Solution of the plane contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-profile

• Autorzy: Arslan O.

Identyfikatory

DOI

10.24423/aom.3207

• Języki publikacji: EN

Abstrakty

EN

A singular integral equation (SIE) approach and a finite element method are developed for the solution of the frictional sliding contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-shape considering the plane strain assumption. An exponential shear modulus variation is introduced through the lateral direction. The field variables are obtained applying the Fourier transformation techniques on the governing partial differential equations. A surface displacement gradient is then utilized to derive a SIE of the second kind. A numerical solution of the SIE is performed by using a collation method and the Gauss quadrature integration techniques for the flat, triangular and circular stamp profiles. Finite element analyses (FEA) of the same contact problems are also performed upon selection of the augmented Lagrange contact-solver in ANSYS. For the incomplete (triangular and circular) stamp problems, an iterative algorithm is developed in order to obtain practically computational solutions for any desired contact lengths. Successful convergence of the SIE results and excellent consistency between the SIE and FEA results are attained, that indicate the reliability of both methods. The change in the thickness is shown to alter the contact behavior of the laterally graded solid significantly.

Słowa kluczowe

EN

frictional sliding contact; laterally graded layer; singular integral equation; finite element method

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2019
• Tom: Vol. 71, nr 6
• Strony: 531--565
• Opis fizyczny: Bibliogr. 28 poz., rys. kolor.

Twórcy

autor

Arslan O.

• Department of Mechanical Engineering, Eskisehir Osmangazi University, Eskisehir 26480, Turkey

Bibliografia

• 1. D.E.Wolfe, J. Singh, Titanium carbide coatings deposited by reactive ion beam-assisted, electron beam-physical vapor deposition, Surface and Coatings Technology, 124, 142–153, 2000.
• 2. K.A. Khor, Z.L. Dong, Y.W Gu, Plasma sprayed functionally graded thermal barrier coatings, Materials Letters, 38, 437–444, 1999.
• 3. C.E. Rousseau, H.V. Tippur, Evaluation of crack tip fields and stress intensity factors in functionally graded elastic materials: cracks parallel to elastic gradient, International Journal Fracture, 114, 1, 87–112, 2002.
• 4. R.J. Butcher, C.E. Rousseau, H.V. Tippur, A functionally graded particulate composite: preparation, measurements and failure analysis, ActaMaterialia, 47, 259–268, 1999.
• 5. S. Surresh, Graded materials for resistance to contact deformation and damage, Science, 292, 2447–51, 2001.
• 6. B. Lawn, Indentation of Ceramics with spheres: A Century after Hertz, Journal of the American Ceramic Society, 81, 1977–1994, 1998.
• 7. M.A Guler, F. Erdogan, Contact mechanics of graded coatings, International Journal of Solids and Structures, 41, 3865–3889, 2004.
• 8. 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, 161–182, 2007.
• 9. P. Chen, S. Chen, Partial slip contact between a rigid punch with an arbitrary tip-shape and an elastic graded solid with a finite thickness, Mechanics of Materials, 59, 24–35, 2013.
• 10. X. Guo, J. Fan, H. Gao, Mechanics of non-slipping adhesive contact on a power-law graded elastic half-space, International Journal of Solids and Structures, 48, 2565–2575, 2011.
• 11. S. Borgi, I. Comez, A receding frictional contact problem between a graded layer and a homogeneous substrate pressed by a rigid punch, Mechanics of Materials, 114, 201–214, 2017.
• 12. M.A. Guler, Y. Alinia, S. Adibnazari, On the rolling contact problem of two elastic solids with graded coatings, International Journal of Mechanical Sciences, 64, 62–81, 2012.
• 13. I. Comez, Contact problem for a functionally graded layer indented by a moving punch, International Journal of Mechanical Sciences, 100, 339–344, 2015.
• 14. H.J. Choi, G.H. Paulino, Thermoelastic contact mechanics for a flat punch sliding over a graded coating/substrate system with frictional heat generation, Journal of the Mechanics and Physics of Solids, 56, 1673–1692, 2008.
• 15. O. Arslan, S. Dag, 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.
• 16. T.S. Vasu, T.K. Bahndakkar, Plane strain cylindrical indentation of functionally graded half-plane with exponentially varying shear modulus in the presence of residual surface tension, International Journal of Mechanical Sciences, 135, 158–167, 2018.
• 17. A. Polat, Y. Kaya, T.S. Ozsahin, Analytical solution to continuous contact problem for a functionally graded layer loaded through two dissimilar rigid punches, Meccanica, 53, 3565–3577, 2018.
• 18. I. Comez, V. Kahya, R. Erdol, Plane receding contact problem for a functionally graded layer supported by two quarter-planes, Archives of Mechanics, 70, 485–504, 2018.
• 19. R. Cremer, D. Neuschutz, A combinatorial approach to the optimization of metastable multicomponent hard coatings, Surface and Coatings Technology, 146, 229–236, 2001.
• 20. V.K. Ganesh, K. Ramakrishna, D.N. Ghista, Biomechanics of bone-fracture fixation by stiffness-graded plates in comparison with stainless-steel plates, Biomedical Engineering Online, 4, 46, 2005.
• 21. K. Ramakrishna, I. Sridhar, S. Sivashanker, K.S. Khong, D.N. Ghista, Design of fracture fixation plate for necessary and sufficient bone stress shielding, JSME International Journal, 47, 1086–1094, 2004
• 22. Z.N. Nejat, M. Jabbari, M. Gahnnad, Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading , International Journal of Mechanical Sciences, 89, 86–99, 2015.
• 23. S. Dag, M.A. Guler, B. Yildirim, C. Ozatag, Sliding frictional contact between a rigid punch and a laterally graded elastic medium, International Journal of Solids and Structures, 46, 4038–4053, 2009.
• 24. S. Dag, M.A. Guler, B. Yildirim, C. Ozatag, Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp, Acta Mechanica, 224, 1773–1789, 2013.
• 25. P. Chen, S. Chen, J. Pengh, Sliding contact between a cylindrical punch and a graded half-plane with an arbitrary gradient direction, Journal of Applied Mechanics, 82, 4, 2015.
• 26. D. Dini, D. Nowell, Flat and rounded fretting contact problems incorporating elastic layers, International Journal of Mechanical Sciences, 46, 1635–1657, 2004.
• 27. F. Erdogan, Mixed boundary value problems in mechanics, [in:] S. Nemat-Nasser [ed.], Mechanics Today, 4, 1–84, 1978.
• 28. M.A. Guler, Contact Mechanics of FGM Coatings, Dissertation, Lehigh University, Bethlehem NY, 2000.