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Plane receding contact problem for a functionally graded layer supported by two quarter-planes

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this study, the plane receding contact problem for a functionally graded (FG) layer resting on two quarter-planes is considered by using the theory of linear elasticity. The layer is indented by a rigid cylindrical punch that applies a concentrated force in the normal direction. While the Poisson’s ratio is kept constant, the shear modulus is assumed to vary exponentially through-the-thickness of the layer. It is assumed that the contact at the layer-punch interface and the layer-substrate interface is frictionless, and only the normal tractions can be transmitted along the contact regions. Applying the Fourier integral transform, the plane elasticity equations are converted to a system of two singular integral equations, in which the contact stresses and the contact widths are unknowns. The singular integral equations are solved numerically by Gauss–Jacobi integration formula. Effects of the material inhomogeneity, the distance between quarter-planes and the punch radius on the contact stresses, the contact widths, and the stress intensity factors at the sharp edges are shown. Although the theoretical analysis is formulated with respect to elastic quarter planes, the numerical studies are carried out only for rigid ones.
Rocznik
Strony
485--504
Opis fizyczny
Bibliogr. 45 poz.
Twórcy
autor
  • Faculty of Engineering Department of Civil Engineering Karadeniz Technical University 61080 Trabzon, Turkey
autor
  • Faculty of Engineering Department of Civil Engineering Karadeniz Technical University 61080 Trabzon, Turkey
autor
  • Faculty of Engineering and Architecture Department of Civil Engineering Avrasya University 61010 Trabzon, Turkey
Bibliografia
  • 1. J. Dundurs, M. Stippes, Role of elastic constants in certain contact problems, Journal of Applied Mechanics, 37, 965-970, 1970.
  • 2. Y. Weitsman, On the unbonded contact between plates and an elastic half space, Journal of Applied Mechanics, 36, 198–202, 1969.
  • 3. S.L. Pu, M.A. Hussain, Note on the unbonded contact between plates and an elastic half space, Journal of Applied Mechanics, 37, 859–861, 1970.
  • 4. L.M. Keer, J. Dundurs, K.C. Tasi, Problems involving a receding contact between a layer and a half-space, Journal of Applied Mechanics, 39, 1115–1120, 1972.
  • 5. M.B. Civelek, F. Erdogan, The axisymmetric double contact problem for a frictionless elastic layer, International Journal of Solids and Structures, 10, 6, 639–659, 1974.
  • 6. M.R. Gecit, Axisymmetric contact problem for a semi-infinite cylinder and a half space, International Journal of Engineering Science, 24, 8, 1245–1256, 1986.
  • 7. M. Ratwani, F. Erdogan, On the plane contact problem for a frictionless elastic layer, International Journal of Solids and Structures, 9, 8, 921–936, 1973.
  • 8. I. Comez, A. Birinci, R. Erdol, Double receding contact problem for a rigid stamp and two elastic layers, European Journal of Mechanics A-Solids, 23, 301–309, 2004.
  • 9. V. Kahya, T.S. Ozsahin, A. Birinci, R. Erdol, A receding contact problem for an anisotropic elastic medium consisting of a layer and a half-plane, International Journal of Solids and Structures, 44, 5695–5710, 2007.
  • 10. H. Adibelli, I. Comez, R. Erdol, Receding contact problem for a coated layer and a half-plane loaded by a rigid cylindrical stamp, Archive of Mechanics, 65, 3, 219–236, 2013.
  • 11. I. Çömez, Frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half-plane, International Journal of Solids and Structures, 47, 7–8, 1090–1097, 2010.
  • 12. A.E. Giannakopoulos, P. Pallot, Two-dimensional contact analysis of elastic graded materials, Journal of the Mechanics and Physics of Solids, 48, 1597–631, 2000.
  • 13. 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, 4038–53, 2009.
  • 14. P. Chen, S. Chen, Contact behaviors of a rigid punch and a homogeneous half-space coated with a graded layer, Acta Mechanica, 223, 563–577, 2012.
  • 15. M.A. Guler, F. Erdogan, Contact mechanics of graded coatings, International Journal of Solids and Structures, 41, 3865–3889, 2004.
  • 16. T.J. Liu, Y.S. Wang, C. Zhang, Axisymmetric frictionless contact of functionally graded materials, Archive of Applied Mechanics, 78, 267–282, 2008.
  • 17. P. Chen, S. Chen, Contact behaviors of a rigid punch and a homogeneous half- space coated with a graded layer, Acta Mechanica, 223, 563–77, 2012.
