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From Simulation to Theory in the Physics of Deformation and Fracture

Published online by Cambridge University Press:  31 January 2011

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Fracture dynamics remains a challenging research topic in materials science, mechanical engineering, mathematics, and nonequilibrium physics. Despite nearly a century of intense investigation, several basic problems remain unsolved. In particular, there is still no fundamental understanding of the distinction between brittle and ductile failure; there is still no definitive explanation of how breaking stresses can be transmitted through plastic zones near crack tips, nor is there an adequate understanding of why the energy-release rate even in brittle fracture is often orders of magnitude larger than the rate at which surface energy is created. These difficulties seem to stem primarily from the lack of an adequate theory of deformation near crack tips, where stresses and strain rates are large.

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Research Article
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Copyright © Materials Research Society 2000

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References

1.Falk, M.L. and Langer, J.S., Phys. Rev. E 57 (1998) p. 7192.CrossRefGoogle Scholar
2.Falk, M.L., Phys. Rev. B 60 (1999) p. 7062.Google Scholar
3. Such internal-state variable models of plastic deformation have been used widely in the description of crystal plasticity. The origin of these ideas are attributable to Hart, E., Acta Metall. 18 (1970) p. 599; and J. Rice, in Constitutive Equations in Plasticity, edited by A. Argon (MIT Press, Cambridge, MA, 1975) p. 23. The term “rate-and-state theory” is widely used in the seismological literature and in recent theories of friction. For seismological references, see A. Ruina, J. Geophys. Res. 88 (1983) p. 10359; and J.H. Dieterich and B.D. Kilgore, Pageoph 143 (1994) p. 283. For related work on friction, see J.M. Carlson and A.A. Batista, Phys. Rev. E 53 (1996) p. 4153.CrossRefGoogle Scholar
4.Lubliner, J., Plasticity Theory (Macmillan, New York, 1990).Google Scholar
5.Hill, R., The Mathematical Theory of Plasticity (Clarendon Press, Oxford, 1960).Google Scholar
6. In the context of crystalline materials, the effect of interparticle potential on ductility has received significant attention. For specific references, see Rice, J.R. and Thomson, R., Philos. Mag. 29 (1974) p. 73; J.R. Rice, J. Mech. Phys. Solids 40 (1992) p. 239; and S.J. Zhou, A.E. Carlsson, and R. Thompson, Phys. Rev. Lett. 72 (1994) p. 852.Google Scholar
7.Srolovitz, D., Vitek, V., and Egami, T., Acta Metall. 31 (1983) p. 335.CrossRefGoogle Scholar
8.Kobayashi, S., Maeda, K., and Takeuchi, S., Acta Metall. 28 (1980) p. 1641.CrossRefGoogle Scholar
9.Maeda, K. and Takeuchi, S., Philos. Mag. A 44 (1981) p. 643.Google Scholar
10.Deng, D., Argon, A., and Yip, S., Philos. Trans. R. Soc. London, Ser. A 329 (1989) p. 549.Google Scholar
11.Spaepen, F., Acta Metall. 25 (1977) p. 407.CrossRefGoogle Scholar
12.Argon, A., Acta Metall. 27 (1979) p. 47.Google Scholar
13.Argon, A. and Kuo, H.,Mater. Sci. Eng. 39 (1979) p. 101.Google Scholar
14.Spaepen, F. and Taub, A., in Physics of Defects, Proc. of the 1981 Les Houches Summer School, Session XXXV, edited by Balian, R., Kleman, M., and Poirier, J.-P. (North-Holland, Amsterdam, 1981) p. 133.Google Scholar
15.Argon, A. and Shi, L., Acta Metall. 31 (1983) p. 499.Google Scholar
16.Cohen, M. and Turnbull, D., J. Chem. Phys. 31 (1959) p. 1164.CrossRefGoogle Scholar
17.Turnbull, D. and Cohen, M.,J. Chem. Phys. 34 (1961) p. 120.CrossRefGoogle Scholar
18.Turnbull, D. and Cohen, M., J. Chem. Phys. 52 (1970) p. 3038.Google Scholar
19.Langer, J.S. and Lobkovsky, A.E., Phys. Rev. E 58 (1998) p. 1568.Google Scholar
20.Langer, J.S. and Lobkovsky, A.E., Phys. Rev. E 60 (1999) p. 6978.Google Scholar
21.Malvern, L.E., Introduction to the Mechanics of a Continuous Medium (Prentice-Hall, Englewood Cliffs, NJ, 1969).Google Scholar
22.Mangion, M.B.M., Cavaille, J.Y., and Perez, J., Philos. Mag. A 66 (1992) p. 773.Google Scholar
23.Hasan, O.A. and Boyce, M.C., Polym. Eng. Sci. 35 (1995) p. 331.Google Scholar
24.Kobayashi, M., Ohno, N., and Igari, T., Int. J. Plasticity 14 (1998) p. 373.Google Scholar
25.Kuhlmann-Wilsdorf, D., Mater. Sci. Eng., A 113 (1989) p. 1.Google Scholar
26.Pampillo, C.A., J. Mater. Sci. 10 (1975) p. 1194.Google Scholar
27.Bulatov, V.V. and Argon, A.S., Modelling Simul. Mater. Sci. Eng. 2 (1994) p. 167.CrossRefGoogle Scholar