Paper Titles

Elastic-Plastic Contact between Hard Metal Particles
p.86

Mechanical Behaviour of Auxetic Microstructures Using Contact Mechanics and Elastoplasticity
p.100

Analysis of Wear Processes for Periodic Loading
p.117

Theoretical and Experimental Investigation on Friction in Lubricated Line Contacts with Different Materials and Textures in Presence of Wear
p.142

The Frictional Contact Problem of a Rigid Stamp Sliding over a Graded Medium
p.155

Numerical Solution of Frictional Contact Problems for Viscoelastic Solids by SGBEM and Quadratic Programming
p.175

Quasistatic Electro-Elastic Contact Modeling Using the Boundary Element Method
p.185

Contact Modeling of the Duct-Concrete Interface in the Evaluation of Multistrand Effect in High Curvature Post-Tensioned Tanks
p.197

Influence of the Main Contact Parameters in Finite Element Analysis of Elastic Bodies in Contact
p.214

HomeKey Engineering MaterialsKey Engineering Materials Vol. 681The Frictional Contact Problem of a Rigid Stamp...

The Frictional Contact Problem of a Rigid Stamp Sliding over a Graded Medium

Article Preview

Abstract:

In this study, the contact problem for a graded elastic half-plane in frictional contact with a rigid stamp is considered. The plane contact problem is assumed to be linear elastic and the Poisson's ratio is assumed to be constant. Analytical formulation of the study includes Fourier transforms of the governing equations and boundary conditions. The resulting integral equation is solved numerically. Contact pressure, in-plane stress and the stress intensity factor at the sharp edges of the contact are evaluated and demonstrated for various stamp profiles. The results are compared with a closed form solution for homogeneous isotropic half-plane indented by rigid stamps. The effects of the nonhomogeneity parameter, coefficient of friction and stamp profiles on the contact and in-plane stresses are analyzed in detail.

You might also be interested in these eBooks

Wear and Contact Mechanics II

Info:

Periodical:

Key Engineering Materials (Volume 681)

Pages:

155-174

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.681.155

Citation:

Cite this paper

Online since:

February 2016

Authors:

M.A. Guler, M. Ozturk, A. Kucuksucu

Keywords:

Contact Mechanics, FGM, Friction, Rigid Stamp, Singular Integral Equation, Sliding Contact

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2016 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] H. Hertz, Vber die beruhrung fester elastischer korper (On the contact of elastic solids), Journal für die reine und angewandte Mathematik 92 (1881) 156–171, (in German).

DOI: 10.1515/9783112342404-004

[2] R. D. Mindlin, Compliance of elastic bodies in contact, Journal of . Applied. Mechanics 16 (1949) 259–268.

DOI: 10.1115/1.4009973

[3] I. N. Sneddon, Fourier Transforms, Mc Graw-Hill, New York, (1951).

[4] N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Groningen, Noordhoff, (1953).

[5] D.A. Spence, The Hertz problem with finite friction, Journal of Elasticity 5 (1975) 297–319.

[6] L. M. Keer, D. B. Mowry, The stress field created by a circular sliding contact on transversely isotropic spheres, International Journal of Solids and Structures 15 (1979) 33–39.

DOI: 10.1016/0020-7683(79)90041-6

[7] G.M.L. Gladwell, Contact Problems in the Classical Theory of Elasticity, Sijtho and Noordho, Alphen aan den Rijn, (1980).

[8] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, (1985).

[9] D.A. Hills, D. Nowell, A. Sackfield, Mechanics of Elastic Contact, Butterworth-Heinemann, Oxford, (1993).

[10] J. R. Barber, Elasticity, 3rd edn. Springer (2009).

[11] J. R. Barber, M. Ciavarella, Contact mechanics, International Journal of Solids and Structures 37 (2000) 29–43.

[12] S. Suresh, M. Olsson, A.E. Giannakopoulos, N.P. Padture, J. Jitcharoen, Engineering the resistance to sliding contact damage through controlled gradients in elastic properties at contact surfaces, Acta Materialia 47 (1999) 3915–3926.

DOI: 10.1016/s1359-6454(99)00205-0

[13] M. Niino, S. Maeda, Recent development status of functionally graded materials, The Iron and Steel Institute of Japan International 30 (1990) 699-703.

DOI: 10.2355/isijinternational.30.699

[14] M. Stuber, S. Ulrich, H. Leiste, A. Kratzsch, H. Holleck, Graded layer design for stress-reduced and strongly adherent super hard amorphous carbon films, Surface and Coatings Technology 116 (1999) 591-598.

DOI: 10.1016/s0257-8972(99)00224-8

[15] Q.R. Hou, J. Gao, Enhanced adhesion of diamond-like carbon films with a composition-graded intermediate layer, Applied Physics a-Materials Science & Processing 68 (1999) 343-347.

DOI: 10.1007/s003390050900

[16] K.L. Choy, E. Felix, Functionally graded diamond-like carbon coatings on metallic substrates, Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 278 (2000) 162-169.

