A comparative study of six fracture loci for DIN1623 St12 steel to predict strip tearing in a tandem cold rolling mill


During tandem cold rolling mill process, strip tearing reduces production rate, damages the rollers, and consequently decreases efficiency of production. Predicting and postponing of this phenomenon leads to less expensive trial and errors in rolling industries. In this research first, DIN1623 St12 steel which is frequently applied in metal forming industries and also Bao–Wierzbicki ductile damage criterion is selected. Then, six curve fitting methods are employed to calibrate the material and are presented in 2D space of equivalent plastic strain to fracture and stress triaxiality. Finally, the achieved fracture loci are validated by comparing corresponding simulation results with experimental tests and the best curve fitting method with aims of high accuracy for tracking the strip tearing in a tandem cold rolling mill process and fewer numbers of required tests is revealed. Eventually, due to engaging this innovative approach, it is possible to trace the strip tearing in tandem cold rolling mill process by performing only two simple tensile tests. Therefore, it is concluded that strip tearing phenomenon can be precisely predicted in tandem cold rolling mill processes by a special focus on calibration of the Bao–Wierzbicki damage criterion in the range of low positive stress triaxiality which causes less number of needed tests.

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\(c,c_{1} ,c_{2}\) :

Damage parameters

\(d_{1} ,d_{2} ,d_{3} ,d_{4}\) :

Damage parameters

\(D\) :

Damage variable

\(e_{u}\) :


\(E\) :

Young’s modulus

\(K\) :

Hardening coefficient

\(n\) :

Hardening power

\(u_{{\text{f}}}\) :

Displacement to fracture

\(\varepsilon_{{{\text{eq}}}}\) :

Equivalent plastic strain

\(\varepsilon_{{\text{f}}}\) :

Equivalent fracture strain at onset of fracture

\(\varepsilon_{{{\text{f}},{\text{s}}}}\) :

Equivalent fracture strain under pure shear

\(\varepsilon_{{{\text{f}},{\text{t}}}}\) :

Equivalent fracture strain under uniaxial tension

\(\eta\) :

Stress triaxiality

\(\eta_{0}\) :

Intersection point of the second and third branches of fracture locus

\(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\) :

Principal stresses

\(\sigma_{{{\text{eq}}}}\) :

Von Mises equivalent stress

\(\sigma_{{\text{m}}}\) :

Mean stress

\(\sigma_{{\text{u}}}\) :

Ultimate stress

\(\sigma_{{y_{0} }}\) :

Initial yield stress


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Correspondence to F. Haji Aboutalebi.

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Asadi, M., Haji Aboutalebi, F. & Poursina, M. A comparative study of six fracture loci for DIN1623 St12 steel to predict strip tearing in a tandem cold rolling mill. Arch Appl Mech (2021). https://doi.org/10.1007/s00419-020-01859-0

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  • Fracture loci
  • Ductile damage criterion
  • Strip tearing
  • Tandem cold rolling mill process
  • DIN1623 St12 steel