TY - JOUR

T1 - Surface–dislocation interaction by various models of surface elasticity

AU - Grekov M.A., null

PY - 2024/2/1

Y1 - 2024/2/1

N2 - The effect of applying different surface elasticity models related to the Gurtin–Murdoch and Steigmann–Ogden theories to the problem on an interaction of a dislocation row with a flat surface of a semi-infinite three-dimensional body is analyzed in the paper. The boundaryconditions in the case of an arbitrary shape of a cylindrical surface under the plane strain are derived within the framework of the Steigmann–Ogden model involving all simplified versions of the Gurtin–Murdoch model and the Gurtin–Murdoch model itself. The boundary condition used in the paper for the flat surface is a particular case of the general one. The analytical solution of the corresponding boundary value problem is obtained in the paper in a closed formfor the elastic field. Based on this solution, some numerical examples of the stress distribution at the surface and the image force acting on each dislocation are presented. It is shown that incorporating the bending resistance of the surface in the Steigmann–Ogden model leads to thedecrease of some stresses and increase the other ones at the surface and to the decrease of the image force, as compared with those obtained by the Gurtin–Murdoch membrane theory of the surface.

AB - The effect of applying different surface elasticity models related to the Gurtin–Murdoch and Steigmann–Ogden theories to the problem on an interaction of a dislocation row with a flat surface of a semi-infinite three-dimensional body is analyzed in the paper. The boundaryconditions in the case of an arbitrary shape of a cylindrical surface under the plane strain are derived within the framework of the Steigmann–Ogden model involving all simplified versions of the Gurtin–Murdoch model and the Gurtin–Murdoch model itself. The boundary condition used in the paper for the flat surface is a particular case of the general one. The analytical solution of the corresponding boundary value problem is obtained in the paper in a closed formfor the elastic field. Based on this solution, some numerical examples of the stress distribution at the surface and the image force acting on each dislocation are presented. It is shown that incorporating the bending resistance of the surface in the Steigmann–Ogden model leads to thedecrease of some stresses and increase the other ones at the surface and to the decrease of the image force, as compared with those obtained by the Gurtin–Murdoch membrane theory of the surface.

KW - Edge dislocations; Steigmann--Ogden model; Surface elasticity models; Stress field; Image force

UR - https://www.mendeley.com/catalogue/41d365b9-7b6f-34cc-a8fb-99a620f34e64/

U2 - 10.1016/j.ijengsci.2023.103989

DO - 10.1016/j.ijengsci.2023.103989

M3 - Article

VL - 195

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

M1 - 103989

ER -