International Journal of Fracture

, Volume 110, Issue 4, pp 351–369 | Cite as

A cohesive model of fatigue crack growth

  • O. Nguyen
  • E.A. Repetto
  • M. Ortiz
  • R.A. Radovitzky
Article

Abstract

We investigate the use of cohesive theories of fracture, in conjunction with the explicit resolution of the near-tip plastic fields and the enforcement of closure as a contact constraint, for the purpose of fatigue-life prediction. An important characteristic of the cohesive laws considered here is that they exhibit unloading-reloading hysteresis. This feature has the important consequence of preventing shakedown and allowing for steady crack growth. Our calculations demonstrate that the theory is capable of a unified treatment of long cracks under constant-amplitude loading, short cracks and the effect of overloads, without ad hoc corrections or tuning.

Cohesive law fatigue finite elements overload short cracks. 

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REFERENCES

  1. Anderson, T. (1995). Fracture Mechanics: Fundamentals and Applications. Boca CRC Press, Boca Raton.Google Scholar
  2. ASTMG47 (1991). Standard Test Method for Determining Susceptibility to Stress Corrosion Cracking of High Strength Aluminum Alloy Products, Vol. 03.02. ASTM, pp. 173–177.Google Scholar
  3. Atkinson, C. and Kanninen, M. (1977). A simple representation of crack tip plasticity: the inclined strip-yield superdislocation model. International Journal of Fracture 13, 151–163.Google Scholar
  4. Barrenblatt, G.I. (1962). The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics 7, 55–129.Google Scholar
  5. Bilby, B. and Swinden, K. (1965). Representation of plasticity at notches by linear dislocation arrays. Proceedings of the Royal Society of London A285, 22–33.Google Scholar
  6. Budiansky, B. and Hutchinson, J. (1978). Analysis of closure in fatigue crack growth. Journal of Applied Mechanics 45, 267–276.Google Scholar
  7. Camacho, G.T. and Ortiz, M. (1996). Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 33, 2899–2938.Google Scholar
  8. Cuitiño, A.M. and Ortiz, M. (1992). A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Engineering Computations 9, 437–451.Google Scholar
  9. Dafalias, Y. (1984). Modelling Cyclic Plasticity: Simplicity Versus Sophistication. Wiley, New York, pp. 153–198.Google Scholar
  10. De-Andrés, A., Pérez, J.L. and Ortiz, M. (1999). Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. International Journal of Solids and Structures 36, 2231–2258.Google Scholar
  11. Donahue, R., Clark, H., Atanmo, P., Kumble, R. and McEvily, A. (1972). Crack opening displacement and the rate of fatigue crack growth. International Journal of Fracture Mechanics 8, 209–219.Google Scholar
  12. Drucker, D. and Palgen, L. (1981). On the stress-strain relations suitable for cyclic and other loading. Journal of Applied Mechanics 48, 479–485.Google Scholar
  13. Dugdale, D.S. (1960). Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8, 100–104.Google Scholar
  14. El Haddad, M., Dowling, N., Topper, T. and Smith, K. (1980). J-integral applications for short fatigue cracks at notches. International Journal of Fracture 16, 15–30.Google Scholar
  15. El Haddad, M., Topper, T. and Smith, K. (1979). Prediction of non-propagating cracks. Engineering Fracture Mechanics 11, 573–584.Google Scholar
  16. Elber, W. (1970). Fatigue crack closure under cyclic tension. Engineering Fracture Mechanics 2, 37–45.Google Scholar
  17. Foreman, R., Keary, V. and Engle, R. (1967). Numerical analysis of crack propagation in cyclic-loaded structures. Journal of Basic Engineering 89, 459–464.Google Scholar
  18. Gilbert, C., Dauskardt, R. and Ritchie, R. (1997). Microstructural mechanisms of cyclic fatigue-crack propagation in grain-bridging ceramics. Ceramics International 23, 413–418.Google Scholar
  19. Gilbert, C., Petrany, R., Ritchie, R., Dauskardt, R. and Steinbrech, R. (1995). Cyclic fatigue in monolithic alumina: mechanisms for crack advance promoted by frictional wear of grain bridges. Journal of Materials Science 30, 643–654.Google Scholar
  20. Gylltoft, K. (1984). A fracture mechanics model for fatigue in concrete. Materials and Structures 17, 55–58.Google Scholar
  21. Hordijk, D. and Reinhardt, H. (1991). Growth of Discrete Cracks under Fatigue Loading. In: Toughening Mechanisms in Quasi-Brittle Materials (edited by Shah, S.), Dordrecht, pp. 541–554.Google Scholar
  22. Kanninen, M. and Atkinson, C. (1980). Application of an inclined-strip-yield crack-tip plasticity model to predict constant amplitude fatigue crack growth. International Journal of Fracture 16, 53–69.Google Scholar
  23. Kanninen, M. and Popelar, C. (1985). Advanced Fracture Mechanics. Oxford University Press, Oxford.Google Scholar
  24. Klesnil, M. and Lukas, P. (1972). Influence of strength and stress history on growth and stabilisation of fatigue cracks. Engineering Fracture Mechanics 4, 77–92.Google Scholar
  25. Laird, C. (1979). Mechanisms and theories of fatigue. In: Fatigue and Microstructure. American Society for Metals, pp. 149–203.Google Scholar
  26. Leis, B., Kanninen, M., Hopper, A., Ahmad, J. and Broek, D. (1983). A Critical Review of the Short Crack Problem in Fatigue. Technical report, Air Force Aeronautical Laboratories Report.Google Scholar
  27. McEvily, A. (1988). On Closure in Fatigue Crack Growth. Technical report, American Society for Testing and Materials, Philadelphia.Google Scholar
