Abstract
This is a review of some concepts in the mechanics of fracture appropriate to interpreting atomistically brittle modes of cracking of crystal lattices and of interfaces between crystalline phases, especially in solids which are normally, or potentially, ductile. Crack tip modelling is first discussed based on elastic-brittle concepts, assuming either that there is no near-tip dislocation activity or, for the time being, neglecting it. That discussion brings out the importance of the Griffith condition and its generalization to a cracking interface (e.g., an embrittled grain boundary), and includes an account of the thermodynamics of interfacial decohesion in presence of (possibly embrittling) segregants. It is suggested that the phenomenology of grain boundary embrittlement by P and Sn in Fe, and of “cohesion enhancement” by C, can be at least partly understood as an effect of the various segregants on altering the work necessary to separate an interface against atomic cohesive forces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.F. Kanninen and C.H. Popelar, Advanced Fracture Mechanics (Oxford, 1985 ).
L.B. Freund and J.W. Hutchinson, J. Mech. Phys. Solids, 33, 169 (1985); L.B. Freund, J.W. Hutchinson and P.S. Lam, Eng. Fracture Mech, 23, 119 (1986).
J.W. Willis, J. Mech. Phys. Solids, 19, 353 (1971); D.L. Clements, Int. J. Eng. Sci., 9, 256 (1971).
P.M. Anderson, Ductile and Brittle Crack Tip Response (Ph.D. Dissertation, Harvard, 1986 ).
A.N. Stroh, Phil Mag., 2, 625 (1958); D.M. Barnett and R.J. Asaro, J. Mech. Phys. Solids, 20, 353 (1972).
R. Thomson, Atomistics of Fracture, 167 (Plenum, ed. Latanision and Pickens, 1983) and Solid State Physics, 39, 1 (1986); B.R. Lawn and T.R. Wilshaw, Fracture of Brittle Solids (Cambridge, 1975 ).
J.R. Rice, J. Mech. Phys. Solids, 26, 61 (1978) and Proc. 8th U.S. Nat. Congr. Appl. Mech., 191 ( Western Periodicals, ed. Kelly, 1979 ).
G.P. Cherepanov, Appl. Math. Mech. (transl. PMM), 21, 476 (1967); J.R. Rice, Fracture: An Advanced Treatise, 2, 191 (Academic, ed. Liebowitz, 1968) and J. Appl. Mech., 25., 379 (1968); J.D. Eshelby, Inelastic Behavior of Solids, 77 (McGraw Hill, ed. Kanninen et al, 1970 ).
J.R. Rice, Effect of Hydrogen on Behavior of Materials, 455 (TMS-AIME, ed. Thompson and Bernstein, 1976); R.J. Asaro, Phil. Trans. Roy. Soc. London, A295., 150 (1980); J.P. Hirth and J.R. Rice, Met. Trans., 11A, 1502 (1980).
G. Tauber and H.J. Grabke, Ber. Bunsenges Phys. Chem., £2, 298 (1978); H. Erhart and H.J. Grabke, Metal Sei., 15, 401 (1981); H. Hänsel, L. Stratmann, H. Keller and H.J. Grabke, Acta Met., 33, 659 (1985); H.J. Grabke, presentation at 1986 NATO Conf. on Phys. and Chem. of Fracture.
M.E. Eberhart, K.H. Johnson, R.P. Messner and C.L. Briant, Atomistics of Fracture, 255 ( Plenum, ed. Latanision and Pickens, 1983 ).
K. Tatsumi, N. Okumura and S. Funaki, Grain Boundary Structure and Related Phenomena, Supplement to Trans. Japan Inst. Metals, 427 (1986).
