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Concepts of Linear and Nonlinear Fracture Mechanics

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Defects and Fracture

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Abstract

After a brief introduction, various fracture mechanics concepts and fracture criteria are examined and their relative merits are discussed. There are two distinct aspects of fracture in the case of several practical materials exhibiting nonlinearity. These are, crack extension and crack growth. Sih’s criterion for predicting the crack extension direction and critical fracture load can be applied for non-self-similar crack extension unlike Griffith’s criterion which was based on self-similar crack extension.

Fracture toughness testing of many practical alloys indicates that most of the effects due to plasticity can be attributed to the phenomenon of slow crack growth. Several of the proposed crack growth laws are examined in this paper and it is shown that the results obtained using the plastic energy method of Lee and Liebowitz have been successfully applied to several uniaxial and biaxial loading cases.

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References

  1. Griffith, A. A., Phil. Trans. Vol. A221, p. 163, 1921.

    ADS  Google Scholar 

  2. Sih, G. C., Methods of analysis and solutions of crack problems, ed. G. C. Sih, Noordhoff, Vol. I, p. XXI-XLV, 1973 and Three-dimensional crack problems, ed. G. C., Sih, Noordhoff, Vol. II, p. XV-LIII, 1975.

    Google Scholar 

  3. Sih, G. C., Recent Advances in Engineering Science, ed. T. S. Chang, Vol. 6, p. 221–234, 1973.

    Google Scholar 

  4. Sih, G. C., Fracture Mechanics, eds. N. Perrone, H. Liebowitz, D. Mulville and W. Pilkey, University Press of Virginia, p. 497–514, 1978.

    Google Scholar 

  5. Lee, J. D. and Liebowitz, H., Engineering Fracture Mechanics, Vol. 9, p. 765–779, 1977.

    Article  Google Scholar 

  6. Paris, P. C., Tada, H., Zahoor, A. and Ernst, H., ASTM STP 668, p. 5–36, 1979.

    Google Scholar 

  7. Lee, J. D. and Liebowitz, H., Computers and Structures, Vol. 8, p. 403–410, 1978.

    Article  MATH  Google Scholar 

  8. Shih, C. F., de Lorenzi, H. G. and Andrews, W. R., ASTM STP 668, p. 65–120, 1979.

    Google Scholar 

  9. Liebowitz, H., Lee, J. D. and Subramonian, N., International Symposium on Fracture Mechanics, Bangalore, India, Feb. 1979.

    Google Scholar 

  10. Liebowitz, H., Lee, J. D. and Subramonian, N., Nonlinear and dynamic fracture mechanics, eds. N. Perrone and S. N. Atluri, ASME, 1979.

    Google Scholar 

  11. Irwin, G. R., J. Appl. Mech., Vol. 24, p. 3, 1957.

    Google Scholar 

  12. Williams, M. L., J. Appl. Mech., Vol. 24, p. 109, 1957.

    MathSciNet  MATH  Google Scholar 

  13. Sih, G. C., Int. Jnl. of Fract. Mech., Vol. 7, p. 39–61, 1971.

    Google Scholar 

  14. Sih, G. C. and Liebowtiz, H., Mathematical Theories of Brittle Fracture, published in “Fracture-An Advanced Treatise”, Academic Press, Vol. 2, Chapter 2, 1968.

    Google Scholar 

  15. Sneddon, I. N. and Lowenbrub, M., Crack problems in the classical theory of elasticity, Wiley, 1969.

    Google Scholar 

  16. Paris, C. P. and Sih, C. G., ASTM STP 381, 1965.

    Google Scholar 

  17. Cherepanov, G. P., Mechanics of brittle fracture ( English ), McGraw-Hill, 1979.

    MATH  Google Scholar 

  18. Hartranft, R. J., Mechanics of Fracture, Vol. 3, ed. G. C. Sih, Noordhoff, 1977.

    Google Scholar 

  19. ASTM Test Method E399–74, Part 10, ASTM, Annual Standards.

    Google Scholar 

  20. Jones, D. L. and Chisholm, D. B., Engr. Fract. Mech., Vol. 7, 1975.

    Google Scholar 

  21. Jones, D. L. and Subramonian, N., (Private Communications).

    Google Scholar 

  22. Chan, S. K., Tuba, I. S. and Wilson, W. K., Engr. Fract. Mech., Vol. 2, p. 1–17, 1970.

    Article  Google Scholar 

  23. Cruse, T. A., ASCE National Struct. Engr. Convention, 1975.

    Google Scholar 

  24. Newman, J. C., Jr., NASA TN D-6376, 1971.

    Google Scholar 

  25. Palaniswamy, K. and Knauss, W. G., Int. Journ. of Fracture Mech., Vol. 8, pp. 114–117, 1972.

    Article  Google Scholar 

  26. Lindsey, G. H., ASTM STP 536, pp. 22–31, 1973.

    Google Scholar 

  27. Ueda, Y., Fracture 1977, Waterloo, Vol. 2, pp. 173–182, 1977.

    Google Scholar 

  28. Liebowitz, H., Lee, J. D. and Subramonian, N., International Fracture Mechanics Conference, Rome, 1980.

    Google Scholar 

  29. Irwin, G. R., Engr. Fract. Mech., Vol. 1, 1968.

    Google Scholar 

  30. Orowan, E., Rep. Progress Physics, Vol. 12, p. 185, 1949.

    Article  ADS  Google Scholar 

  31. Dugdale, D. S., Jnl. of the Mech. and Phys. of Solids, Vol. 8, p. 100, 1960.

    Article  ADS  Google Scholar 

  32. Hutchinson, J. W., Jnl. of the Mech. and Phys. of Solids, Vol. 16, 1968.

    Google Scholar 

  33. Liebowitz, H. and Eftis, J., Engr. Fract. Mech., Vol. 3, 1971.

    Google Scholar 

  34. Jones, D. L., Poulose, P. K., Etfis, J. and Liebowitz, H., Engr. Fract. Mech., Vol. 10, 1978.

    Google Scholar 

  35. De Koning, A. U., NLR Report MP 75035 U, National Aerospace Lab., The Netherlands, 1975.

    Google Scholar 

  36. Newman, J. C., Jr., ASTM STP 637, 1976.

    Google Scholar 

  37. Kanninen, M. F., Rybicki, E. F., Stonesifer, R. B., Brock, D., Rosenfield, A. R., Marschall, C. W. and Hahn, G. J., ASTM STP 668, pp. 121–150, 1979.

    Google Scholar 

  38. Hsu, Y. C. and Forman, R. G., Engr. Fract. Mech., Vol. 7, pp. 743–750, 1975.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. The George Washington University, Washington, D.C., 20006, USA

    H. Liebowitz, J. D. Lee & N. Subramonian

Authors
  1. H. Liebowitz
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  2. J. D. Lee
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  3. N. Subramonian
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Editor information

Editors and Affiliations

  1. Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, Pennsylvania, USA

    G. C. Sih

  2. Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland

    H. Zorski

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© 1982 Martinus Nijhoff Publishers, The Hague

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Liebowitz, H., Lee, J.D., Subramonian, N. (1982). Concepts of Linear and Nonlinear Fracture Mechanics. In: Sih, G.C., Zorski, H. (eds) Defects and Fracture. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7520-3_14

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  • DOI: https://doi.org/10.1007/978-94-011-7520-3_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-011-7522-7

  • Online ISBN: 978-94-011-7520-3

  • eBook Packages: Springer Book Archive

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