PSI - Issue 32

L.V. Stepanova et al. / Procedia Structural Integrity 32 (2021) 261–272 Author name / Structural Integrity Pro edi 00 (2019) 000–000

271 1

(

)

(

)

(

)

1

3/2

1 2

2

1

5/2

equal to 0.5 are following:

,

,

,

1 37.314 / a Pa c м =

15.251 /

3 9.311 / a Pa c м =

a

Pa c м

= −

(

)

(

)

(

)

(

)

2 2 0 a = ,

1 4

3

1 5

7/2

2

3/2

2

5/2

,

,

,

,

0.045 /

1.522 /

37.314 /

3 7.651 / a Pa c м =

a

Pa c м

a

Pa c м

a

Pa c м

= −

= −

=

1

(

)

(

)

(

)

1 5

7/2

2

5/2

2

3

,

,

.

0.988 /

3 7.651 / a Pa c м =

0.337 /

a

Pa c м

a

Pa c м

= −

= −

4

Fig. 15. The stress tensor component 22 σ : blue line shows the analytical solution with the obtained coefficients and red lines show the atomistic distribution.Mixed mode loading, 0.5 e M = . Thus, the over-deterministic method makes it possible to reconstruct the coefficients of the multi-point Williams series expansion from MD simulations. 3. Conclusions The study presents the method of determination of continuum fracture mechanics parameters (stress intensity factors, T-stress and higher-order terms of Williams series expansion of the stress field in the vicinity of the crack tip in an isotropic linear elastic materials) using molecular dynamics simulations. Based on the procedure of the over-deterministic method the continuum fracture mechanics parameters for Mode I and Mixed Mode loading are found. Reconciliation of continuum and atomistic models is demonstrated. Atomistic simulations clearly show that the angular distributions of the stress tensor components are very similar to the

analytical solution. Acknowledgements The work is supported by the Russian Science Foundation (project 21-11-00346).

References

Cheng, S.-H., Sun, C.T., 2011. Applicability of continuum fracture mechanics in atomic system. Proc. ASME. IMECE2011. 8, 283-288.