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


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.


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

List of symbols


Gurson plastic potential


Stress tensor of porous aggregate


Effective stress of porous aggregate


Mean stress of porous aggregate


Deviatoric stress tensor of porous aggregate


Deviatoric part of total strain

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

Deviatoric part of plastic strain

q1, q2, q3

Gurson’s parameters


Shear modulus


Bulk modulus/Hardening coefficient in stress–strain law


Hardening constant


Current yield stress of matrix material


J Integral


Strain tensor

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

Plastic strain tensor

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

Effective plastic strain


Mean strain


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


Void volume fraction

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

Void growth rate due to nucleation

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

Void growth rate due to growth


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia

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