A model is proposed that enables the direct use of apparent fracture toughness values, KQ, as measured from fracture specimens with dimensions too small to produce a valid measure of KIc. The approach is not intended to predict KIc from KQ values measured on subsize specimen as has been previously attempted by others, but rather to use KQ values directly for applications in which the geometry dictates that the use of KIc would be in appropriate. The predicted value is within 30 percent of the measured values which compares to a previous prediction that is six times too high.
An earlier investigation [1] examined the effect of crack length on the apparent fracture toughness of Indiana limestone. Fracture toughness, Kic , has been used extensively in modeling fracture in brittle metals while the effective surface energy, Yeff, is more common for rock fracture [2,3,4,5,6]. Several attempts have been made to predict tensile strengths from effective surface energy with assumptions as to the natural flaw geometry [2,3]. Typically one assumes that the most severe flaw is a "penny-shaped" flaw oriented perpendicular to the stress axis. This provides a prediction of tensile strength that is usually four to ten times higher than the measured value (e.g., six times higher for Indiana limestone as calculated by Hoagland et al.. [3]). A likely explanation of this discrepancy was proposed by Hoagland et al..[3] which likened the zone of micro cracking that is observed to form at a crack tip in a rock to the plastic zone that forms at the tip of a crack in a metal. This implies that a linear elastic parameter such as KIc or Yeff may not apply when the zone of inelastic behavior (plasticity or micro-cracking) is not small when compared to the crack length.
