K. A. Mushankova, L. V. Stepanova
ATOMISTIC DETERMINATION OF STRESS FIELDS IN SAMPLES WITH DEFECTS
DOI: 10.17804/2410-9908.2022.3.036-046 The main goal of the study is the atomistic determination of the static stress-strain state at the crack tip in isotropic and anisotropic linearly elastic materials by the molecular dynamics method implemented in the open source LAMMPS (Large-scale Atomistic/Molecular Massively Parallel Simulator). An extensive class of computational experiments has been carried out for a single-crystal copper specimen with a central crack in the LAMMPS. The circumferential distributions of the stress tensor components obtained by molecular dynamics are compared with the angular distributions of brittle fracture continuum mechanics, i.e. with Williams’ analytical solution to the problem of an infinite plate loaded with a central crack in a linearly elastic isotropic material. The comparison of the angular distributions of the stress tensor components gained in the framework of atomistic modeling and the angular distributions obtained from the classical solution of continuum mechanics has shown that, at the nanoscale level, the stress fields are in good agreement with their macroscopic values.
Keywords: molecular dynamics approach, classical fracture mechanics, embedded atom potential (EAM), crack propagation References:
- 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, 2012, vol. 49 (3–4), pp. 556–566. DOI: 10.1016/j.ijsolstr.2011.10.024.
- Stepanova L.V., Yakovleva E.M. Mixed-mode loading of the cracked plate under plane stress conditions. Vestnik PNIPU. Mekhanika, 2014, No. 3, pp. 129–162. DOI: 10.15593/perm.mech/2014.3.08. (In Russian).
- Rashidi Moghaddam M., Ayatollahi M.R., Berto F. The application of strain energy density criterion to fatigue crack growth behavior of cracked components. Theoretical and Applied Fracture Mechanics, 2018, vol. 97, pp. 440–447. DOI: 10.1016/j.tafmec.2017.07.014.
- 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 specimen. Theoretical and Applied Fracture Mechanics, 2018, vol. 97, pp. 419–425. DOI: 10.1016/j.tafmec.2017.07.004.
- Malíková L., Veselý V., Seitl S. Estimation of the crack propagation direction in a mixed-mode geometry via multi-parameter fracture criteria. Frattura ed Integrità Strutturale, 2015, 9 (33), 25–32. DOI: 10.3221/igf-esis.33.04.
- 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, 2016, vol. 117, pp. 518–526. DOI: 10.1016/j.commatsci.2016.02.032.
- Andric P., Curtin W.A. New theory for Mode I crack-tip dislocation emission. Journal of the Mechanics and Physics of Solids, 2017, vol. 106, pp. 315–337. DOI: 10.1016/j.jmps.2017.06.006.
- Gao Ying-jun, Deng Qian-qian, Huang Li-lin, Ye Li, Wen Zhen-chuan, Luo Zhi-rong. Atomistic modeling for mechanism of crack cleavage extension on nano-scale. Computational Materials Science, 2017, vol. 130, pp. 64–75. DOI: 10.1016/j.commatsci.2017.01.003.
- Cui C.B., Beom H.G. Molecular dynamics simulation of edge cracks in copper and aluminium single crystals. Materials Science and Engineering A, 2014, vol. 609, pp. 102–109. DOI: 10.1016/j.msea.2014.04.101.
- 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, 2016, vols. 100–101, pp. 11–28. DOI: 10.1016/j.ijsolstr.2016.06.032.
- Hardy R.J. Formulas for determining local properties in molecular-dynamics simulations: shock waves. Journal Chemical Physics, 1982, vol. 76, pp. 622–628. DOI: 10.1063/1.442714.
- Berinskii I.E., Dvas N.G., Krivtsov A.M., et al. Uprugie i teplovye svoystva idealnykh kristallov [Theoretical Mechanics. Elastic Properties of Monoatomic and Diatomic Crystals: educational book, ed., A.M. Krivtsov], St. Petersburg, Izd-vo Politekhn. Un-ta, 2009. (In Russian).
- Gaillac Romain, Pullumbi Pluton and Coudert François-Xavier. ELATE: an open-source online application for analysis and visualization of elastic tensors. Journal of Physics: Condensed Matter, 2016, vol. 28 (27), 275201. DOI: 10.1088/0953-8984/28/27/275201.
Article reference
Mushankova K. A., Stepanova L. V. Atomistic Determination of Stress Fields in Samples with Defects // Diagnostics, Resource and Mechanics of materials and structures. -
2022. - Iss. 3. - P. 36-46. - DOI: 10.17804/2410-9908.2022.3.036-046. -
URL: http://eng.dream-journal.org/issues/2022-3/2022-3_368.html (accessed: 12/02/2024).
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