Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences		 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936
Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 
Issues > Archive of Issues > 2012-4 > pp.415-425

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212
<< Previous article | Volume 47, Issue 4 / 2012 | Next article >>
R.L. Salganik and K.B. Ustinov, "Deformation Problem for an Elastically Fixed Plate Modeling a Coating Partially Delaminated from the Substrate (Plane Strain)," Mech. Solids. 47 (4), 415-425 (2012)
Year 2012 Volume 47 Number 4 Pages 415-425
DOI 10.3103/S0025654412040061
Title Deformation Problem for an Elastically Fixed Plate Modeling a Coating Partially Delaminated from the Substrate (Plane Strain)
Author(s) R.L. Salganik (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, salganik@ipmnet.ru)
K.B. Ustinov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, ustinov@ipmnet.ru)
Abstract An asymptotic solution of the problem indicated in the title is obtained at distances large compared with the plate width and some promising methods for its use, in particular, for calculating the coefficients in the boundary conditions of the plate elastic fixation which models a coating partially delaminated from the substrate, are outlined. The possibility of considering the delamination in the approximation of the plate weak bending (the plate approximation) and the possibility of neglecting the tangential stress action along the contact boundary are implemented. The substrate is considered as a half-infinite elastic solid. This solution was obtained by using the Fourier transform and the solution of the resulting equation by the Wiener-Hopf method. The obtained asymptotic solution can be used to study problems related to coating delamination, especially on soft thick substrata.
Keywords substrate, coating, elastic fixation, elastic fixation coefficient, Fourier transform, Wiener-Hopf method, asymptotics
References
1.  J. W. Hutchinson and Z. Suo "Mixed Mode Cracking in Layered Materials," in Advances in Applied Mechanics, Ed. by J. W. Hutchinson and T. Y. Wu (1992), Vol. 29, pp. 63-191.
2.  B. Cotterell and Z. Chen, "Buckling and Cracking of Thin Film on Compliant Substrates under Compression," Int. J. Fract. 104 (2), 169-179 (2000).
3.  H. H. Yu and J. W. Hutchinson, "Influence of Substrate Compliance on Buckling Delamination of Thin Film," Int. J. Fract. 113 (1), 39-55 (2000).
4.  G. Parry, J. Colin, C. Coupeau, et al., "Effect of Substrate Compliance on the Global Unilateral Post-Buckling of Coatings: AFM Observations and Finite Element Calculations," Acta Mat. 53 (2), 441-447 (2005).
5.  B. Audoly and A. Boudaoud, "Buckling of a Stiff Film Bound to a Compliant Substrate (Part I). Formulation, Linear Stability of Cylindrical Patterns, Secondary Bifurcation," J. Mech. Phys. Solids 56, 2401-2421 (2008).
6.  S. Faulhaber, C. Mercera, M.-W. Moon, et al., "Buckling Delamination in Compressed Multilayers on Curved Substrates with Accompanying Ridge Cracks," J. Mech. Phys. Solids 54, 1004-1028 (2006).
7.  R. V. Goldstein, K. B. Ustinov, and A. V. Chentsov, "Buckling of Delaminated Coatings: Effects of Substrate Compliance and Coating Thickness," in 2nd Conf. "From Nanoparticles and Nanomaterials to Nanodevices and Nanosystems", Rhodes, Greece, 2009, Book of Abstracts, p. 192.
8.  K. B. Ustinov and A. V. Chentsov, Analytic and Numerical Modeling of the Loss of Stability of the Coating Delaminated from the Substrate, Preprint No. 926 (IPMekh RAN, Moscow, 2010) [in Russian].
9.  R. L. Salganik, A. A. Mishchenko, and A. A. Fedotov, "Electromechanical Effects in Material with Cracks and Rough Coating in Buckling Delamination," Vestnik MAI 16 (4), 130-138 (2009).
10.  R. L. Salganik, A. A. Fedotov, and A. A. Mishchenko, "Thermal Stressing Effects in Materials with Rough Coating Caused by Electromagnetic Radiation Energy Dissipation," in Proc. PACAM XI. 11th Pan-American Congr. Appl. Mech. 2010. Foz do Iguaçu, PR, Brazil, 2009, p. 0353.
11.  K. B. Ustinov, A. V. Dyskin, and L. N. Germanovich, "Asymptotic Analysis of Extensive Crack Growth Parallel to Free Boundary," in 3rd Int. Conf. Localized Damage 94 (Comput. Mech. Publ., Southampton, 1994), pp. 623-630.
12.  A. V. Dyskin, L. N. Germanovich, and K. B. Ustinov, "Asymptotic Analysis of Crack Interaction with Free Boundary," Int. J. Solids Struct. 37, 857-886 (2000).
