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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3. Conclusions The study presents the method of determination of continuum fracture mechanics parameters (stress intensity factors, T-stress and higher-order terms of Williams series expansion of the stress field in the vicinity of the crack tip in an isotropic linear elastic materials) using molecular dynamics simulations. Based on the procedure of the over-deterministic method and the minimization of the objective function introduced the continuum fracture mechanics parameters for Mode I and Mixed Mode loading are found. Reconciliation of continuum and atomistic models is demonstrated. Atomistic simulations clearly show that the angular distributions of the stress tensor components are very similar to the analytical solution. We recognize that the work presented here only represents first steps in analysis of connections of two approaches. Several development steps would be needed for further progress. Nevertheless, the comparison carried out here clearly shows the similarity of the angular distributions of stresses in the vicinity of the crack tip. The further study is needed to delve into coupling two approaches of fracture processes description. Acknowledgements The work is supported by the Russian Science Foundation (project 21-11-00346). References Beltz, G.E., Machova, A., 2004. Effect of T-stress on dislocation emission in iron. Scripta Mater 59(4), 483-487. Beltz, G.E., Machova, A., 2007. Reconcillation of continuum and atomistic models for the ductile versus brittle response of iron. Modell Simul Mater Sci Eng 15(2), 65. Cheng, S.-H., Sun, C.T., 2011. Applicability of continuum fracture mechanics in atomic system. Proc. ASME. IMECE2011 8, 283-288. Dehaghani, M.Z., Mashhadzadeh, A.H., Salmankhani, A., Karami, Z., Habibzaden, S., Ganjali, M.R., Saeb, M.R.,2020. Fracture toughness and crack propagation behavior of nanoscale beryllium oxide graphene-like structures: A molecular dynamics simulation analysis. Engineering fracture Mechanics 235, 107194. Hello, G., 2018. Derivation of complete crack-tip stress expansions from Westergaard-Sanford solutions. International Journal of Solids and Structures 144-145, 265-275. Gallo, P., 2020. Some Considerations on Stress Intensity Factor at Atomic Scale. In: Gdoutos E., Konsta-Gdoutos M. (eds) Proceedings of the Third International Conference on Theoretical, Applied and Experimental Mechanics. ICTAEM 2020. Structural Integrity 16. 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. 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, 315-322. Mai, N.T., Choi, S.T., 2018. Atomic-scale mutual integrals for mixed-mode fracture: Abnormal fracture toughness of grain boundaries in graphene. International Journal of Solids and Structures 138, 205-216. Roy, S., Roy A., 2019. A computational investigation of length-scale effects in the fracture behaviour of a graphene sheet using the atomistic J integral. Engineering Fracture Mechanics 207, 165-180. Shimada, T., Ouchi, K., Chihara, Y., Kitamura, T., 2015. Breakdown of Continuum Fracture Mechanics at the Nanoscale. Sci Rep 5, 8596. Singh, D., Sharma, P., Parashar, A., 2019. Atomistic simulations to study crack tip behavior in single crystal of bcc niobium and hcp zirconium. Current Applied Physics 19, 37-43. Stepanova, L., Bronnikov, S. A., 2020. Computational study of the mixed-mode crack behavior by molecular dynamics method and the multi Parameter crack field description of classical fracture mechanics. Theoretical and Applied Fracture Mechanics 109, 102691. Stepanova, L.V., Belova, O.N., 2021. A molecular dynamics analysis of mixed mode crack growth. AIP Conference Proceedings 2371, 020012. Tsai, J.-L., Tzeng, S.-H., Tzou, Y.-J., 2010. Characterizing the fracture parameters of a graphene sheet using atomistic simulation and continuum mechanics. International Journal of Solids and Structures 47, 503-509. Wilson, M.A., Grutzik, S.J., Chandross, M. 2019. Continuum stress intensity factors from atomistic fracture simulations. Comput. Methods Appl. Mech. Engrg 354, 732-749.