The Application of Fracture Mechanics to Ice Problems

  • K J Miller
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

Linear elastic fracture mechanics concerns the application of crack tip characterizing parameters to the study of instability phenomena of cracked bodies. These parameters are G, the strain energy release rate, K, the stress intensification factor, and CTOD, the crack tip opening displacement. Successful applications are associated with brittle fracture studies and fatigue crack propagation in metals when plasticity is limited. For non-linear elastic behaviour of crack tip material the J contour integral is an improved parameter.

None of these parameters however quantify the propagation of cracks, rather they are concerned with the initiation situation; cf. the relation between yield point and plastic flow behaviour of materials. Thus G, K, CTOD and J do not quantify stable crack growth although they have been used as characterizing parameters for crack growth in ductile materials. The difficulty in the quantification of crack initiation and growth are the roles played by plasticity, time dependent deformation and differing fracture processes and recent developments have centred on C* and a crack growth parameter G.

All of these parameters will be briefly reviewed and their relevance to the fracture of ice outlined both from a theoretical and an experimental viewpoint.

Keywords

Fatigue Brittle Recrystallization EPFM 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Miller, K. J. Traverse of the Staunings Alps, North-East Greenland. Alpine Journal 81 (1976) 143-152Google Scholar
  2. [2]
    Griffith, A. A. The phenomena of rupture and flow in solids. Phil.Trans.Roy.Soc. 1921 A22l, 163 - 198Google Scholar
  3. [3]
    Irwin, G. R. Fracture dynamics. Fracturing of metals A.S.M. Cleveland 1948Google Scholar
  4. [4]
    Orowan E. Fracture and strength of solids Rep. Phys. Soc. Prog. Phys. 12 (1948/49) 185 - 232ADSCrossRefGoogle Scholar
  5. [5]
    Irwin, G. R. and Kies, J. A. Fracturing and fracture dynamics. Weld. J. Res. Suppl. 17 (1952) 95s - 103sGoogle Scholar
  6. [6]
    Irwin, G. R. Analysis of stresses and strains near the end of a crack traversing a plate. J.App.Mech. 24 (1957) 361 - 364Google Scholar
  7. [7]
    Knott, J. F. Fundamentals of Fracture Mechanics (1973) ButterworthsGoogle Scholar
  8. [8]
    Liu, H. W. and Miller K. J. Fracture toughness of freshwater ice. J. Glac. 22 (1979) 135 - 143ADSGoogle Scholar
  9. [9]
    Rooke, D. P. and Cartwright, D. J. Compendium of Stress Intensity factors. HMSO 1976Google Scholar
  10. [10]
    Liu, H. W. Discussion in Fracture toughness testing and its applications. ASTM (1965) S.T.P. 381 p. 23 - 29Google Scholar
  11. [11]
    Dugdale, D. S. Yielding of steel sheets containing slits J. Mech. Phys. Solids. 8 (1960) 100 - 104ADSCrossRefGoogle Scholar
  12. [12]
    Barenblatt, G. I. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7 (1962) 55 - 111MathSciNetCrossRefGoogle Scholar
  13. [13]
    Wells, A. A. Unstable crack propagation in metals: cleavage and fast fracture. Crack Propagation Symposium, Cranfield 1961Google Scholar
  14. [14]
    Burdekin, F. M. and Stone, D.E.W. The crack opening displacerrent approach to fracture mechanics in yielding materials. J. Strain Analysis 1 (1966) 145 - 153CrossRefGoogle Scholar
  15. [15]
    Rice, J. R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mechanics. (1968) 379 - 386Google Scholar
