TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=85065447056&partnerID=8YFLogxK

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

UR - http://www.mendeley.com/research/stress-concentration-analysis-nanosized-thinfilm-coating-rough-interface

UR - https://proxy.library.spbu.ru:3693/item.asp?id=41793483

U2 - 10.1007/s00161-019-00780-4

DO - 10.1007/s00161-019-00780-4

M3 - Article

AN - SCOPUS:85065447056

VL - 31

SP - 1863

EP - 1871

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 6

ER -