PSI - Issue 18

Giuseppe Pitarresi et al. / Procedia Structural Integrity 18 (2019) 330–346 Author name / Structural Integrity Procedia 00 (2019) 000–000

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11

Table 4. Values of SIF and T-Stress for R=0 from the LSF method ( r min =5 px; r max =18, 24, 43, 116 px).

Number of Williams’ terms

1

2

3

4

5

6

8

10

12

FEM

r max/(W-a) =0.15; number of input data points=804

R 2

0.9769 0.9813

0.9814 0.9902 0.9906 0.9927 0.9927 0.9928

0.9928

22.22

 K [MPa×m 0.5 ]

26.28

24.72 -24.26

24.78

21.92

21.44

19.99

19.28

20.20

20.20

   MPa 

0.00

-24.83 -138.56 -162.82 -258.67 -313.88 -220.57

-220.57

r max/(W-a) =0.20; number of input data points=1508

R 2 

0.9819 0.9819

0.982 0.9906 0.9912 0.9922 0.9924 0.9924

0.9924

22.22

 K [MPa×m 0.5 ]

26.17

26.05 -1.61

26.16

23.35

22.80

21.82

20.90

21.01

21.01

   MPa 

0.00

-3.01 -103.83 -128.90 -187.81 -252.53 -241.65

-241.65

r max/(W-a) =0.35; number of input data points=5005

R 2 

0.9719 0.983

0.9861 0.9886 0.9897 0.9901 0.9908 0.9909

0.9909

 K [MPa×m 0.5 ]

25.04

27.74 29.52

28.38

26.86

26.13

25.55

23.97

23.74

23.94

22.22

   MPa 

0.00

18.28 -25.45 -51.63 -79.70 -167.54 -183.19

-166.40

r max/(W-a) =0.95; number of input data points=35093

R 2 

0.8083 0.862

0.9388 0.9529 0.9766 0.9837 0.989 0.9902

0.9905

22.22

 K [MPa×m 0.5 ]

20.07

25.91 40.71

28.19 -0.06

31.67

28.45

30.64

28.72 -4.51

27.22 -73.59

26.28

   MPa 

0.00

66.20 -10.37 57.88

-127.43

Table 5. Values of SIF and T-Stress for R=-1 from the LSF method ( r min =5 px; r max =18, 24, 43, 116 px).

Number of Williams’ terms

1

2

3

4

5

6

8

10

12

FEM

r max/(W-a) =0.15; number of input data points=804

R 2

-3.3424 0.3961

0.7913 0.9449 0.9449 0.9459 0.9464 0.9479

0.9479

21.78

 K [MPa×m 0.5 ]

19.31

5.00

8.74

4.95

4.95

5.28

5.62

7.59

7.59

   MPa 

0.00 -223.20

-259.82 -410.38 -410.73 -388.71 -364.06 -172.11

-172.11

r max/(W-a) =0.20; number of input data points=1508

R 2 

-1.5263 0.4641

0.8025 0.9581 0.9599 0.9606 0.9608 0.9618

0.9618

21.78

 K [MPa×m 0.5 ]

19.60

6.72

10.09

5.61

5.23

5.52

5.48

7.04

7.04

   MPa 

0.00 -179.88

-223.27 -383.66 -400.90 -383.64 -388.59 -249.31

-249.31

r max/(W-a) =0.35; number of input data points=5005

R 2 

0.1287 0.6116

0.8268 0.9462 0.9707 0.9712 0.9717 0.9719

0.9721

 K [MPa×m 0.5 ]

19.63

10.82 -96.30

13.46

8.22

6.48

6.18

5.54

6.22

6.81

21.78

   MPa 

0.00

-142.12 -292.28 -355.26 -369.50 -405.67 -355.63

-307.70

r max/(W-a) =0.95; number of input data points=35093

R 2 

0.677 0.6814

0.8419 0.8528 0.9612 0.9615 0.9802 0.9819

0.982

21.78

 K [MPa×m 0.5 ]

17.21

16.05 -8.09

18.34

16.21

11.41

11.07

7.23

5.95

5.99

   MPa 

0.00

-49.14 -89.70 -203.65 -214.02 -347.86 -406.91

-403.32

(a)

(b)

32

1

N w =1 N w =2 N w =3 N w =4 N w =6 N w =8 N w =10

N w =1 N w =2 N w =3 N w =4 N w =6 N w =8 N w =10

30

0.95

28

0.9

26

24

0.85

22

0.8

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 r max /(W-a) 18

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 r max /(W-a) 0.75

Fig. 7. (a) Evolution of R 2 with r

max and N w ; (b) variation of  K with r max and N w . Both plots are obtained for the case of R=0.1. The data input area has a constant r min /( w - a )=0.04.