface melting of rotating bands. Wear 38, 235–243 (1976) · doi:10.1016/0043-1648(76)90073-9 |
| [27] | Ortiz M., Simo J.C.: An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int. J. Numer. Methods Eng. 23(3), 353–366 (1986) · Zbl 0585.73058 · doi:10.1002/nme.1620230303 |
| [28] | Rigney, D.A., Hirth, J.P.: Plastic-deformation and sliding friction of metals. Wear, 345–370 (1979) |
| [29] | Simo, J.C., Hughes, T.J.R.: On the variational foundations of assumed strain methods. J. Appl. Mech. Trans. ASME, 51–54 (1986) · Zbl 0592.73019 |
| [30] | Taylor, G.I., Quinney, H.: The latent energy remaining in a metal after cold working. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci., 0307–0326 (1934) |
| [31] | Voyiadjis G.Z., Abed F.H.: Microstructral based models for BCC and FCC metals with temperature and strain rate dependency. Mech. Mater. 37, 355–378 (2005) · doi:10.1016/j.mechmat.2004.02.003 |
| [32] | Voyiadjis G.Z., Abed F.H.: Effect of dislocation density evolution on the thermo-mechanical response of metals with different crystal structures at low and high strain rates and temperatures. Arch. Mech. 57, 299–343 (2005) · Zbl 1126.74011 |
| [33] | Voyiadjis G.Z., Abu Al-Rub R.K.: Nonlocal gradient-dependent thermodynamics for Modeling scale-dependent plasticity. Int. J. Multiscale Comput. Eng. 5, 295–323 (2007) · doi:10.1615/IntJMultCompEng.v5.i3-4.110 |
| [34] | Voyiadjis, G.Z., Deliktas, B.: Theoretical and experimental characterization for the inelastic behavior of the micro-/nanostructured thin films using strain gradient plasticity with interface energy. J. Eng. Mater. Technol. Trans. ASME, 131 (2009a) |
| [35] | Voyiadjis, G. Z., Deliktas, B.: Mechanics of strain gradient plasticity with particular reference to decomposition of the state variables into energetic (2009b) · Zbl 1213.74068 |
| [36] | Voyiadjis G.Z., Deliktas, B.: Modeling strengthening and softening in inelastic nanocrystalline materials with reference to the triple junction and grain boundaries using strain gradient plasticity (to be submitted) (2009c) · Zbl 1272.74073 |
| [37] | Voyiadjis G.Z., Deliktas B., Aifantis E.C.: Multiscale analysis of multiple damage mechanisms coupled with inelastic behavior of composite materials. J. Eng. Mech. ASCE 127, 636–645 (2001) · doi:10.1061/(ASCE)0733-9399(2001)127:7(636) |
| [38] | Voyiadjis, G.Z., Deliktas, B., Lodygowski, A.: Non-local modeling of heterogeneous media to assess high velocity contact using coupled viscoplasticity damage mode (submitted) (2009) |
| [39] | Wang, X.J., Rigney, D.A.: Sliding behavior of Pb–Sn alloys. Wear, 290–301 (1995) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
