Deformation of two welded half-spaces due to inclined shear and tensile point dislocations and a centre of dilation

Abstract

Closed-form analytical expressions are obtained for the displacements caused by an inclined shear or tensile point dislocation located in an elastic half-space which is in welded contact with another elastic half-space along a plane interface. These expressions are valid for arbitrary values of the Poisson's ratios of the two media and for arbitrary observer locations. The derivation is straightforward and uses the body force equivalence of the shear and tensile point dislocations and the Rongved [1995. Force interior to one of two joined semi-infinite solids. In: Bogdanoff, J.L. (Ed.), Proceedings of the 2nd Midwestern Conference on Solid Mechanics, Purdue University, Indiana, Res. Ser. 129, pp. 1-13] solution for a point force in terms of the Papkovich-Neuber displacement potentials. The solution for an arbitrary point displacement dislocation can be expressed as a linear combination of the solutions for six fundamental point sources, viz. vertical strike-slip, horizontal strike-slip, vertical dip-slip, 45° dip-slip, centre of dilation and horizontal dipole without moment. While the solutions for a vertical strike-slip, a vertical dip-slip and a horizontal dipole were presented in an earlier paper ([Kumari, G., Singh, S.J., Singh, K., 1992. Phys. Earth Planet. Int. 73, 53-76] referred to as Paper I), the solutions for the remaining three sources are given in the present paper. An error in the results for a horizontal dipole in Paper I is also corrected.