Mathematical Modelling of Nonlinear Phenomena in Fracture Mechanics

  • M. P. Wnuk
Part of the International Centre for Mechanical Sciences book series (CISM, volume 314)


In damage-tolerant and structural-integrity analyses, the residual strength of a flawed component must be evaluated. For brittle materials, linear-elastic fracture mechanics (LEFM) concepts, such as plane-strain fracture toughness, KIc, are used. For materials that exhibit large amounts of plasticity at the crack tip prior to failure, LEFM techniques must be extended to incorporate new notions such as J-integral, CTOD, CTOA, R-curve and Ct-integral. Introduction of these quantities and the demonstration of their applications in materials and designs pertinent to the engineering fields will be the primary theme of these lectures.


Crack Front Linear Elastic Fracture Mechanic Nonlinear Phenomenon Creep Crack Growth Ductility Index 
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  1. 1.
    G. P. Cherepanov, 1968, Prikladnaya Mat. Mekhanika (English version), Vol. 32, p. 1050.Google Scholar
  2. 2.
    M. P. Wnuk, 1971, Int. J. Fracture, Vol. 7, pp. 383–407.Google Scholar
  3. 3.
    W. Obreimov, 1930, Proc. Royal Soc., Vol. Al27, p. 290.Google Scholar
  4. 4.
    H. Feng and M. P. Wnuk, 1989, “Cohesive Models for Quasistatic Cracking in Inelastic Solids,” submitted to Int. J. Fracture.Google Scholar
  5. 5.
    I. Hunsacharoonroj and M. P. Wnuk, 1987, “Material Resistance to Cracking and Relation Between the CTOD and J-integral for Strain-hardening Ramberg-Osgood Solid,” Ph.D. Thesis and yet an unpublished report, Univ. of Wisconsin-Milwaukee.Google Scholar
  6. 6.
    A. A. Griffith, 1921, Phil. Trans. Royal Soc., London, Vol. 221, pp. 163–198.Google Scholar
  7. 7.
    W. Weibull, 1939, Ing. Veterskaps Akad. Hanal, No. 151.Google Scholar
  8. 8.
    W. Weibull, 1951, J. Appl. Mechanics, Vol. 18, p. 293.MATHGoogle Scholar
  9. 9.
    A. de S. Jayatilaka and K. Trustrum, 1983, J. Mater. Sci., Vol. 18.Google Scholar
  10. 10.
    H. E. Daniels, 1945, Proc. Royal Soc. London, Vol. A183, p. 405.MATHMathSciNetGoogle Scholar
  11. 11.
    A. M Hasofer, 1968, Int. J. Fracture, Vol. 4.Google Scholar
  12. 12.
    M. P. Wnuk, 1974, J. Appl. Mechanics, Vol. 41, pp. 234–242.CrossRefMATHGoogle Scholar
  13. 13.
    M. P. Wnuk, 1983, in “Modelling Problems in Crack Tip Mechanics,” Editor J. T. Pindera, Martinus Nijhoff Publishers, pp. 91–109.Google Scholar
  14. 14.
    M. P. Wnuk and D. T. Read, 1986, Int. J. Fracture, Vol. 31, pp. 161–171.CrossRefGoogle Scholar
  15. 15.
    R. Narasimhan, A. J. Rosakis and J. F. Hall, 1987, J. Appl. Mechanics, Vol. 109, pp. 838–845 (Part I), and pp. 846–853 (Part II).Google Scholar
  16. 16.
    M. P. Wnuk, 1972, in Proceedings of Int. Conf. on Dynamic Crack Propagation, Editor G. C. Sih, published by Noordhoff, The Netherlands.Google Scholar
  17. 17.
    J. R. Rice and E. P. Sorensen, 1978, J. Mech. Phys. Solids, Vol 25, pp. 163–186.CrossRefGoogle Scholar
  18. 18.
    M. P. Wnuk and T. Mura, 1983, Mechanics of Materials, Vol. 2, p 33–46.CrossRefGoogle Scholar
  19. 19.
    M. P. Wnuk, Z. P. Bazant and E. Law, 1984, J. Theor. Appl. Fracture Mechanics, Vol. 2, pp. 259–286.CrossRefGoogle Scholar
  20. 20.
    W. W. Gerberich, 1977, Int. J. Fracture, Vol. 13, pp. 535–538.Google Scholar
  21. 21.
    I. N. Sneddon and M. Lowengrub, 1969, “Crack Problems in the Classical Theory of Elasticity,” SIA Series in Appl. Math., publ. by John Wiley and Sons.Google Scholar
  22. 22.
    M. P. Wnuk, 1979a, in Proceedings of ICM3, Vol. 3, Cambridge, Pergamon Press, pp. 549–561.Google Scholar
  23. 23.
    M. P. Wnuk, 1979b, Int. J. Fracture, Vol. 15, pp. 553–581.CrossRefGoogle Scholar
  24. 24.
