PSI - Issue 37

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

999

5

Guinea, Rojo and Elices (2004) calculated, by using the finite element method and the displacement extrapolation technique, the solutions of the maximum SIF (at the point of the crack front closest to the surface) for cylindrical geometries, with an inner circular crack placed eccentrically in relation to the bar axis, when they were subjected to remote tensile load. The results were fitted by the authors to an interpolation expression considering the asymptotic behavior when the crack size and the ligament depth vanish, as follows:

(4)

IA 0 = K f K

where K 0 (reference value) is the SIF of a circular crack (penny-shape crack) of diameter d in an infinite medium subjected to remote tensile stress σ , that can be obtained with the following expression taken from the handbook of Tada, Paris and Irwin (2000):

2

d

K

=

 

(5)

0

2



and f is the shape function that depends on the d / D and 2 b / D dimensionless parameters, as follows:



   

C

5

3

) ( ) +

i 1 = 

i 1 = 

(

(

)

(

) (

)

ln 1 

   

2i 1 2

2i

2 ln d D C d D b D  2

1 = +

f

i0 C d D

+

+

+

 

i2

(6)





i1

(

) ( d D b D 2

)



The parameter b is the minimum distance from the crack front (point A) to the cylinder surface. Thus, the parameter 2 b / D is related to the d / D and ε / D dimensionless parameters (used in this paper to characterize study geometry) with the following expression: ( ) ( ) ( ) 2 1 2 b D d D D  = − − (7)

The coefficients C i0 , C i1 and C i2 corresponding to equation (6) are shown in Table 2.

Table 2. C i0 , C i1 and C i2 coefficients of equation (6). i C i0 C i1 C i2 1 0.01242 -0.3097 1.185 2 -6.388 1.547 -3.723 3 16.89 -0.8769 2.628 4 -9.838 5 -1.228

Fig. 7 shows the SIF ratio at point A K IA / K I,sym (maximum SIF value along the crack front) obtained in the present paper together with the results derived from the expression by Guinea, Rojo and Elices (2004) for the relative crack diameters d / D = 0.3 and 0.5 and different relative crack eccentricities ε / D . In both K IA / K I,sym - ε / D curves a similar trend is observed, with greater closeness between them for d / D = 0.5 than for d / D = 0.3. In addition, the values obtained by Guinea, Rojo and Elices (2004) are greater than those provided by the present paper, except for the relative crack diameter d / D = 0.5 and high relative crack eccentricities ε / D > 0.14.