Multi layered finite element analysis of graded coatings in frictional rolling contact

ADMT Journal

مقاله 1، دوره 8، شماره 1، خرداد 2015، صفحه 1-12   

نویسندگان

R. Jahedi؛ S. Adibnazari^*

Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

چکیده

A plain strain analysis of frictional rolling contact on an elastic graded coating is presented in this paper. Finite element method is applied to gain an understanding of the stresses and contact zone properties caused during rolling contact. The effects of friction, material stiffness ratio and coating thickness on stresses in contact zone and coating/substrate interface are studied. Shear modulus of softening and stiffening graded coatings change with exponential, power law and linear functions. The substrate is homogenous and the rigid cylindrical roller moves in a steady state condition with constant velocity. The coating is modeled in multi layers and a 2-D hard contact of rolling surfaces is considered. The analytical results verify the present method and show a good agreement. It is shown that thinner thicknesses have more effects on stresses and energy density, but these effects are not seen for thicknesses larger than a specific limit.

کلیدواژه‌ها

Frictional Rolling Contact؛ Finite Element Method؛ Graded Coating؛ Geometrical Effects

مراجع

[1]   Dahm, K. L., “Thin coatings with graded elastic properties”, Proc IMechE Part J: J. Engineering Tribology, Vol. 222, No. 3, 2008, pp. 249-259.

[2]   Dag, S., Erdogan, F., “A surface crack in a graded medium loaded by a sliding rigid stamp”, Eng. Fract. Mech., Vol. 69, No. 14-16, 2002, pp. 1729-1751.

[3]   Guler, M. A., Erdogan, F., “Contact mechanics of graded coatings”, Int. J. Solids Struct., Vol. 41, No. 14, 2004, pp. 3865-3889.

[4]   Ding, S. H., Li, X., “Anti-plane problem of periodic interface cracks in a functionally graded coating-substrate structure”, Int. J. Fract., Vol. 153, No. 1, 2008, pp. 53-62.

[5]   Jin, Z. H., “Effect of thermal property gradients on the edge cracking in a functionally graded coating”, Surf. Coat. Technol., Vol. 179, No. 2, 2004, pp. 210-214.

[6]   Nami, M. R., Eskandari, H., “Three-dimensional investigation of stress intensity factors in a cracked cylinder made of functionally graded materials”, Mech. Based Des. Struct. Mach., Vol. 40, No. 2, 2012, pp. 206-217.

[7]   Alwahdi, F., Franklin, F. J. and Kapoor, A., “The effect of partial slip on the wear rate of rails”, Wear, Vol. 258, No. 7, 2005, pp. 1031-1037.

[8]   Vasica, G., Franklin, F. J. and Fletcher, D. I., “Influence of partial slip and direction of traction on wear rate in wheel-rail contact”, Wear, Vol. 270, No. 3, 2011, pp. 163-171.

[9]   Suresh, S., Olsson, M. and Giannakopoulos, A. E., “Engineering the resistance to sliding contact damage through controlled gradients in elastic properties at contact surfaces”, Acta Mater, Vol. 47, No. 14, 1999, pp. 3915-3926.

[10]     Ke, L., Wang, Y., “Two dimensional contact mechanics of functionally graded materials with arbitrary spatial variations of material properties”, Int. J. Solids Struct., Vol. 43, No. 18, 2006, pp. 5779-5798.

[11]     Ke, L., Wang, Y., “Two dimensional sliding frictional contact of functionally graded materials”, Eur. J. Mech., Vol. 26, No. 1, 2007, pp. 171-188.

[12]     Liu, T., Xing, Y., “Analysis of graded coatings for resistance to contact deformation and damage based on a new multi-layer model,” Int. J. Mech. Sci., Vol. 81, 2014, pp. 158-164.

[13]     Banichuk, N. V., Ivanova, S. and Makeev, E. V., “Finding of rigid punch shape and optimal contact pressure distribution”, Mech Based Des. Struct. Mach., Vol. 38, 2010, pp. 417-429.

[14]     Guler, M. A., Erdogan, F., “Contact mechanics of two deformable elastic solids with graded coatings”, Mech. Mater., Vol. 38, No. 7, 2006, pp. 633-647.

