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Probabilistic fracture kinetics theory and constitutive laws

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Fracture Kinetics of Crack Growth

Part of the book series: Mechanical Behavior of Materials ((MBOM,volume 1))

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Abstract

It was shown in Chapters 1 and 2 that the physical process of crack growth is the net effect of the random breaking and healing of atomic bonds; that the randomness itself results from the stochastic fluctuations of the atomic vibrational amplitude; and that this fluctuation is, in fact, the thermal energy that controls the rate of atomic breaking and healing steps. It was also demonstrated that the rate theory of statistical mechanics rigorously describes the average rate of the random breaking and healing activations by the elementary rate constant k. Because the rate of activations associated with any macroscopic crack movement is very large — 108 S-1, give or take a few orders of magnitude — random fluctuation is not perceived on this scale. Nevertheless, it has very significant and often essential consequences on crack growth.

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References

Part 1

  1. R. A. Heller (ed.): Probabilistic Aspects of Fatigue, ASTM STP 511, American Society for Testing and Materials (1971).

    Google Scholar 

  2. R. E. Little and J. C. Ekvall (eds.): Statistical Analysis of Fatigue Data, ASTM STP 744, American Society for Testing and Materials (1979).

    Google Scholar 

  3. J. M. Bloom and J. C. Ekvall (eds.): Probabilistic Fracture Mechanics and Fatigue Methods: Applications for Structural Design and Maintenance, ASTM STP 798, American Society for Testing and Materials (1981).

    Google Scholar 

  4. W. Feller, : An Introduction to Probability Theory and its Applications, Vol. 1, Wiley (1970).

    Google Scholar 

  5. D. T. Philips, A. Ravindron and J. J. Solberg: Operations Research: Principles and Practice, Wiley (1976).

    Google Scholar 

  6. A. S. Krausz and K. Krausz: The inherently probabilistic character of subcritical fracture processes, Trans. Soc. Mech. Eng. Design, Special Issue: Reliability, Stress Analysis, and Failure Prevention 104 (1982), pp. 666–670.

    Article  Google Scholar 

  7. A. S. Krausz, K. Krausz and D. Necsulescu: Reliability theory of stochastic fracture processes in sustained loading: Part I, Z. Naturforsch. 38a (1983), pp. 719–502.

    Google Scholar 

  8. Takeo Yokobori: Fracture, fatigue and yielding of materials as a stochastic process, Kolloid Z. 166(1) (1959), pp. 20–24.

    Article  CAS  Google Scholar 

  9. S. D. Brown: Multibarrier kinetics approach to subcritical crack growth in glasses and ceramics, Am. Ceram. Soc. Bull. 55(4) (1976), pp. 395–401.

    Google Scholar 

  10. A. S. Krausz and K. Krausz: The theory of non-steady state fracture kinetics analysis, Part 1: General theory of crack propagation, Eng. Fract. Mech. 13 (1980), pp. 751–758.

    Article  Google Scholar 

  11. A. S. Krausz, J. Mshana and K. Krausz: The theory of non-steady state fracture kinetics analysis; Part II: Non-steady state crack propagation in stress corrosion cracking, Eng. Fract. Mech. 13 (1980), pp. 759–766.

    Article  Google Scholar 

  12. A. S. Krausz: Crack-size distribution in homogeneous solids, Int. J. Fract. 15 (1979), pp. 337–342.

    CAS  Google Scholar 

  13. A. S. Krausz and J. Mshana: Steady-state fracture kinetics of crack front spreading, Int. J. Fract. 19 (1982), pp. 277–293.

