Skip to main content
SpringerLink
Log in

Stress analysis of a substrate coated by nanomaterials with vacancies subjected to uniform extension load

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this study, a stress analysis of a substrate coated by nanomaterials with a vacancy under uniform extension load is investigated. The behavior of the coated substrate is modeled with the behavior of a two-layered beam, in which one of the layers is elastic and described by the continuous medium and the second layer consists of a nanomaterial with damage of a vacancy. The extension of the coating is carried out by stretching of the first layer, which lies on the substrate and by the cohesive forces between the layers. It is assumed that vacancies do not vary along the width of the substrate. The constitutive equations of the first layer (i.e., an elastic substrate) are given in the framework of Hooke’s law and the constitutive equations of the second layer; that is, the coating is carried out by taking into account discreteness of the nanomaterial with a vacancy. The expressions for the determination of the contact pressure and stresses of the substrate with a nanocoating that have vacancies are obtained. In addition, damage conditions for the substrate and nanocoating are determined. Finally, carrying out some computations, effects of the characteristics of a nanocoating with and without vacancies on the values of contact pressure and stresses of the coated substrate have been studied.

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

Similar content being viewed by others

References

  1. Gleiter H.: Nanocrystalline solids. J. Appl. Crystallogr. 24, 79–90 (1991)

    Article  Google Scholar 

  2. Subramanian C., Strafford K.N.: Review of multicomponent and multilayer coatings for tribological applications. Wear 165, 85–95 (1993)

    Article  Google Scholar 

  3. Luo J.F., Liu Y.J., Berger E.J.: Interfacial stress analysis for multicoating systems using an advanced boundary element method. Comput. Mech. 24, 448–455 (2000)

    Article  MATH  Google Scholar 

  4. Dahotre N.B., Nayak S.: Nanocoatings for engine application. Surf. Coating. Tech. 194, 58–67 (2005)

    Article  Google Scholar 

  5. Rogers J.A., Bao Z.: Printed plastic electronics and paperlike displays. Polym. Sci. Part A Polym. Chem. 40, 3327–3334 (2002)

    Article  Google Scholar 

  6. Park S., Jayaraman S.: Smart textiles: wearable electronic systems. MRS Bull. 28, 585–591 (2003)

    Article  Google Scholar 

  7. Lewis J.: Material challenge for flexible organic devices. Mater. Today 9, 38–45 (2006)

    Article  Google Scholar 

  8. Lu N.S., Wang X., Suo Z., Vlassak J.: Metal films on polymer substrates stretched beyond 50 %. Appl. Phys. Lett. 91, 221909 (2007)

    Article  Google Scholar 

  9. Krivtsov A.M., Morozov N.F.: On mechanical characteristics of nanocrystals. Phys. Solid State 44, 2260–2265 (2002)

    Article  Google Scholar 

  10. Goldstein R.V., Morozov N.F.: Mechanics of deformation and fracture of nanomaterials and nanotechnology. Phys. Mesomech. 10, 235–246 (2007)

    Article  Google Scholar 

  11. Meyers M.A., Mishra A., Benson D.J.: Mechanical properties of nanocrystalline materials. Prog. Mater. Sci. 51, 427–556 (2006)

    Article  Google Scholar 

  12. Chen T., Dvorak G.J., Yu C.C.: Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mech. 188, 39–54 (2007)

    Article  MATH  Google Scholar 

  13. Loboda O., Krivtsov A.M.: Determination of mechanical properties of nanostructures with complex crystal lattice using moment interaction at microscale. Rev. Adv. Mater. Sci. 20, 143–147 (2009)

    Google Scholar 

  14. Kadkhodapour J., Ziaei-Rad S., Karimzadeh F.: Finite-element modeling of rate dependent mechanical properties in nano-crystalline materials. Comput. Mater. Sci. 45, 1113–1124 (2009)

    Article  Google Scholar 

  15. Pallab B., Weng G.J.: Mechanics of a nanocrystalline coating and grain-size dependence of its plastic strength. Mech. Mater. 43, 496–504 (2011)

