Abstract
A multiscale cohesive zone model (MCZM) that combines finite element method with atomistic modeling is applied to simulate fracture of amorphous materials and polycrystalline solids. In order to apply MCZM to model amorphous materials, the Cauchy–Born rule is linked with the Parrinello–Rahman MD method to associate atom configurations with material deformation by using molecular statics (MS). We found the algorithm allows us to simulate ductile fracture of amorphous materials successfully. In addition, the methodology is applied to model the amorphous grain boundaries of polycrystalline solids, and we show that it can capture ductile fracture of polycrystalline metals.
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Dolbow, J.O.H.N., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131–150 (1999)
Stolarska, M., Chopp, D.L., Mos, N., Belytschko, T.: Modelling crack growth by level sets in the extended finite element method. Int. J. Numer. Methods Eng. 51(8), 943–960 (2001)
Xu, X.P., Needleman, A.: Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solids 42(9), 1397–1434 (1994)
Camacho, G.T., Ortiz, M.: Computational modelling of impact damage in brittle materials. Int. J. Solids Struct. 33(20–22), 2899–2938 (1996)
Shet, C., Chandra, N.: Analysis of energy balance when using cohesive zone models to simulate fracture processes. J. Eng. Mater. Technol. 124(4), 440–450 (2002)
Ren, B., Li, S.: Modeling and simulation of large-scale ductile fracture in plates and shells. Int. J. Solids Struct. 49(18), 2373–2393 (2012)
Silling, S.A.: Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48(1), 175–209 (2000)
Silling, S.A., Lehoucq, R.B.: Peridynamic theory of solid mechanics. Adv. Appl. Mech. 44, 73–168 (2010)
Hori, M., Oguni, K., Sakaguchi, H.: Proposal of FEM implemented with particle discretization for analysis of failure phenomena. J. Mech. Phys. Solids 53(3), 681–703 (2005)
Oguni, K., Wijerathne, M.L.L., Okinaka, T., Hori, M.: Crack propagation analysis using PDS-FEM and comparison with fracture experiment. Mech. Mater. 41(11), 1242–1252 (2009)
Wijerathne, M.L.L., Oguni, K., Hori, M.: Numerical analysis of growing crack problems using particle discretization scheme. Int. J. Numer. Methods Eng. 80(1), 46–73 (2009)
Francfort, G.A., Marigo, J.J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319–1342 (1998)
Bourdin, B., Francfort, G.A., Marigo, J.J.: Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48(4), 797–826 (2000)
Bourdin, B.: Numerical implementation of the variational formulation for quasi-static brittle fracture. Interfaces Free Bound. 9(3), 411–430 (2007)
Bourdin, B., Francfort, G.A., Marigo, J.J.: The variational approach to fracture. J. Elast. 91(1–3), 5–148 (2008)
Takaishi, T., Kimura, M.: Phase field model for mode III crack growth in two dimensional elasticity. Kybernetika 45(4), 605–614 (2009)
Rountree, C.L., Kalia, R.K., Lidorikis, E., Nakano, A., Van Brutzel, L., Vashishta, P.: Atomistic aspects of crack propagation in brittle materials: multimillion atom molecular dynamics simulations. Ann. Rev. Mater. Res. 32(1), 377–400 (2002)
Goel, S., Faisal, N.H., Luo, X., Yan, J., Agrawal, A.: Nanoindentation of polysilicon and single crystal silicon: molecular dynamics simulation and experimental validation. J. Phys. D: Appl. Phys. 47(27), 275304 (2014)
Miller, R.E., Tadmor, E.B.: A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods. Model. Simul. Mater. Sci. Eng. 17(5), 053001 (2009)
Liu, X., Li, S., Sheng, N.: A cohesive finite element for quasi-continua. Comput. Mech. 42(4), 543–553 (2008)
Zeng, X., Li, S.: A multiscale cohesive zone model and simulations of fractures. Comput. Methods Appl. Mech. Eng. 199(9), 547–556 (2010)
Li, S., Zeng, X., Ren, B., Qian, J., Zhang, J., Jha, A.K.: An atomistic-based interphase zone model for crystalline solids. Comput. Methods Appl. Mech. Eng. 229, 87–109 (2012)
Qian, J., Li, S.: Application of multiscale cohesive zone model to simulate fracture in polycrystalline solids. J. Eng. Mater. Technol. 133(1), 011010 (2011)
He, M., Li, S.: An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method. Comput. Mech. 49(3), 337–355 (2012)
Urata, S., Li, S.: Higher order Cauchy–Born rule based multiscale cohesive zone model and prediction of fracture toughness of silicon thin films. Int. J. Fract. 203, 159–181 (2017)
Urata, S., Li, S.: A multiscale model for amorphous materials. Comput. Mater. Sci. 135, 64–77 (2017)
Needleman, A.: A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54(3), 525–531 (1987)
Needleman, A.: An analysis of decohesion along an imperfect interface. Int. J. Fract. 42(1), 21–40 (1990)
Ericksen, J.L.: On the Cauchy–Born rule. Math. Mech. Solids 13(3–4), 199–220 (2008)
Fan, H., Li, S.: Multiscale cohesive zone modeling of crack propagations in polycrystalline solids. GAMM-Mitteilungen 38(2), 268–284 (2015)
Lyu, D., Fan, H., Li, S.: A hierarchical multiscale cohesive zone model and simulation of dynamic fracture in metals. Eng. Fract. Mech. 163, 327–347 (2016)
Liu, L., Li, S.: A finite temperature multiscale interphase zone model and simulations of fracture. J. Eng. Mater. Technol. 134(3), 031014 (2012)
Tersoff, J.: Empirical interatomic potential for silicon with improved elastic properties. Phys. Rev. B 38(14), 9902 (1988)
Li, S., Urata, S.: An atomistic-to-continuum molecular dynamics: theory, algorithm, and applications. Comput. Methods Appl. Mech. Eng. 306, 452–478 (2016)
Parrinello, M., Rahman, A.: Polymorphic transitions in single crystals: a new molecular dynamics method. J. Appl. Phys. 52(12), 7182–7190 (1981)
Chen, Y., Lee, J.D.: Multiscale modeling of polycrystalline silicon. Int. J. Eng. Sci. 42(10), 987–1000 (2004)
Stemmer, S., Streiffer, S.K., Browning, N.D., Basceri, C., Kingon, A.I.: Grain boundaries in barium strontium titanate thin films: structure, chemistry and influence on electronic properties. Interface Sci. 8(2–3), 209–221 (2000)
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Urata, S., Li, S. (2018). Simulation of Ductile Fracture in Amorphous and Polycrystalline Materials by Multiscale Cohesive Zone Model. In: van Meurs, P., Kimura, M., Notsu, H. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications II. CoMFoS 2016. Mathematics for Industry, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-6283-4_4
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