Interaction between an edge dislocation and a bridged crack with surface elasticity

• Published in: Archive of applied mechanics (1991) Vol. 87; no. 10; pp. 1739 - 1768
• Main Authors: Yang, Moxuan, Wang, Xu, Feng, Xi-Qiao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2017; Springer Nature B.V
• Subjects: Boundary value problems; Chebyshev approximation; Classical Mechanics; Collocation methods; Crack bridging; Crack tips; Differential equations; Edge dislocations; Elasticity; Engineering; Image force; Mathematical models; Original; Position (location); Singularities; Surface tension; Theoretical and Applied Mechanics; Tips; Crack bridging; Equilibrium position; Cauchy singular integro-differential equation; Image force; Edge dislocation; Surface elasticity
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-017-1284-3

We examine the contribution of crack bridging and surface elasticity to the elastic interaction between a finite crack and an edge dislocation. The surface effect on the crack faces is incorporated by using the continuum-based surface/interface model of Gurtin and Murdoch. The crack faces are subjected to both normal and shear bridging forces, and the bridging stiffnesses are allowed to vary arbitrarily along the crack. The residual surface tension is taken to be zero in our discussion. The Green’s function method is utilized to reduce the boundary value problem to three first-order Cauchy singular integro-differential equations, which are solved numerically by combining the Chebyshev polynomials and the collocation method. A general formula is derived for calculating the image force acting on the edge dislocation. Our analysis indicates that the stresses exhibit both the weak logarithmic and the strong square root singularities at the crack tips. We note that both crack bridging and surface elasticity influence the magnitude and direction of the image force acting on the edge dislocation. Particularly, the results show that the dislocation may have four stable and two unstable equilibrium positions due to the presence of surface elasticity. In addition, the number and location of the equilibrium positions depend on both surface elasticity and crack bridging.