    Article  Google Scholar 

Part 2

  1. W. Feller: An Introduction to Probability Theory and its Applications, Vol. 1, Wiley (1970).

    Google Scholar 

  2. D. T. Philips, A. Ravindran and J. J. Solberg, Operations Research: Principles and Practice, Wiley (1976).

    Google Scholar 

  3. A. B. Clarke and R. L. Disney: Probability and Random Processes for Engineers and Scientists, Wiley (1970).

    Google Scholar 

  4. N. Wax (ed.): Selected Papers on Noise and Stochastic Processes, Dover (1954).

    Google Scholar 

  5. A. S. Krausz: Crack-size Distribution in Homogeneous Solids, Int. J. Fract. 15 (1979), pp. 337–342.

    CAS  Google Scholar 

  6. W. Jost: Diffusion in Solids, Liquids, Gases, Academic Press (1960).

    Google Scholar 

  7. P. G. Shewmon: Diffusion in Solids, McGraw-Hill (1963).

    Google Scholar 

  8. J. Crank: The Mathematics of Diffusion, Oxford University Press (1956).

    Google Scholar 

  9. P. C. Jordan: Chemical Kinetics and Transport, Plenum Press (1979).

    Google Scholar 

  10. R. M. Barrer: Diffusion in and Through Solids, Cambridge (1941).

    Google Scholar 

  11. J. R. Manning: Diffusion Kinetics for Atoms in Crystals, D. Van Nostrand (1968).

    Google Scholar 

  12. A. S. Krausz, K. Krausz and D. Necsulescu: Reliability theory of stochastic fracture processes in sustained loading: Part I, Z. Naturforsch. 38a (1983), pp. 719–722.

    Google Scholar 

  13. A. S. Krausz: The random walk theory of crack propagation, Eng. Fract. Mech. 12 (1979), pp. 499–504.

    Article  Google Scholar 

  14. W. J. Moore, Physical Chemistry, 3rd edn., Prentice-Hall (1962).

    Google Scholar 

  15. A. S. Krausz and K. Krausz: The theory of non-steady state fracture kinetics analysis, Part 1: General theory of crack propagation, Eng. Fract. Mech. 13 (1980), pp. 751–758.

    Article  Google Scholar 

  16. A. S. Krausz, J. Mshana and K. Krausz: The theory of non-steady state fracture kinetics analysis; Part II: Non-steady state crack propagation in stress corrosion cracking, Eng. Fract. Mech. 13 (1980), pp. 759–766.

    Article  Google Scholar 

  17. A. S. Krausz and K. Krausz: A unified fracture kinetics representation of the three regions of stress corrosion cracking, Int. J. Fract. 23 (1983), pp. 169–175.

    Article  Google Scholar 

  18. A. S. Krausz and K. Krausz: A fracture kinetics representation of fatigue crack propagation rate, Proc. of the 2nd International Conference on Fatigue and Fatigue Thresholds (C. H. Beevers, J. Bachlund, P. Lukas, J. Schijive and R. O. Ritchie, eds.) (1984), pp. 497–510.

    Google Scholar 

  19. R. P. Wei and J. D. Landes: Correlation between sustained-load and fatigue crack growth in high-stress steels, Mat. Res. Standards 9(7) (1969), pp. 25–27.

    Google Scholar 

  20. A. J. McEvily and R. P. Wei: in Corrosion Fatigue: Chemistry, Mechanics and Microstructure, NACE-2, National Association of Corrosion Engineers (1973), p. 381.

    Google Scholar 

  21. R. P. Wei and G. W. Simmons: Environment enhanced fatigue crack growth in high-strength steels, Stress Corrosion Cracking and Hydrogen Embrittlement of Iron Base Alloys (R. W. Staehle, J. Hochman, R. D. McCright and J. E. Slater, eds.), NACE Vol. 5, National Association of Corrosion Engineers (1977), pp. 751–765.

    Google Scholar 

  22. R. P. Wei and G. Shim:Fracture Mechanics and Corrosion Fatigue, (T. W. Crooker and B. N. Leis, eds.), ASTM STP 801, American Society for Testing and Materials (1983), pp. 5–25.

    Google Scholar 

  23. M. O. Speidel: Corrosion Fatigue in Fe-Ni-Cr Alloys, Stress Corrosion Cracking and Hydrogen Embrittlement in Iron Base Alloys (R. W. Staehle, J. Hochman, R. D. McCright and J. E. Slater, eds.), NACE Vol. 5, National Association of Corrosion Engineers (1977), pp. 1071–1094.

