Molecular dynamic modeling of stress fields in plates with a central crack made of materials with a face-centered cubic lattice
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 4, pp. 68-82 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The purpose of this study is to determine the stress-strain state at the atomistic level using molecular dynamic modeling of the structure of the material, which were selected as single crystals of copper and aluminium. A series of computational experiments were carried out on plates with a central crack in the LAMMPS open code. Also, LAMMPS conducted experiments on cubic samples from the same materials to find the tensor components of elastic modules. The visualizations obtained in the OVITO software package are shown, which show the distribution of stress tensor components over different time steps for copper and aluminum single crystals. The work presents graphs showing the dependence of the stress tensor components on the polar angle, obtained by atomistic and classical approaches. The comparison showed that the stress fields at the nanoscale level are in good agreement with their macroscopic magnitudes, so a continuum approach can be applied at the atomistic level.
Keywords: molecular dynamics approach, normal loading, embedded atom potential (EAM), crack propagation.
@article{VSGU_2021_27_4_a4,
     author = {K. A. Mushankova and L. V. Stepanova},
     title = {Molecular dynamic modeling of stress fields in plates with a central crack made of materials with a face-centered cubic lattice},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {68--82},
     year = {2021},
     volume = {27},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2021_27_4_a4/}
}
TY  - JOUR
AU  - K. A. Mushankova
AU  - L. V. Stepanova
TI  - Molecular dynamic modeling of stress fields in plates with a central crack made of materials with a face-centered cubic lattice
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2021
SP  - 68
EP  - 82
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VSGU_2021_27_4_a4/
LA  - ru
ID  - VSGU_2021_27_4_a4
ER  - 
%0 Journal Article
%A K. A. Mushankova
%A L. V. Stepanova
%T Molecular dynamic modeling of stress fields in plates with a central crack made of materials with a face-centered cubic lattice
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2021
%P 68-82
%V 27
%N 4
%U http://geodesic.mathdoc.fr/item/VSGU_2021_27_4_a4/
%G ru
%F VSGU_2021_27_4_a4
K. A. Mushankova; L. V. Stepanova. Molecular dynamic modeling of stress fields in plates with a central crack made of materials with a face-centered cubic lattice. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 27 (2021) no. 4, pp. 68-82. http://geodesic.mathdoc.fr/item/VSGU_2021_27_4_a4/

[1] Hello G., Tahar M.B., Roelandt J.-M., “Analytical determination of coefficients in crack-tip stress expansions for a finite crack in an infinite plane medium.”, International Journal of Solids and Structures, 49:3–4 (2012), 556–566 | DOI

[2] Stepanova L.V., Yakovleva E.M., “Mixed-mode loading of the cracked plate under plane stress conditions”, PNRPU Mechanics Bulletin, 2014, no. 3, 129–162 | DOI

[3] Rashidi Moghaddam M., Ayatollahi M., Berto F., “The application of strain energy density criterion to fatigue crack growth behavior of cracked components”, Theoretical and Applied Fracture Mechanics, 97 (2018), 440–447 | DOI

[4] Razavi M.J., Aliha M.R.M., Berto F., “Application of an average strain energy density criterion to obtain the mixed mode fracture load of granite rock tested with the cracked asymmetric four-point bend specimens”, Theoretical and Applied Fracture Mechanics, 97 (2018), 419–425 | DOI

[5] Malikova L., Vesely V., Seitl S., “Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria”, Frattura ed Integrita Strutturalle, 2015, no. 33, 25–32 | DOI

[6] Chandra S., Kumar N.N., Samal M.K., Chavan V.M., Patel R.J., “Molecular dynamics simulation of crack growth behavior in Al in the presence of vacancies”, Computational Materials Science, 117 (2016), 518–526 | DOI

[7] Andric P., Curtin W.A., “New theory for Mode I crack-tip dislocation emission”, Journal of Mechanics and Physics of Solids, 106 (2017), 315–337 | DOI

[8] Gao Y.-J., Deng Q.-Q., Huang L.Ye, Wen Z.C., Luo Zhi-R., “Atomistic modeling for mechanism of crack cleavage extension on nano-scale”, Computational Materials Science, 130 (2017), 64–75 | DOI

[9] Cui C.B., Beom H.G., “Molecular dynamics simulation of edge cracks in copper and aluminium single crystals”, Materials Science and Engineering: A, 609 (2014), 102–109 | DOI

[10] Stepanova L.V., Mathematical methods of fracture mechanics, FIZMATLIT, M., 2009, 336 pp. (in Russ.)

[11] Hellan K., Introduction to Fracture Mechanics, transl. from English, Mir, M., 1988, 364 pp. (in Russ.)

[12] Stepanova L.V., Roslyakov P.S., “Multi-parameter description of the crack-tip stress field: Analytic determination of coefficients of crack-tip stress expansions in the vicinity of the crack tips of two finite cracks in an infinite plane medium”, International Journal of Solids and Structures, 100–101 (2016), 11–28 | DOI

[13] Berinsky I.E., Dvas N.G., Krivtsov A.M., Kudarova A.M., Kuzkin V.A., Le-Zakharov A.A., Loboda O.S., Neugebauer I.I., Podolskaya E.A., Theoretical mechanics. Elastic and thermal properties of ideal crystals, textbook, Izd-vo Politekhn. un-ta, Saint Petersburg, 2009, 144 pp. (in Russ.)

[14] Gaillac R., Pullumbi P., Coudert F.-X., “ELATE: an open - source online application for analysis and visualization of elastic tensors”, Journal of Physics: Condensed Matter, 28:27 (2016), 275201 | DOI

[15] Guide to using the LAMMPS package

[16] Guide to using the OVITO package

[17] Sobhit Singh, Logan Lang, Viviana Dovale-Farelo, Uthpala Herath, Pedram Tavadze, Francois-Xavier Coudert, Aldo H. Romero, “MechElastic: A Python library for analysis of mechanical and elastic properties of bulk and 2D materials”, Computer Physics Communications, 267 (2021), 108068 | DOI