    Article  Google Scholar 

  16. Wolf D., Yamakov V., Philpot S.R., Mukherjee A., Gleiter H.: Deformation of nanocrystalline materials by molecular-dynamics simulation: relationship to experiments?. Acta Mater. 53, 1–40 (2005)

    Article  Google Scholar 

  17. Bialas M.: Finite element analysis of stress distribution in thermal barrier coatings. Surf. Coating Tech. 202, 6002–6010 (2008)

    Article  Google Scholar 

  18. Wernik J.M., Meguid S.A.: Atomistic-based continuum modeling of the nonlinear behavior of carbon nanotubes. Acta Mech. 212, 167–179 (2010)

    Article  MATH  Google Scholar 

  19. Zhang Y.M., Gu Y., Chen J.T.: Stress analysis for multilayered coating systems using semi-analytical BEM with geometric non-linearities. Comput. Mech. 47, 493–504 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. Pallab B., Weng G.J.: A micro-continuum model for the creep behavior of complex nanocrystalline materials. Int. J. Eng. Sci. 49, 155–174 (2011)

    Article  Google Scholar 

  21. Chai H., Josell D.: Fracture behavior of nano-layered coatings under tension. Thin Solid Films 519, 331–336 (2010)

    Article  Google Scholar 

  22. Miller D.C., Foster R.R., Zhang Y., Jen S.-H., Bertrand J.A., Lu Z., Seghete D., O’Patchen J.L., Yang R., Lee Y.-C., George S.M., Dunn M.L.: The mechanical robustness of atomic-layer- and molecular-layer-deposited coatings on polymer substrates. J. Appl. Phys. 105, 093527 (2009)

    Article  Google Scholar 

  23. Zhu X.F., Zhang B., Gao J., Zhang G.P.: Evaluation of the crack-initiation strain of a Cu–Ni multilayer on a flexible substrate. Scripta Materialia 60, 178–181 (2009)

    Article  Google Scholar 

  24. Civalek O., Demir C.: Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory. Appl. Math. Model. 35, 2053–2067 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Guisbiers G.: Schottky defects in nanoparticles. J. Phys. Chem. C 115, 2616–2621 (2011)

    Article  Google Scholar 

  26. Panin S.V.: Plastic deformation and fracture caused by coating-substrate mismatch at mesoscale. Theor. Appl. Fract. Mech. 35, 1–8 (2001)

    Article  Google Scholar 

  27. Karakasidis T.E., Charitidis C.A.: Vacancy effect on the elastic constants of layer-structured nanomaterials. Theor. Appl. Fract. Mech. 51, 195–201 (2009)

    Article  Google Scholar 

  28. Alizada A.N., Sofiyev AH.: Modified Young’s moduli of nanomaterials taking into account the scale effects and vacancies. Meccanica 46, 915–920 (2011)

    Article  MathSciNet  Google Scholar 

  29. Xie S.F., Chen S.D., Soh A.K.: The effect of atomic vacancies and grain boundaries on mechanical properties of gan nanowires. Chin. Phys. Lett. 28, 066201 (2011)

    Article  Google Scholar 

  30. Alizada A.N., Sofiyev A.H.: On the mechanics of deformation and stability of the beam with a nanocoating. J. Reinforced Plastics Compos. 30, 1583–1595 (2011)

    Article  Google Scholar 

  31. Wang C.M., Reddy J.N., Lee K.H.: Shear Deformable Beams and Plates. Elsevier, UK (2000)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mechanics, Azerbaijan State Marine Academy, Baku, Azerbaijan

    A. N. Alizada

  2. Department of Civil Engineering, Suleyman Demirel University, 32260, Isparta, Turkey

    A. H. Sofiyev

  3. Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Bahcesehir University, Istanbul, Turkey

    N. Kuruoglu

Authors
  1. A. N. Alizada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. H. Sofiyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Kuruoglu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. H. Sofiyev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alizada, A.N., Sofiyev, A.H. & Kuruoglu, N. Stress analysis of a substrate coated by nanomaterials with vacancies subjected to uniform extension load. Acta Mech 223, 1371–1383 (2012). https://doi.org/10.1007/s00707-012-0649-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-012-0649-5

Keywords

Search

Navigation