The Hertz indentation test and Auerbach's law

Abstract

Hertz indentation tests commonly yield fracture loads approximately proportional to the radius of the indenter. Two quite different explanations of this so-called 'Auerbach law' have been given: one depending primarily on the presence of flaws with a wide range of sizes, and the other on the details of the varying stress field close to the indentor. A computer simulation shows that it is quite likely that the surfaces with different distributions of flaws may exhibit mean fracture loads roughly proportional to the radius of the indenter, but that in this case the individual measurements of the fracture load will show considerable scatter about the mean. As some specimens obey Auerbach's law well with a relatively small scatter on the load, it seems that for these specimens one must take account of the considerable stress gradients in the stress field near the indenter as discussed by Frank and Lawn (1967).