Metallurgical and Materials Transactions A

, Volume 40, Issue 2, pp 354–364 | Cite as

Finite Element Modeling of Plane Strain Toughness for 7085 Aluminum Alloy

  • M.E. Karabin
  • F. BarlatEmail author
  • R.T. Shuey


In this work, the constitutive model for 7085-T7X (overaged) aluminum alloy plate samples with controlled microstructures was developed. Different lengths of 2nd step aging times produced samples with similar microstructure but different stress-strain curves (i.e., different nanostructure). A conventional phenomenological strain-hardening law with no strain gradient effects was proposed to capture the peculiar hardening behavior of the material samples investigated in this work. The classical Gurson–Tvergaard potential, which includes the influence of void volume fraction (VVF) on the plastic flow behavior, as well as an extension proposed by Leblond et al.,[3] were considered. Unlike the former, the latter is able to account for the influence of strain hardening on the VVF growth. All the constitutive coefficients used in this work were based on experimental stress-strain curves obtained in uniaxial tension and on micromechanical modeling results of a void embedded in a matrix. These material models were used in finite element (FE) simulations of a compact tension (CT) specimen. An engineering criterion based on the instability of plastic flow at a crack tip was used for the determination of plane strain toughness K Ic . The influence of the microstructure was lumped into a single state variable, the initial void volume fraction. The simulation results showed that the strain-hardening behavior has a significant influence on K Ic .


Aging Time Stress Triaxiality Void Growth Compact Tension Specimen Void Volume Fraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors gratefully acknowledge Drs. Mark James and John Brockenbrough, Alcoa Technical Center, for their critical review of this manuscript.


