Modelling plastic zones and the brittle-ductile transition

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 355, Issue 1731, 1997, Pages 1991-2002

  Hirsch, P B ^a   Roberts, S G ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042894633     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1997.0101     Document Type: Article

References (30)

1. Bilby, B. A. & Swinden, K. H. 1965 The representation of plasticity at notches by linear arrays of dislocations. Proc. R. Soc. Lond. A 285, 22-33.
2. Bilby, B. A., Cottrell, A. H. & Swinden, K. H. 1963 The spread of plastic yield from a notch. Proc. R. Soc. Lond. A 272, 304-314.
3. Chang, S.-J. & Ohr, S. M. 1981 Dislocation-free zone model of fracture. J. Appl. Phys. 52, 7174-7181.
4. Creager, M. & Paris, P. C. 1967 Elastic field equations for blunt cracks with reference to stress corrosion cracking. Int. J. Fracture Mech. 3, 247-252.
5. Devincre, B. & Roberts, S. G. 1996 Three dimensional simulation of dislocation-crack interactions in B.C.G. metals at the mesoscopic scale. Acta Metall. 44, 2891-2900.
6. Dugdale, D. S. 1960 Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100-108.
7. George, A. & Michot, G. 1993 Dislocation loops at crack tips: nucleation and growth - an experimental study in silicon. Mater. Sci. Engng A 164, 118-134.
8. Griffith, A. A. 1921 The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond. A 221, 163-197.
9. Hirsch, P. B. 1995 Crack-tip plasticity and quasi-brittle fracture of single crystals. In Plastic deformation of ceramics (ed. R. Bradt, C. Brooks & J. Routbort), pp. 1-20. New York: Plenum.
10. Hirsch, P. B. & Roberts, S. G. 1991 The brittle-ductile transition in silicon. Phil. Mag. A 64, 55-80.
11. Hirsch, P. B. & Roberts, S. G. 1996 Comment on the brittle-to-ductile transition: a cooperative dislocation generation instability: dislocation dynamics and the strain-rate dependence of the transition temperature. Acta Mater. 44, 2361-2371.
12. Hirsch, P. B., Roberts, S. G. & Samuels, J. 1989 The brittle-ductile transition in silicon. II. Interpretation. Proc. R. Soc. Lond. A 421, 25-53.
13. Hutchinson, J. W. 1948 Plastic stress and strain fields at a crack tip. J. Mech. Phys. Solids 16, 337-347.
14. Knott, J. F. 1973. Fundamentals of fracture mechanics. London: Butterworths.
15. Lakshmanan, V. & Li, J. C. M. 1988 Edge dislocations emitted along inclined planes from a mode I crack. Mat. Sci. Eng. A 104, 95-104.
16. Levy, N., Marcal, P. V., Ostergren, W. J. & Rice, J. R. 1971 Small scale yielding near a crack in plane strain: a finite element analysis. Int. J. Fracture Mech. 7, 143-156.
17. Lin, I.-H. & Thomson, R. 1986 Cleavage, dislocation emission and shielding for cracks under general loading. Acta Metall 34, 187-206.
18. Majumdar, B. S. & Burns, S. J. 1981 Crack tip shielding - an elastic theory of dislocations and dislocation arrays near a sharp crack. Acta Metall. 29, 579-588.
19. Rice, J. R. & Johnson, M. A. 1970 Inelastic behaviour of solids (ed. M. F. Kanninen et al.). McGraw-Hill.
20. Rice, J. R. & Rosengren, G. F. 1968 Plane strain deformation near a crack tip in a power-law hardening material. J. Mech. Phys. Solids 16, 1-12.
21. Ritchie, R. O., Knott, J. F. & Rice, J. R. 1973 On the relationship between critical tensile stress and fracture toughness in mild steel. J. Mech. Phys. Solids 21, 395-410.
22. Roberts, S. G., Booth, A. S. & Hirsch, P. B. 1994 Dislocation activity and brittle-ductile transitions in single crystals. Mat. Sci. Engng A 176, 91-98.
23. Roberts, S. G., Hirsch, P. B., Booth, A. S., Ellis, M. & Serbena, F. C. 1993 Dislocations, cracks and brittleness in single crystals. Physica Scripta T 49, 420-426.
24. Samuels, J. & Roberts, S. G. 1989 The brittle-ductile transition in silicon. I. Experiments. Proc. R. Soc. Lond. A 421, 1-23.
25. Serbena, F. C. & Roberts, S. G. 1994 The brittle-to-ductile transition in germanium. Acta Metall. Mater. 42, 2505-2510.
26. Thomson, R. 1986 Physics of fracture in solid state physics (ed. H. Ehrenreich & D. Turnbull), vol. 39, pp. 1-129. New York: Academic.
27. Tracey, D. M. 1976 Finite element solutions for crack-tip behaviour in small scale yielding. J. Engng Mater. Technol. 98, 146-151.
28. Vitek, V. 1976 Yielding on inclined planes at the tip of a crack loaded in uniform tension. J. Mech. Phys. Solids 24, 263-275.
29. Warren, P. D. 1989 The brittle-ductile transition in silicon: the influence of preexisting dislocation arrangements. Scripta Metall. 23, 637-642.
30. Weertman, J., Lin, I.-H. & Thomson, R. 1983 Double slip plane crack model. Acta Metall. 31, 473-482.