Semi-analytical solution for mode I penny-shaped crack in a soft inhomogeneous layer

An axisymmetric elastostatics problem for a penny-shaped crack placed in the middle of a inhomogeneous (FGM) elastic layer is considered. It is assumed that the elastic modulus of the layer varies through the thickness symmetrically with respect to the crack plane. Several specific distributions of the moduli variations have been analysed. We report a semi-analytical approximate solution for the determination of the stress intensity factor for the distributions considered. The obtained solution is accurate enough and can be applied in engineering applications for the analysis of crack propagation in FGM and hydrofracture growth in elastic reservoirs.