13.  K. B. Ustinov, "On the Refinement of Boundary Conditions for the Beam Model of the Cantilever of the Atomic Force Microscope and Their Influence on the Interpretation of the Measurement Results," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 182-188 (2008) [Mech. Solids (Engl. Transl.) 43 (3), 470-476 (2008)].
14.  H. H. Yu, M. Y. He, and J. W. Hutchinson, "Edge Effects in Thin Film Delamination," Acta Mater. 49, 93-107 (2001).
15.  R. L. Salganik, "Temporal Effects in Brittle Fracture," Probl. Prochn., No. 2, 79-85 (1971) [Strength of Materials (Engl. Transl.) 3 (2), 200-206 (1971)].
16.  L. Banks-Sills and R. L. Salganik, "An Asymptotic Approach Applied to Longitudinal Crack in an Adhesive Layer," Int. J. Fract. 68 (1), 55-73 (1994).
17.  R. L. Salganik, "Model of a Crack-Like Wave of Inelastic Deformation in a Solid (Crack in Silver)," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 1, 48-60 (1970) [Mech. Solids (Engl. Transl.)].
18.  R. L. Salganik, "Film Buckling on a Layer in the Case of Jumpwise Variation of Their Characteristics and in the Case of the Layer Contact with a Solid," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 4, 86-97 (1988) [Mech. Solids (Engl. Transl.)].
19.  V. M. Alexandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Interlayers (Nauka, Moscow, 1983) [in Russian].
20.  G. Ya. Popov and L. Ya. Tikhonenko, "Two-Dimensional Problem of the Contact between a Semi-Infinite Beam and an Elastic Wedge," Prikl. Mat. Mekh. 38 (2), 312-320 (1974) [J. Appl. Math. Mech. (Engl. Transl.) 38 (2), 284-292 (1974)].
21.  S. G. Lekhnitskii, Theory of Elasticity of Anisotropic Body (Gostekhizdat, Moscow-Leningrad, 1950) [in Russian].
22.  B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon Press, London etc., 1958; Izd-vo Inostr. Lit., Moscow, 1962).
23.  R. L. Salganik, "Thin Layer with Jumpwise Characteristics in and Infinite Elastic Body," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 154-163 (1977) [Mech. Solids (Engl. Transl.)].
24.  V. M. Entov and R. L. Salganik, "On the Prandtl Brittle Fracture Model," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 6, 87-99 (1968) [Mech. Solids (Engl. Transl.)].
25.  R. V. Goldstein and A. B. Konovalov, "Asymptotic Analysis of the 3D Problem on a Crack-Delamination in a Two-Layer Plate," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 62-71 (1996) [Mech. Solids (Engl. Transl.) 96 (3), 53-60 (1996)].
26.  A. N. Zlatin and A. A. Khrapkov, "A Semi-Infinite Crack Parallel to the Boundary of the Elastic Half-Plane," Dokl. Akad. Nauk SSSR 31, 1009-1010 (1986) [Sov. Phys. Dokl. (Engl. Transl.) 31 (12), 1009-1010 (1986)].
27.  R. L. Salganik, "The Brittle Fracture of Cemented Bodies," Prikl. Mat. Mekh. 27 (5), 957-962 (1963) [J. Appl. Math. Mech. (Engl. Transl.) 27 (5), 1468-1478 (1963)].
28.  V. M. Malyshev and R. L. Salganik, "The Strength of Adhesive Joints Using the Theory of Crack," Int. J. Fract. Mech. 1 (2), 114-128 (1965).
29.  L. I. Slepyan, Mechanics of Cracks (Sudostroenie, Leningrad, 1981) [in Russian].
30.  K. B. Ustinov and A. V. Chentsov, Problem of an Elastically Fixed Plate Modeling a Coating Partially Delaminated from the Substrate, Preprint No. 948 (IPMekh RAN, Moscow, 2010) [in Russian].
31.  S. A. Nazarov and O. R. Polyakova, "Stress Intensity Factors for Parallel Cracks Lying Close Together in a Plane Region," Prikl. Mat. Mekh. 54 (1), 132-140 (1990) [J. Appl. Math. Mech. (Engl. Transl.) 54 (1), 105-115 (1990)].
32.  M. A. Grekov, Singular Plane Problem of Elasticity (Izd-vo St. Petersburg Univ., St.Petersburg, 2001) [in Russian].
Received 18 November 2010
Link to Fulltext
<< Previous article | Volume 47, Issue 4 / 2012 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia • (+7 495) 434-3538 • mechsol@ipmnet.ru • https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS 		© Mechanics of Solids
webmaster		 Rambler's Top100