Statistical properties of threshold and notch derived estimations of the critical distance according to the line method of the theory of critical distances

The theory of critical distances is based on the definition of a material-dependent length L. Here, we investigate the statistical properties of L deduced from the crack threshold or a suitable notched specimen geometry. Monte Carlo simulations are done for best-fitting analytical functions to express mean, standard deviation and skewness of L. Standard-deviation-to-mean ratio is the lowest for the threshold-derived L estimation and decreases with notch sharpness. The minimum notch severity to achieve the desired accuracy in L estimation is identified. The impact of these statistical properties on the prediction of independent notched and cracked configurations is evaluated.