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Journal of Materials Science

, Volume 43, Issue 6, pp 1897–1909 | Cite as

A complete GTN model for prediction of ductile failure of pipe

  • S. AcharyyaEmail author
  • S. Dhar
Article

Abstract

The micro mechanical model by Gurson–Tvergaard–Needleman is widely used for the prediction of ductile fracture. Some material properties (Gurson parameters) used as material input in this model for simulation are estimated experimentally from specimen level. In this article an attempt has been made to tune the values of some of these Gurson’s parameters by comparing the simulated results with the experimental results in the specimen level (axisymmetric tensile bar and CT specimens). An elastic–plastic finite element code has been developed together with Gurson–Tvergaard–Needleman model for void nucleation and growth. The initial value of fc is determined from Thomason’s limit load model and then tuned on the basis of best prediction of the failure of one-dimensional tensile bar. Then the load versus load line displacement and J versus \({\Updelta}\)a results for CT specimen are generated with the same code and the value of fn is tuned to match the simulated J versus \(\Updelta\)a results with the experimental results. Lastly the same code and the Gurson’s parameters obtained are used to simulate the load versus load point displacement and crack growth for pipe with circumferential crack under four point bending. The simulated results are compared with the experimental results to assess the applicability of the whole method. In the proposed material modelling, post-yielding phenomena and necking of the tensile bar are simulated accordingly and strain softening due to void nucleation and growth has been taken care of properly and drop in stress is implicitly simulated through a model. Incremental plasticity theory with arc length method is used for the nonlinear displacement control problem.

Keywords

Void Growth Void Volume Fraction Circumferential Crack Load Line Displacement Gurson Model 

List of symbols

ϕ

Gurson plastic potential

σij

Stress tensor of porous aggregate

σeq

Effective stress of porous aggregate

σm

Mean stress of porous aggregate

\(\sigma_{ij}^{\prime}\)

Deviatoric stress tensor of porous aggregate

γij

Deviatoric part of total strain

\(\gamma_{ij}^{\rm p}\)

Deviatoric part of plastic strain

q1, q2, q3

Gurson’s parameters

G

Shear modulus

K

Bulk modulus/Hardening coefficient in stress–strain law

h

Hardening constant

σc

Current yield stress of matrix material

J

J Integral

ɛij

Strain tensor

\(\varepsilon_{ij}^{\rm p}\)

Plastic strain tensor

\(\varepsilon_{\rm eq}^{\rm p}\)

Effective plastic strain

\(\bar{\varepsilon}\)

Mean strain

n

Hardening exponent of stress–strain law

\(\bar{\varepsilon}^{\rm p}\)

Mean plastic strain

\(\{{\dot{\varepsilon}^{\rm e}}\}\)

Elastic strain rate vector

\(\{{\dot{\varepsilon}^{\rm p}}\}\)

Plastic strain rate vector

f

Void volume fraction

\({\dot{f}_{\rm nu}} \)

Void growth rate due to nucleation

\({\dot{f}_{\rm gr}} \)

Void growth rate due to growth

References

  1. 1.
    Mackenzie JHAC, Hancock JW, Brown DK (1977) Eng Fract Mech 9:167CrossRefGoogle Scholar
  2. 2.
    Gurland J (1972) Acta Metall 20:735CrossRefGoogle Scholar
  3. 3.
    Argon AS, Im J (1975) Metall Trans 6A:839CrossRefGoogle Scholar
  4. 4.
    Rosselier G (1987) Nucl Eng Des 105:97CrossRefGoogle Scholar
  5. 5.
    Gurson AL (1977) J Eng Mater Tech 99:2CrossRefGoogle Scholar
  6. 6.
    Tvergaard V, Needleman A (1984) Acta Metall 32:157CrossRefGoogle Scholar
  7. 7.
    Cheng, Yiu (1998) In: International Conference on non linear Mechanics, ICNM, pp 175–180Google Scholar
  8. 8.
    Decamp K, Bauvineau L, Besson J, Pineau A (1997) Int J Fracture 88:1CrossRefGoogle Scholar
  9. 9.
    Ragab AR (2000) Int J Fract 105:391CrossRefGoogle Scholar
  10. 10.
    Pineau A (1997) 14th Trans. 14th Int Conf Struct Mech SmiRt 14, Lyon, 1997Google Scholar
  11. 11.
    Lee JH, Zhang Y (1994) J Eng Mater Tech 116:69CrossRefGoogle Scholar
  12. 12.
    Qiu YP, Weng GJ (1993) Int J Plast 6:271CrossRefGoogle Scholar
  13. 13.
    Zhang ZL, Thaulow C, Ødegård J (2000) Eng Fract Mech 67(2):155CrossRefGoogle Scholar
  14. 14.
    Rakin M, Cvijovic Z, Grabulov V, Putic S (2004) Eng Fract Mech 71(4–6):813CrossRefGoogle Scholar
  15. 15.
    Pavankumar TV, Samal MK, Chattopadhyay J, Dutta BK, Kushwaha HS, Roos E, Seidenfuss M (2005) Int J Pressure Vessels Piping 82(5):386CrossRefGoogle Scholar
  16. 16.
    Mkaddem A, Hambli R, Potiron A (2004) Int J Adv Manuf Tech 23:451CrossRefGoogle Scholar
  17. 17.
    Qian XD, Choo YS, Liew JYR, Wardenier J (2005) J Struct Eng 131:768CrossRefGoogle Scholar
  18. 18.
    Teng X, Wierzbick T, Hiermaier S, Rohr I (2005) Int J Struct Sol 42:2929CrossRefGoogle Scholar
  19. 19.
    Chu C, Needleman A (1980) J Eng Mater Tech 102:249CrossRefGoogle Scholar
  20. 20.
    Batoz JL, Dhatt G (1979) Int J Num Meth Eng 14:1262CrossRefGoogle Scholar
  21. 21.
    Crisfield MA (1987) In: Owen DR, Hinton E, Onate E (eds) Computational plasticity Part-I. Pineridge Press, pp 133–159Google Scholar
  22. 22.
    Bathe KJ (1997) Finite element procedures. Printice Hall of IndiaGoogle Scholar
  23. 23.
    Chattopadhyay J, Dutta BK, Kushwaha HS (2000) Int J Pressure Vessels Piping 77:455CrossRefGoogle Scholar
  24. 24.
    Thomason PF (1990) Acta Metall 33:1079CrossRefGoogle Scholar
  25. 25.
    Zahoor A (1992) Int J Pressure Vessels Piping 51:1Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia

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