PSI - Issue 50

L.V. Stepanova et al. / Procedia Structural Integrity 50 (2023) 275–283 Author name / Structural Integrity Procedia 00 (2021) 000 – 000

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realized by molecular dynamics method. Within the context of the continuum solid mechanics – based approach the higher-order factors of the Max Williams series expansions are determined from the closed form solutions for the infinite plane medium with the central crack and from the finite element analysis for the single edge notched plate. The finite element analysis allows us to estimate stress tensor components and then the over-deterministic method to compute the amplitude coefficients of the Max Williams series expansion is involved. The coefficients of the Max Williams series power expansion are reckoned by the over-deterministic method based on the atomistic stresses calculated via the Virial formalism. The reconciliation of the results captured by two techniques is evidently observed. The originality of the presented work is begotten by scrutiny and comparability of two materials with cubic singony and two approaches based on continuum mechanics and discrete molecular dynamics method. The comparison performed can serve as a backend or an engine for understanding the relations and interactions of failure processes at two scales. Acknowledgements The work was supported by Russian Foundation for Basic Research (project 20-31-90082). References Birang, O. S.E., Steinmann, P., 2021. Discrete configurational mechanics for the computational study of atomistic fracture mechanics. Forces in Mechanics, 2, 100009. Gao, H., Huang, Y., Abraham, F.F., 2001. Continuum and atomistic of intersonic crack propagation. Journal of the Mechanics and Physics of Solids, 49, 2113. Buehler, M.J., Gao, H., Huang, Y., 2004. Atomistic and continuum studies of stress and strain fields near a rapidly propagating crack in a harmonic lattice. Theoretical and Applied Fracture Mechanics, 41, 21. Chakraborty, S., Ghost, S., 2021. Crystal plasticity phase – field model with crack tip enhancement through a concurrent atomistic-continuum model, Journal of the Mechanics and Physics of Solids, 155, 104563. Diaz, A., Gu, B., Li, Y., Plimpton, S.J., McDowell, L., Chen, Y., 2022. A parallel algorithm for the concurrent atomistic-continuum methodology. Journal of Computational Physics, 463, 111140. Karihaloo, B.L., Xiao, Q.Z., 2001. Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. Eng. Fract. Mechanics 68(15), 1609-1630. Li, Y., Zheng, K., 2021. Crack tip field coefficients analyses based on the extended finite element method using over-deterministic displacement field fitting method. Theoretical and applied Fracture Mechanics 113, 102971. Liu, P., Ju, Y., Fu, G., Ren, Z., 2020. Visualization of full-field stress evolution during 3D penetrated crack propagation through 3D printing and frozen stress techniques. Engineering Fracture Mechanics 236, 107222. Machova, A., Uhnakova, A., Hora, P., 2017. Growth of 3D edge cracks in mode I and T-stress on the atomistic level. Computational Materials Science, 138, 315. Malikova, L., Vesely, V., 2014. Significance of higher-order terms of the Williams expansion for plastic zone extent estimation demonstrated on a mixed-mode geometry. Procedia Structural Integrity 2014, 3 1383-1388. Peng, Y., Ji R., Phan, T., Gao, W., Levitas, V.I., Xiong, L., 2022. An atomistic-to-microscale computational analysis of the dislocation pileup induced local stresses near an interface in plastically deformed two-phase materials, Acta Materialia, 226, 117663. Stepanova, L.V., Belova, O.N., 2022. Coefficients of the Williams power expansion of the near crack stress field in continuum linear elastic fracture mechanics at the nanoscale. Theoretical and Applied Fracture Mechanics, 119, 103298. Stepanova, L.V., Belova, O.N., Bronnikov, S.A., 2021. Atomistic Determination of Fracture Mechanics Parameters, Procedia Structural Integrity, 32, 261-272. Stepanova, L.V., Roslyakov, P.S., 2016. Complete Williams asymptotic expansion of the stress field near the crack tip: analytical solutions, interference-optic methods and numerical experiments. AIP Conference 1785, 030029.