Abstract
This paper investigates the buckling of a bi-layered material with functionally graded coating including a pre-existing interface crack. In order to investigate this phenomenon which is of particular interest to the tribological community, the stresses due to sliding cylindrical loading were determined. Solutions for stresses are obtained by use of Fourier transform technique. These stress fields under such loading are strongly affected by various parameters such as friction coefficient, indenter tip radius, film thickness, etc. Therefore, to assess the coating strength reliably, the mechanical stress field developed by mixed normal and tangential surface pressure was analyzed by considering the affected parameters. The mechanical properties of the FG coating are assumed to vary exponentially through the thickness. On the basis of stress analysis, a satisfactory framework was developed to study the buckling of FG coatings. An interface crack was assumed to model the actually occurring flaws in such coated systems, and the critical buckling stress was obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barovich D., Kingsley S.C., Ku T.C.: Stress on a thin strip or slab with different elastic properties from that of the substrate due to elliptically distributed load. Int. J. Eng. Sci. 2, 253–268 (1964)
Gupta P.K., Walowit J.A.: Contact stress between an elastic cylinder and a layered elastic solid. ASME. J. Lubr. Technol. 94, 250–257 (1974)
King R.B., O’Sullivan T.C.: Sliding contact stresses in a two dimensional layered elastic half-space. Int. J. Solids Struct. 23, 581–597 (1987)
Sonia Oliveira A.G., Bower A.F.: An analysis of fracture and delamination in thin coating subjected to contact loading. Wear 198, 15–32 (1996)
Patterson T., Orloff D.I., Bloom F.: Delamination buckling and spalling of plasma-sprayed thermal barrier coatings. Math. Comput. Model. 35, 165–190 (2002)
Yu H., Hutchinson J.W.: Delamination of thin film strips. Thin Solid Films 423, 54–63 (2003)
Zhou L., Ni J., He Q.: Study on failure mechanism of the coated carbide tool. Int. J. Refract. Metals Hard Mater. 25, 1–5 (2007)
Gao Y.F., Xu H.T., Oliver W.C., Pharr G.M.: Effective elastic modulus of film-on-substrate systems under normal and tangential contact. J. Mech. Phys. Solids 56, 402–416 (2008)
Shakeri M., Sadough A., Rashahmadi S.: Elastic stress analysis of bi-layered isotropic coating and substrate subjected to line scratch indentation. J. Mater. Process. Technol. 196, 213–221 (2008)
Cheng Zh., Gao D., Zhong Zh.: Crack propagating in functionally graded coated with arbitrarily distributed material properties bonded to homogeneous substrate. Acta Mach. Sol. Sinica 23, 437–446 (2010)
Guo L., Wang Zh., Zhang L.: A fracture mechanics problem of a functionally graded layered structure with an arbitrarily oriented crack crossing the interface. Mech. Mater. 46, 69–82 (2012)
Timoshenko S., Goodier J.N.: Theory of Elasticity. 2nd edn. McGraw-Hill, New York (1951)
Asaro R.J., Lubarda V.A.: Mechanics of Solids and Materials. Cambridge University Press, Cambridge (2006)
Sad, M.H.: Elasticity Theory, Applications and Numerics. 2nd ed., p. 124, Elsevier (2009)
Timoshenko S.P., Krieger S.W.: Theory of Plates and Shells. 2nd edn. McGraw-Hill, NY (1959)
Ugural A.C.: Stresses in Plates and Shells. 2nd edn. McGraw-Hill, NY (1998)
Alinia, M.M.: Theory of Plates and Shells, 2nd ed. Ashian-Tehran (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rash Ahmadi, S., Maroufi, F. & Ghahremanijou, J. Buckling of a functionally graded coated solid subjected to sliding contact loading. Acta Mech 225, 553–562 (2014). https://doi.org/10.1007/s00707-013-0977-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-013-0977-0