A multilayer film coating with slightly curved boundary

Research output

19 Citations (Scopus)

Abstract

Surface irregularity is often a source of stress concentrations. They can be reduced by proper matching of dissimilar surface layers. In this connection, a 2-D model of an isotropic multilayer film-substrate composite with rough surface is considered, in order to examine an influence of physical and geometrical properties of the components on the stress state of a boundary. Using the complex variable representations and boundary perturbation technique, the problem is reduced to the set of Fredholm integral equations of the second kind for an arbitrary shape of the boundary. The solution is given in terms of Fourier series for the periodic shape. In the case of a bilayer film coating, numerical results obtained with the use of the first-order approximation demonstrate effects of the boundary shape, thickness and elastic properties of the layers and the substrate on the stress state of a rough surface.
Original languageEnglish
Pages (from-to)61-74
JournalInternational Journal of Engineering Science
Volume89
DOIs
Publication statusPublished - 2015

Fingerprint

Curved Boundary
Multilayer films
Coating
Multilayer
Coatings
Rough Surface
Substrate
Perturbation techniques
Stress Concentration
Perturbation Technique
Fourier series
Elastic Properties
Complex Variables
Fredholm Integral Equation
Irregularity
Substrates
Integral equations
Stress concentration
Composite
First-order

Scopus subject areas

  • Mathematics(all)

Cite this

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title = "A multilayer film coating with slightly curved boundary",
abstract = "Surface irregularity is often a source of stress concentrations. They can be reduced by proper matching of dissimilar surface layers. In this connection, a 2-D model of an isotropic multilayer film-substrate composite with rough surface is considered, in order to examine an influence of physical and geometrical properties of the components on the stress state of a boundary. Using the complex variable representations and boundary perturbation technique, the problem is reduced to the set of Fredholm integral equations of the second kind for an arbitrary shape of the boundary. The solution is given in terms of Fourier series for the periodic shape. In the case of a bilayer film coating, numerical results obtained with the use of the first-order approximation demonstrate effects of the boundary shape, thickness and elastic properties of the layers and the substrate on the stress state of a rough surface.",
keywords = "Multilayer film coating, Rough surface, Stress concentration",
author = "M.A. Grekov and S.A. Kostyrko",
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journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier",

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T1 - A multilayer film coating with slightly curved boundary

AU - Grekov, M.A.

AU - Kostyrko, S.A.

PY - 2015

Y1 - 2015

N2 - Surface irregularity is often a source of stress concentrations. They can be reduced by proper matching of dissimilar surface layers. In this connection, a 2-D model of an isotropic multilayer film-substrate composite with rough surface is considered, in order to examine an influence of physical and geometrical properties of the components on the stress state of a boundary. Using the complex variable representations and boundary perturbation technique, the problem is reduced to the set of Fredholm integral equations of the second kind for an arbitrary shape of the boundary. The solution is given in terms of Fourier series for the periodic shape. In the case of a bilayer film coating, numerical results obtained with the use of the first-order approximation demonstrate effects of the boundary shape, thickness and elastic properties of the layers and the substrate on the stress state of a rough surface.

AB - Surface irregularity is often a source of stress concentrations. They can be reduced by proper matching of dissimilar surface layers. In this connection, a 2-D model of an isotropic multilayer film-substrate composite with rough surface is considered, in order to examine an influence of physical and geometrical properties of the components on the stress state of a boundary. Using the complex variable representations and boundary perturbation technique, the problem is reduced to the set of Fredholm integral equations of the second kind for an arbitrary shape of the boundary. The solution is given in terms of Fourier series for the periodic shape. In the case of a bilayer film coating, numerical results obtained with the use of the first-order approximation demonstrate effects of the boundary shape, thickness and elastic properties of the layers and the substrate on the stress state of a rough surface.

KW - Multilayer film coating

KW - Rough surface

KW - Stress concentration

U2 - 10.1016/j.ijengsci.2014.12.001

DO - 10.1016/j.ijengsci.2014.12.001

M3 - Article

VL - 89

SP - 61

EP - 74

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

ER -