Quasistatic approach to wheel - rail contact problems with elastic graded materials
DOI:
https://doi.org/10.2478/v10174-010-0003-4Keywords:
rolling contact problem, elastic graded materials, quasistatic methodAbstract
Graded materials are generally two - phase composities with continously varying volume fraction. Numerous experiments indicate that used as the coatings attached to the conventional steel body and interfacial zones they can reduce the magnitude of mechanically and/or thermally induced stresses. In this paper the wheel - rail contact problem including friction and wear is considered. The rail is assumed to be covered with a coating. The mechanical properties of the coating material depend on its distance to the rail surface and are governed by power law. In the paper quasistatic approach to solve numerically this rolling contact problem is employed. This approach is based on the assumption that for the observer moving with the rolling wheel the displacement of the rail is independent on time. Finite element method is used as a discretization method. Numerical results are provided and discussed.
References
Choi I. S., Dao M., Suresh S.: Mechanics of indentation of plastically graded materials I: Analysis, Journal of Mechanics and Physics of Solids, 2008, Vol. 56, Issue I, pp. 157-171.
Chudzikiewicz A., Myslinski A.: On wheel - rail contact problem with material properties varing with depth, submitted to Proceedings of Applied Mathematics and Mechanics.
Chudzikiewicz A., Myslinski A.: Rolling contact problem with the generalized Coulomb friction, Proceedings of Applied Mathematics and Mechanics, 2006, Volume 6, Issue I, pp. 299-300.
Chudzikiewicz A., Myslinski A.: Thermoelastic wheel - rail contact problem with temperature dependent friction coefficient, CD-ROM Proceedings of III European Conference on Com- putational Mechanics, Solids, Structures and Coupled Problems in Engineering, CA. Mota Soares et.al. (eds.), Lisbon, Portugal, 5-9 June 2006, CIMNE, 2006.
Chudzikiewicz A., Myslinski A., Nagorski Z., Piotrowski J.: Comparison of numerical methods for solution of thermoelastic wheel - rail contact problems with friction, CD-ROM Proceedings of XVI International Conference on Computer Methods in Mechanics, June 21-24, 2005, Częstochowa, Poland, ISBN: 83-921605-7-6, 2005.
Chudzikiewicz A., Zochowski A., Myslinski A.: Quasistatic versus Kalker approach for solving rolling contact problems, The Archive of Transport, 1992, Vol. 4, pp. 103-120.
Ertz M., Knothe K.: A comparison of analytical and numerical methods for the calculation of temperatures in wheel - rail contact, Wear, 2002, vol. 253, pp. 498-508.
Giannakopoulos A.E., Pallot P.: Two dimensional contact analysis of elastic graded materials, Journal of Mechanics and Physics of Solids, 2000, Vol. 48, Issue 8, pp. 1597-1631.
Han W., Sofonea M.: Quasistatic contact problems in viscoelasticity and viscoplasticity, AMS and IP, 2002, pp. 104-110.
Hiensch M., Larsson P.O., Nilsson 0., Levy D., Kapoor A., Franklin E, Nielsen J., Ringsberg J.W., Josefson B.L.: Two-material rail development: field test results regarding rolling contact fatigue and squeal noise behaviour, Wear, 2005, Vol. 258, No 7-8, pp. 964-972.
Hansaka M., Mamada S., Sato K.: Development of rail noise isolating material, Quarterly Report of RTRI, 2007, Vol. 48, No.4, pp. 215-220.
Jang Y. H., Ahn S.: Frictionally-excited thermoelastic instability on functionally graded material, Wear, 2007, Vol. 262, pp. 1102-1112.
Lee D., Barber J.R., Thouless M.D.: Indentation of an elastic half space with material properties varing with depths, International Journal of Engineering Science, 2008, in press.
Kalker J.J.: Three dimensional elastic bodies in rolling contact. Kluwer Academic Publishers, 1990.
Ke L.L., Wang YS.: Fretting contact with finite friction of a functionally graded coating with arbitraly varing elastic modulus. Part I: normal loading, Part II tangential loading, The Journal of Strain Analysis for Engineering Design, 2007, Vol. 42, No 5, pp. 293-304 (Part I), pp. 305-313 (Part ll).
Mahmoud FF, AI Shafei A.G.: A quasistatic analysis for thermoviscoelastic contact problems, The Journal of Strain Analysis for Engineering Design, 2008, Vol. 43, No 7, pp. 655-672.
Meng Re., Ludema K.e.: Wear models and predictive equations: their form and content, Wear, 1995, pp. 443-457.
Myslinski A., Zochowski A.: A numerical analysis of rolling contact problems using quasistatic variational formulation, Computers & Structures, 1991, Vol. 40, pp. 1261-1266.
Myslinski A.: Level set method for optimization of contact problems, Engineering Analysis with Boundary Elements, 2008, Vol. 32, pp. 986-994.
Oden J.T., Kikuchi N.: Contact problems in elasticity: A study of variational inequalities and finite element method, SIAM, Philadelphia, 1988.
Paczelt I., Mroz Z.: Optimal shape of contact interfaces due to wear in the steady relative motion, Int. J. Solids Struct., 2007, Vol. 44, pp. 895-925.
Paulk Y., Zastrau B.: 2D rolling contact problem involving frictional heating, International Journal of Mechanical Sciences, 2002, Vol. 44, Issue 12, pp. 2573-2584.
Panagiotopoulos P.D.: Inequality Problems in Mechanics and Applications, Birkhauser, 1985. (24] B.N. Pschenichnyj: The Linearization Method, Optimization, 1987, Vol. 18, pp. 179-196.
Serkan D.: Contact Mechanics of Graded Materials: Analysis Using Singular Integrated Equations, in Multiscale and Functionally Graded Materials 2006, AIP Conference Proceedings, 2008, Vol. 973, pp. 820-825.
Suresh S.: Graded materials for resistance to contact deformation and damage, Science, 2001, Vol. 292, pp. 2447-2451.
Sextro W: Dynamical Contact Problems with Friction, Springer, Berlin, 2007, pp. 160-163. (28] M.
Shillor M., Sofonea J., Telega J.: Models and Analysis of Quasistatic Contact: Variational Methods, Springer, Berlin, 2004, pp. 174-175.
Ringsberg J.W, Franklin FJ., Josefson B.L., Kapoor A., Nielsen J.e.O.: Fatigue evaluation of surface coated railway rails using shakedown theory, finite element calculations, and lab and field trials, International Journal of Fatigue, 2005, Vol. 27, No 6, pp. 680-694.
Wriggers P.: Computational Contact Mechanics, Second Edition, Springer, Berlin, 2006, pp. 368-376.
Yang J., Ke L.L.: Two - dimensional contact problem for a coating - graded layer - substarate structure under a rigid cylindrical punch, International Journal of Mechanical Sciences, 2008, Vol. 50, pp. 985-994.
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