PSI - Issue 37

Jesús Toribio et al. / Procedia Structural Integrity 37 (2022) 989–994 Jesús Toribio / Procedia Structural Integrity 00 (2021) 000 – 000

993 5

4. SIF solutions A closed-form solution for the maximum dimensionless SIF K IA /(σ rem (π D )

1/2 ) results has been carried out by means

of polynomial equations (using the least squares method) in function of the parameters d / D and ε / D : For symmetrical case (maximum error: 0.5%),

   

   

4

3

2

K

      d D

      d D

      d D

      d D

( ) IA,sym D

=

−

+

−

+

33.542

90.653

93.636

45.482

9.535

(4)

1 2

rem  

For applied tensile load and no contact (maximum error: 1.0%),

K

       

3

2

K

      d D

      d D

      d D





IA,F No ontact C

IA,sym

=

+ − 1 2 1 76.90

+

−

+

182.21

146.30

( ) D

( ) D

1 2

rem  

rem  

(5)

    +       49.44 D

For applied tensile load and contact (maximum error: 2.5%),

K

3

2

2

             d D D           d D D

          d D D

      d D       d D





( ) IA,F Contact D

= −

+

−

+

69.07

172.07

352.20

1 2

rem  

3

2

2

       D

       D

      d D

+

+

−

+

−

+

314.01

97.77

112.79

68.18

55.33

(6)

     +   D

+

35.08

12.60

5. Conclusions As the eccentricity of the ligament increases, so does the difference between the SIF values along the crack front. From a certain value of the misalignment, as a consequence of the bending effect, the crack remains closed in the area near the point of lower depth B at which the SIF is equal to zero. References ASTM, 2012. Standard test method for linear-elastic plane-strain fracture toughness K Ic of metallic materials (ASTM E399), ASTM, West Conshohocken, USA. Benthem, J.P., Koiter, W.T., 1973. Asymptotic approximations to crack problems. In: G.C. Sih (Ed.), Method of Analysis and Solutions of Crack Problems, Noordhoft International Publishing, Croningen, pp. 131 – 178. Bueckner, H.C., 1965. Discussion on stress analysis of cracks. In: P.C. Paris, G.C. Sih (Eds.), Fracture Toughness Testing and its Applications (ASTM STP 381), ASTM, West Conshohocken, USA, pp. 82 – 83. Dieter, G.E., 1988. Mechanical Metallurgy SI edition, McGraw-Hill, Singapore. Gray, T.G.F., 1977. Convenient closed form stress intensity factors for common crack configurations. International Journal of Fracture 13, 65 – 75. Ibrahim, R.N., Kotousov, A., 1999. Eccentricity correction for the evaluation of fracture toughness from cylindrical notched test small specimens. Engineering Fracture Mechanics 64, 49 – 58. Ibrahim, R.N., Stark, H.L., 1990. Establishing K 1c from eccentrically fatigue cracked small circumferentially grooved cylindrical specimens. International Journal of Fracture 44, 179 – 188.