Estimating the probabilities of triggering brittle fracture associated with the defects in the materials

A method for determining the probabilities of initiating fracture, associated with the defects in the materials, is proposed. Using the observed failure frequency distributions over the existing groups of defects, the individual probabilities of triggering fracture associated with the defects are obtained. The new theory proposed also allows the description of the influence of specimen size on probability of fracture. The concept ‘detrimental factor’ characterising the groups of defects is introduced and a method for determining the most deleterious group of defects is proposed. It is also demonstrated that the existing models pertinent to probability of fracture and the Weibull distribution function are special cases of the proposed new theory. Only in these special cases are the existing statistical models suitable to calculate the probability of brittle fracture. It has been demonstrated that in the general case, particularly if the number density of the defects is relatively small and the ratio of the stressed volume to the calibration volume is relatively large, only the new theory should be applied.