  28. Needleman, A. (1987). A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 54, 525–531.Google Scholar
  29. Needleman, A. (1990a). An analysis of decohesion along an imperfect interface. International Journal of Fracture 42, 21–40.Google Scholar
  30. Needleman, A. (1990b). An analysis of tensile decohesion along an interface. Journal of the Mechanics and Physics of Solids 38, 289–324.Google Scholar
  31. Needleman, A. (1992). Micromechanical modeling of interfacial decohesion. Ultramicroscopy 40, 203–214.Google Scholar
  32. Neumann, P. (1974). The geometry of slip processes at a propagating fatigue crack. Acta Metallurgica 22, 1155–1178.Google Scholar
  33. Ortiz, M. (1996). Computational micromechanics. Computational Mechanics 18, 321–338.Google Scholar
  34. Ortiz, M. and Pandolfi, A. (1999). Finite-deformation irreversible cohesive elements for three-dimensional crackpropagation analysis. International Journal for Numerical Methods in Engineering 44, 1267–1282.Google Scholar
  35. Ortiz, M. and Popov, E. (1985). Accuracy and stability of integration algorithms for elastoplastic constitutive relations. International Journal for Numerical Methods in Engineering 21, 1561–1576.Google Scholar
  36. Ortiz, M. and Quigley, J. (1991). Adaptive mesh refinement in strain localization problems. Computer Methods in Applied Mechanics and Engineering 90, 781–804.Google Scholar
  37. Ortiz, M. and Suresh, S. (1993). Statistical properties of residual stresses and intergranular fracture in ceramic materials. Journal of Applied Mechanics 60, 77–84.Google Scholar
  38. Pandolfi, A. and Ortiz, M. (1998). Solid modeling aspects of three-dimensional fragmentation. Engineering with Computers 14, 287–308.Google Scholar
  39. Paris, P., Bucci, R., Wessel, E., Clark, W. and Mager, T. (1972). An extensive study on low fatigue crack growth rates in A533 and A508 steels. Technical Report ASTM STP 513. American Society for Testing and Materials, Philadelphia.Google Scholar
  40. Paris, P. and Erdogan, F. (1963). A critical analysis of crack propagation laws. Journal of Basic Engineering 85, 528–534.Google Scholar
  41. Paris, P., Gomez, M. and Anderson, W. (1961). A rational analytic theory of fatigue. The trend in engineering 13, 9–14.Google Scholar
  42. Prager, M. (1956). A new method of analyzing stress and strains in work-hardening plastic solids. Journal of Applied Mechanics 23, 493–496.Google Scholar
  43. Radovitzky, R. and Ortiz, M. (1999). Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Computer Methods in Applied Mechanics and Engineering 172, 203–240.Google Scholar
  44. Repetto, E.A., Radovitzky, R. and Ortiz, M. (1999). Finite element simulation of dynamic fracture and fragmentation of glass rods. Computer Methods in Applied Mechanics and Engineering, in press.Google Scholar
  45. Rice, J. (1967). Mechanics of Crack-Tip Deformation and Extension by Fatigue. Technical report, American Society for Testing and Materials, Philadelphia.Google Scholar
  46. Rice, J. and Beltz, G. (1994). The activation-energy for dislocation nucleation at a crack. Journal of the Mechanics and Physics of Solids 42, 333–360.Google Scholar
  47. Simo, J. and Laursen, T. (1992). An augmented Lagrangian treatment of contact problems involving friction. Computers and Structures 42, 97–116.Google Scholar
  48. Starke, E. and Williams, J. (1989). Microstructure and the Fracture Mechanics of Fatigue Crack Propagation. Technical report, American Society for Testing and Materials, Philadelphia.Google Scholar
  49. Suresh, S. (1991). Fatigue of Materials. Cambridge University Press, Cambridge.Google Scholar
  50. Tvergaard, V. and Hutchinson, J.W. (1996). Effect of strain dependent cohesive zone model on predictions of interface crack growth. Journal de Physique IV 6, 165–172.Google Scholar
  51. von Euw, E., Hertzberg, R. and Roberts, R. (1972). Delay Effects in Fatigue-Crack Propagation. Technical report, American Society for Testing and Materials, Philadelphia.Google Scholar
  52. Weertman, J. (1966). Rate of growth of fatigue cracks calculated from the theory of infinitesimal dislocations distributed on a plane. International Journal of Fracture Mechanics 2, 460–467.Google Scholar
  53. Wheeler, O. (1972). Spectrum loading and crack growth. Journal of Basic Engineering 94, 181–186.Google Scholar
  54. Willenborg, J., Engle, R. and Wood, R. (1971). A Crack Growth Retardation Model Using an Effective Stress Concept. Technical Report AFFDL-TM–71–1-FBR, Air Force Flight Dynamics Laboratory Report.Google Scholar
  55. Xu, G., Argon, A. and Ortiz, M. (1995). Nucleation of dislocations from crack tips under mixed-modes of loading – Implications for brittle against Ductile behavior of crystals. Philosophical Magazine A – Physics of Condensed Matter Structure Defects and Mechanical Properties 72, 415–451.Google Scholar
  56. Xu, X.P. and Needleman, A. (1994). Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 42, 1397–1434.Google Scholar
  57. Yankelevsky, D. and Reinhardt, H. (1989). Uniaxial behavior of concrete in cyclic tension. Journal of Structural Engineering 115, 166–182.Google Scholar
  58. Ziegler, H. (1959). A modification of Prager's hardening rule. Quarterly of Applied Mathematics 17, 55–65.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • O. Nguyen
    • 1
  • E.A. Repetto
    • 1
  • M. Ortiz
    • 1
  • R.A. Radovitzky
    • 1
  1. 1.Graduate Aeronautical LaboratoriesCalifornia Institute of TechnologyPasadenaUSA

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