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Atomistic Aspects of Fracture Modelling in the Framework of Continuum Mechanics

Published online by Cambridge University Press:  10 February 2011

F. Cleri
F. Cleri*
Affiliation:
Divisione Materiali Avanzati, ENEA, Centro Ricerche Casaccia, C.P. 2400, 00100 Roma, (Italy)
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Abstract

The validity and predictive capability of continuum models of fracture rests on basic informations whose origin lies at the atomic scale. Examples of such crucial informations are, e.g., the explicit form of the cohesive law in the Barenblatt model and the shear-displacement relation in the Rice-Peierls-Nabarro model. Modem approaches to incorporate atomic-level information into fracture modelling require to increase the size of atomic-scale models up to millions of atoms and more; or to connect directly atomistic and macroscopic, e.g. finite-elements, models; or to pass information from atomistic to continuum models in the form of constitutive relations. A main drawback of the atomistic methods is the complexity of the simulation results, which can be rather difficult to rationalize in the framework of classical, continuum fracture mechanics. We critically discuss the main issues in the atomistic simulation of fracture problems (and dislocations, to some extent); our objective is to indicate how to set up atomistic simulations which represent well-posed problems also from the point of view of continuum mechanics, so as to ease the connection between atomistic information and macroscopic models of fracture.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 538: Symposium J – Multiscale Modelling of Materials , 1998 , 441
Copyright
Copyright © Materials Research Society 1999

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References

1. Liebowitz, H. (ed.), “Fracture: An Advanced Treatise. Vol.11: Mathematical Fundamentals”, Academic Press, New York, 1968; G.C. Sih, H. Nisitani and T. Ishihara (eds.), “Role of Fracture Mechanics in Modem Technology”, Elsevier, Amsterdam, 1987; M.H. Aliabadi and D.P. Rooke, “Numerical Fracture Mechanics”, Kluwer, Dordrecht, 1991.Google Scholar
2. Griffith, A.A., Philos. Trans. Royal Soc. (London) A 221 (1920) 163.Google Scholar
3. Selinger, R.L. Blumberg, Mecholsky, J.J, Carlsson, A. E. and Fuller, E. R. Jr (eds.), “Fracture-Instability Dynamics, Scaling and Ductile/Brittle Behavior”, MRS vol. 409, Pittsburgh, 1996; A.K. Cheetam et al., J. Comput.-Aided Mater. Design 3 (1996) 1.Google Scholar
4. Gerberich, W.W. et al., Acta Metall. Mater. 43 (1995) 1569.Google Scholar
5. Ashurst, W.T. and Hoover, W.G., Phys. Rev., B 14 (1976) 1465.Google Scholar
6. Lomdahl, P.S. et al., Int. J. Mod. Phys. C42 (1993) 1075.Google Scholar
7. Abraham, F.F et al., Phys. Rev. Lett. 73 (1994) 272.Google Scholar
8. Holian, B.L. and Ravelo, R., Phys. Rev. B 51 (1995) 11275.Google Scholar
9. Nakano, A., Kalia, R.K. and Vashista, P., Phys. Rev. Lett. 73 (1994) 2336.Google Scholar
10. Zhou, S.J. et al., Phys. Rev. Lett. 76 (1996) 2318.Google Scholar
11. Mullins, D. and Dokainish, A., Phil. Mag. A 46 (1982) 771.Google Scholar
12. Kohloff, S., Gumbsch, P. and Fischmeister, H.F., Phil. Mag. A 64 (1991) 851.Google Scholar
13. Tadmor, E.B., Ortiz, M. and Phillips, R., Phil. Mag. A 73 (1996) 1529.Google Scholar
14. Miller, R. and Phillips, R., Phil. Mag. A 73 (1996) 803.Google Scholar
15. Kaxiras, E. and Duesbery, M.S., Phys. Rev. Lett. 70 (1993) 3752.Google Scholar
16. Cleri, F., Yip, S., Wolf, D. and Phillpot, S.R., Phys. Rev. Lett. 79 (1997) 1309; Acta Mater. 45 (1997) 4993.Google Scholar
17. Love, A.E.H., Appendix B in “A Treatise on the Mathematical Theory of Elasticity”, 4th ed., Dover, , New York, 1944; M. Born and K. Huang, “Dynamical Theory of Crystal Lattices”. Oxford University Press, Oxford, 1954.Google Scholar
18. Cleri, F., Phillpot, S.R., Wolf, D. and Yip, S., J. Am. Cer. Soc. 81 (1998) 503.Google Scholar
19. Allen, M.P. and Tildesley, D.J., “Computer simulation of liquids”, Oxford Science Publications, Oxford, 1989.Google Scholar
20. Parrinello, M. and Rahman, A., J. Appl. Phys. 52 (1981) 7182.Google Scholar
21. Cheung, K.S. and Yip, S., Phys. Rev. Lett. 65 (1990) 2804.Google Scholar
22. Hoagland, R.G., Daw, M.S. and Hirth, J.P., J. Mater. Res. 6 (1991) 2565.Google Scholar
23. Lekhnitskii, S.G., pp.153–162 in “Theory of Elasticity of an Anisotropic Elastic Body”, Holden-Day, San Francisco, 1963.Google Scholar
24. Parton, V.Z. and Morozov, E.M., pp.103–123 in “Mechanics of Elastic-Plastic Fracture”, Hemisphere, Washington, 1989.Google Scholar
25. Bulatov, V., Abraham, F.F., Kubin, L., Devincre, B and Yip, S., Nature 391 (1998) 669.Google Scholar