Shear loaded interface crack under the influence of friction: A finite difference solution

Formulation of the elastic two-dimensional problem of contact with friction is presented. Two-dimensional equilibrium equations and boundary conditions in an orthogonal curvilinear co-ordinate system are written explicitly. The above formulation is solved with the aid of the finite difference technique. An iterative algorithm which does not require load increments is employed for solving interface fracture problems with contact and friction subjected to a monotonically increasing load. The J-integral is extended for problems in which there is friction along the crack faces. Stress intensity factors are calculated by means of the J-integral, as well as an asymptotic expansion of the tangential shift. Two problems are analysed: (1) a crack in homogeneous material in the presence of friction involving stationary contact; and (2) an interface crack in the presence of friction involving receding contact. Results are compared to those found by analytical and semi-analytical methods which are presented in the literature, as well as to those obtained by means of the finite element method. The accuracy of the results establishes the reliability of the finite difference analysis, as well as the post-processors. In addition, a problem involving stick conditions is considered. It is observed that with increasing friction, the normal gaps and tangential shifts decrease. The size of the contact zone increases and values of the stress intensity factor decrease.