Experience in modeling inclined cracks in materials with cubic crystal structure

K. A. Mushankova   ; L. V. Stepanova

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 4, pp. 106-116

Résumé

In this work, a good coincidence of atomistic and continuum stress fields at the crack tip under mixed mode loading conditions in an anisotropic medium with cubic symmetry of elastic properties is revealed. The atomic stress distributions associated with the crack tip are obtained using the molecular dynamics method. Continuum distributions are obtained from the theoretical solution of the problem of determining the stress-strain state at the crack tip, based on the methods of the elasticity theory of anisotropic media and the subsequent decomposition of complex potentials by eigenfunctions. In the framework of a molecular dynamics computational experiment, a single-crystal face-centered copper at low temperature was considered in order to isolate the elastic mode of deformation of a single crystal, and the embedded atom potential was used. A distinctive feature of the conducted molecular dynamic modeling is the consideration of a crack that makes up various angles with planes of symmetry of the crystal. In the vicinity of the crack tip, points lying in annular regions at different distances from the crack tip and of different thickness were selected, and the dependences of the stress tensor components depending on the polar angle were plotted. A comparison of the angular dependencies obtained by atomistic calculation and using a theoretical solution showed their good consistency. It is found that the similarity of the angular dependences of the stress tensor components is observed for all the studied values of two angles: the angle between the axis of symmetry of the crystal lattice (in the plane of the plate) and the direction of the crack and the angle between the action of the tensile load and the crack line. By virtue of this property of solutions, it can be concluded that solutions of continuous fracture mechanics can serve to describe stress fields at atomistic distances from the crack tip.

Détail

Keywords: molecular dynamics method, atom implementation potential, cubic system, stress fields.

Bibliographie

[1] Cui Y., Chew H.B., “Machine-Learning Prediction of Atomistic Stress along Grain Boundaries”, Acta Materialia, 222 (2022), 117387 | DOI

[2] Li R., Chew H.B., “Grain boundary traction signatures: Quantitative Predictors and Dislocation Emission”, Physical Review Letters, 117:8 (2016), 085502 | DOI

[3] Li R., Chew H.B., “Grain boundary traction signatures: Quantifying the asymmetrical dislocation emission processes under tension and compression”, Journal of the Mechanics and Physics of Solids, 103 (2017), 142–154 | DOI

[4] Wu W.-P., Yao Z.-Z., “Molecular dynamics simulation of stress distribution and microstructure evolution ahead of a growing crack in single crystal nickel”, Theoretical and Applied Fracture Mechanics, 62 (2012), 67–75 | DOI

[5] Yamakov V., Saether E., Phillips D.R., Glaessgen E.H., “Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum”, Journal of the Mechanics and Physics of Solids, 54:9 (2006), 1899–1928 | DOI | Zbl

[6] Egami T., “Atomic level stress”, Progress in Materials Science, 56:6 (2011), 637–653 | DOI

[7] Tsai D.H., “The virial theorem and stress calculation in molecular dynamics”, Journal of Chemical Physics, 70:3 (1979), 1375–1382 | DOI

[8] Nartin R.M., “First-Principles Calculation of Stress”, Physical Review Letters, 50:9 (1983), 697–700 | DOI

[9] Nielsen O.N., Martin R.M., “Quantum-mechanical theory of stress and force”, Physical Review B, 32:6 (1985), 3780 | DOI

[10] Maranganti R., Sharma P., “Revisiting quantum notions os stress”, Proceedings of the Royal Society A, 466:2119 (2010), 2097–2116 | DOI | MR | Zbl

[11] Maranganti R., Sharma P., Wheeler L., “Quantum notions of stress”, Journal of Aerospace Engineering, 20:1 (2007), 22–37 | DOI

[12] Shiihara Y., Kohyama M., Ishibashi S., “Ab initio local stress and its application to Al (111) surfaces”, Physical Review B, 81:7 (2010), 075441 | DOI

[13] Wang H., Kohyama M., Tanaka S., Shiihara Y., “Ab initio local-energy and local-stress analysis of tensile behaviours of titl grain boundaries in Al and Cu”, Modelling and Simulation in Materials Science and Engineering, 25:1 (2017), 015005 | DOI