DOI: 10.1016/s0921-5093(99)00569-9

[17] S. Suresh, Graded materials for resistance to contact deformation and damage, Science 292 (2001) 2447-2451.

DOI: 10.1126/science.1059716

[18] L. Prchlik, S, Sampath, J, Gutleber, G, Bancke, A.W. Ruff, Friction and wear properties of WC-Co and Mo-Mo2C based functionally graded materials, Wear 249 (2001) 1103-1115.

DOI: 10.1016/s0043-1648(01)00839-0

[19] I. Dahan, U. Admon, N. Frage, J. Sariel, M.P. Dariel, J.J. Moore, The development of a functionally graded TiC-Ti multilayer hard coating, Surface and Coatings Technology 137 (2001) 111-115.

DOI: 10.1016/s0257-8972(00)01122-1

[20] Y. Liu, E.I. Meletis, Tribological behavior of DLC coatings with functionally gradient interfaces, Surface and Coatings Technology 153 (2002) 178-183.

DOI: 10.1016/s0257-8972(01)01688-7

[21] V. Stoica, R. Ahmed, T. Itsukaichi, S. Tobe, Sliding wear evaluation of hot iso-statically pressed (HIPed) thermal spray cermet coatings, Wear 257 (2004) 1103-1124.

DOI: 10.1016/j.wear.2004.07.016

[22] S. Stewart, R. Ahmed, T. Itsukaichi, Contact fatigue failure evaluation of post-treated WC-NiCrBSi functionally graded thermal spray coatings, Wear 257 (2004) 962-983.

DOI: 10.1016/j.wear.2004.05.008

[23] A. Valarezo, G. Bolelli, W.B. Choi, S. Sampath, V. Cannillo, L. Lusvarghi, R. Rosa, Damage tolerant functionally graded WC-Co/Stainless Steel HVOF coatings, Surface and Coatings Technology 205 (2010) 2197-2208.

DOI: 10.1016/j.surfcoat.2010.08.148

[24] G. Bolelli, V. Cannillo, L. Lusvarghi, R. Rosa, A. Valarezo, W.B. Choi, R. Dey, C. Weyant, S. Sampath, Functionally graded WC-Co/NiAl HVOF coatings for damage tolerance, wear and corrosion protection, Surface and Coatings Technology 206 (2012).

DOI: 10.1016/j.surfcoat.2011.11.018

[25] X. Wang, K.S. Hwang, M. Koopman, Z.Z. Fang, L.H. Zhang, Mechanical properties and wear resistance of functionally graded WC-Co., International Journal of Refractory Metals & Hard Materials 36 (2013) 46-51.

DOI: 10.1016/j.ijrmhm.2012.04.011

[26] A.E. Giannakopoulos, S. Suresh, Indentation of solids with gradients in elastic properties: Part I. Point force solution, International Journal of Solids and Structures 34 (1997a) 2357-2392.

DOI: 10.1016/s0020-7683(96)00171-0

[27] A.E. Giannakopoulos, S. Suresh, Indentation of solids with gradients in elastic properties: Part II. Axisymetric indenter, International Journal of Solids and Structures 34 (1997b) 2393-2428.

DOI: 10.1016/s0020-7683(96)00172-2

[28] S. Suresh, A.E. Giannakopoulos, J. Alcala, Spherical indentation of compositionally graded materials: Theory and experiments, Acta Materialia 45 (1997) 1307-1321.

DOI: 10.1016/s1359-6454(96)00291-1

[29] S. Suresh, M. Olsson, A.E. Giannakopoulos, N.P. Padture, J. Jitcharoen, Engineering the resistance to sliding-contact damage through controlled gradients in elastic properties at contact surfaces, Acta Materialia 47 (1999) 3915-3926.

DOI: 10.1016/s1359-6454(99)00205-0

[30] M.A. Guler, F. Erdogan, Contact mechanics of graded coatings, International Journal of Solids and Structures 41 (2004) 3865-3889.

DOI: 10.1016/j.ijsolstr.2004.02.025

[31] M.A. Guler, F. Erdogan, Contact mechanics of two deformable elastic solids with graded coatings, Mechanics of Materials 38 (2006) 633-647.

DOI: 10.1016/j.mechmat.2005.11.006

[32] M.A. Guler, F. Erdogan, The frictional sliding contact problems of rigid parabolic and cylindrical stamps on graded coatings, International Journal of Mechanical Sciences 49 (2007) 161–182.

DOI: 10.1016/j.ijmecsci.2006.08.006

[33] M.A. Guler, F. Erdogan, S. Dag, The frictional contact problem of sliding rigid parabolic stamps on graded materials, Multiscale and Functionally Graded Materials 973 (2008) 784-789.

DOI: 10.1063/1.2896881

[34] A.E. Giannakopoulos, P. Pallot, Two-dimensional contact analysis of elastic graded materials, Journal of Mechanics and Physics of Solids 48 (2000) 1597-1631.

DOI: 10.1016/s0022-5096(99)00068-x

[35] L.L. Ke, Y.S. Wang, Two-dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties, International Journal of Solids and Structures 43 (2006) 5779-5798.

