Skip to main content
SpringerLink
Log in

Surface effects on delamination of a thin film bonded to an elastic substrate

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The delamination of a circular thin film at micro/nanoscale is studied using the Kirchhoff plate theory incorporating surface effects in this paper. Bending of a clamped circular nanoplate subjected to a concentrated force at the center or a uniformly distributed force over a lateral surface is solved. The bending deflection is derived in closed form. The adhesion energy and its release rate for delamination are determined when surface effects are taken into account. The influences of surface residual stress and surface elasticity along with the film’s size on the energy release rate of debonding advance or interfacial adhesion of a thin film bonded to an elastic substrate are analyzed for applied loading or given displacements. Analytic results are compared with experimental data and satisfactory agreement is confirmed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Assadi A, Farshi B (2010) Vibration characteristics of circular nanoplates. J Appl Phys 108(7):074312

    Article  Google Scholar 

  • Boddeti NG, Koenig SP, Long R, Xiao J, Bunch JS, Dunn ML (2013) Mechanics of adhered pressurized graphene blisters. J Appl Mech 80(4):041044

    Article  Google Scholar 

  • Cao Z, Wang P, Gao W, Tao L, Suk JW, Ruoff RS, Akinwande D, Huang R, Liechti KM (2014) A blister test for interfacial adhesion of large-scale transferred graphene. Carbon 69(4):390–400

    Article  Google Scholar 

  • Cao Z, Tao L, Akinwande D, Huang R, Liechti KM (2015) Mixed-mode interactions between graphene and substrates by blister tests. J Appl Mech 82(8):081008

    Article  Google Scholar 

  • Cotterell B, Chen Z (1997) The blister test—transition from plate to membrane behaviour for an elastic material. Int J Fract 86(3):191–198

    Article  Google Scholar 

  • Cuenot S, Freigny C, Demoustier-Champagne S, Nysten B (2004) Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys Rev B 69(16):1124–1133

    Article  Google Scholar 

  • Dauskardt RH, Lane M, Ma Q, Krishna N (1998) Adhesion and debonding of multi-layer thin film structures. Eng Fract Mech 61(1):141–162

    Article  Google Scholar 

  • Deng C, Jiang J, Liu F, Fang L, Wang J, Li D, Wu J (2015) Influence of graphene oxide coatings on carbon fiber by ultrasonically assisted electrophoretic deposition on its composite interfacial property. Surface Coat Technol 272(8):176–181

    Article  Google Scholar 

  • Elizalde MR, Sanchez JM, Martinez-Esnaola JM, Pantuso D, Scherban T, Sun B, Xu G (2003) Interfacial fracture induced by cross-sectional nanoindentation in metal-ceramic thin film structures. Acta Mater 51(14):4295–4305

    Article  Google Scholar 

  • Gavan KB, Westra HJR, van der Drift EWJM, Venstra WJ, van der Zant HSJ (2009) Size-dependent effective young’s modulus of silicon nitride cantilevers. Appl Phys Lett 94(23):233108

    Article  Google Scholar 

  • Godin M, Tabard-Cossa V, Miyahara Y, Monga T, Williams PJ, Beaulieu LY, Bruce LR, Grutter P (2010) Cantilever-based sensing: the origin of surface stress and optimization strategies. Nanotechnology 21(7):075501

    Article  Google Scholar 

  • Goyal S, Srinivasan K, Siegmund T, Subbarayan G (2010) On instability-induced debond initiation in thin film systems. Eng Fract Mech 77(8):1298–1313

    Article  Google Scholar 

  • Grossmann A, Erley W, Hannon JB, Ibach H (1996) Giant surface stress in heteroepitaxial films: invalidation of a classical rule in epitaxy. Phys Rev Lett 77(1):127–130

    Article  Google Scholar 

  • Guo S, Wan KT, Dillard DA (2005) A bending-to-stretching analysis of the blister test in the presence of tensile residual stress. Int J Solids Struct 42(9–10):2771–2784

    Article  Google Scholar 

  • Gurtin ME, Murdoch AI (1975) A continuum theory of elastic material surfaces. Arch Ration Mech Anal 57(4):291–323

    Article  Google Scholar 

  • Gurtin ME, Murdoch AI (1978) Surface stress in solids. Int J Solids Struct 14(6):431–440

    Article  Google Scholar 

  • He LH, Lim CW, Wu BS (2004) A continuum model for size-dependent deformation of elastic films of nano-scale thickness. Int J Solids Struct 41(3–4):847–857

    Article  Google Scholar 

  • Ibach H (1997) The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures. Surf Sci Rep 29(5):195–263

    Article  Google Scholar 

  • Jeng YR, Tan CM (2006) Investigation into the nanoindentation size effect using static atomistic simulations. Appl Phys Lett 89(89):251901

    Article  Google Scholar 

  • Kanninen MF, Popelar CA, Saunders H (1985) Advanced fracture mechanics. Oxford University Press, Oxford

    Google Scholar 

  • Kim BC, Park SW, Lee DG (2008) Fracture toughness of the nano-particle reinforced epoxy composite. Compos Struct 86(1–3):69–77

