Issue 35

S. Blasón et alii, Frattura ed Integrità Strutturale, 35 (2016) 187-195; DOI: 10.3221/IGF-ESIS.35.22

5

Geometric factor according to standard Fit Z(a*)

4.5

4

3.5

3

2.5

2

1.5

1

0.2

0.3

0.4

0.5

0.6

0.7

a*

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.

300

a a a a

=3.4 mm =3.6 mm =4.0 mm =4.5 mm

0

0

250

0

0

200

150

 [MPa]

100

50

0

0

5

10

15

N [cycles]

x 10 4

Figure 10: S-N field in propagation as derived from the crack growth curves.

C ONCLUSIONS

T

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.

194