Issue 78

S. Vantadori et alii, Fracture and Structural Integrity, 78 (2026) 432-453; DOI: 10.3221/IGF-ESIS.78.25

different slope in the bilogarithmic da dN - K  representation. In contrast, for

0.75 R  , only two sub-stages are observed,

with Sub-Stage IIb being almost negligible. By applying the Paris law ( /

m da dN C K   ) to each identified sub-stage, the corresponding parameters, namely the exponent m and the coefficient logC are determined. The results are summarised in Fig. 10 using a representation commonly adopted in the literature, where logC is plotted as a function of m , thus enabling a direct comparison among the different fatigue ratios and crack-growth sub-stages.

-9

R 0.10 0.50 0.75

Sub-Stage II a b c

-10

-13 COEFFICIENT, logC [-] -12 -11

2 3 4 5 6 7 8 EXPONENT, m [-] -14

Figure 10: Values of logC and m for the sub-stages identified at the three investigated fatigue ratios.

The transition points 

 , / K da dN  , defined as the coordinates where the regression lines of two adjacent sub-stages

intersect, are reported in Tab. 3 for each examined R value.

SUB-STAGE II

From a to b

From b to c

From a to c

R

/ da dN

/ da dN

/ da dN

K 

K 

K 

[MPam 0.5 ]

[m/cycle] 1.66 (10) -8

[MPam 0.5 ]

[m/cycle] 1.22 (10) -7

[MPam 0.5 ]

[m/cycle]

7.22

-

-

0.10

5.85

0.50

4.13

9.46 (10) -9

5.62

8.22 (10) -8

-

-

0.75

-

-

-

-

3.30

9.56 (10) -9

Table 3: Data points 

 , / K da dN  marking the transition between adjacent sub-stages for R = 0.10, 0.50, and 0.75.

The occurrence of sub-stages characterised by different slopes within the Paris regime of fatigue crack propagation - commonly referred to as multilinear behaviour - has been widely reported in conventional Al alloys subjected to various heat treatments [36-38]. This behaviour is primarily attributed to changes in the dominant damage mechanisms, as well as to the interaction between the crack tip plastic zone and the underlying microstructural features. Three main mechanisms can be identified, as summarized below.

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