PSI - Issue 28

Jesús Toribio et al. / Procedia Structural Integrity 28 (2020) 2382–2385 Jesús Toribio et al. / Procedia Structural Integrity 00 (2020) 000–000

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3

3. Numerical results In Fig. 3 the dimensionless SIF K I,sym / σ (π D )

1/2 is represented against the relative inner crack diameter d / D for the symmetric case (crack without eccentricity respect to the bar axis, ε = 0), σ being the remote stress. The SIF increases with the relative inner crack diameter; the results agree with the solution provided by Tada et al. (2000).

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.3 0.4 0.5 0.6 0.7 0.8 Present paper Tada et al. (2000) d/D K I,sym /  (  D) 1/2

Fig. 3. Dimensionless SIF K I,sym / σ (π D ) 1/2 vs . relative inner crack diameter d / D for the symmetric case. The evolution of SIF ratio K I / K I,sym along the crack front (depicting its points by means of θ angle) for ε / D from 0 (symmetric case) to 0.175 with increments of 0.0125 and for d / D = 0.3 and 0.5, can be observed in Fig. 4. For non symmetric cases, inner crack eccentricity makes the SIF vary along the crack front, decreasing from point A to point B.

1.20

1.04

d/D=0.3

d/D=0.5

 /D

 /D

1.15

1.03

1.10

1.02

K I /K I,sym

K I /K I,sym

1.05

1.01

1.00

1.00

0.95

0.99

0 30 60 90 120 150 180  (º) A B

0 30 60 90 120 150 180  (º) A B

(a) (b) Fig. 4. SIF ratio K I / K I,sym along the crack front (characterized by the angle θ ) for ε / D from 0 to 0.175 with increments of 0.0125: (a) d / D = 0.3; (b) d / D = 0.5. Fig. 5 shows the SIF ratio at point A K IA / K I,sym (maximum value) and the SIF ratio at point B K IB / K I,sym (minimum value) as a function of relative inner crack eccentricity ε / D (for d / D = 0.3 and 0.5). For a given crack diameter, the eccentricity raises the SIF at point A. In addition, the rise of crack eccentricity or crack diameter raises the differences between SIFs at different points of the crack, thereby increasing even more the eccentricity itself when the cracks propagate by fatigue. The tensile loading