PSI - Issue 28

Jesús Toribio et al. / Procedia Structural Integrity 28 (2020) 2396–2403 Jesús Toribio et al. / Procedia Structural Integrity 00 (2020) 000–000

2401

6

4. Macro-approach to fatigue crack growth An innovative procedure for estimating the real crack propagation rate (in the form of Paris law of fatigue crack growth) was proposed by Toribio et al. (2014) where the non-linear crack configuration (crack morphology at the micro-level) was taken into account on the basis of the variations in crack morphology (degree and periodicity of micro-crack kinks, deviations or deflections), so that a correction was made in the matter of the cyclic crack growth rate by considering the actual physical crack growth rate (the real length of propagation is different from the projected one in the global mode I direction of crack advance). The procedure leads to the two different fatigue propagation laws (represented in Fig. 8).

10 -6

da/dN - Hot rolled da/dN - Cold drawn da*/dN - Hot rolled da*/dN - Cold drawn

10 -7

Fatigue crack rate (m/cycle)

10 -8

10

20

30

40 50

SIF range (MPam 1/2 )

Fig. 8. Conventional Paris Laws (CPLs) d a /d N and Actual Paris Laws (APLs) d a */d N for the hot rolled bar and the cold drawn wire.

The Conventional Paris Law (CPL) evaluated on the basis of the virtual crack advance in global mode I , i.e., without considering the micro-deflections. Therefore, the crack length a is measured in the transverse direction of the bar or the wire and represents the projection of the real fatigue crack path in the direction of virtual (theoretical) crack advance in global mode I. This CPL takes the form: d a /d N = C ∆ K m (1) where C and m are the conventional Paris coefficients of the material given in Table 3. Table 3. Conventional and actual Paris coefficients of the materials (units for d a /d N in m/cycle and Δ K in MPam 1/2 ).

Steel

C *

m *

C

m

Hot rolled bar

5.3·10 -12

3.0

3.3·10 -12

3.2

Cold drawn wire

4.1·10 -12

3.0

3.2·10 -12

3.2

The Actual Paris Law (APL) is evaluated on the basis of the actual crack advance in local mixed mode I+II , i.e., considering the micro-deflections. The actual crack length a* is measured in the real deflected direction of advance, following the real or physical fatigue crack path in the actual direction of micro-crack advance and considering the micro-deflections and the tortuosity of the fatigue crack path (with zig-zag shape).