Interaction of edge dislocation array with bimaterial interface incorporating interface elasticity. (April 2020) - Grekov, M.A.; Sergeeva, T.S.
Highlights: Misfit dislocation array parallel to a bimaterial interface is considered. Gurtin–Murdoch surface elasticity model and complex variables are used. Explicit formulas for stresses are derived allowing for interface tension. Interaction of dislocations with the interface is studied at the nanoscale. Effect of interface elasticity on stress field and image forces is revealed. Abstract: 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.