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Assessment of void growth models from porosity measurements in cold-drawn copper bars

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Abstract

This work investigates void growth in cold-drawn copper bars containing a fine dispersion of small inclusions at which voids nucleate. Using the Rice and Tracey (RT), the Gurson-Tvergaard (GT), and the Gurson-Leblond-Perrin (GLP) void growth models, a procedure is proposed for deriving the porosity distribution from density measurements on specimens sectioned from the neck of a tensile bar. This procedure allows identification of the parameters of the models. The effect of strain hardening on porosity evolution is analyzed by comparing the behavior of the material in the cold-drawn state (n≈0.1) and in the recrystallized state (n≈0.4). Inclusion dimensions and distributions were found to be identical in these two states. The parameter α of the RT model is found to depend on n, whereas the parameter q of the Gurson-type models does not vary with n. Numerical modeling of porosity variations in notched, round copper bars shows that both the parameter α and the parameter q in the GT model depend on the stress triaxiality in the recrystallized material, whereas the parameter q remains a constant in the GLP model. Accounting for the ellipsoidal void shapes and for the presence of the inclusion significantly affects the prediction of porosity variations.

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References

  1. F.A. McClintock: J. Appl. Mech., 1968, vol. 35, pp. 363–71.

    Google Scholar 

  2. J.R. Rice and D.M. Tracey: J. Mech. Phys. Solids, 1969, vol. 17, pp. 201–17.

    Article  Google Scholar 

  3. A.L. Gurson: J. Eng. Mater. Technol., 1977, vol. 99, pp. 2–15.

    Google Scholar 

  4. A. Needleman: J. Appl. Mech., 1972, vol. 39, pp. 964–70.

    Google Scholar 

  5. V. Tvergaard: Int. J. Fract., 1981, vol. 17, pp. 389–407.

    Article  Google Scholar 

  6. B. Marini, F. Mudry, and A. Pineau: Eng. Fract. Mech., 1985, vol. 6, pp. 989–96.

    Article  Google Scholar 

  7. G. Perrin and J.-B. Leblond: Int. J. Plast., 1990, vol. 6, pp. 677–99.

    Article  Google Scholar 

  8. J.-B. Leblond, G. Perrin, and J. Devaux: Eur. J. Mech., A/Solids, 1995, vol. 4, pp. 499–527.

    Google Scholar 

  9. V. Tvergaard and A. Needleman: Acta Metall., 1984, vol. 32, pp. 157–69.

    Article  Google Scholar 

  10. J. Koplik and A. Needleman: Int. J. Solids Struct., 1990, vol. 24, pp. 835–53.

    Article  Google Scholar 

  11. R. Becker, A. Needleman, O. Richmond, and V. Tvergaard: J. Mech. Phys. Solids, 1988, vol. 36, pp. 317–51.

    Article  Google Scholar 

  12. C.L. Hom and R.M. McMeeking: J. Appl. Mech., 1989, vol. 56, pp. 309–17.

    Article  Google Scholar 

  13. M.J. Worswick and R. Pick: J. Mech. Phys. Solids, 1990, vol. 38, pp. 601–25.

    Article  Google Scholar 

  14. W. Brocks, S. Hao, and D. Steglich: Proc. Euromech-Mecamat 96, Fontainebleau, A. Pineau and G. Rousselier, eds., Les Editions de Physique, Les Ulis, France, 1996, pp. 43–52.

    Google Scholar 

  15. F.M. Beremin: in Three-Dimensional Constitutive Relations and Ductile Fracture, S. Nemat-Nasser, ed., North-Holland Publishing Company, Amsterdam, 1981, pp. 185–205.

    Google Scholar 

  16. D.M. Tracey: Eng. Fract. Mech., 1971, vol. 3, pp. 301–15.

    Article  Google Scholar 

  17. H. Andersson: J. Mech. Phys. Solids, 1977, vol. 25, pp. 217–33.

    Article  Google Scholar 

  18. B. Budiansky, J.W. Hutchinson, and S. Slutsky: in Mechanics of Solids, H.G. Hopkins and M.J. Sewell, eds., Pergamon Press, Oxford, United Kingdom, 1982, pp. 13–45.

