Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch

doi:10.1007/s10483-022-2885-7

Abstract

Abstract: This paper studies the contact vibration problem of an elastic half-space coated with functionally graded materials (FGMs) subject to a rigid spherical punch. A static force superimposing a dynamic time-harmonic force acts on the rigid spherical punch. Firstly, we give the static contact problem of FGMs by a least-square fitting approach. Next, the dynamic contact pressure is solved by employing the perturbation method. Lastly, the dynamic contact stiffness with different dynamic contact displacement conditions is derived for the FGM coated half-space. The effects of the gradient index, coating thickness, internal friction, and punch radius on the dynamic contact stiffness factor are discussed in detail.

Key words: contact vibration, functionally graded material (FGM), spherical punch, perturbation method

2010 MSC Number:

74H60

Xin LYU, Liaoliang KE, Jiayong TIAN, Jie SU. Contact vibration analysis of the functionally graded material coated half-space under a rigid spherical punch. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1187-1202.

TrendMD

References

[1] SURESH, S. and MORTENSEN, A. Fundamentals of Functionally Graded Materials:Processing and Thermomechanical Behavior of Graded Metals and Metal-ceramic Composites, IOM Communications Ltd., London (1998)
[2] LI, W. and HAN, B. Research and application of functionally gradient materials. IOP Conference Series:Materials Science and Engineering, 394, 1-7(2018)
[3] SURESH, S. Graded materials for resistance to contact deformation and damage. Science, 292, 2447-2451(2001)
[4] LIU, T. J. and WANG, Y. S. Axisymmetric frictionless contact problem of a functionally graded coating with exponentially varying modulus. Acta Mechanica, 199, 151-165(2008)
[5] VASILIEV, A. S., VOLKOV, S. S., BELOV, A. A., LITVINCHUK, S. Y., and AIZIKOVICH, S. M. Indentation of a hard transversely isotropic functionally graded coating by a conical indenter. International Journal of Engineering Science, 112, 63-75(2017)
[6] PATRA, R., BARIK, S. P., and CHAUDHURI, P. K. Frictionless contact between a rigid indentor and a transversely isotropic functionally graded layer. International Journal of Applied Mechanics and Engineering, 23, 655-671(2018)
[7] GULER, M. A. and ERDOGAN, F. The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings. International Journal of Mechanical Sciences, 49, 161-182(2007)
[8] CHOI, H. J. On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch. Journal of Mechanical Science and Technology, 23, 2703-2713(2009)
[9] CHEN, P. J., CHEN, S. H., and PENG, J. Sliding contact between a cylindrical punch and a graded half-plane with an arbitrary gradient direction. Journal of Applied Mechanics, 82, 041008(2015)
[10] HU, Y., ZHOU, L., DING, H. H., TAN, G. X., LEWIS, R., LIU, Q. Y., GUO, J., and WANG, W. J. Investigation on wear and rolling contact fatigue of wheel-rail materials under various wheel/rail hardness ratio and creepage conditions. Tribology International, 143, 106091(2020)
[11] LORENZ, S. J., SADEGHI, F., TRIVEDI, H. K., ROSADO, L., KIRSCH, M. S., and WANG, C. A continuum damage mechanics finite element model for investigating effects of surface roughness on rolling contact fatigue. International Journal of Fatigue, 143, 105986(2021)
[12] FU, P. L., ZHAO, J. Z., ZHANG, X., KANG, G. Z., WANG, P., and KAN, Q. H. Elastic shakedown analysis of two-dimensional thermo-elastic rolling/sliding contact for a functionally graded coating/substrate structure with arbitrarily varying thermo-elastic properties. Composite Structures, 280, 114891(2022)
