Probability of Hertzian fracture
Abstract
The indentation strength of brittle solids is traditionally characterized by Auerbach's law, which predicts a linear relationship between the load required to initiate a Hertzian cone crack and the radius of a spherical indentor. This paper reviews both the energy balance and flaw statistical explanations of Auerbach's law. It is shown that Auerbach's law in the strictest sense only applies to wellabraded specimens. A novel application of Weibull statistics is presented which allows the distribution of fracture loads to be predicted for any specimen surface condition for a given indentor size. The indentation strength of a brittle solid, for both spherical and cylindrical indentors, is shown to be influenced by both its surface flaw statistics and the degree of interfacial friction. It is observed that the indentation strength of sodalime glass is increased by a factor of about three times that expected for frictionless contact, and that for a fully bonded indentor, conical fractures cannot occur.
 Publication:

Journal of Materials Science
 Pub Date:
 April 1994
 DOI:
 10.1007/BF01154702
 Bibcode:
 1994JMatS..29.2216F
 Keywords:

 Cracks;
 Fractures (Materials);
 Fracturing;
 Indentation;
 Surface Defects;
 Weibull Density Functions;
 Brittleness;
 Friction;
 Glass;
 Interfacial Tension;
 Tensile Stress;
 Structural Mechanics