    Google Scholar 

  24. B. R. Lawn and T. R. Wilshaw: Fracture of Brittle Solids, Cambridge University Press (1975).

    Google Scholar 

  25. A. S. Krausz and K. Krausz: The theory of thermally activated fracture: environment assisted crack propagation, Canad. Metall. Quarterly 23 (1984), pp. 107–113.

    CAS  Google Scholar 

  26. A. G. Evans: A method for evaluating the time-dependent failure characteristics of brittle materials — and its application to polycrystalline alumina, J. Mater. Sci. 7(10) (1972), pp. 1137–1146.

    Article  CAS  Google Scholar 

  27. R. D. Carter, E. W. Lee, E. A. Starke, Jr. and C. J. Beevers: The effect of microstructure and environment on fatigue crack closure of 7475 aluminum alloy, Metall. Trans. 15A (1984), pp. 555–563.

    CAS  Google Scholar 

  28. W. W. Stinchcomb and K. L. Reitsnider: Fatigue damage mechanisms in composite materials: A review, in Fatigue Mechanisms (J. T. Fong, ed.), ASTM STP 675, American Society for Testing and Materials (1979), pp. 763–787.

    Google Scholar 

  29. A. S. Krausz, K. Krausz and D.-S. Necsulescu: Probabilistic Fracture Kinetics of ‘Natural’ Composites, (H. T. Hahn, ed.), ASTM STP 907, American Society for Testing and Materials (1986), pp. 73–83.

    Chapter  Google Scholar 

  30. M. F. Kanninen and C. H. Popelar: Advanced Fracture Mechanics, Oxford University Press (1985).

    Google Scholar 

  31. S. W. Tsai and H. T. Hahn: Introduction to Composite Materials, Technomic (1980).

    Google Scholar 

  32. A. Kelly: Strong Solids, Oxford University Press (1973).

    Google Scholar 

  33. M. R. Pigott: Load Bearing Fibre Composites, Pergamon Press (1980).

    Google Scholar 

  34. A. S. Argon: Fracture of composites, in Treatise on Materials Science and Technology, Vol. 1 (H. Herman, ed.), Academic Press (1972), pp. 79–114.

    Google Scholar 

  35. V. A. Petrov and A. N. Orlov: Statistical kinetics of thermally activated fracture, Int. J. Fract. 12 (1976), pp. 231–238.

    Article  Google Scholar 

  36. H. Ishikawa, A. Tsurui and A. Utsumi: A stochastic model of fatigue crack growth in consideration of random propagation resistance, Proc. of the 2nd International Conference on Fatigue and Fatigue Thresholds (C. H. Beevers, J. Bachlund, P. Lukas, J. Schijve and R. O. Ritchie, eds.) (1984), pp. 511–520.

    Google Scholar 

  37. R. Arone: A stochastic model for fatigue crack growth, Proc. of the 2nd International Conference on Fatigue and Fatigue Thresholds (C. H. Beevers, J. Bachlund, P. Lukas, J. Schijve and R. O. Ritchie, eds.) (1984), pp. 521–527.

    Google Scholar 

  38. S. B. Batdorf and H. L. Heinisch, Jr.: Fracture statistics of brittle materials with surface cracks, Eng. Fract. Mech. 11 (1978), pp. 831–891.

    Article  Google Scholar 

  39. S. Aoki and M. Sakata: Statistical approach to delayed failure of brittle materials, Int. J. Fract. 16 (1980), pp. 459–469

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Ottawa, Ontario, Canada

    A. S. Krausz (Faculty of Engineering) & K. Krausz (Faculty of Engineering)

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  1. A. S. Krausz
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  2. K. Krausz
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© 1988 Kluwer Academic Publishers

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Krausz, A.S., Krausz, K. (1988). Probabilistic fracture kinetics theory and constitutive laws. In: Fracture Kinetics of Crack Growth. Mechanical Behavior of Materials, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1381-3_3

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  • DOI: https://doi.org/10.1007/978-94-009-1381-3_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7116-1

  • Online ISBN: 978-94-009-1381-3

  • eBook Packages: Springer Book Archive

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