Initiation and propagation of a penny-shaped crack in a finitely deformed incompressible elastic medium

The effects that the initial lateral stress has on the initiation and the propagation of a penny-shaped crack are investigated on the basis of the theory of small deformations superposed on finite deformation for an incompressible elastic material. Using the methods of the Laplace and Hankel transforms, the crack shape function and the stress distribution with singularities in the crack plane are obtained in closed forms for the crack propagating at a constant speed in the Mooney material. The dynamic stress-intensity factor is obtained as a function of the initial lateral stretch and the ratio of the crack speed to the shear wave speed. For the same crack speed, the value of the dynamic stress-intensity factor increases with increasing lateral stretch, but decreases if the lateral compression increases.The dynamic solutions reduce to the associated static solutions at zero crack speed. For the stationary crack, the stress-intensity factor is shown to be independent of the initial stress. However, the initial lateral stretch increases, but the lateral compression decreases the value of the critical stress required for the initiation of crack growth on the basis of the Griffith theory. The central crack opening displacement is shown to decrease if the lateral stretch increases or the lateral compression decreases.