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

Statistical significance of notch fatigue prognoses based on the strain-energy–density method: Application to conventionally and additively manufactured materials

“…Specifically, the notch depth of an axisymmetric V-notched specimen was designed to maximize the intensity of the notch singular stress term in order to minimize the sensitivity of the inverse search to experimental uncertainties. Recent investigations [49] about the statistical distribution of the inverse estimation of L pointed out the crucial role played by the notch radius R: the coefficient of variation (CV, standard deviation to mean ratio) of L depends, as expected, on the CV of the input quantities, viz. the plain and notch fatigue strength, and is amplified by a factor that is an increasing function of the ratio R/L.…”

“…the plain and notch fatigue strength, and is amplified by a factor that is an increasing function of the ratio R/L. As already observed in [49,50], it is clear that reliable fatigue assessments are only possible when the notch geometry used to get L or R 1 is considerably sharper than that of the notch to be calculated.…”

“…The present paper is aimed at extending the investigations done in [49] on the critical distance L to the statistical distribution of the inverse estimation of R 1 . The key concept that we want to develop here is that the amplitude ( )…”

Theory of critical distances: A discussion on concepts and applications

“…Other works investigated critical distance estimation methods. For instance, Santus et al 74,78,85 proposed a refined methodology for critical distance estimation based on the inverse search method and they provided a sensitivity analysis based on the specimen geometry. In this method, critical distance is estimated considering an, up to this point, unmentioned aspect.…”

“…By using relatively low stress gradients, small variations of the fatigue limit introduce large alterations in critical distance value whereas, in sharp notches, contained error on L bring to large error in the reference stress and, consequently, on strength assessment. Moreover correction functions are introduced in Santus et al 74,78 Then, Benedetti and Santus 85 studied the statistical properties of the thus determined critical distance.…”