PSI - Issue 2_A

Larisa Stepanova et al. / Procedia Structural Integrity 2 (2016) 1789–1796 Stepanova L.V., Roslyakov P.S. / Structural Integrity Procedia 00 (2016) 000–000

1795

7

σ

σ

σ

σ

12 4

/

12 4

/

^

12

12

N=9,10

r=r/a=0.45 ^

r=r/a=0.45

1.2

N=13

N=5,6 N=7,8

N=11,12

N=9

N=30,40,50,150,200

1

1

0.8

0.8

N=50,150,200

0.6

N=3,4

0.6

0.4

0.4

N=1,2

0.2

0.2

θ

θ

-1

-2

2

3

1

0

-2

3

1

0

2

-1

-3

-3

Fig. 7. Angular distributions of the stress components σ 12 near the crack tip z = b at di ff erent distances from the crack tip

σ

σ

σ

σ

12 4

/

12 4

/

12

12

N=40

N=50,150,200

r=r/a=0.75 ^

r=r/a=0.75 ^

N=13,14

N=11,12

N=15,16

1.4

N=7,8

N=30

1

N=17,18 N=19,20

N=3,4

N=9,10

N=5,6

1.2

N=30

0.8

1

0.8

0.6

N=50,150,200

0.6

0.4

N=1,2

0.4

0.2

0.2

θ

θ

-3

2

0

-1

-1

2

3

1

0

3

-2

1

-2

-3

Fig. 8. Angular distributions of the stress components σ 12 near the crack tip z = b at di ff erent distances from the crack tip

5. Summary

The paper has aimed at determining closed-form expressions for coe ffi cients in crack-tip stress expansions for two finite collinear cracks of equal lengths in an infinite plane medium subjected to mixed mode load. The method is based on the complex variable theory and the classical Koloso ff -Muskhelishvili approach. The asymptotic expansion of the Koloso ff -Muskhelishvili’s potential in the vicinity of the crack tips allows to find the analytical presentation for coe ffi cients of the complete M. Williams asymptotic expansion. The analytical solution gives the dependence of the amplitude coe ffi cients on the lengths of the crack and the applied loads. It is shown that together with the leading term including the stress intensity factor and term called T-stress it is necessary to hold the higher-order terms in the asymptotic solutions for the stress field. The obtained solutions permit to construct the asymptotic stress field expansion containing arbitrary preassigned number of higher-order terms. The analytical expressions for the coe ffi cients of the higher-order terms obtained in this study can be used for examination of the results obtained by the over-deterministic method employed both the FE data and the experimental data from the photoelasticity technique, the holographic interferometry method, the DIC technique (see Ayatollahi and Nejati (2010), Akbardoost and Rastin