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

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Abstract

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.

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Abbreviations

E :

instantaneous Young’s modulus

\(\overline \varepsilon\) :

equivalent plastic strain

E 0 :

initial Young’s modulus of chord modulus model

E a :

saturated Young’s modulus of chord modulus model

ξ :

material parameter of chord modulus model

r b :

plastic strain ratio of balanced biaxial test

m :

exponent parameter of Yld2000-2d model

α 1∼8 :

material parameter of Yld2000-2d model

ε :

logarithmic strain tensor

C :

stiffness matrix

v :

poisson’s ratio

f :

yield function

\(\overline \sigma\) :

effective stress

σ :

cauchy stress tensor

a :

back-stress tensor or center of yield surface

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

size of yield function

K :

material parameter of size of yield function

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

material parameter of size of yield function

n :

material parameter of size of yield function

C :

material parameter of Chaboche model

γ :

material parameter of Chaboche model

β :

center of bounding surface

c :

material parameter of center of bounding surface

K :

material parameter of size of yield function

θ before :

angle before springback in 3-point bending

θ after :

angle after springback in 3-point bending

Δθ :

angle difference in three-point bending

L :

length of a beam

b :

width of a beam

h :

height of a beam

M :

moment

R :

distance from neutral plane of beam to center of curvature

Y :

yield strength

δ :

degree of asymmetry

κ 0 :

maximum curvature

κ * :

springback amount

e :

elastic

p :

plastic

1, 2:

direction

T :

tension

C :

compression

Max :

maximum

s :

symmetry

a :

asymmetry

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Acknowledgement

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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Authors and Affiliations

  1. School of Mechanical Engineering, Pusan National University, Busan, 46241, Korea

    Jaebong Jung, Yong Chan Hur, Byung-Min Kim & Ji Hoon Kim

  2. Metal Forming Technology Team, LG Electronics, 222 LG-ro, Jinwi-myeon, Pyeongtaek-si, Gyeonggi, 17709, Korea

    Sungwook Jun

  3. Press Die Research Team, NARA Mold & Die Co., Ltd., 675 Gongdan-ro, Seongsan-gu, Changwon-si, Gyeongnam, 51555, Korea

    Hyun-Seok Lee

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  1. Jaebong Jung
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Correspondence to Ji Hoon Kim.

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This paper was significantly extended and modified from the original paper presented in Asia-Pacific Symposium on Engineering Plasticity and its Applications 2018, and recommended by the Scientific & Technical Committee for journal publication.

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Jung, J., Hur, Y.C., Jun, S. et al. Constitutive Modeling of Asymmetric Hardening Behavior of Transformation-Induced Plasticity Steels. Int.J Automot. Technol. 20 (Suppl 1), 19–30 (2019). https://doi.org/10.1007/s12239-019-0124-6

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