DOI: 10.1016/j.ijsolstr.2005.06.081

[36] L.L. Ke, Y.S. Wang Two-dimensional sliding frictional contact of functionally graded materials, European Journal of Mechanics a-Solids 26 (2007) 171-188.

DOI: 10.1016/j.euromechsol.2006.05.007

[37] L.L. Ke, Y.S. Wang, Fretting contact of two dissimilar elastic bodies with functionally graded coatings, Mechanics of Advanced Materials and Structures 917 (2010) 433-447.

DOI: 10.1080/15376494.2010.483327

[38] S. Chidlow, M. Teodorescu, N. Vaughan, A solution method for the sub-surface stresses and local deflection of a semi-infinite inhomogeneous elastic medium, Applied Mathematical Modeling 36 (2012) 3486-3501.

DOI: 10.1016/j.apm.2011.10.006

[39] F. Erdogan, M. Ozturk On the singularities on contact and fracture mechanics, ASME Journal of Applied Mechanics 75 (2008) 051111.

[40] F. Erdogan, P.F. Joseph, Mechanical modeling of multilayered films on an elastic substrate Part I: analysis, Part II: results and discussion, ASME Journal of Electronic Packaging 112 (1990) 309–326.

DOI: 10.1115/1.2904384

[41] F. Erdogan, G.D. Gupta, The problem of an elastic stiffener bonded to a half-plane, ASME Journal Applied Mechanics 38 (1971) 937–941.

DOI: 10.1115/1.3408978

[42] M.A. Guler, Mechanical modeling of thin films and cover plates bonded to graded substrates, ASME Journal of Applied Mechanics 75 (2008) 051105.

DOI: 10.1115/1.2936237

[43] M.A. Guler, Y. F. Gulver, E. Nart, Contact analysis of thin films bonded to graded coatings, International Journal of Mechanical Sciences 55 (2012) 50–64.

DOI: 10.1016/j.ijmecsci.2011.12.003

[44] Y. Alinia, M.A. Guler, S. Adibnazari, The effect of material property grading on the rolling contact stress field, Mechanics Research Communications 55 (2014) 45-52.

DOI: 10.1016/j.mechrescom.2013.10.014

[45] Y. Alinia, M.A. Guler, S. Adibnazari, On the contact mechanics of a rolling cylinder on a graded coating Part 1: Analytical formulation, Mechanics of Materials, 68 (2014) 207-216.

DOI: 10.1016/j.mechmat.2013.08.010

[46] M.A. Guler, S. Adibnazari, Y. Alinia, Tractive rolling contact mechanics of graded coatings, International Journal of Solids and Structures 49 (2012) 929-945.

DOI: 10.1016/j.ijsolstr.2011.12.005

[47] M.A. Guler, Y. Alinia, S. Adibnazari, On the contact mechanics of a rolling cylinder on a graded coating. Part 2: Numerical results, Mechanics of Materials 66 (2013) 134-159.

DOI: 10.1016/j.mechmat.2013.07.014

[48] I. Bakirtaş, The contact problem of an orthotropic non-homogeneous elastic half-space, International Journal of Engineering Science 2 (1984) 347-359.

DOI: 10.1016/0020-7225(84)90070-3

[49] I. Bakirtaş, Solution of certain elasticity problems for a medium with varying modulus of elasticity, Ph. D. Dissertation, Istanbul, Istanbul Technical University, 1977 (in Turkish).

[50] M.A. Guler, The problem of a rigid punch with friction on a graded elastic medium, MS. Thesis, Lehigh University, (1996).

[51] S. Dag, M. A. Guler, B. Yildirim, A. C. Ozatag, Sliding frictional contact between a rigid punch and a laterally graded elastic medium, International Journal of Solids and Structures, 46 (2009) 4038–4053.

DOI: 10.1016/j.ijsolstr.2009.07.023

[52] S. Dag, M. A. Guler, B. Yildirim, A. C. Ozatag, Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp, Acta Mechanica 224 (2013) 1773–1789.

DOI: 10.1007/s00707-013-0844-z

[53] B.R. Lawn, Fracture of Brittle Solids, 2nd. edn. Cambridge University Press, Cambridge, U.K., (1993).

[54] M.A. Guler, Contact Mechanics of FGM Coatings: An integral equation approach, VDM Verlag , (2009).

[55] F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quarterly of Applied Mathematics 29 (1972) pp.525-534.

DOI: 10.1090/qam/408277

[56] A.C. Kaya and F. Erdogan, On the solution of integral equation with a generalized Cauchy kernel, Quarterly of Applied Mathematics xiv (1987) 455-469.

DOI: 10.1090/qam/910453

[57] F. Erdogan, G. D. Gupta and T. S. Cook, Numerical solution of singular integral equations, method of analysis and solution of crack problems, G.C. Sixth (ed. ), Noordhoff, Int. Publ. Leyden, pp.368-425, (1973).

DOI: 10.1007/978-94-017-2260-5_7