TY - JOUR

T1 - Interaction of edge dislocation array with bimaterial interface incorporating interface elasticity

AU - Grekov, M

AU - Sergeeva, T. S.

PY - 2020/4

Y1 - 2020/4

N2 - We extend the analytical method developed earlier for constructing periodic Green functions in the case of a half plane with surface stress to the problem on an interaction between the dislocation array (misfit dislocations) and the interface in bimaterial at the nanoscale. We use the complete Gurtin–Murdoch surface elasticity model for the interface under plane strain conditions, incorporating the interface stress and interface tension. Based on Goursat–Kolosov's complex potentials, Muskhelishvili's representations and original superposition technique, we reduce the solution of the problem to the singular integro-differential equation in complex displacement at the interface and derive analytical formulas for the elastic field in the explicit form suitable for numerical investigations. Numerical results are obtained by neglecting residual interface stress (interface tension) in order to reveal the pure effect of interface properties due to deformation. Bearing in mind that strength and fracture of heterogeneous and crystalline materials is essentially influenced by the stress field at the interface and the dislocation mobility, we give the numerical results of analyzing the stress distribution at the interface and image forces acting on dislocations at the nanoscale depending on the dislocation-interface distance, period of the array and stiffness ratio of the bimaterial.

AB - We extend the analytical method developed earlier for constructing periodic Green functions in the case of a half plane with surface stress to the problem on an interaction between the dislocation array (misfit dislocations) and the interface in bimaterial at the nanoscale. We use the complete Gurtin–Murdoch surface elasticity model for the interface under plane strain conditions, incorporating the interface stress and interface tension. Based on Goursat–Kolosov's complex potentials, Muskhelishvili's representations and original superposition technique, we reduce the solution of the problem to the singular integro-differential equation in complex displacement at the interface and derive analytical formulas for the elastic field in the explicit form suitable for numerical investigations. Numerical results are obtained by neglecting residual interface stress (interface tension) in order to reveal the pure effect of interface properties due to deformation. Bearing in mind that strength and fracture of heterogeneous and crystalline materials is essentially influenced by the stress field at the interface and the dislocation mobility, we give the numerical results of analyzing the stress distribution at the interface and image forces acting on dislocations at the nanoscale depending on the dislocation-interface distance, period of the array and stiffness ratio of the bimaterial.

KW - Bimaterial

KW - Edge dislocation array

KW - Elastic field

KW - Image forces

KW - Interface elasticity

KW - Superposition technique

KW - FIELDS

KW - ENERGY

KW - SIZE-DEPENDENT INTERACTION

KW - NANO-INHOMOGENEITIES

KW - BEHAVIOR

KW - SURFACE ELASTICITY

KW - MECHANICS

KW - INCLUSION

KW - STRESS

KW - EMISSION

UR - http://www.scopus.com/inward/record.url?scp=85079347046&partnerID=8YFLogxK

UR - https://proxy.library.spbu.ru:3693/item.asp?id=43246703

UR - https://www.mendeley.com/catalogue/649405ed-e479-35d1-b70f-0ab5ca6dcf1c/

U2 - 10.1016/j.ijengsci.2020.103233

DO - 10.1016/j.ijengsci.2020.103233

M3 - Article

AN - SCOPUS:85079347046

VL - 149

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

M1 - 103233

ER -