Mode-I pressurized axisymmetric penny-shaped crack in graded interfacial zone with variable modulus and Poisson's ratio

This paper presents an analytical treatment to the fracture problem of a Mode-I pressurized penny-shaped crack in a graded interfacial zone or FGMs interlayer with variable shear modulus and Poisson's ratio. An efficient multilayered model is proposed to address the general form of material inhomogeneity. The mixed boundary value problem is reduced to a Fredhom integral equation of the second kind. The solution procedure is also extended to address the Leonov-Panasyuk-Dugdale plastic crack. Analytical solutions in explicit form are derived for the full stress fields at the crack plane, Mode-I stress intensity factor (SIF), crack opening displacement (COD), T-Stress and plastic zone in terms of the solution of the integral equations. Numerical results of SIF, elastic stress fields, COD, T-Stress and length of plastic zone are presented to quantitively explore the effects of material inhomogeneity on the fracture response. It is demonstrated that the graded Poisson's ratio has non-negligible influences on COD and T-Stress under certain condition. The present solutions can be used to advanced fracture analysis of pressurized crack in engineering composite material.