    Article  Google Scholar 

  • Kim CI, Schiavone P, Ru CQ (2010) The effects of surface elasticity on an elastic solid with mode-III crack: complete solution. J Appl Mech 77(2):293–298

    Google Scholar 

  • Koenig SP, Boddeti NG, Dunn ML, Bunch JS (2011) Ultrastrong adhesion of graphene membranes. Nat Nanotechnol 6(9):543–546

    Article  Google Scholar 

  • Lee C, Wei X, Kysar JW, Hone J (2008) Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321:385–388

    Article  Google Scholar 

  • Li X-F (2006) Effects of an elastic substrate on the interfacial adhesion of thin films. Surf Coat Technol 200(16–17):5003–5008

    Article  Google Scholar 

  • Lim CW, He LH (2004) Size-dependent nonlinear response of thin elastic films with nano-scale thickness. Int J Mech Sci 46(11):1715–1726

    Article  Google Scholar 

  • Liu H-Y, Wang G-T, Mai Y-W, Zeng Y (2011) On fracture toughness of nano-particle modified epoxy. Compos B Eng 42(8):2170–2175

    Article  Google Scholar 

  • Marshall DB, Evans AG (1984) Measurement of adherence of residually stressed thin films by indentation. I. Mechanics of interface delamination. J Appl Phys 56(10):2632–2638

    Article  Google Scholar 

  • Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(11):139–147

    Article  Google Scholar 

  • Mogilevskaya SG, Crouch SL, Stolarski HK (2008) Multiple interacting circular nano-inhomogeneities with surface/interface effects. J Mech Phys Solids 56(6):2298–2327

    Article  Google Scholar 

  • Ru CQ (2010) Simple geometrical explanation of gurtin-murdoch model of surface elasticity with clarification of its related versions. Science China 53(3):536–544

    Google Scholar 

  • Sanchez JM, El-Mansy S, Sun B, Scherban T, Fang N, Pantuso D, Ford W, Elizalde MR, Martinez-Esnaola JM, Martin-Meizoso A, Gil-Sevillano J, Fuentes M, Maiz J (1999) Cross-sectional nanoindentation: a new technique for thin film interfacial adhesion characterization. Acta Mater 47(17):4405–4413

    Article  Google Scholar 

  • Selvadurai APS (2007) On adhesion energy estimates derived from the pressurized brittle delamination of a flexible thin film. Acta Mater 55(14):4679–4687

    Article  Google Scholar 

  • Serenyi M, Frigeri C, Szekrrnyes Z (2013) On the formation of blisters in annealed hydrogenated a-Si layers. Nanoscale Res Lett 8(1):84–90

    Article  Google Scholar 

  • Serrano JR, Cahill DG (2005) Laser-induced blistering of thin \(\text{ Sio }_{2}\) on Si. Nanoscale Microscale Thermophys Eng 9(2):155–164

    Article  Google Scholar 

  • Shenoy VB (2005) Atomistic calculations of elastic properties of metallic FCC crystal surfaces. Phys Rev B 71(9):094104

    Article  Google Scholar 

  • Son D, Jeong JH, Kwon D (2003) Film-thickness considerations in microcantilever-beam test in measuring mechanical properties of metal thin film. Thin Solid Films 437(1–2):182–187

    Article  Google Scholar 

  • Sun CT, Zhang H (2003) Size-dependent elastic moduli of platelike nanomaterials. J Appl Phys 93(2):1212–1218

    Article  Google Scholar 

  • Sun J-Y, Hu J-L, He X-T, Zheng Z-L, Geng H-H (2011) A theoretical study of thin film delamination using clamped punch-loaded blister test: energy release rate and closed-form solution. J Adhes Sci Technol 25(16):2063–2080

    Article  Google Scholar 

  • Wan KT, Shu G, Dillard DA (2003) A theoretical and numerical study of a thin clamped circular film under an external load in the presence of a tensile residual stress. Thin Solid Films 425(425):150–162

    Article  Google Scholar 

  • Wang H, Li X, Tang G, Shen Z (2013) Effect of surface stress on stress intensity factors of a nanoscale crack via double cantilever beam model. J Nanosci Nanotechnol 13(1):477–482

    Article  Google Scholar 

  • Williams JG (1997) Energy release rates for the peeling of flexible membranes and the analysis of blister tests. Int J Fract 87(3):265–288

    Article  Google Scholar 

  • Wu CH (1999) The effect of surface stress on the configurational equilibrium of voids and cracks. J Mech Phys Solids 47(12):2469–2492

    Article  Google Scholar 

  • Wu J-X, Li X-F, Tang A-Y, Lee KY (2017) Free and forced transverse vibration of nanowires with surface effects. J Vib Control 23(13):2064–2077

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11672336) and the Open Foundation of State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, PRC (No. GZ1712).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, People’s Republic of China

    Y. Yang & X.-F. Li

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    K. Y. Lee & X.-F. Li

Authors
  1. Y. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Y. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X.-F. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to X.-F. Li.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Lee, K.Y. & Li, XF. Surface effects on delamination of a thin film bonded to an elastic substrate. Int J Fract 210, 81–94 (2018). https://doi.org/10.1007/s10704-018-0262-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-018-0262-2

Keywords

Search

Navigation