  1. 1.
    A.L. Gurson: J. Eng. Mater. Technol., 1977, vol. 99, pp. 2–15Google Scholar
  2. 2.
    V. Tvergaard: Int. J. Fract., 1981, vol. 17, pp. 389–406CrossRefGoogle Scholar
  3. 3.
    J.B. Leblond, G. Perrin, J. Devaux: Eur. J. Mech. A, Solids, 1995, vol. 14, pp. 499–527zbMATHMathSciNetGoogle Scholar
  4. 4.
    J.T. Staley: Materials Selection and Design, ASM, Materials Park, OH, 1997, pp. 381–89Google Scholar
  5. 5.
    R.T. Shuey and A.J. den Bakker: Advances in the Metallurgy of Aluminum Alloys, M. Tiryakioglu, ed., ASM INTERNATIONAL, Metals Park, OH, 2001, pp. 189–94Google Scholar
  6. 6.
    J.T. Staley: Properties Related to Fracture Toughness, STP 605, ASTM, Philadelphia, PA, 1976, pp. 71–103Google Scholar
  7. 7.
    G.T. Hahn, A.R. Rosenfield: Metall. Trans. A, 1975, vol. 6A, pp. 653–70Google Scholar
  8. 8.
    P. Tanaka, C.A. Pampillo, and J.R. Low, Jr.: Review of Developments in Plane Strain Fracture Toughness Testing, ASTM Special Technical Publication No. 463, ASTM, Philadelphia, PA, 1970, pp. 191–215Google Scholar
  9. 9.
    J.C.W. Van de Kasteele, D. Broek: Eng. Fract. Mech., 1977, vol. 9, pp. 625–35CrossRefGoogle Scholar
  10. 10.
    D. Broek: Eng. Fract. Mech., 1973, vol. 5, pp. 55–56CrossRefGoogle Scholar
  11. 11.
    R.T. Shuey, F. Barlat, M.E. Karabin, and D.J. Chakrabarti: Metall. Mater. Trans. A, 2009, vol. 40A, DOI  10.1007/s11661-008-9703-2
  12. 12.
    G.T. Hahn and A.R. Rosenfield: Applications Related Phenomena in Titanium Alloys, ASTM Special Technical Publication No. 432, ASTM, Philadelphia, PA, 1968, pp. 5–32Google Scholar
  13. 13.
    P.F. Thomason: Int. J. Fract. Mech., 1971, vol. 7, pp. 409–19Google Scholar
  14. 14.
    T.L. Anderson: Fracture Mechanics—Fundamental and Applications, CRC Press, Boca Raton, FL, 1995Google Scholar
  15. 15.
    E. Van der Giessen, A. Needleman: Annu. Rev. Mater. Res., 2002, vol. 32, pp. 141–62CrossRefGoogle Scholar
  16. 16.
    W. Brocks: in Continuum Scale Simulation of Engineering Materials–Fundamentals–Microstructures–Process Applications, D. Raabe, F. Roters, F. Barlat, L.-Q. Chen, eds., Wiley-VCH Verlag GmbH, Berlin, 2004, pp. 621–37CrossRefGoogle Scholar
  17. 17.
    D. Steglich: in Continuum Scale Simulation of Engineering Materials–Fundamentals–Microstructures–Process Applications, D. Raabe, F. Roters, F. Barlat, L.-Q. Chen, eds., Wiley-VCH Verlag GmbH, Berlin, 2004, pp. 817–28CrossRefGoogle Scholar
  18. 18.
    T. Pardoen, Y. Brechet: Philos. Mag., 2004, vol. 84, pp. 269–97CrossRefADSGoogle Scholar
  19. 19.
    T. Pardoen, J.W. Hutchinson: Acta Mater., 2003, vol. 51, pp. 133–48CrossRefGoogle Scholar
  20. 20.
    R.M. McMeeking: J. Mech. Phys. Solids, 1977, vol. 25, pp. 357–81CrossRefGoogle Scholar
  21. 21.
    A. Needleman, V. Tvergaard: J. Mech. Phys. Solids, 1987, vol. 35, pp. 151–83zbMATHCrossRefADSGoogle Scholar
  22. 22.
    T. Pardoen, J.W. Hutchinson: J. Mech. Phys. Solids, 1999, vol. 48, pp. 2467–512CrossRefGoogle Scholar
  23. 23.
    R. Becker, A. Needleman, S. Suresh, V. Tvergaard, A.K. Vasudévan: Acta Metall., 1989, vol. 37, pp. 99–120CrossRefGoogle Scholar
  24. 24.
    T. Pardoen, D. Dumont, A. Deschamp, Y. Brechet: J. Mech. Phys. Solids, 2003, vol. 51, pp. 637–65zbMATHCrossRefADSGoogle Scholar
  25. 25.
    F.A. McClintock: J. Appl. Mech., 1968, vol. 35, pp. 363–71Google Scholar
  26. 26.
    J.R. Rice, D.M. Tracey: J. Mech. Phys. Solids, 1969, vol. 17, pp. 201–17CrossRefADSGoogle Scholar
  27. 27.
    A.C. Mackenzie, J.W. Hancock, D.K. Brown: Eng. Fract. Mech., 1977, vol. 9, pp. 167–88CrossRefGoogle Scholar
  28. 28.
    M.H. Porch, H.F. Fischmeister: Eng. Fract. Mech., 1992, vol. 43, pp. 581–88CrossRefGoogle Scholar
  29. 29.
    S. Jun: Eng. Fract. Mech., 1993, vol. 44, pp. 789–806CrossRefADSGoogle Scholar
  30. 30.
    M.R. Hill, T.L. Panontin: Eng. Fract. Mech., 2002, vol. 69, pp. 2163–2218CrossRefGoogle Scholar
  31. 31.
    D.M. Tracey: Eng Fract. Mech., 1971, vol. 3, pp. 301–15CrossRefGoogle Scholar
  32. 32.
    G. Perrin, J.-B. Leblond, and J. Devaux: ECF 8-Fracture Behaviour and Design of Materials and Structures, Engineering Materials Advisory Services Ltd., Torino, Italy, Oct. 1–5, 1990, vol. I, pp. 427–32Google Scholar
  33. 33.
    R. Becker: J. Mech. Phys. Solids, 1987, vol. 35, pp. 577–99CrossRefADSGoogle Scholar
  34. 34.
    V. Tvergaard: Adv. Appl. Mech., 1990, vol. 27, pp. 83–147zbMATHCrossRefGoogle Scholar
  35. 35.
    J. Faleskog, C.F. Shih: Int. J. Fract., 1997, vol. 89, pp. 355–73CrossRefGoogle Scholar
  36. 36.
    Z.H. Li, C. Wang, C.Y. Chen: Int. J. Plast., 2003, vol. 19, pp. 213–34zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    J. Koplik, A. Needleman: Int. J. Solids Struct., 1988, vol. 24, pp. 835–53CrossRefGoogle Scholar
  38. 38.
    ABAQUS, version 6.5, ABAQUS, Inc., Providence, RI, 2004Google Scholar
  39. 39.
    J.-B. Leblond: Mécanique de la rupture fragile et ductile, Lavoisier, Paris, 2003zbMATHGoogle Scholar
  40. 40.
    J.W. Hancock, M.J. Cowling: Met. Sci., 1980, vol. 14, pp. 293–304CrossRefGoogle Scholar
  41. 41.
    T. Ohira, T. Kishi: Mater. Sci. Eng., 1986, vol. 78, pp. 9–19CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2008

Authors and Affiliations

  1. 1.Alloy Technology and Materials Research DivisionAlcoa Technical CenterPittsburghUSA
  2. 2.Materials Mechanics Laboratory, Graduate Institute of Ferrous Technology (GIFT)Pohang University of Science and Technology (POSTECH)PohangRepublic of Korea

Personalised recommendations