[13] WANG, Z., YU, C., and WANG, Q. An efficient method for solving three-dimensional fretting contact problems involving multilayered or functionally graded materials. International Journal of Solids and Structures, 66, 46-61(2015)
[14] EL-BORGI, S., USMAN, S., and GÜLER, M. A. A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate. International Journal of Solids and Structures, 51, 4462-4476(2014)
[15] YAN, J. and MI, C. W. A receding contact analysis for an elastic layer reinforced with a functionally graded coating and pressed against a half-plane. Journal of Mechanical Science and Technology, 33, 4331-4344(2019)
[16] YAYLACI, M., ADIYAMAN, G., ONER, E., and BIRINCI, A. Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM. Computers and Concrete, 27, 199-210(2021)
[17] JIN, F., GUO, X., and GAO, H. J. Adhesive contact on power-law graded elastic solids:the JKRDMT transition using a double-Hertz model. Journal of the Mechanics and Physics of Solids, 61, 2473-2492(2013)
[18] CHIDLOW, S. J., CHONG, W. W. F., and TEODORESCU, M. On the two-dimensional solution of both adhesive and non-adhesive contact problems involving functionally graded materials. European Journal of Mechanics-A/Solids, 39, 86-103(2013)
[19] KUDISH, I. I., VOLKOV, S. S., VASILIEV, A. S., and AIZIKOVICH, S. M. Lubricated point heavily loaded contacts of functionally graded materials, part 2, lubricated contacts. Mathematics and Mechanics of Solids, 23, 1081-1103(2018)
[20] KANETA, M., MATSUDA, K., and NISHIKAWA, H. Effects of thermal properties of contact materials and slide-roll ratio in elastohydrodynamic lubrication. Journal of Tribology, 144, 061603(2022)
[21] NAYAK, P. R. Contact vibrations. Journal of Sound and Vibration, 22, 297-322(1972)
[22] SEIMOV, V. M. Application of the orthogonal polynomial method to dynamic contact problems. Soviet Applied Mechanics, 8, 52-58(1972)
[23] BROCK, L. M. Frictionless indentation by an elastic punch:a dynamic Hertzian contact problem. Journal of Elasticity, 8, 381-392(1978)
[24] BROCK, L. M. Dynamic analysis of non-symmetric problems for frictionless indentation and plane crack extension. Journal of Elasticity, 8, 273-283(1978)
[25] BEDDING, R. J. and WILLIS, J. R. The dynamic indentation of an elastic half-space. Journal of Elasticity, 3, 289-309(1973)
[26] BEDDING, R. J. and WILLIS, J. R. High speed indentation of an elastic half-space by conical or wedge-shaped indentors. Journal of Elasticity, 6, 195-207(1976)
[27] GEORGIADIS, H. G., BROCK, L. M., and RIGATOS, A. P. Dynamic indentation of an elastic half-plane by a rigid wedge:frictional and tangential-displacement effects. International Journal of Solids and Structures, 32, 3435-3450(1995)
[28] SABOT, J., KREMPF, P., and JANOLIN, C. Non-linear vibrations of a sphere-plane contact excited by a normal load. Journal of Sound and Vibration, 214, 359-375(1998)
[29] STREATOR, J. L. Dynamic contact of a rigid sphere with an elastic half-space:a numerical simulation. Journal of Tribology, 125, 25-32(2003)
[30] MA, Q. L., KAHRAMAN, A., PERRET-LIAUDET, J., and RIGAUD, E. An investigation of steady-state dynamic response of a sphere-plane contact interface with contact loss. Journal of Applied Mechanics, 74, 249-255(2007)
[31] ARGATOV, I. I. Slow vertical motions of an elliptic punch on an elastic half-space. International Journal of Engineering Science, 46, 711-724(2008)
[32] ARGATOV, I. I. Slow vertical motions of a spherical indenter on an elastic half-space. The Quarterly Journal of Mechanics and Applied Mathematics, 65, 129-140(2012)
[33] POPOV, M., POPOV, V. L., and POHRT, R. Relaxation damping in oscillating contacts. Scientific Reports, 5, 1-9(2015)