  16. [16]
    Hutchinson, J. W. Singular behaviour at the end of a tensile crack in a hardening material J.Mech.Phys.Solids. 16 (1968) 13 - 31ADSMATHCrossRefGoogle Scholar
  17. [17]
    Rice, J. R. and Rosengren, G. F. Plane strain deformation near a crack tip in a power-law hardening material J. Mech.Phys.Solids 16(1968) 1 - 12ADSMATHCrossRefGoogle Scholar
  18. [18]
    Eshelby, J. D. Solid State Physics 3, Ed Seitz F. & Turnbull D. New York (1956) 79 - 144Google Scholar
  19. [19]
    Cherepanov, G. P. J.App.Math.Mech. 31 (1967) 503 - 512MATHGoogle Scholar
  20. [20]
    Landes, J. D. and Begley J. A. A Fracture Mechanics Approach to creep crack growth. Westinghouse Res.Lab.Rep. (1974) 74–1E7-FESGT-PlGoogle Scholar
  21. [21]
    Nikbin, K. M., Webster, G. A., and Turner, C. E. A comparison of methods of correlating creep crack growth. Proc. ICF 4 (1977) 627–634Google Scholar
  22. [22]
    Ellison, E. G., and Walton, D. Fatigue, creep and cyclic creep crack propagation in a 1% Cr-Mo-V Steel. Instn.mech.engrs. (1973/74). 1,p173.1 - 173.12Google Scholar
  23. [23]
    Rice, J. R. An examination of the fracture mechanics energy balance from the point of view of continuum mechanics ICF 1 (1966) p309 - 340. 1st Inst.Conf. on Fracture, Sendai, Japan 1965, Japanese Society for Strength & Fracture of Materials 1966Google Scholar
  24. [24]
    Kfouri, A. P., and Miller, K. J. Crack Separation Energy Rates in Elastic - Plastic Fracture Mechanics. Proc.lnstn.mech.Engs. 190 (1976) 571–584. First published as a Cambridge University Report (1974) CUED/C-Mat/TRl8Google Scholar
  25. [25]
    Rice, J. R. and Johnson, M. A. Inelastic behaviour of Solids Ed. M.F. Kanninen et al. McGraw-Hill, New York (1960) 641–672Google Scholar
  26. [26]
    Miller, K. J. and Kfouri, A. P. A comparison of Elastic-Plastic Fracture Parameters in Biaxial Stress-States ASTM STP 668 (1979) 214–228Google Scholar
  27. [27]
    Kfouri, A. P. and Miller, K. J. The effect of load biaxiality on the fracture toughness parameters J and G.Proc. ICF 4 (1977) 241–245Google Scholar
  28. [28]
    Kfouri, A. P. and Rice J. R. Elastic/Plastic Separation Energy Rate for Crack Advance in Finite Growth Steps Proc. ICF4, 1, (1977) 43 - 59Google Scholar
  29. [29]
    Miller, K. J. Fatigue under complex stress. Metal Science Journal August/September 1977 432 - 438Google Scholar
  30. [30]
    Howard, 1. C. Models of the reduction of fracture toughness due to hydrogen in strong steels. Proc. ICM3 2 (1979) 463 - 474Google Scholar
  31. [31]
    Goodman, D. J. and Tabor, D. Fracture toughness of ice: a preliminary account of some new experiments. J. Glac. 21 (1978) 651 - 660ADSGoogle Scholar
  32. [32]
    Gold, L. W., Crack Formation in Ice Plates by Thermal Shock. Canadian J. Physics 41 (1963) 1712–1738ADSCrossRefGoogle Scholar
  33. [33]
    Miller, K. J., Sheffield University 1978 Greenland Expedition Report. To be published.Google Scholar
  34. [34]
    Smith, R. A., The application of fracture mechanics to the problem of crevasse penetration. J. Glac. 17(1976) 223–228ADSGoogle Scholar
  35. [35]
    Fletcher, N. H. The Chemical Physics of Ice Cambridge University Press 1970CrossRefGoogle Scholar

Copyright information

© Springer-Verlag, Berlin, Heidelberg 1980

Authors and Affiliations

  • K J Miller
    • 1
  1. 1.University of SheffieldEngland

Personalised recommendations