Abstract
We use the perturbation method to construct a solution of the plane problem of elasticity for a film-foundation composite where the film surface is weakly curved. In the case where the film surface has a periodic shape, the problem solution in each approximation is represented in terms of Fourier series with coefficients expressed in terms of quadrature. In the first approximation, we obtain the stresses on the film surface and on the interphase surface in terms of the surface curvature, the film average thickness, and the film-to-foundation Young’s modulus ratio.
Similar content being viewed by others
References
P. Kordos and J. Novak (Editors), Heterostructure Epitaxy and Devices — HEAD’97 (Kluwer, Dordrecht, 1998).
L. B. Freund, “Evolution of Waviness on the Surface of a Strained Elastic Solid due to Stressdriven Diffusion,” Int. J. Solids Struct. 32(6/7), 911–923 (1995).
H. Gao and W. D. Nix, “Surface Roughness of Heteroepitaxial Thin Films,” Annu. Rev. Mater. Sci. 29, 173–209 (1999).
A.M. Andrews, J. S. Speck, A. E. Romanov, et al., “Modeling Cross-Hatch Surface Morphology in Growing Mismatched Layers,” J. Appl. Phys. 91(4), 1933–1943 (2002).
M. A. Grekov, “Weakly Curved Crack near the Boundary of Junction of Two Different Materials,” Vestnik St. Petersburg. Univ. Ser. 1, No. 1, 93–100 (2008).
M. A. Grekov and N. F. Morozov, “Some Modern Methods in Mechanics of Cracks,” in Operator Theory: Advances and Applications, Vol. 191: Modern Analysis and Applications. Ed. by V. Adanyan et al. (Birkhäuser, Basel, 2009), pp. 127–142.
H. Gao, “A Boundary Perturbation Analysis for Elastic Inclusions and Interfaces,” Int. J. Solids Struct. 28(6), 703–725 (1991).
M. A. Grekov and S. N. Makarov, “Stress Concentration near a Slightly Curved Part of an Elastic Body Surface,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 53–61 (2004) [Mech. Solids (Engl. Transl.) 39 (6), 40–46 (2004)].
M. A. Grekov, Singular Plane Problem of Elasticity (Izd-vo St. Petersburg Univ., St.Petersburg, 2001) [in Russian].
M. A. Grekov and S. A. Kostyrko, “Stressed State of Thin Coating under the Action of a Periodic System of Surface Concentrated Forces,” Vestnik St. Peterburg. Univ. Ser. 10, No. 4, 99–107 (2004).
A. M. Lin’kov, Complex Method of Boundary Integral Equations in Elasticity (Nauka, St. Petersburg, 1999) [in Russian].
J. Dundurs, “Edge-Bonded Dissimilar Orthogonal Elastic Wedges under Normal and Shear Loading,” Trans. ASME. J. Appl. Mech. 36(3), 650–652 (1969).
N. I. Muskhelishvili, Some Fundamental Problems of Mathematical Elasticity Theory (Nauka, Moscow, 1966) [in Russian].
H. Gao, “Stress Concentration at Slightly Undulating Surfaces,” J. Mech. Phys. Solids 39(4), 443–458 (1991).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.I. Vikulina, M.A. Grekov, S.A. Kostyrko, 2010, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2010, No. 6, pp. 16–28.
About this article
Cite this article
Vikulina, Y.I., Grekov, M.A. & Kostyrko, S.A. Model of film coating with weakly curved surface. Mech. Solids 45, 778–788 (2010). https://doi.org/10.3103/S0025654410060038
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654410060038