A crack on a cycloid rough bimaterial interface

Abstract

We conduct an analytical study of a finite mode III Griffith or Zener-Stroh crack lying on a cycloid rough interface between an elastic body and a rigid substrate. Closed-form expressions of the analytic function characterizing the stress and displacement fields are derived via the solution of a Riemann-Hilbert problem with discontinuous coefficients. Stress distributions are obtained in both Cartesian and curvilinear coordinate systems. In general, the stresses exhibit a square root singularity at the two interface crack tips and at all cusp tips. Cusps located on the interface crack surface behave as cracks while those outside the interface crack act as anticracks or rigid line inclusions. The stress intensity factors scaling the square root singularity in the stresses are extracted from the full-field solutions. When one crack tip is lodged only at a cusp tip, the stronger r−3/4 and the weaker r−1/4 power-type singularities at this crack-cusp tip are observed and the stress intensity factors scaling these power-type singularities are derived.