Stress concentration analysis of nanosized thin-film coating with rough interface

Research output

2 Citations (Scopus)

Abstract

The boundary perturbation method combined with the superposition principle is used to calculate the stress concentration along the arbitrary curved interface of an isotropic thin film coherently bonded to a substrate. In the case of plane strain conditions, the boundary value problem is formulated for a four-phase system involving two-dimensional constitutive equations for bulk materials and one-dimensional equations of Gurtin–Murdoch model for surface and interface. Static boundary conditions are formulated in the form of generalized Young–Laplace equations. Kinematic boundary conditions describe the continuous of displacements across the surface and interphase regions. Using Goursat–Kolosov complex potentials, the system of boundary equations is reduced to a system of the integral equations via first-order boundary perturbation method. Finally, the solution of boundary value problem is obtained in terms of Fourier series. The numerical analysis is then carried out using the practically important properties of ultra-thin-film materials.

Original languageEnglish
Pages (from-to)1863-1871
Number of pages9
JournalContinuum Mechanics and Thermodynamics
Volume31
Issue number6
Early online date3 May 2019
DOIs
Publication statusPublished - 1 Nov 2019

Fingerprint

stress concentration
Boundary value problems
Stress concentration
Boundary conditions
coatings
boundary value problems
Thin films
Coatings
Ultrathin films
Fourier series
thin films
Constitutive equations
boundary conditions
Integral equations
Numerical analysis
perturbation
Kinematics
binary systems (materials)
plane strain
constitutive equations

Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)

Cite this

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title = "Stress concentration analysis of nanosized thin-film coating with rough interface",
abstract = "The boundary perturbation method combined with the superposition principle is used to calculate the stress concentration along the arbitrary curved interface of an isotropic thin film coherently bonded to a substrate. In the case of plane strain conditions, the boundary value problem is formulated for a four-phase system involving two-dimensional constitutive equations for bulk materials and one-dimensional equations of Gurtin–Murdoch model for surface and interface. Static boundary conditions are formulated in the form of generalized Young–Laplace equations. Kinematic boundary conditions describe the continuous of displacements across the surface and interphase regions. Using Goursat–Kolosov complex potentials, the system of boundary equations is reduced to a system of the integral equations via first-order boundary perturbation method. Finally, the solution of boundary value problem is obtained in terms of Fourier series. The numerical analysis is then carried out using the practically important properties of ultra-thin-film materials.",
keywords = "Boundary perturbation method, Interface roughness, Stress concentration, Thin film",
author = "Sergey Kostyrko and Mikhail Grekov and Holm Altenbach",
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T1 - Stress concentration analysis of nanosized thin-film coating with rough interface

AU - Kostyrko, Sergey

AU - Grekov, Mikhail

AU - Altenbach, Holm

PY - 2019/11/1

Y1 - 2019/11/1

N2 - The boundary perturbation method combined with the superposition principle is used to calculate the stress concentration along the arbitrary curved interface of an isotropic thin film coherently bonded to a substrate. In the case of plane strain conditions, the boundary value problem is formulated for a four-phase system involving two-dimensional constitutive equations for bulk materials and one-dimensional equations of Gurtin–Murdoch model for surface and interface. Static boundary conditions are formulated in the form of generalized Young–Laplace equations. Kinematic boundary conditions describe the continuous of displacements across the surface and interphase regions. Using Goursat–Kolosov complex potentials, the system of boundary equations is reduced to a system of the integral equations via first-order boundary perturbation method. Finally, the solution of boundary value problem is obtained in terms of Fourier series. The numerical analysis is then carried out using the practically important properties of ultra-thin-film materials.

AB - The boundary perturbation method combined with the superposition principle is used to calculate the stress concentration along the arbitrary curved interface of an isotropic thin film coherently bonded to a substrate. In the case of plane strain conditions, the boundary value problem is formulated for a four-phase system involving two-dimensional constitutive equations for bulk materials and one-dimensional equations of Gurtin–Murdoch model for surface and interface. Static boundary conditions are formulated in the form of generalized Young–Laplace equations. Kinematic boundary conditions describe the continuous of displacements across the surface and interphase regions. Using Goursat–Kolosov complex potentials, the system of boundary equations is reduced to a system of the integral equations via first-order boundary perturbation method. Finally, the solution of boundary value problem is obtained in terms of Fourier series. The numerical analysis is then carried out using the practically important properties of ultra-thin-film materials.

KW - Boundary perturbation method

KW - Interface roughness

KW - Stress concentration

KW - Thin film

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UR - https://doi.org/10.1007/s00161-019-00780-4

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