PSI - Issue 39

Larisa Stepanova et al. / Procedia Structural Integrity 39 (2022) 748–760 Author name / Structural Integrity Procedia 00 (2019) 000–000

756

9

e)

Fig. 9. a) angular distributions of stresses for

0.33 obtained for the ring area with the inner radius 5 A and the outer radius 15; b) angular obtained for the ring area with the inner radius 10 A and the outer radius 15; second picture; c) angular obtained for the ring area with the inner radius 5 A and the outer radius 15; d) angular distributions of e M =

distributions of stresses for distributions of stresses for

e M =

0.33

e M =

0.66

stresses for 1 e M = obtained for the ring area with the inner radius 15 A and the outer radius 20A; e) angular distributions of stresses for 1 e M = obtained for the ring area with the inner radius 10 A and the outer radius 15.

The computed values of the coefficients of the Williams series expansion obtained by the over-deterministic method are given in Tables 1-5. The surprisingly good agreement between coefficients obtained by molecular dynamics simulations and continuum linear elastic fracture mechanics can be observed.

Table 1. The computed values of the Williams series expansion, Mode I loading Coefficients of the Williams power expansion, Mode I Coefficients, MD method Coefficients,

Analytical Solutions 70,67885

70,67885

1

1/2

1 , a MPa m ⋅

-25.0000

-25.0000

1 2 , a MPa

17.68451

17.68563

1

1/2

− ⋅

3 , a MPa m

-2.21245

-2.21269

1

3/2

− ⋅

5 , a MPa m

0.55344

0.55367

1

5/2

− ⋅

7 , a MPa m

-0.17012

-0.17318

1

7/2

− ⋅

9 , a MPa m

0.05991

0.06067

1 11 , a MPa m − ⋅ 13 , a MPa m − ⋅ 15 , a MPa m − ⋅ 1 1

9/2

-0.00191

-0.00227

11/2

0.00815

0.00895

13/2