PSI - Issue 37

Jesús Toribio et al. / Procedia Structural Integrity 37 (2022) 995–1000 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000 – 000

998

4

Fig. 5 plots the SIF ratio at point A K IA / K I,sym (maximum) and the SIF ratio at point B K IB / K I,sym (minimum) as a function of the inner crack eccentricity ε / D ( d / D = 0.3 and 0.5). For a given crack diameter, the SIF at point A increases with the eccentricity, while the SIF at point B decreases for small eccentricities and increases for high eccentricities. 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 applied at the bar ends generates a bending stress caused by the eccentricity of the inner crack, thus provoking a rotation in the sample, which increases with the crack deviation from the bar axis (Fig. 6).

1.20

1.03

d/D=0.3

d/D=0.5

K IA /K I,sym

1.15

1.02

K IA /K I,sym

1.10

1.01

K IB /K I,sym

K I /K I,sym

K I /K I,sym

1.05

K IB /K I,sym

1.00

1.00

0.99

0.95

0.00

0.05

0.10

0.15

0.20

0.00

0.05

0.10

0.15

0.20

 /D

 /D

(a) (b) Fig. 5. SIF ratio at point A K IA / K I,sym and SIF ratio at point B K IB / K I,sym vs . relative inner crack eccentricity ε / D : (a) d / D = 0.3; (b) d / D = 0.5.

(a) (c) Fig. 6. Initial and deformed cracked bar (contour bands correspond with the normal component in axial direction of the stress tensor): (a) ε / D = 0; (b) ε / D = 0.0875; (c) ε / D = 0.175. (b)

The maximum SIF results (point A) have been fitted to an exponential expression as a function of the relative crack eccentricity ε / D for the two relative crack diameters studied, d/D = 0.3 and 0.5. The coefficients A 0 , A 1 and A 2 corresponding to this equation are shown in Table 1. ( ) ( ) IA I,sym 0 1 2 D K K A A A  = + (3)

Table 1. A 0 , A 1 and A 2 coefficients of equation (3).

d/D 0.3

A 0

A 1

A 2

0.9957 0.9787

0.004188 0.02214

48676

0.5

385545