[34] POPOV, M., POPOV, V. L., and POPOV, N. V. Reduction of friction by normal oscillations. I. Influence of contact stiffness. Friction, 5, 45-55(2017)
[35] KORUK, H. Modelling small and large displacements of a sphere on an elastic half-space exposed to a dynamic force. European Journal of Physics, 42, 055006(2021)
[36] GLUSHKOV, Y. V., GLUSHKOVA, N. V., and KIRILLOVA, Y. V. The dynamic contact problem for a circular punch adhering to an elastic layer. Journal of Applied Mathematics and Mechanics, 56, 675-679(1992)
[37] YANG, J. and KOMVOPOULOS, K. Dynamic indentation of an elastic-plastic multi-layered medium by a rigid cylinder. Journal of Tribology, 126, 18-27(2004)
[38] ESKANDARI-GHADI, M., PAK, R. Y. S., and ARDESHIR-BEHRESTAGHI, A. Transversely isotropic elastodynamic solution of a finite layer on an infinite subgrade under surface loads. Soil Dynamics and Earthquake Engineering, 28, 986-1003(2008)
[39] ZHANG, P., LIU, J., LIN, G., and WANG, W. Y. Axisymmetric dynamic response of the multilayered transversely isotropic medium. Soil Dynamics and Earthquake Engineering, 78, 1-18(2015)
[40] WANG, X. M., KE, L. L., and WANG, Y. S. Dynamic response of a coated half-plane with hysteretic damping under a harmonic Hertz load. Acta Mechanica Solida Sinica, 33, 449-463(2020)
[41] YU, H. Y. and LEE, S. Time-harmonic elastic singularities and oscillating indentation of layered solids. IMA Journal of Applied Mathematics, 85, 542-563(2020)
[42] OGI, H., HIRAO, M., TADA, T., and TIAN, J. Y. Elastic-stiffness distribution on polycrystalline Cu studied by resonance ultrasound microscopy:Young's modulus microscopy. Physical Review B, 73, 174107(2006)
[43] TIAN, J. Y., OGI, H., TADA, T., and HIRAO, M. Young's modulus mapping on SCS-6 SiC_f/Ti-6Al-4V composite by electromagnetic-resonance-ultrasound microscopy. Journal of Applied Physics, 94, 6472-6476(2003)
[44] TIAN, J. Y., OGI, H., TADA, T., and HIRAO, M. Vibration analysis on electromagneticresonance-ultrasound microscopy (ERUM) for determining localized elastic constants of solids. Journal of the Acoustical Society of America, 115, 630-636(2004)
[45] LYU, X., KE, L. L., SU, J., and TIAN, J. Y. Axisymmetric contact vibration analysis of a rigid spherical punch on a piezoelectric half-space. International Journal of Solids and Structures, 210, 224-236(2021)
[46] LYU, X., SU, J., TIAN, J. Y., and KE, L. L. Dynamic contact response of an elastic sphere on a piezoelectric half-space. Applied Mathematical Modelling, 100, 16-32(2021)
[47] O'SULLIVAN, T. C. and KING, R. B. Sliding contact stress field due to a spherical indenter on a layered elastic half-space. Journal of Tribology, 110, 235-240(1988)
[48] OZTURK, M. and ERDOGAN, F. Axisymmetric crack problem in bonded materials with a graded interfacial region. International Journal of Solids and Structures, 33, 193-219(1996)
[49] JOHNSON, K. L. Contact Mechanics, Cambridge University Press, Cambridge University (1985)
[50] ERDOGAN, F. and GUPTA, G. D. On the numerical solution of singular integral equations. Quarterly of Applied Mathematics, 29, 525-534(1972)
[51] SUNG, T. Vibrations in semi-infinite solids due to periodic surface loading. Symposium on Dynamic Testing of Soils, 156, 35-68(1954)
[52] BYCROFT, G. Forced vibrations of a rigid circular plate on a semi-infinite elastic space and on an elastic stratum. Philosophical Transactions of The Royal Society A:Mathematical Physical and Engineering Sciences, 248, 327-368(1956)
[53] BARKAN, D. D. Dynamics of Bases and Foundations, McGraw-Hill Book Company, New York (1962)
[54] TIAN, J. Y. Anisotropy influence of cubic solid on dynamic Hertzian contact stiffness for a vibrating rigid indenter. American Journal of Engineering and Applied Sciences, 3, 56-63(2010)