PSI - Issue 28

R.M. Zhabbarov et al. / Procedia Structural Integrity 28 (2020) 1768–1773 Author name / Structural Integrity Procedia 00 (2019) 000–000

1771

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Fig. 1. Typical mesh containing singular elements near the crack tips.

Fig. 2. Distribution of the von Mises equivalent stress in the vicinity of the right crack tip (left), distributions of the stress components 11  (center) and 22  in the vicinity of the crack tip (right).

250 σ 11

σ 11

σ 11

N=1

150

150

200

N=3

N=2

150

100

100

100

Abaqus

Abaqus

50

50

50

Abaqus

0

0

0

-50

-50

-50

-100

-100

θ

-100

θ

3 θ

-2

1

2

-1

0

3

-3

-2

1

2

-3

-2

-1

0

-1

0

3

2

-3

1

Fig. 3. Distribution of the stress component 11  at the distance from the crack tip 0.033 r cm  : the red curve shows the one-term asymptotic solution (left), the two-term asymptotic solution (center), the three-term asymptotic solution (right), the blue points show the FEM solution.

σ 11

σ 11

100

100

N=7

N=2

50

50

Abaqus

Abaqus

0

0

-50

-50

-100

-100

θ

θ

-2

1

-2

1

2

2

-1

0

-1

0

3

3

-3

-3

0.059 r cm  : the red curve shows the two-term asymptotic

Fig. 4. Distribution of the stress component 11  at the distance from the crack tip

solution (left), the seven-term asymptotic solution (right), the blue points show the FEM solution