Constitutive Modeling of Asymmetric Hardening Behavior of Transformation-Induced Plasticity Steels

  • Jaebong Jung
  • Yong Chan Hur
  • Sungwook Jun
  • Hyun-Seok Lee
  • Byung-Min Kim
  • Ji Hoon KimEmail author


Transformation-induced plasticity (TRIP) steels are part of advanced high strength steels capable of phase transformation, having good strength and ductility. The transformation rate is known to be dependent on the stress state, which may lead to asymmetric hardening behaviour for TRIP steels with compressive flow stresses larger than tensile ones. Sheet stamping products of TRIP steels show complex springback because of the asymmetry in addition to the large strength, which will complicate the analysis of sheet metal forming processes. In this work, the asymmetric hardening behaviour of a TRIP steel with a tensile strength of 1180 MPa was measured using the sheet tension-compression tester. An asymmetric hardening model was developed by introducing an off-centred bounding surface for the kinematic back-stress evolution, to depict the asymmetric hardening behaviour. The model parameters of the proposed constitutive equations were obtained from the stressstrain curves under tension followed by compression. The stress-strain curves were well captured by the developed constitutive model, whereas the conventional symmetric model fails to describe the asymmetric hardening behaviour of the TRIP steel. For validation, load-displacement curve and springback angles of three-point bending test were compared with the predictions by the proposed model.

Key words

Transformation-induced plasticity (TRIP) Asymmetry Combined isotropic-kinematic hardening rule Springback Phase transformation 



instantaneous Young’s modulus

\(\overline \varepsilon\)

equivalent plastic strain


initial Young’s modulus of chord modulus model


saturated Young’s modulus of chord modulus model


material parameter of chord modulus model


plastic strain ratio of balanced biaxial test


exponent parameter of Yld2000-2d model


material parameter of Yld2000-2d model


logarithmic strain tensor


stiffness matrix


poisson’s ratio


yield function

\(\overline \sigma\)

effective stress


cauchy stress tensor


back-stress tensor or center of yield surface

\({\overline \sigma_{{\rm{iso}}}}\)

size of yield function


material parameter of size of yield function

\({\overline \varepsilon_{\rm{0}}}\)

material parameter of size of yield function


material parameter of size of yield function


material parameter of Chaboche model


material parameter of Chaboche model


center of bounding surface


material parameter of center of bounding surface


material parameter of size of yield function


angle before springback in 3-point bending


angle after springback in 3-point bending


angle difference in three-point bending


length of a beam


width of a beam


height of a beam




distance from neutral plane of beam to center of curvature


yield strength


degree of asymmetry


maximum curvature


springback amount






1, 2














This work was supported by the Small and Medium Business Administration of Korea (SMBA) grant funded by the Korean government (MOTIE) (No. S2315965) and the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (2012R1A5A1048294) and the Ministry of Science and ICT (2015R1C1A1A01051620).


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Copyright information

© KSAE/112-04 2019

Authors and Affiliations

  • Jaebong Jung
    • 1
  • Yong Chan Hur
    • 1
  • Sungwook Jun
    • 2
  • Hyun-Seok Lee
    • 3
  • Byung-Min Kim
    • 1
  • Ji Hoon Kim
    • 1
    Email author
  1. 1.School of Mechanical EngineeringPusan National UniversityBusanKorea
  2. 2.Metal Forming Technology TeamLG ElectronicsGyeonggiKorea
  3. 3.Press Die Research TeamNARA Mold & Die Co., Ltd.GyeongnamKorea

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