Slip and edge effect in complete contacts - Qiu, H; Qiu, Hui (2008)
﻿ The general problem of an anticrack, present in a simple domain and subject to general remote loading is solved using distributed line forces, acting as strain nuclei, along the line of the anticrack. Subsequently, both dislocations and point forces are used as strain nuclei to achieve mixed boundary value conditions. The influence function for a pair of forces applied to the faces of a semi-infinite notch is found and finally this is used to find the true closure length and interfacial contact pressure. When a sharp-edged indenter is pressed into a half plane material in the half-plane is displaced and 'laps around' the edges of the punch, possibly making contact with the side faces. This phenomenon is quantified within (coupled) half-plane theory, and applied first to an idealised indenter having the cross section of a trapezium, and then to a semi-infinite indenter. The latter allows an asymptotic form to be found which, through a generalised stress intensity factor may be collocated into the edge of any notionally sharp-edged indentation problem. The effect of surface strains on the local slip angle, when an infinite cylinder is slid skew-wise across an elastically similar half-plane is found. It is shown that local frictional orthogonality is not completely consistent with global orthogonality. The problems of a square-ended and an almost square-ended rigid punch sliding with both plane and anti-plane velocity components are studied. It is shown that, for a truly complete contact, if the contacting body is incompressible, convection effects are absent. Introducing either: (a) local rounding or (b) finite compressibility of the contacting body into the problem introduces convection, giving rise to an inconsistency between the global and local requirement of the orthogonal friction law. The state of stress in a three-quarter-plane undergoing antiplane shear deformation is studied, due to the presence of a screw dislocation along one of the projection lines extending from the free surfaces. A simple, accurate formula for the state of stress along the line is found, providing a useful kernel for the solution of crack and contact edge slip problems. The state of stress induced in an axi-symmetric solid formed from a half-space and a bonded semi-infinite rod, by a family of ring dislocations of arbitrary Burgers vector is found. Particular care is given to the interaction between the Cauchy singularity near the dislocation core and the geometric singularity at the rod/half-space junction. Torsional contact between a semi-infinite elastic rod with square ends and an elastically similar half-space was then solved using the ring dislocations as influence functions. This provides an excellent illustration of the imposition of orthogonality condition for a complete contact.