Mathematical modelling of the interface crack propagation in a pre-stressed fiber reinforced elastic composite

A pre-stressed fiber reinforced elastic composite containing an interface crack in the mode three of classical fracture is considered. The boundary conditions of our problem are leading to a homogeneous and a non-homogeneous Riemann-Hilbert problem. Using the theory of Cauchy's integral and the numerical analysis we determine the incremental fields in the vicinity of the crack tips. The cases of elliptical type and parabolical type of incremental antiplane shear forces are considered. Extending the validity of Sih's criterion we obtain the critical values of the incremental stresses which are producing crack propagation and the crack propagation direction. A numerical example in the case of constant antiplane shear stress regarding the propagation of an antiplane interface crack in graphite-epoxy is considered.