PSI - Issue 42

M. Yakovlev et al. / Procedia Structural Integrity 42 (2022) 1619–1625 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1623

5

To determine the range of a stable solution, an analysis of the numerical solution convergence was carried out. Figure 4 shows SIF values depending on the distance to the crack tip, which is normalized to the crack length b . It should be noted that in the range of r/b from 8∙10 -3 m to 4∙10 -2 m, there is a region of stable solution, in which K takes approximately constant values. Thus, in this work, to calculate the approximation functions K , the distance from the crack tip r/b = = 1∙10 -2 m was chosen.

Fig. 4. SIFs distributions in the specimen deepest point ( φ = 90°, θ = 0°).

To compare the results for the same configurations of semi-elliptical crack fronts using Murakami ’s handbook (1987) SIFs were calculated. SIFs were calculated using the following equations that were obtained by Newman and Raju (1981):

( ) s F E k a t W   b b b a

( , , , ) 

K

=

1

(6)

1/ 2 1.65

( ) 1 1.464 b E k a  =  +

         

 

(7)

2 b b F M M M gf f t t        = + +               4 1 2 3 s

w

(8)

b a

1 1.13 0.09 = −

M

(9)

1

−

b a





0.54 0.89 0.2

M

= − +

 +   

2

(10)

1

24

−

3 0.5 0.65  = − + + −         14 1 b a b a   

M

(11)

  

2

b           t

2

1 0.1 0.35 

(1 sin( )) − 

g

= + +

(12)

1/ 4

2 1 cos(2 ) 1 cos(2 ) 2 2  +  −  + 

  

b a

f

=       



 

(13)

1/ 2



   

   

   

a b W t



sec

f

= 

w

2

 

(14)