On the nucleation of cavities in planar elasticity

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

Volumn 355, Issue 1734, 1997, Pages 2417-2458

  Levy, A J ^a  

^a SYRACUSE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 5344228392     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1997.0142     Document Type: Article

References (31)

1. Argon, A. S. & Im, J. 1975 Separation of second phase particles in spheroidized 1045 steel, cu-0.6 pct cr alloy, and maraging steel in plastic straining. Metall. Trans. A 6, 839-851.
2. Argon, A. S., Im, J. & Safoglu, R. 1975 Cavity formation from inclusions in ductile fracture. Metall. Trans. A 6, 825-837.
3. Ball, J. M. 1982 Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Phil. Trans. R. Soc. Lond. A 306, 557-611.
4. Cox, T. B. & Low, J. R. 1974 An investigation of the plastic fracture of AISI 4340 and 18 nickel-200 grade maraging steels. Metall. Trans. 5, 1457-1470.
5. Ferrante, J., Smith, J. R. & Rose, J. H. 1982 Universal binding energy relations in metallic adhesion. In Microscopic aspects of adhesion and lubrication (ed. J. M. Georges), pp. 19-30. New York: Elsevier.
6. Fisher, J. R. & Gurland, J. 1981 Void nucleation in spheroidized carbon steels. 2. model. Metal Sci. 15, 193-202.
7. Goods, S. H. & Brown, L. M. 1979 The nucleation of cavities by plastic deformation. Acta. Metall. 27, 1-15.
8. Gradshteyn, I. S. & Ryzhik, I. M. 1994 In Table of integrals, series and products (ed. A. Jeffrey). New York: Academic.
9. Griffith, A. A. 1920 The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. Lond. A 221, 163-198.
10. Guckenheimer, J. & Holmes, P. 1983 Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Berlin: Springer.
11. Gurtin, M. E. 1984 The linear theory of elasticity. In Mechanics of solids (ed. C. Truesdell), vol. 2, pp. 1-273. Berlin: Springer.
12. Hahn, G. T. & Rosenfield, A. R. 1966 Effects of second-phase particles on ductility. Air Force Materials Laboratory Technical Report AFML-TR-65-409.
13. Hirsch, M. W. & Smale, S. 1974 Differential equations, dynamical systems and linear algebra. New York: Academic.
14. Horgan, C. O. & Polignone, D. A. 1995 Cavitation in nonlinear elastic solids: a review. Appl. Mech. Rev. 48, 471-485.
15. Knops, R. J. & Wilkes, E. W. 1973 Theory of elastic stability. In Mechanics of solids (ed. C. Truesdell), vol. 3, pp. 125-302. Berlin: Springer.
16. Levy, A. J. 1991 The debonding of elastic inclusions and inhomogeneities. J. Mech. Phys. Solids 39, 477-505.
17. Levy, A. J. 1993 Corrigendum. J. Mech. Phys. Solids 41, 213.
18. Levy, A. J. 1994 Separation at a circular interface under biaxial load. J. Mech. Phys. Solids 42, 1087-1104.
19. Levy, A. J. 1995 Nonsymmetric cavity formation at a circular inclusion under remote equibiaxial load. J. Mech. Phys. Solids 43, 1003-1024.
20. Levy, A. J. 1996 The effective dilatational response of fiber reinforced composites with nonlinear interface. J. Appl. Mech. 63, 357-364.
21. MAPLE 1994 Waterloo Maple Software, Waterloo.
22. Mikhlin, S. G. 1960 Linear integral equations. Delhi: Hindustan Publishing.
23. Muskhelishvili, N. I. 1953 Some basic problems of the mathematical theory of elasticity. Groningen: Noordhoff.
24. Needleman, A. 1987 A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54, 525-531.
25. Nutt, S. R. & Needleman, A. 1987 Void nucleation at fiber ends in Al-SiC composites. Scripta Met. 21, 705-710.
26. Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical recipes in fortran. Cambridge University Press.
27. Rogers, H. C. 1960 The tensile fracture of ductile metals. AIME Trans. 218, 498-506.
28. Tanaka, K., Mori, T. & Nakamura, T. 1970 Cavity formation at the interface of a spherical inclusion in a plastically deformed matrix. Phil. Mag. 21, 267-279.
29. Tricomi, F. G. 1985 Integral equations. New York: Dover.
30. Watson, G. N. 1995 A treatise on the theory of Bessel functions. Cambridge University Press.
31. Wiggins, S. 1990 Introduction to applied nonlinear dynamical systems and chaos. Berlin Springer.