  We consider an infinite bi-material plane containing a semi-infinite crack
situated on a soft imperfect interface. The crack is loaded by a general
asymmetrical system of forces distributed along the crack faces. On the basis
of the weight function approach and the fundamental reciprocal identity, we
derive the corresponding boundary integral formulation, relating physical
quantities. The boundary integral equations derived in this paper in the
imperfect interface setting show a weak singularity, in contrast to the perfect
interface case, where the kernel is of the Cauchy type. We further present
three alternative variants of the boundary integral equations which offer
computationally favourable alternatives for certain sets of parameters.
