PSI- Issue 9

Jesús Toribio / Procedia Structural Integrity 9 (2018) 317–322

320

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Author name / Structural Integrity Procedia 00 (2018) 000–000

5. Anisotropy of fatigue resistance and crack paths: conventional and actual Paris Laws

The afore-said local anisotropy of fatigue resistance allows a correction of the fatigue crack growth equation (Paris Law) to consider the real fatigue crack path in local mixed mode instead of the apparent fatigue crack path in global mode I . Fig. 5 shows the locally anisotropic fatigue crack paths in the hot rolled bar and in the cold drawn wire. As the drawing degree rises, the average deviation angle increases and the average deflection length decreases. This implies more frequent deflections in the cold drawn wire that in the hot rolled bar, cf. Fig. 5.

l

l

θ

θ l

l

Fig. 5. Locally anisotropic fatigue crack paths in the hot rolled bar (left) and in the cold drawn wire (right).

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, 2017) 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. 6. On one hand, 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. On the other hand, the Actual Paris Law (APL) evaluated on the basis of the actual crack advance in local mixed mode I+II , i.e., considering the micro-deflections. Therefore, the actual crack length a* is measured in the real deflected direction of advance, i.e., following the real or physical fatigue crack path in the actual direction of micro crack advance and taking into account the micro-deflections and the tortuosity of the fatigue crack path (with zig zag shape, cf. Fig. 5).

10 -6

10 -6

Hot rolled bar Cold drawn wire

Hot rolled bar Cold drawn wire

10 -7

10 -7

da/dN (m/cycle)

da/dN (m/cycle)

10 -8

10 -8

10

20

30

40 50

10

20

30

40 50

Δ K (MPam 1/2 )

Δ K (MPam 1/2 )

Fig. 6. Conventional Paris Laws (CPLs; left) and Actual Paris Laws (APLs, right) for both materials.