PSI - Issue 13

Yuebao Lei / Procedia Structural Integrity 13 (2018) 571–577 Y Lei/ Structural Integr ty P o edi 00 (2018) 000–000

575

15

15

(a)

(b)

Predicted (Opt-2 FAC) FE, pure tension ( λ=0) FE, combined tension and bending (λ=0.5)

Predicted (Opt-2 FAC) FE, pure tension ( λ= λ1=0) FE, bi-axial tension (λ1=0.5) FE, bi-axial tension (λ1=1)

10

10

FE, pure bending ( λ=∞) a / t =0.5, a / c =0.6, c/W=0.25 Ramberg-Osgood material n =5, α =1, σ o =340 MPa FE: Lei (2004(1),(2),(3))

J / J e

J / J e

a / t =0.4, a / c =0.2, c/W=0.0625 Ramberg-Osgood material n =5, α =1, σ o =200 MPa FE: Wang (2006)

5

5

0

0

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

ϭ ref / ϭ o

ϭ ref / ϭ o

Fig.2 Comparison of normalised J values at the deepest point between FE and the predictions using the reference stress method for plates with semi-elliptical surface cracks: (a) combined tension and bending and (b) bi-axial loading

8

15

(b)

(a)

Predicted (Opt-2 FAC) FE, a/t=0.1 FE, a/t=0.3 FE, a/t=0.5 FE, a/t=0.75 Cylinder R m / t =5, circumferental internal crack: θ / π=0.25 Ramberg-Osgood material

Predicted (Opt-2 FAC) FE, a/t=0.1, a/c=0.022 FE, a/t=0.4, a/c=0.089 FE, a/t=0.75, a/c=0.168 Cylinder R m / t =5, axial internal crack Ramberg-Osgood material

6

10

J / J e

4

J / J e

n =3, α =1, σ o =400 MPa FE: Kim et al. (2004)

5

n =5, α =1, σ o =400 MPa FE: Kim et al. (2002)

2

0

0

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

σ ref /  0

σ ref /  0

15

15

(c)

(d)

Predicted (Opt-2 FAC) FE, a/t = 0.1 FE, a/t = 0.2 FE, a/t = 0.4 FE, a/t = 0.5 Cylinder R m / t =4.5, circumferental external crack: θ / π=0.12 Ramberg-Osgood material n =5, α =1, σ o =400 MPa FE: Chiodo and Ruggieri (2010)

Predicted (Opt-2 FAC) FE, a/t=0.1 FE, a/t=0.3 FE, a/t=0.5 FE, a/t=0.75 Cylinder R m / t =5, circumferental internal crack: θ / π=0.25 Ramberg-Osgood material

10

10

J / J e

J / J e

5

5

n =5, α =1, σ o =400 MPa FE: Kim et al. (2002)

0

0

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

σ ref /  0

σ ref /  0

Fig. 3 Comparison of normalised J values at the deepest point between FE and the predictions using the reference stress method for cylinders with axial/circumferential semi-elliptical surface cracks: (a) axial internal cracks under pressure, (b) circumferential internal cracks under pressure, (c) circumferential internal cracks under global bending and (d) circumferential external cracks under global bending

8

(a)

8

(b)

Predicted (Opt-2 FAC) FE, internal crack, pressure FE, external crack, in-plane bending

Predicted (Opt-2 FAC) FE, internal crack, pressure FE, internal crack, out-of-plane bending FE, internal crack, in-plane+out-of-plane bending

6

6

FE, internal crack, in-plane bending+pressure FE, internal crack, in-plane+out-of-plane bending Elbow R c / r m =4, r m / t =10 Axial semi-elliptical cracks

J / J e

4

Elbow R c / r m =4, or 6, r m / t =10 Circumferential semi-elliptical cracks

J / J e

4

a/t=0.25, a/c=1/3 n =6, σ y =185 MPa FE: Kayser(2016)

a/t=0.25, a/c=1/3 n =6, σ y =185 MPa FE: Kayser(2016)

2

2

0

0

0.0

0.5

1.0

1.5

0.0

0.5

1.0

1.5

σ ref /  y

σ ref /  y

Fig. 4 Comparison of normalised J values at the deepest point between FE and the predictions using the reference stress method for elbows with axial/circumferential semi-elliptical surface cracks: (a) axial cracks and (b) circumferential cracks