PSI - Issue 57

6

Hultgren & Barsoum/ Structural Integrity Procedia 00 (2023) 000 – 000

Gustav Hultgren et al. / Procedia Structural Integrity 57 (2024) 428–436

433

Table 1. Analytical expressions for the stress concentration factor. Reference Stress concentration factor Tsuji (1990) 0.446 t,Tsuji 1 1.015 K Q f  = +

(7) (8)

1

h  

Q

=

2 W r t         −  

2.8

   

    

W

1 exp 0.90 − −



2

h

(9)

f

=



   

    

W



1 exp 0.90 − −

2 2 h

Fitting range Weld toe radius / : 0.0033 0.1 r t −

Monahan (1995)

0.454

r −       t

(10)

0.37

t,Monahan 1 0.388 = +

K



Parameter validity Weld toe radius / : 0.02 0.067 r t − Flank angle :30 60  − o o

Hellier et al. (2014)

2

2

3

r       t

L       t

r       t

L       t

L       t

2 0.012 104  +

3 0.614 0.18  +

0.889 0.302 3.44  = − +

0.529

0.633

K

+

+

−

+

, t Hellier

4

2

L       t

r       t

L       t

r L          t t

r       t

L     −      t   64.3 r t  

(11)

2

2

0.018

35.5

0.153

4.38

30.6

0.219

−

−

−

+

+

−









2

2

2

0.299 r             L t t −

0.263

L       t

r L             t t

r L          t t

0.68

0.041

54.5

0.595

+

−

+

+





Parameter validity Weld toe radius / : 0.01 0.067 r t − Flank angle :30 60  − o o

Wang et al. (2020)

(12) (13) (14) (15)

1 1.394 (/) () ((/) ) f r t f f r t   = +    

, t Wang K f r t

0.145

3 6.400 ( / ) 6.802 ( / ) 3.277 ( / ) 2.692 r t r t r t +  −  +  − 2

( /) 1.824( /) r t = 

−

3 ) 1.532 (     =− −+ −− −+ 2 ) 3.395 ( ( ) 0.278 ( f   

) 4.967

3 )) 12.703 (( / ) ( r t 

2 )) 5.761 (( / ) ( r t

(( /)( )) 10.016(( /)( f r t r t   =−  Parameter validity Weld toe radius / : 0.003 0.36 r t − Flank angle :20 90  − o o

)) 1.182

   − +

   − + 

   − +

The stress concentration factors obtained through the analytical expressions proposed by Tsuji (1990) and Wang 142 et al. (2021) are compared with the simulation results for three specimens, 10, 18 and 13, in Fig. 6. Despite variations 143 in geometric characteristics, these specimens exhibit similar distributions of the ratio sec nom    (as shown in Fig. 3). 144 The discrepancies observed among the simulation results are presented in Fig. 6, ranging from the least critical 145 geometry (left) to the most critical geometry (right). Notably, two distinct geometric differences exist among the 146 specimens. Firstly, the middle specimen (18) possesses the sharpest weld transition radii, approximately 0.4 mm 147 smaller than the other two specimens. Secondly, the two specimens on the left side in Fig. 6 (10 and 13) lack any 148 undercut, whereas the rightmost specimen has an average undercut depth slightly exceeding 0.2 mm. The top of the 149 figure displays the corresponding geometries of the specimens, with surface plots that illustrate the ratio between the 150 sectional and nominal stress. The disagreement observed between the analytical expressions and the simulated values 151 in Fig. 5 is partly attributed to the findings in Fig. 6. These results reveal that the oscillations in the simulated stress 152 outcomes exhibit a considerably slower rate than the measured weld toe radii, with which the analytical expressions 153 are strongly correlated. The interaction of neighbouring cross-section geometries in the finite element simulations 154