Symmetric failure of the halfspace with penny-shaped cracks in compression

Abstract

The three-dimensional axisymmetric problem is investigated for a halfspace with penny-shaped crack parallel to the free surface. A uniform compression is applied parallel to the crack plane. The Griffith-Irwin theory is not applicable to this configuration of load and crack geometry since all the stress intensity factors are zero. Instead, a stability criterion will be invoked within the framework of the three-dimensional linearized stability theory. Reference can be made to previous works [5,6] involving compressible and incompressible elastic bodies. Use was made of an arbitrary form of the elastic potential for high subcritical deformations and for two variants of the theory of small subcritical deformations that involved equal and unequal roots of the characteristics equation [6]. It was found that consideration of the mutual influence of the subsurface crack and the free surface results in a considerable reduction of the theoretical strength limit. This was previously derived for infinite material with a crack. Examples of potentials with equal roots are discussed: the Bartenev-Khazanovich (incompressible bodies) and harmonic potential (compressible bodies).