Issue 35

S. Blasón et alii, Frattura ed Integrità Strutturale, 35 (2016) 187-195; DOI: 10.3221/IGF-ESIS.35.22 194 Figure 9: Fitting of function Z(a*). d- Derivation of the S-N field Finally, the S-N field in propagation can be derived from former information using Expr. (7). Fig. 10 shows the S-N field in which both axes representing non-dimensional variables. The information gained from both models, that is that representing the probabilistic S-N field and that related to the crack growth rate curve as proposed here, provide a basis for the probabilistic interpretation to the Kitagawa-Takahashi diagram [10]. First, it seems possible to assign crack sizes to iso-probabilistic curves in the S-N field, making use of the El Haddad equation, and second, the asymptotic character of the S-N field allow a true endurance limit to be defined, thus extending the concept and application of the Kitagawa-Takahashi diagram for finite number of cycles (limited propagating cracks) and infinite number of cycles (non-propagating cracks) according to the asymptotic value of the fatigue limit for N→ ∞. Finally, the study of variability of the crack growth rate curve is facilitated by the normalizing concept that includes the consideration of the threshold stress intensity factor ΔK th as a model parameter. Figure 10: S-N field in propagation as derived from the crack growth curves. C ONCLUSIONS he main conclusions derived from this work are: - The validity of the methodology proposed is confirmed for fitting experimental data to the crack growth rate curve of one steel used for crankshafts. Also the crack growth curves a-N curves for different initial crack size values and load, or remote stress range. - This opens new perspectives for the crack growth prediction under variable loading. - The derivation of the S-N requires further study in order to solve scale problems observed. 0.2 0.3 0.4 0.5 0.6 0.7 1 1.5 2 2.5 3 3.5 4 4.5 5 a* Geometric factor according to standard Fit Z(a*) 0 5 10 15 x 10 4 0 50 100 150 200 250 300 N [cycles]  [MPa] a 0 =3.4 mm a 0 =3.6 mm a 0 =4.0 mm a 0 =4.5 mm T