Viscoplasticity and the dynamics of brittle fracture

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 62, Issue 1 B, 2000, Pages 1351-1360

  Langer, J S ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CRACK PROPAGATION; MATHEMATICAL MODELS; PLASTIC DEFORMATION; STRENGTH OF MATERIALS; STRESS ANALYSIS; STRESS INTENSITY FACTORS; VISCOELASTICITY; YIELD STRESS;

PLASTIC YIELD STRESS;

BRITTLE FRACTURE;

EID: 0034229466     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.62.1351     Document Type: Article

References (29)

1. J. Lubliner, Plasticity Theory (Macmillan, New York, 1990).
2. R. Hill, The Mathematical Theory of Plasticity (Clarendon Press, Oxford, 1960).
3. L.B. Freund, Dynamic Fracture Mechanics (Cambridge University Press, New York, 1990).
4. Melvin F. Kanninen and Carl H. Popelar, Advanced Fracture Mechanics (Oxford University Press, New York, 1985).
5. N.A. Fleck and J.W. Hutchinson, J. Mech. Phys. Solids 41, 1825 (1993).
6. N.A. Fleck, G.M. Muller, M.F. Ashby, and J.W. Hutchinson, Acta Metall. Mater. 42, 475 (1994).
7. N.A. Fleck and J.W. Hutchinson, in Advances in Applied Mechanics, edited by J.W. Hutchinson and T.Y. Wu (Academic Press, New York, 1996), Vol 33.
8. L.B. Freund and J.W. Hutchinson, J. Mech. Phys. Solids 33, 169 (1985).
9. J.S. Langer and A.E. Lobkovsky, J. Mech. Phys. Solids 46, 1521 (1998).
10. G.I. Barenblatt, Adv. Appl. Mech. 7, 56 (1962).
11. D.S. Dugdale, J. Mech. Phys. Solids 8, 100 (1960).
12. E.S.C. Ching, J.S. Langer, and H. Nakanishi, Phys. Rev. E 53, 2864 (1996).
13. X.-P. Xu, A. Needleman, and F. Abraham, Modell. Simul. Mater. Sci. Eng. 5, 489 (1997).
14. M.L. Falk and J.S. Langer, Phys. Rev. E 57, 7192 (1998).
15. A. Ruina, J. Geophys. Res. 88, 10359 (1983).
16. J.H. Dieterich and B.D. Kilgore, PAGEOPH 143, 283 (1994).
17. J.M. Carlson and A.A. Batista, Phys. Rev. E 53, 4153 (1996).
18. J.S. Langer and A.E. Lobkovsky, Phys. Rev. E (to be published).
19. A.A. Griffith, Philos. Trans. R. Soc. London, Ser. A 221, 163 (1920).
20. N.I. Muskhelishvili, Some Basic Problems in the Mathematical Theory of Elasticity (Noordhoff, Groningen, Holland, 1975).
21. Equation (4.9) is a well-known formula. A derivation is contained in J.S. Langer, in Chance and Matter, proceedings of the Les Houches Summer School, Session XLVI, edited by J. Souletie, J. Vannimenus, and R. Stora (North-Holland, Amsterdam, 1987).
22. Lawrence E. Malvern, Introduction to the Mechanics of a Continuous Medium (Prentice-Hall, Englewood Cliffs, NJ, 1969).
23. J.S. Langer and D. Rabinowitz (unpublished).
24. For a brief review and references regarding viscous fingering, see J.S. Langer, Science 243, 1150 (1989). While they look superficially similar, the viscous fingering and fracture problems are very different from one another. In fingering, pattern selection is controlled by surface tension. According to the present analysis of the fracture problem, although surface tension is important, it is the plastic yield stress that is essential in determining the growth mode.
25. M.L. Falk, Phys. Rev. E (to be published).
26. S.J. Zhou, P.S. Lomdahl, R. Thomson, and B.L. Holian, Phys. Rev. Lett. 76, 2318 (1996).
27. D. Holland and M. Marder, Phys. Rev. Lett. 80, 746 (1998); J. Hauch, D. Holland, M. Marder, and H.L. Swinney, ibid. 82, 3823 (1999).
28. D. Holland and M. Marder, Phys. Rev. Lett. 80, 746 (1998); J. Hauch, D. Holland, M. Marder, and H.L. Swinney, ibid. 82, 3823 (1999).
29. Marder [27] and private communication.