    Google Scholar 

  19. R. Becker, R.E. Smelser, O. Richmond, and E.J. Appleby: Metall. Trans. A, 1989, vol. 20A, pp. 853–61.

    CAS  Google Scholar 

  20. M. Gologanu, J.-B. Leblond, and J. Devaux: J. Mech. Phys. Solids, 1993, vol. 41, pp. 1723–54.

    Article  Google Scholar 

  21. A.B. Richelsen and V. Tvergaard: Acta Metall. Mater., 1994, vol. 42, pp. 2561–77.

    Article  Google Scholar 

  22. J. Faleskog and C.F. Shih: J. Phys. Mech. Solids, 1997, vol. 45, pp. 21–39.

    Article  CAS  Google Scholar 

  23. N.A. Fleck, J.W. Hutchinson, and V. Tvergaard: J. Phys. Mech. Solids, 1989, vol. 37, pp. 515–40.

    Article  Google Scholar 

  24. H. Yamamoto: Int. J. Fract., 1978, vol. 14, pp. 347–65.

    Article  Google Scholar 

  25. R.J. Bourcier, D.A. Koss, R.E. Smelser, and O. Richmond: Acta Metall., 1986, vol. 34, pp. 2443–53.

    Article  CAS  Google Scholar 

  26. E.M. Dubensky and D.A. Koss: Metall. Trans. A, 1987, vol. 18A, pp. 1887–95.

    CAS  Google Scholar 

  27. R. Becker: J. Mech. Phys. Solids, 1987, vol. 35, pp. 577–99.

    Article  Google Scholar 

  28. A.W. Thompson: Metall. Trans. A, 1987, vol. 18A, pp. 1877–86.

    CAS  Google Scholar 

  29. A. Needleman and A.S. Kushner: Eur. J. Mech., A/Solids, 1990, vol. 3, pp. 193–206.

    Google Scholar 

  30. A. Pineau and P. Joly: in Defect Assessment in Components—Fundamentals and Applications ESIS/EGF9, J.G. Blauel and K.H. Schwalbe, eds., Mechanical Engineering Publications, London, 1991, pp. 381–414.

    Google Scholar 

  31. Y. Huang, J.W. Hutchinson, and V. Tvergaard: J. Mech. Phys. Solids, 1991, vol. 39, pp. 223–41.

    Article  Google Scholar 

  32. V. Tvergaard and A. Needleman: Int. J. Solids Struct., 1995, vol. 32, pp. 1063–77.

    Article  Google Scholar 

  33. M. Gologanu, J.-B. Leblond, G. Perrin, and J. Devaux: in Continuum Micromechanics, P. Suquet, ed., Springer-Verlag, New York, NY, 1997, preprint.

    Google Scholar 

  34. N.A. Fleck and J.W. Hutchinson: Adv. Appl. Mech., 1997, vol. 33, pp. 295–361.

    Article  Google Scholar 

  35. A. Benzerga, J. Besson and A. Pineau: 3ème Colloque National en Calcul des Structures, Giens, France, 1997, preprint.

  36. L.M. Brown and J.D. Embury: Proc. 3rd Int. Conf. on Strength of Metals and Alloys, Institute of Metals, London, 1973, pp. 164–69.

    Google Scholar 

  37. P.F. Thomason: Ductile Fracture of Metals, Pergamon Press, Oxford, United Kingdom, 1990.

    Google Scholar 

  38. T. Pardoen, I. Doghri, and F. Delannay: Acta Mater., 1998, vol. 46, pp. 541–52.

    Article  CAS  Google Scholar 

  39. P.W. Bridgman: Studies in Large Plastic Flow and Fracture, in Metallurgy and Metallurgical Engineering Series, R.F. Mehl, consulting ed., McGraw-Hill Book Company, Inc., New York, NY, 1952.

    Google Scholar 

  40. D.M. Norris, Jr., B. Moran, J.K. Scudder, and D.F. Quinones: J. Mech. Phys. Solids, 1978, vol. 26, pp. 1–19.

    Article  Google Scholar 

  41. Y. Huang: J. Appl. Mech., 1991, vol. 58, pp. 1084–85.

    Google Scholar 

  42. G. Leroy, J.D. Embury, G. Edwards, and M.F. Ashby: Acta Metall., 1981, vol. 29, pp. 1509–22.

    Article  CAS  Google Scholar 

  43. T. Pardoen: Ph.D. Thesis, Université Catholique de Louvain, Louvainla-Neuve, Belgium, 1998.

    Google Scholar 

  44. R.T. de Hoff and F.N. Rhisnes: Microscopie Quantitative, Masson, Paris, France, 1972.

    Google Scholar 

  45. B. Baudelet: Mise en Forme des Métaux et Alliages, Ecole d’Ete de Métallurgie Physique de Villars-sur-Ollon, 1975, Editions du CNRS, Paris, 1976.

    Google Scholar 

  46. A. Needleman: J. Mech. Phys. Solids, 1972, vol. 20, pp. 111–24.

    Article  Google Scholar 

  47. A.S. Argon, J. Im, and A. Needleman: Metall. Trans. A, 1975, vol. 6A, pp. 815–24.

    CAS  Google Scholar 

  48. A. Needleman and J.R. Rice: in Mechanics of Sheet Metal Forming, D.P. Koistinen and N.M. Wang, eds., Plenum Press, New York, NY, 1978, pp. 237–67.

    Google Scholar 

  49. J.M. Duva and J.W. Hutchinson: Mech. Mater., 1984, vol. 3, pp. 41–54.

    Article  Google Scholar 

  50. R. Chaouadi: Ph.D. Thesis, Katholieke Universiteit Leuven and SCK-CEN, MOL, Belgium, 1995.

    Google Scholar 

  51. B.A. Senior, F.W. Noble, and B.L. Eyre: Acta Metall., 1986, vol. 34, pp. 1321–27.

    Article  CAS  Google Scholar 

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  1. the Département Des Sciences, Des Matériaux et Procédés at Université Catholique De Louvain, B-1348, Louvain-la-Neuve, Belgium

    T. Pardoen (Research Assistant) & F. Delannay (Professor)

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  1. T. Pardoen
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  2. F. Delannay
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Pardoen, T., Delannay, F. Assessment of void growth models from porosity measurements in cold-drawn copper bars. Metall Mater Trans A 29, 1895–1909 (1998). https://doi.org/10.1007/s11661-998-0014-4

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  • DOI: https://doi.org/10.1007/s11661-998-0014-4

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