Transition from ductile tearing to cleavage fracture: A cell-model approach

  • L. Xia
  • L. Cheng
Article

Abstract

The fracture resistance of ferritic steels in the ductile/brittle transition regime is controlled by the competition between ductile tearing and cleavage fracture. Under typical conditions, a crack initiates and grows by ductile tearing but, ultimately, failure occurs by catastrophic cleavage fracture. In this computational study cleavage fracture is treated by a weakest link mechanism in conjunction with brittle microcrack statistics. The cleavage model also accounts for the competition between the nucleation of voids from the carbide inclusions on grain boundaries and the unstable cracking of these inclusions precipitating catastrophic cleavage fracture. The probabilistic treatment for the transition to catastrophic cleavage is phrased in terms of the Weibull stress, σ_W, reaching measurable material-specific values. The successful application of this cleavage fracture model hinges on an accurate description of the evolution of the stress field during crack growth by ductile tearing. This is accomplished by using cell elements endowed with the micro-separation characteristics of ductile tearing. Load-displacement behavior, ductile tearing resistance and transition to cleavage fracture are investigated for three different test geometries. Crack geometry, microstructure and ductile crack growth exert strong effects on the transition from ductile tearing to cleavage fracture. The model predicts trends in ductile/brittle transition that are consistent with experimental data.

Transition ductile tearing cleavage fractue cell model. 