[14] Cui Y., Chew H.B., “A simple numerical approach for reconstructing the atomic stresses at grain boundaries from quantum-mechanical calculations”, Journal of Chemical Physics, 150:14 (2019), 144702 | DOI

[15] Nicholson D.M., Ojha M., Egami T., “First-principles local stress in crystalline and amorphous metals”, Journal of Physics: Condensed Matter, 25:43 (2013), 435505 | DOI

[16] Koch C.T., Ozdol V.B., Van Aken P.A., “An efficient, simple, and precise way to map strain with nanometer resolution in semiconductor devices”, Applied Physics Letters, 96:9 (2010), 091901 | DOI

[17] Hytch M, Houdeller, Hue F., Snoeck E., “Nano scale holographic interferometry for strain measurements in electronic devices”, Nature, 453:7198 (2008), 1086–1089 | DOI

[18] Beche A., Rouviere J.L., Barnes J.P., Cooper D., “Strain measurement at the nanoscale: Comparison between convergent beam electron diffraction, nano-beam electron diffraction, high resolution imaging and dark field electron holography”, Ultramicroscopy, 131 (2013), 10–23 | DOI

[19] Legros M., “In situ mechanical TEM: Seeing and measuring under stress with electrons”, Comptes Rendus Physique, 15 (2014), 224–240 | DOI

[20] Li Y.-M., Zhang B., “Cracking direction in grapheme under mixed mode loading”, Engineering Fracture Mechanics, 289 (2022), 109434 | DOI

[21] Min B., Chen X., Li Ke, Wang Z., “Multiscale study of enhancing the fracture properties of interfacial transition zone: Insights from molecular dynamics and finite element simulations”, Construction and Building Materials, 409 (2023), 133846 | DOI

[22] Stepanova L.V., Belova O.N., “Identification of stress intensity factors, T-stresses and higher-order coefficients of regular terms in the Williams series expansion through molecular dynamics simulations”, PNRPU Mechanics Bulletin, 2023, no. 2, 47–77 (In Russ.) | DOI

[23] Mushankova K.A., Stepanova L.V., “Influence of high-order terms in the solution generalizing the approach of M. Williams, taking into accounr the anisotropy of the material”, Vestnik Samarskogo universiteta. Estestvennonauchnaya seriya – Vestnik of Samara University. Natural Science Series, 29:2 (2023), 30–40 (In Russ.) | DOI | DOI | MR

[24] Stepanova L.V., Belova O.N., “Coefficients of the williams power expansion of the near crack tip stress field in continuum linear elastic fracture mechanics at the nanoscale”, Theoretical and Applied Fracture Mechanics, 119 (2022), 103298 | DOI

[25] Stepanova L.V., Belova O.N., “Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion and their evaluation through molecular dynamics simulations”, Mechanics of Advanced Materials and Structures, 30:19 (2023), 3862–3884 | DOI

[26] Mushankova K.A., Stepanova L.V., “Molecular dynamic modeling of stress fields in plates with a central crack made of materials with a face-centered cubic lattice”, Vestnik Samarskogo universiteta. Estestvennonauchnaya seriya – Vestnik of Samara University. Natural Science Series, 27:4 (2021), 68–82 (In Russ.) | DOI

[27] Nejati M., Ghouli S., Ayatollahi M.R., “Crack tip asymptotic fields in anisotropic planes: Importance of higher order terms”, Applied Mathematical Modelling, 91 (2021), 837–862 | DOI | MR | Zbl

[28] Ayatollahi M.R., Nejati M., Ghouli S., “The finite element over-deterministic method to calculate the coefficients of the crack tip asymptotic fields in anisotropic planes”, Engineering Fracture Mechanics, 231 (2020), 106982 | DOI | MR

[29] Sakha M., Nejati M., Aminzadeh A., Ghouli S., Saar M.O., “On the validation of mixed-mode I/II crack growth theories for anisotropic rocks”, International Journal of Solids and Structures, 241 (2022), 111484 | DOI

[30] Admal N.C., Tadmor E.B., “A unified interpretation of stress in molecular systems”, Journal of Elasticity, 100:1–2 (2010), 63–143 | DOI | MR | Zbl