PSI - Issue 40

L.V. Stepanova et al. / Procedia Structural Integrity 40 (2022) 392–405 Stepanova L.V., Belova O.N. / Structural Integrity Procedia 00 (2022) 000 – 000

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2. Comparisons of the continuum and atomistic approaches The stress distributions obtained by molecular dynamics simulations are shown in figs. 14, 15 by red points. The blue lines illustrate the reconstructed theoretical analytical Williams solution whereas red points are immediately obtained from molecular dynamics calculations. The plots clearly show the qualitative coincidence of the atomistic approach and conventional continuum fracture mechanics descriptions.

Fig. 14. The stress tensor components: blue line shows the analytical solution with the obtained coefficients and red points show the atomistic distributions for Mode I crack

The conventional over-deterministic method allows us to calculate the high-order coefficients of the multi-point Williams series expansion (1) where the first five coefficients for Mode I crack have been kept. The results are ( ) 1 3/2 1 72.528 / a Pa mm = , ( ) 1 2 2 27.517 / a Pa mm = − , ( ) 1 5/2 3 21.406 / a Pa mm = , ( ) 1 3 4 0.033 / a Pa mm = − , ( ) 1 7/2 5 2.844 / a Pa mm = − . The values of the higher order terms for Mixed Mode loading with the mixity parameter ( ) ( ) ( ) 22 12 0 2 / arctan lim , 0 / , 0 e r M r r      → = = =