International Journal of Fracture

, Volume 58, Issue 2, pp 137–156 | Cite as

A finite element investigation of quasi-static and dynamic asymptotic crack-tip fields in hardening elastic-plastic solids under plane stress

Part II: Crack growth in power-law hardening materials
  • Xiaomin Deng
  • Ares J. Rosakis


This is the second half of a two-part finite element investigation of quasi-static and dynamic crack growth in hardening elastic-plastic solids under mode I plane stress, steady state, and small-scale yielding conditions. The hardening materials are assumed to obey the von Mises yield criterion and the associated flow rule, and are characterized by a Ramberg-Osgood type power-law effective stress-strain curve. The asymptotic feature of the crack-tip stress and deformation fields, and the influence of hardening and crack propagation speed on these fields as well as on the size and shape of the crack-tip active plastic zone, are addressed in detail. The results of this study strongly suggest the existence of stress and strain singularities of the type [ln(R o/r )]s (s>0) at r=0, where r is the distance to the crack tip and R0 is a length scaling parameter, which is consistent with the predictions of asymptotic analyses of variable-separable type by Gao et al. [1–4]. Difficulties in estimating the values of R0 and s by fitting the results of the present full-field study to the type of singularities shown above are analyzed, and quantititive differences between the results of this study and those of the asymptotic analyses are discussed. As expected, findings presented here share many similarities with those reported in the first part of this study [5] for crack growth in linear hardening solids. A prominent common feature of crack growth in these two types of hardening materials is that as the level of hardening decreases and the crack propagation speed increases, a secondary yield zone emerges along the crack surface, and kinks in the angular variations of the stress and velocity fields begin to develop near where elastic unloading is taking place.


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  1. 1.
    Y.C. Gao, X.T. Zhang and K.C. Hwang, International Journal of Fracture 21 (1983) 301–317.Google Scholar
  2. 2.
    Y.C. Gao and K.C. Hwang, in Advances in Fracture Research, Proceedings of the 5th International Conference on Fracture, Vol. 2, D. Francois et al. (eds.), (1981) 669–682.Google Scholar
  3. 3.
    Y.C. Gao and S. Nemat-Nasser, Mechanics of Materials 2 (1983) 305–317.CrossRefGoogle Scholar
  4. 4.
    Z. Zhang and Y.C. Gao, Acta Mechanica Sinica 4 (1988) 22–34.Google Scholar
  5. 5.
    X. Deng and A.J. Rosakis, International Journal of Fracture 57 (1992) 291–308.Google Scholar
  6. 6.
    R.H. Dean and J.W. Hutchinson, in Fracture Mechanics: Twelfth Conference, ASTM STP 700, American Society for Testing and Materials (1980) 383–405.Google Scholar
  7. 7.
    J. Christoffersen and J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 27 (1979) 465–487.CrossRefGoogle Scholar
  8. 8.
    P.S. Lam, ‘Numerical Analysis of Stable Crack Growth in Elastic-plastic Materials in Small Scale and General Yielding’, Ph.D. thesis, University of Illinois at Urbana-Champaign (1982).Google Scholar
  9. 9.
    X. Luo, X. Zhang and K. Hwang, in Proceedings of ICF International Symposium on Fracture Mechanics (Beijing), Science Press, Beijing, China (1984) 138–145.Google Scholar
  10. 10.
    E.P. Sorensen, International Journal of Fracture 14 (1978) 485–500.Google Scholar
  11. 11.
    R. Narasimhan, A.J. Rosakis and J.F. Hall, Journal of Applied Mechanics 54 (1987) 846–853.Google Scholar
  12. 12.
    X. Deng and A.J. Rosakis, Finite Elements in Analysis and Design 7 (1990) 181–191.CrossRefGoogle Scholar
  13. 13.
    X. Deng, ‘Dynamic Crack Propagation in Elastic-plastic Solids’, Ph.D. thesis, California Institute of Technology, Pasadena, CA 91125 (1990).Google Scholar
  14. 14.
    X. Deng and A.J. Rosakis, Journal of the Mechanics and Physics of Solids 39 (1991) 682–722.CrossRefGoogle Scholar
  15. 15.
    Y.C. Gao, International Journal of Fracture 34 (1987) 111–129.Google Scholar
  16. 16.
    L.B. Freund and A.S. Douglas, Journal of the Mechanics and Physics of Solids 30 (1982) 59–74.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Xiaomin Deng
    • 1
  • Ares J. Rosakis
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

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