  • 18. J. Yang, L.L Ke, Two-dimensional contact problem for a coating–graded layer–substrate structure under a rigid cylindrical punch, International Journal of Mechanical Science, 50, 985–994, 2008.
  • 19. S.J. Chidlow, M. Teodorescu, Sliding contact problems involving inhomogeneous materials comprising a coating-transition layer-substrate and a rigid punch, International Journal of Solids and Structures, 51, 10, 1931–1945, 2014.
  • 20. J. Liu, L.L. Ke, Y.S. Wang, J.Yang, F. Alam, Thermoelastic frictional contact of functionally graded materials with arbitrarily varying properties, International Journal of Mechanical Science, 63, 86–98, 2012.
  • 21. J.J. Mao, L.L Ke, Y.S.Wang, Thermoelastic contact instability of a functionally graded layer and a homogeneous half-plane, International Journal of Solids and Structures, 51, 3962–3972, 2014.
  • 22. J.J. Mao, L.L Ke, Y.S. Wang, J. Yang, S. Kitipornchai, Thermoelastic instability of functionally graded coating with arbitrarily varying properties considering contact resistance and frictional heat, Applied Mathematical Modelling, 43, 521–537, 2017.
  • 23. S. El-Borgi, R. Abdelmoula, L. Keer, A receding contact problem between a functionally graded layer and a homogeneous substrate, International Journal of Solids and Structures, 43, 658–674, 2006.
  • 24. S. El-Borgi, S. Usman, M.A. Güler, A frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate, International Journal of Solids and Structures, 51, 25, 4462-4476, 2014.
  • 25. M. Rhimi, S. El-Borgi, N. Lajnef, A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate, Mechanics of Materials, 43, 12, 787–798, 2011.
  • 26. İ. Çömez, S. El-Borgi, V. Kahya, R.Erdöl, Receding contact problem for two-layer functionally graded media indented by a rigid punch, Acta Mechanica, 227, 9, 2493–2504, 2016.
  • 27. S. El-Borgi, İ. Çömez, 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.
  • 28. J. Yan, X. Li, Double receding contact plane problem between a functionally graded layer and an elastic layer, European Journal of Mechanics A-Solids, 53, 143–150, 2015.
  • 29. J. Yan, C. Mi, Double contact analysis of multilayered elastic structures involving functionally graded materials, Archives of Mechanics, 69, 3, 199–221, 2017.
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  • 36. M. Bakioglu, Kamalarla Mesnetlendirilmis Elastik Seritler için Bir Karısık Sınır Değer Problemi, Dissertation, Istanbul Technical University, Istanbul, 1977 [in Turkish].
  • 37. L.M. Keer, J.C. Lee, T. Mura, A contact problem for the elastic quarter space, International Journal of Solids and Structures, 20, 5, 513–524, 1984.
  • 38. O. Aksogan, S. Akavci, A.A. Becker, The solution of the nonsymmetrical contact problem of an elastic layer supported by two elastic quarter-planes using three different methods, Çukurova Üniversitesi Mühendislik ve Mimarlık Fakültesi Dergisi, 12, 1–13, 1997.
  • 39. M. Yaylaci, A. Birinci, The receding contact problem of two elastic layers supported by two elastic quarter-planes, Structural Engineering and Mechanics, 48, 2, 241–255, 2013.
  • 40. G. Adıyaman, A. Birinci, E. Öner, M. Yaylacı, A receding contact problem between a functionally graded layer and two homogeneous quarter planes, Acta Mechanica, 227, 6, 1753–1766, 2016.
  • 41. F. Erdogan, Mixed boundary value problems in mechanics, [in:] S. Nemat-Nasser, Mechanics Today, vol. 4, Pergamon Press, New York, 1978.
  • 42. S. Krenk, On quadrature formulas for singular integral equations of the first and the second kind, Quarterly of Applied Mathematics, 33, 225–232, 1975.
  • 43. F. Erdogan, G. Gupta, On the numerical solutions of singular integral equations, Quarterly of Applied Mathematics, 29, 525–534, 1972.
  • 44. S. Krenk, On the use of the interpolation polynomial for solutions of singular integral equations, Quarterly of Applied Mathematics, 33, 479–484, 1975.
  • 45. M. Comninou, Stress singularity at a sharp edge in contact problems with friction, Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 27, 4, 493–499, 1976.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5acf1dac-60e5-40c8-99ce-0bd44e254e2a
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