References

  1. Anderson, T.L. and Dodds, Jr. R.H. (1991). Specimen size requirements for fracture toughness testing in the transition region. Journal of Testing and Evaluation 19, 123–134.CrossRefGoogle Scholar
  2. Bakker, A. and Koers, R.W.J. (1991). Defect Assessment in Components — Fundamentals and Applications, ESIS/EGF9. (Edited by J.G. Blauel and K.-H. Schwalbe) Mechanical Engineering Publications, London, 613–632.Google Scholar
  3. Beremin, F.M. (1983). A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metallurgical Transactions A 14A, 2277–2287.ADSGoogle Scholar
  4. Betegón, C. and Hancock, J.W. (1990). ECF 8 Fracture Behaviour and Design of Materials and Structures, Volume II, (Edited by D. Firraro) Engineering Materials Advisory Services, Ltd., Warly, U.K., 999–1002.Google Scholar
  5. Brückner-Foit, A., Nikishkov, G.P. and Munz, D. (1996). Prediction of cleavage probability using higher order terms of the crack tip field. 1st European Mechanics of Materials Conference. EUROMECH-MECAMAT'96, France.) To appear.Google Scholar
  6. Chu, C.C. and Needleman, A. (1980). Void nucleation effects in biaxially stretched sheets. Journal of Engineering Materials and Technology, 102, 249–256.CrossRefGoogle Scholar
  7. Curry, D.A. and Knott, J.F. (1979). Effect of microstructure on cleavage fracture toughness of quenched and tempered steels. Metal Science 13, 341–345.Google Scholar
  8. Evans, A.G. (1983). Statistical aspects of cleavage fracture in steel. Metallurgical transactions A 14A, 1349–1355.ADSGoogle Scholar
  9. Faleskog, J.P. and Shih, C.F. (1997). Micromechanics of coalescence — I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids. Journal of the Mechanics and Physics of Solids 45, 21–50.CrossRefADSGoogle Scholar
  10. Gao, X., Faleskog, J. and Shih, C.F. Analysis of ductile to cleavage transition in part-through cracks using a cell model incorporating statistics. Submitted for publication.Google Scholar
  11. Gumbel, E.J. (1958). Statistics of Extremes, Columbia University Press, New York.MATHGoogle Scholar
  12. Gurson, A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth: Part I — Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology 99, 2–15.Google Scholar
  13. Kirk, M.T., Koppenhoefer, K.C. and Shih, C.F. (1993). Effects of constraint on specimen dimensions needed to obtain structurally relevant toughness measures. In Constraint Effects in Fracture, ASTM STP 1171, (Edited by E.M. Hackett, K.-H. Schwalbe and R.H. Dodds), 79–103.Google Scholar
  14. Koers, R.W.J., Krom, A.H.M. and Bakker, A. (1994). Prediction of cleavage fracture in the brittle to ductile transition region of a ferritic steel. In Constraint Effects in Fracture, Theory and Applications, ASTM STP 1244, (Edited by M. Kirk and A. Bakker), 191–208.Google Scholar
  15. Lin, T., Evans, A.G. and Ritchie, R.O. (1986). A statistical model of brittle fracture by transgranular cleavage. Journal of the Mechanics and Physics of Solids 34, 477–497.CrossRefADSGoogle Scholar
  16. Minami, F., Brückner-Foit, A., Munz D. and Trolldenier, B. (1992). Estimation procedure for the Weibull parameter used in the local approach. International Journal of Fracture 54, 197–210.Google Scholar
  17. Mudry, F. (1987). A local approach to cleavage fracture. Nuclear Engineering and Design 105, 65–76.CrossRefGoogle Scholar
  18. Pineau, A. (1981). Review of fracture micromechanisms and a local approach to predicting crack resistance in low strength steels. Advances in Fracture Research: ICF5 Conference (Edited by D. Francois et al.), 533–577.Google Scholar
  19. Ritchie, R.O., Knott, J.K. and Rice, J.R. (1973). On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids 21, 395–410.CrossRefADSGoogle Scholar
  20. Ruggieri, C. and Dodds, R.H. (1996). A transferability model for brittle fracture including constraint and ductile tearing effects: A probabilistic approach. International Journal of Fracture 79, 309–340.CrossRefGoogle Scholar
  21. Ruggieri, C., Panontin, T.L. and Dodds, R.H. (1996). Numerical modeling of ductile crack growth in 3-D using computational cell elements. International Journal of Fracture 82, 67–95.CrossRefGoogle Scholar
  22. Shih, C.F. and Xia, L. (1994). Modeling crack growth resistance using computational cells with microstructurally-based length scales. In Constraint Effects in Fracture, Theory and Applications, ASTM STP 1244 (Edited by M. Kirk and A. Bakker), 163–190.Google Scholar
  23. Sumpter, J.D.G. (1993). In An experimental investigation of T stress approach. Constraint Effects in Fracture, ASTM STP 1171 (Edited by E.M. Hackett, K.-H. Schwalbe and R.H. Dodds), 492–502.Google Scholar
  24. Tvergaard, V. (1981). Influence of voids on shear band instabilities under plane strain conditions. International Journal of Fracture 17, 389–407.CrossRefGoogle Scholar
  25. Wallin, K. (1993). Statistical aspects of constraint with emphasis to testing and analysis of laboratory specimens in the transition region. In Constraint Effects in Fracture, ASTM STP 1171 (Edited by E.M. Hackett, K.-H. Schwalbe and R.H. Dodds), 264–288.Google Scholar
  26. Wallin, K., Saario, T. and Törrönen, K. (1984). Statistical model for carbide induced brittle fracture in steel. Metal Science 18, 13–16.CrossRefGoogle Scholar
  27. Wang, Y.Y. (1991). A two-parameter characterization of elastic-plastic crack-tip and applications to cleavage fracture, Ph. D. Thesis. Department of Mechanical Engineering, MIT.Google Scholar
  28. Xia, L. and Shih, C.F. (1995). Ductile crack growth — I. A numerical study using computational cells with microstructurally-based length scales. Journal of the Mechanics and Physics of Solids 43, 233–259.MATHCrossRefADSGoogle Scholar
  29. Xia, L. and Shih, C.F. (1995). Ductile crack growth — II. Void nucleation and geometry effects on macroscopic fracture behavior. Journal of the Mechanics and Physics of Solids 43, 1953–1981.MATHCrossRefADSGoogle Scholar
  30. Xia, L. and Shih, C.F. (1996). Ductile crack growth — III. Transition to cleavage fracture incorporating statistics. Journal of the Mechanics and Physics of Solids 44, 603–639.CrossRefADSGoogle Scholar
  31. Xia, L., Shih, C.F. and Hutchinson, J.W. (1995). A computational approach to ductile crack growth under large scale yielding conditions. Journal of the Mechanics and Physics of Solids 43, 389–413.MATHCrossRefADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • L. Xia
    • 1
  • L. Cheng
    • 1
  1. 1.Division of EngineeringBrown UniversityProvidenceUSA

Personalised recommendations