C.L. White, R.A. Padgett, C.T. Liu and S.M. Yalisov, Scripta Met., 18, 1417 (1984); C.T. Liu, C.L. White and J.A. Horton, Acta Met., 33, 213 (1985); C.L. White, J. Vac. Sei. Technol., A4, 1633 (1986).
a) A. Kelly, W. Tyson and A. Cottrell, Phil. Mag., 15, 567 (1967); (b) J.R. Rice and R. Thomson, Phil. Mag. 29, 73 (1974); (c) D.D. Mason, Phil. Mag., 39, 455 (1979); (d) T. Yokobori, A.T. Yokobori Jr. and A. Kamei, Int. J. Fracture, 11, 781 (1975) and 12, 519 (1976); (e) S.M. Ohr, Mat. Sci. Eng., 72, 1 (1985); (f) M.P. Seah and D. Hondros, Atomistics of Fracture, 855 (Plenum, ed. Latanision and Pickens, 1983); (g) J.E. Sinclair and M.W. Finnis, ibid, 1047; (h) I.H. Lin and R. Thomson, Acta Met., 34, 187 (1986).
M.S. Daw and M.I. Baskes, Phys. Rev. Lett., 1285 (1983) and Phys. Rev. B, 29, 6443 (1984); M.I. Baskes, Mat. Res. Soc. Bull, 9, no. 4, 14 (1986).
a) M.L. Jokl, V. Vitek and C.J. McMahon Jr., Acta Met., 28, 1479 (1980); (b) J.F. Knott, Atomistics of Fracture, 209 (Plenum, ed. Latanision and Pickens, 1983); (c) P. Haasen, ibid, 707; (d) K. Sieradzki and R.C. Newman, Phil Mag., A51, 95 (1985), and R.C. Newman and K. Sieradzki, Scripta Met., 17, 621 (1983); (e) I.H. Lin and R.M. Thomson, J. Mat. Res., 1, 73 (1986).
E.W. Hart, Int. J. Solids Structures, 16, 807 (1980).
J.R. Rice, Fundamentals of Deformation and Fracture, 33 (Cambridge, ed. Bilby et al, 1985 ).
(a) P.M. Anderson and J.R. Rice, Scripta Met.,20,1467 (1986); (b) J.S. Wang, P.M. Anderson and J.R. Rice,in press, Proc. 5th Int. Conf. on Mechanical Behavior of Materials, Beijing, 1987 (Pergamon); (c) P.M. Anderson and J.R. Rice, manuscript, 1986.
F. Prinz, H.O.K. Kirchner and G. Schoek, Phil, Mag., A38 321 (1978); F. Prinz, A. Korner and H.O.K. Kirchner, Phil. Mag. Ml, 441 (1983).
H. Vehoff and P. Neumann, Acta Met., 27, 915 (1979) and 28 265 (1980); H. Vehoff, W. Rothe and P. Neumann, Proc. 5th Int. Cong. Fracture, 1, 265 (1981); H. Vehoff and W.Rothe, Acta Met., 11, 1781 (1983).
J.R. Rice and R. Nikolic, J. Mech. Phys. Solids, 33, 595 (1985).
J.R. Rice, Mechanics of Solids, 539 (Pergamon, ed. Hopkins and Sewell, 1982) and J. Mech. Phys. Solids, 21, 63 (1973); W.J. Drugan, J.R. Rice and T.L. Sham, J. Mech. Phys. Solids, 30, 447 (1982) and 31, 191 (1983).
A.S. Tetelman and W.D. Robertson, Acta Met., 11, 415 (1963).
P.A. Mataga, High Strain Rate Crack Growth (Ph.D. Dissertation, Harvard, 1986 ).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Martinus Nijhoff Publishers, Dordrecht
About this chapter
Cite this chapter
Rice, J.R. (1987). Mechanics of Brittle Cracking of Crystal Lattices and Interfaces. In: Latanision, R.M., Jones, R.H. (eds) Chemistry and Physics of Fracture. NATO ASI Series, vol 130. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3665-2_3
Download citation
DOI: https://doi.org/10.1007/978-94-009-3665-2_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8140-5
Online ISBN: 978-94-009-3665-2
eBook Packages: Springer Book Archive