A ductile damage-based vertex model for predictor—controller of forming limit at different strain rates with experimental validations

  • Farid Hosseini Mansoub
  • Ali Basti
  • Abolfazl Darvizeh
  • Asghar ZajkaniEmail author


In the present paper, a predictive strain-rate-dependent model of localized necking is developed by using a modified Vertex theory. A novel ductile damage-based criterion is proposed to control the necking parameters including on stress triaxiality, strain-hardening exponent, and Lode parameters. As a characterization parameter, elastic modulus is eventually chosen to measure the ductile damage during process of plastic deforming. Furthermore, a user-defined material subroutine is developed to finite element simulation by ABAQUS software, according to original formulations, in order to create linkage between related essential models. A typical strain rate-dependent metal is selected to validate the modified Vertex theory. To examine the accuracy of the results from present simulated study, the applicability is considered to compare with the experimental results. Tests of forming are also performed for St 13 sheets to measure forming limit diagram (FLD). It should be noted that the simulated FLDs are in good agreement with the experimental data. However, this correlation at low strain rates is better than high strain rates. Results revealed that level of FLD for the material St 13 increases with enhancing the strain rates. However, this increase will be infinitesimal for the lower strain rates as compared to the higher ones.


Ductile damage Triaxiality Lode parameter Strain rate Forming limit diagrams Vertex theory 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Farid Hosseini Mansoub
    • 1
  • Ali Basti
    • 2
  • Abolfazl Darvizeh
    • 2
  • Asghar Zajkani
    • 3
    Email author
  1. 1.Department of Mechanical EngineeringUniversity of GuilanRashtIran
  2. 2.Department of Mechanical EngineeringUniversity of GuilanRashtIran
  3. 3.Department of Mechanical EngineeringImam Khomeini International UniversityQazvinIran

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