A Finite Element Procedure for Sliding Contact Problems Involving Heterogeneous Coefficient of Friction

Year 2020, , 197 - 205, 01.03.2020

Onur Arslan

https://doi.org/10.2339/politeknik.469932

Abstract

A new finite element procedure is developed for the
analysis of sliding contact problems involving spatially varying coefficient of
friction. The problem is implemented using APDL (ANSYS Parametric Design
Language) considering the Augmented Lagrange method as the contact solver. Upon
discretization of the contact interface into multiple contact pairs, a sequence
of steps is followed to evaluate the resultant friction force required for the
sliding contact. As a case study, heterogeneous-friction contact problem
between an orthotropic laterally graded half-plane and a rigid flat stamp is
investigated under plane strain assumption. The proposed iterative procedure is
proved reliable by comparing the results to those generated by a SIE (Singular
Integral Equation) approach for isotropic laterally graded half-planes. Extra
results are presented to reveal the effects of problem parameters on the
contact stresses and the friction force. The paper outlines a convenient
numerical solution for an advance sliding contact problem, and the results can
be used in validation purposes of experimental and analytical studies. 

Keywords

Heterogeneous friction coefficient, sliding frictional contact, laterally graded materials, finite element method

References

• Surresh S., ''Graded materials for resistance to contact deformation and damage'', Science, 292: 2447–2451, (2001)
• Zhang Y., ''Overview: Damage resistance of graded ceramic restorative materials'', Journal of the European Ceramic Society, 32: 2623-2632, (2012)
• Wolfe D. E. and Singh J., ''Titanium carbide coatings deposited by reactive ion beam-assisted, electron beam–physical vapor deposition'', Surface and Coating Technology, 124: 142-153, (2000)
• Khor, K. A., Dong, Z. L. and Gu, Y. W., ''Plasma sprayed functionally graded thermal barrier coatings'', Material Letters, 38: 437–444 (1999)
• Sampath S., Herman H., Shimoda N. and Saito T., ''Thermal spray processing of FGMs'', MRS Bulletin, 20: 27-31 (1995)
• Kaysser W.A. and Ilschner B., ''FGM research activities in Europe'', MRS Bulletin, 20: 22-26, (1995)
• Shi D., Lin Y. and Ovaert T.C., ''Indentation of an orthotropic half-space by a rigid ellipsoidal indenter'', Journal of Tribology-Transactions of the ASME, 125: 223–231, (2003)
• Swanson S.R., ''Hertzian contact of orthotropic materials'', International Journal of Solids and Structures, 41: 1945–1959, (2004)
• Rodriguez N.V., Masen M.A. and Schipper D.J., ''A contact model for orthotropic viscoelastic materials'', International Journal of Mechanical Sciences, 74: 91–98, (2013)
• Dong X.Q., Zhou Y.T., Wang L.M., Ding S.H. and Park, J.B., ''Stress state of two collinear stamps over the surface of orthotropic materials'', Archive of Applied Mechanics, 84: 639–656, (2014)
• Zhou Y.T., Lee K.Y. and Jang Y.H., ''Indentation theory on orthotropic materials subjected to a frictional moving punch'', Archives of Mechanics, 66: 71–94, (2014)
• Zhou Y.T. and Lee K.Y., ''Exact solutions of a new 2D frictionless contact model for orthotropic piezoelectric materials indented by a rigid sliding punch'', Philosophical Magazine, 92: 1937–1965, (2012)
• Guler M.A., ''Closed-form solution of the two-dimensional sliding frictional contact problem for an orthotropic medium'', International Journal of Mechanical Sciences, 87:72–88, (2014)
• Kucuksucu A., Guler M.A. and Avci A., ''Mechanics of sliding frictional contact for a graded orthotropic half-plane'', Acta Mechanica, 226: 3333–3374 (2015)
• Guler M.A., Kucuksucu A., Yilmaz K.B. and Yildirim B., ''On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium'', International Journal of Mechanical Sciences, 120: 12-29, (2017)
• Arslan O. and Dag S., ''Contact mechanics problem between an orthotropic graded coating and a rigid punch of an arbitrary profile'', International Journal of Mechanical Sciences, 135: 541-554, (2018)
• Babilio E., ''Dynamics of an axially functionally graded beam under axial load'', The European Physical Journal Special Topics, 222: 1519–1539, (2013)
• Baron C. and Naili S., ''Propagation of elastic waves in a fluid-loaded anisotropic functionally graded waveguide: Application to ultrasound characterization'', The Journal of the Acoustical Society of America, 127: 1307-1317, (2010)
• Borrelli A., Horgan C. and Patria M. C., ''Exponential decay of end effects in anti-plane shear for functionally graded piezoelectric materials'', Proceedings of the Royal Society of London A-Mathematical and Physical Sciences, 460: 1193-1212, (2004)
• Arslan O., ''Computational contact mechanics analysis of laterally graded orthotropic half-planes'', World Journal of Engineering, 14: 145-154, (2017)
• Dag S., Guler M.A., Yildirim B. and Ozatag A.C., ''Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp'', Acta Mechanica, 224, 1773-1789, (2013)
• Dag S., ''Consideration of spatial variation of the friction coefficient in contact mechanics analysis of laterally graded materials'', ZAMM-Journal of Applied Mathematics and Mechanics, 96: 121-36, (2016)
• Khajehtourian R., Adibnazari S. and Tash, S., ''The influence of grain size and grain size distribution on sliding frictional contact in laterally graded materials'', Applied Mechanics and Materials, 157: 964-969, (2012)
• Dag S. and Erdogan F., ''A surface crack in a graded medium loaded by a sliding rigid stamp'', Engineering Fracture Mechanics, 69: 1729-1751, (2002)
• Hills D.A. and Nowell D., ''Mechanics of fretting fatigue'', Kluwer Academic Publishers, Netherlands, (1994)
• Vadivuchezhian K., Sundar S. and Murthy H., ''Effect of variable friction coefficient on contact tractions'', Tribology International, 44: 1433-1442, (2011)
• Ren L. and Zhang Y., ''Sliding contact fracture of dental ceramics: Principles and validation'', Acta Biomaterialia, 10: 3243–3253, (2014)
• Ballard P., ''Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities'' Journal of the Mechanics and Physics of Solids, 97: 225-259, (2016)