Batdorf and Crose (1) combined the statistical analysis of failure for brittle materials by Weibull (2) with an appropriate fracture criterion based on fracture mechanics theory and extended this notion to multiaxial stress states. If an appropriate form of crack distribution is chosen, the cumulative failure probability function proposed by Batdorf and Crose (1) reduces to the Weibull distribution for uniaxial tensile stress states. In this work, we will show that the approximation of an infinitesimally small volumetric element may have been prematurely employed by Batdorf and Crose (1) in obtaining failure probability for an arbitrary volumetric element $ΔV$. The widely used failure probability formula based on this approximation may present some errors under certain conditions. We will derive an alternative formula without the use of this unnecessary approximation.

Batdorf and Crose (1) introduced the solid angle...