AN INTERFACE CRACK BETWEEN ELASTIC-MATERIALS WHEN THERE IS DRY FRICTION

An analytic solution of the plane problem of a crack (finite or semi-i nfinite) along the interface between two elastic half-planes is given. Under tensile and shear forces, the crack opens over an interval (unk nown in advance). In the vicinity of the crack tips the edges join smo othly and Coulomb's law of dry friction applies. The materials are per fectly bonded everywhere except along the crack. A closed exact soluti on is found in the case of a semi-infinite crack. The slip direction, the slip zone length, and formulae for the contact stress and displace ment jumps are determined. The problem of a finite crack is reduced to the vector (third-order) Riemann problem in the theory of analytic fu nctions, for which an effective solution is constructed by the method proposed in [1]. An explicit relationship between the smaller and larg er slip zone lengths is found by asymptotic analysis. A numerical anal ysis is carried out. Situations are determined in which the coefficien t of friction has practically no effect on the length of the slip zone (to within 5%) and when the effect is substantial (20% or more). An e ffective analytic solution is found for Comninou's equation [2], which corresponds to the problem of an interface crack ignoring the frictio n between its edges.