Abstract
Molecular dynamics is applicable only for a small region of simulation. To simulate a large region it is necessary to combine molecular dynamics with continuum mechanics. Previously we proposed a new model in which molecular dynamics was combined with micromechanics. A molecular dynamics model was applied to the crack tip region and a micromechanics model to the surrounding region. In that model, however, crack propagation simulation must be stopped when the crack tip reaches the boundary of the two regions. In this paper the previous model is improved by moving the molecular dynamics region successively with crack propagation. The improved model may be applied to simulate limitless crack propagation. In order to examine the validity of the improved model, we simulate α-iron. The calculation cost with the improved model is less than a tenth of that of the previous model although the results are equal to each other. The crack tip opening displacement calculated with this model is almost equal to the analytical solution derived by Rice.
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References
Cheung, K.S. and Yips, S. (1990). Brittle–ductile transition in intrinsic fracture behavior of crystals. Physical Review Letters 65–22, 2804–2807.
Chou, Y.T. (1967). Dislocation pile–ups against a locked dislocation of different Burgers vector. Journal of Applied Physics 38, 2080–2085.
deCelis, B., Argon, A.S. and Yip, S. (1983). Molecular dynamics simulation of crack tip process in alpha–iron and copper. Journal of Applied Physics 54–9, 4864–4878.
Eshelby, J.D., Frank, F.C. and Nabarro, F.R.N. (1951). The equilibrium of linear arrays of dislocations. Philosophical Magazine 42, 351–364.
Eshelby, J.D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings, Royal Society London A241, 376–396.
Hirth, J.P., Hoagland, R.G. and Gehlen, P.C. (1974). The interaction between line force arrays and planar cracks. International Journal of Solids and Structures 10–9, 977–984.
Johnson, R.A. (1964). Interstitials and vacancies in α–iron. Physical Review 134–5, 1329–1336.
Kanninen, M.F. and Gehlen, P.C. (1971). Atomic simulation of crack extension in BCC iron. International Journal of Fracture Mechanics 7, 471–474.
Kitagawa, H., Nakatani, A. and Shibutani, Y. (1994). Molecular dynamics study of crack processes associated with dislocation nucleated at the tip. Materials Science and Engineering A176, 263–269.
Kohlhoff, S., Schmauder, S. and Gumbsch, P. (1988). A new method for coupled elastic–atomistic modeling. (Edited by V. Vitek and D.J. Srolovitz), Large atomistic simulation of materials – Beyond pair potentials –, Plenum Press, 411–418.
Kohlhoff, S. and Gumbsch, P. and Fichmeister, H.F. (1991). Crack propagation in b.c.c. crystals studied with a combined finite–element and atomistic model. Philosophical Magazine 64–4, 851–878.
Lekhnitski, S.G. (1968). Anisotropic Plates, Gordon and Breach.
Mullins, M. and Dokanish, F. (1982). Simulation of the (001) plane crack in α1;–iron employing a new boundary scheme. Philosophical Magazine 46–5, 771–787.
Mullins, M. (1982). Molecular dynamics simulation of propagating cracks. Scripta Metallurgica 16, 663–666.
Noguchi, H. and Furuya, Y. (1997). A method of seamlessly combining a crack tip molecular dynamics enclave with a linear elastic outer domain in simulating elastic–plastic crack advance. International Journal of Fracture, 87–4, 309–329.
Rice, J.R. (1974). Limitations to the small scale yielding approximation for crack tip plasticity. Journal of The Mechanics and Physics of Solids 22, 17–26.
Sinclair, J.E., Gehlen, P.C., Hoagland, R.G. and Hirth, J.P. (1978). Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling. Journal of Applied Physics 49–7, 3890–3897.
Weertman, J. and Weertman, J.R. (1964). Elementary dislocation theory, The Macmillan Company.
Weiner, J.H. and Pear, M. (1975). Crack and dislocation propagation in an idealized crystal model. Journal of Applied Physics 46–6, 2398–2405.
Woodcock, L.V. (1971). Isothermal molecular dynamics calculations for liquid salts. Chemical Physics Letters 10–3, 257–261.
Yang, W., Tan, H. and Guo, T. (1994). Evolution of crack tip process zones. Modeling and Simulation in Materials Science and Engineering 2, 767–782.
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Furuya, Y., Noguchi, H. A combined method of molecular dynamics with micromechanics improved by moving the molecular dynamics region successively in the simulation of elastic--plastic crack propagation. International Journal of Fracture 94, 17–31 (1998). https://doi.org/10.1023/A:1007520010603
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DOI: https://doi.org/10.1023/A:1007520010603