Surface flaw distributions in brittle materials and Hertzian fracture

Abstract

Refined mode I and mode II stress intensity factors for short cracks perpendicular to a free surface driven by a Hertzian indenter have been calculated for the case where the sphere and substrate are made of the same material. Computer simulations of Hertzian indentation tests for a variety of random surface flaw distributions show that the ring crack is expected to form outside the contact radius in all cases and that for spheres of small radii, the fracture load is expected to be proportional to the sphere radius (Auerbach's law). Reconstruction of the surface flaw distribution using the “searched area” concept is described. A useful analytical approximation for the stress intensity factors is also presented.