    M. P. Wnuk, 1980, “Stability of Tearing Fracture,” lecture given at Int. Symposium on Plasticity and Nonlinear Mechanics, Dourdan, France, eds. D. Zarka and S. Nemat-Nasser.Google Scholar
  25. 25.
    M. P. Wnuk and S. Sedmak, 1980, ASTM STP 743, pp. 500–508.Google Scholar
  26. 26.
    K. B. Broberg, 1977, in Proceedings of Int. Conference on “Fracture Mechanics and Technology” held in Hong Kong, Vol. 2, pp. 837–862, eds. G. C. Sih and C. L. Chow, publisher Sijthoff and Noordhoff.Google Scholar
  27. 27.
    M. P. Wnuk and W. G. Knauss, 1970, Int. J. Solids and Structures, Vol. 6, pp. 995–1009.CrossRefGoogle Scholar
  28. 28.
    R. J. Nuismer, 1974, J. Appl. Mechanics, Vol. 41, pp. 631–634.CrossRefMATHGoogle Scholar
  29. 29.
    R. A. Schapery, 1975, Int. J. Fracture, Vol. 11, pp. 141–159 (Part I) and pp. 549–562 (Part II).Google Scholar
  30. 30.
    S. R. Swanson, 1976, J. Spacecraft, Vol. 13, No. 9.Google Scholar
  31. 31.
    H. Riedel, 1987, “Fracture at High Temperatures,” Springer-Verlag, Berlin.Google Scholar
  32. 32.
    H. Riedel, 1989, “Recent Advances in Modelling Creep Crack Growth,” in Proceedings of ICF7, Vol. 2, pp. 1495–1523, eds. K. Salama, K. Ravi-Chandar, D.M.R. Taplin, P. Rama Rao, publisher Pergamon Press.Google Scholar
  33. 33.
    A. Saxena, 1989, ibid., pp. 1675–1688.Google Scholar
  34. 34.
    G. A. Webster, 1989, ibid., pp. 1689–1697.Google Scholar
  35. 35.
    W. G. Knauss, 1970, Int. J. Fracture, Vol. 6, pp. 7–20.Google Scholar
  36. 36.
    r. Mohanty and M. P. Wnuk, 1972, “Experimental Verification of Equation for Creep Crack Motion,” unpublished Progress Report for NSF, SDSU, Grant No. GH-43605.Google Scholar
  37. 37.
    C. A. Wells, 1986, “On Life Analysis of Longitudinal Seam Welds in Hot Reheat Piping,” RTI Report, Palo Alto, CA.Google Scholar
  38. 38.
    C. Y. Hui and H. Riedel, 1981, Int. J. Fracture, Vol. 17, pp. 409425.Google Scholar
  39. 39.
    C. Y. Hui, 1983, in ASTM STP 803, pp. 1573–1593.Google Scholar
  40. 40.
    J. D. Landes and J. A. Begley, 1979, in ASTM STP 590, pp. 128–148.Google Scholar
  41. 41.
    A. Saxena, T. T. Shih and H. A. Ernst, 1984, in ASTM STP 833, pp. 516–531.Google Scholar
  42. 42.
    J. L. Bassani, D. E. Hawk and A. Saxena, 1986, to appear in ASTM STP 995 on “Nonlinear Fracture Mechanics.”Google Scholar
  43. 43.
    A. Saxena, 1986, in ASTM STP 905, pp. 185–201.Google Scholar
  44. 44.
    K. M. Nikbin and G. A. Webster, 1981, in Proceedings of Symposium on Micro and Macro-Mechanics of Crack Growth, Metallurgical Society of AIME, pp. 107–117.Google Scholar
  45. 45.
    M. P. Wnuk, 1984, in Proceedings of Int. Conference on Computer-Aided Analysis and Design of Concrete Structures, Part I, held in Split, Yugoslavia, eds. F. Damjanié, E. Hinton, D.R.J. Owen, N. Bieanie and V. Simovie, pp. 163–177.Google Scholar
  46. 46.
    H. Tada, P. C. Paris and G. R. Irwin, 1973, “The Stress Analysis of Cracks Handbook, Del Research Corp., Hellertown, PA.Google Scholar
  47. 47.
    M. P. Wnuk and R. D. Kriz, 1985, Int. J. Fracture, Vol. 28, pp. 121–138.CrossRefGoogle Scholar
  48. 48.
    C. F. Shih, 1983, “Tables of the Hutchinson-Rice-Rosengren Singular Field Quantities,” Brown University Report MRL E-147, Providence, RI.Google Scholar
  49. 49.
    S. N. Atluri, 1981. Atluri, 1981, “Path Independent Integrals in Finite Elasticity and Inelasticity with Body Forces, Inertial and Arbitrary Crack Face Conditions,” ONR Progress Report, Georgia Institute of Technology, Atlanta, GA; also in Eng. Fract. Mech., 1982, Vol. 16, No. 3, pp. 341–364.CrossRefGoogle Scholar
  50. 50.
    M. P. Wnuk, 1981, J. Appl. Mechanics, Vol. 48, pp. 500–508.CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • M. P. Wnuk
    • 1
  1. 1.University of Wisconsin-MilwaukeeMilwaukeeUSA

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