PSI - Issue 37

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

997

3

3. Numerical results For the symmetric case (crack without eccentricity in relation to the bar axis, ε = 0), the handbook of Tada, Paris and Irwin (2000) provides the following expression for the calculation of the SIF ( σ being the remote tensile stress): ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 3 I,sym 2 1 2 1 0.5 0.625 0.421 2 1 d D d K d D d D d D d D      −     = + − +      −  (2) In Fig. 3, the dimensionless SIF K I,sym / σ (π D ) 1/2 is plotted vs the inner crack diameter d / D for the symmetric case, together with the results of Tada, Paris and Irwin (2000), It is seen that the SIF increases with the inner crack diameter and the agreement is excellent between the results of the present paper and those by Tada, Paris and Irwin (2000). This happens for a wide range of inner crack diameters ( d / D from 0.3 to 0.8).

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, Paris and Irwin (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.

1.04

1.20

d/D=0.3

d/D=0.5

 /D

 /D

1.03

1.15

1.02

1.10

K I /K I,sym

K I /K I,sym

1.01

1.05

1.00

1.00

0.99

0.95

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.