Exact implementation of subcritical crack growth into a Weibullian strength distribution under constant stress rate conditions

The strength of brittle materials showing the phenomena of the so-called slow or subcritical crack growth (SCG) is derived analytically for constant stress rate conditions. The approach is based on a Paris-law type relationship (i.e. power law) which describes the growth rate of pre-existing cracks (i.e. crack-like flaws) in terms of the stress intensity factor. The tensile strength of a given specimen is defined as the tensile stress, when the stress intensity factor reaches the fracture toughness (Griffith-criterion). In this paper a closed-form solution of the apparent strength with respect to the inert strength, the stress rate, etc., is presented. Based on that expression the change of a Weibullian inert strength distribution will be derived analytically with respect to the stress rate. By using dimensionless parameters the minimum amount of independent variables has been extracted.