[15]     Singha, M. K., Prakash, T., “Finite element analysis of functionally graded plates under transverse load”, Finite Elem. Anal. Des., Vol. 47, No. 4, 2011, pp. 453-460.

[16]     Rohwer, K., Rolfes, R., “Calculating 3D stresses in layered composite plates and shells”, Mech. Compos. Mater., Vol. 34, No. 4, 1998, pp. 355-362.

[17]     Birman, V., Byrd, L. W., “Modeling and analysis of functionally graded materials and structures”, Appl. Mech. Rev., Vol. 60, No. 5, 2007, pp. 197-216.

[18]     Cho, R., Ha, D. Y., “Averaging and finite element discretization approaches in the numerical analysis of functionally graded materials”, J. Mater. Sci. Technol., Vol. 302, No. 2, 2000, pp. 287-296.

[19]     Ray, M. C., Sachade, H. M., “Finite element analysis of smart functionally graded plates”, Int. J. Solids Struct., Vol. 43, No. 18, 2006, pp. 5468-5484.

[20]     Rabczuk, T., Areias, PMA., “A mesh free thin shell for arbitrary evolving cracks based on an external enrichment”, Computer Modeling Eng. Sci., Vol. 16, No. 1, 2006, pp. 115-130.

[21]     Diao, D., Kandori, A., “Finite element analysis of the effect of interfacial roughness and adhesion strength on the local delamination of hard coating under sliding contact”, Tribol. Int., Vol. 39, No. 9, 2006, pp. 849-855.

[22]     Dag, S., Guler, M. A., “Sliding frictional contact between a rigid punch and a laterally graded elastic medium”, Int. J. Solids Struct., Vol. 46, No. 22, 2009, pp. 4038-4053.

[23]     Adibnazari, S., Khajehtourian, R. and Tashi, S., “The sliding frictional contact problem in two dimensional graded materials loaded by a flat stamp”, Adv. Mat. Res., Vol. 463-464, 2012, pp. 336-342.

[24]     Guler, M. A., Adibnazari, S. and Alinia, Y., “Tractive rolling contact mechanics of graded coatings”, Int. J. Solids Struct., Vol. 49, No. 6, 2012, pp. 929-945.

[25]     Alinia, Y., Guler, M. A. and Adibnazari, S., “On the contact mechanics of a rolling cylinder on a graded coating. Part 1: analytical formulation”, Mech. Mater., Vol. 68, 2014, pp. 207-216.

[26]     Guler, M. A., Alinia, Y. and Adibnazari, S., “On the contact mechanics of a rolling cylinder on a graded coating. Part 2: numerical results”, Mech. Mater., Vol. 66, 2013, pp. 134-159.

[27]     Guler, M. A., Alinia, Y. and Adibnazari, S., “On the rolling contact problem of two elastic solids with graded coatings”, Int. J. Mech. Sci., Vol. 64, No. 1, 2012, pp. 62-81.

[28]     Alinia, Y., Guler, M. A. and Adibnazari, S., “The effect of material property grading on the rolling contact stress field”, Mech. Res. Commun., Vol. 55, 2014, pp. 45-52.

[29]     Hills, D. A., Nowell, D. and Sackfield, A., “Mechanics of Elastic Contact”, 1st ed., Oxford Press, Butterworth-Heinemann, 1993, chap. 2.

[30]     Peixoto, D. F. C., Castro, P. M. de., “Nonlinear analysis of the wheel/rail contact”, Ph.D. Dissertation, Mechanical Eng. Dept., University of Porto, Portugal, 2011.

[31]     Yang, J., Ke, L., “Two-dimensional contact problem for a coating– graded layer– substrate structure under a rigid cylindrical punch”, Int. J. Mech. Sci., Vol. 50, No. 6, 2008, pp. 985-994.

[32]     Halme, J., Andersson, P., “Rolling contact fatigue and wear fundamentals for rolling bearing diagnostics - state of the art”, Proc IMechE Part J: J Engineering Tribology, Vol. 224, 2010, pp. 377-393.