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

Abstract

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig.17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24

Abbreviations

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

Damage parameters

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

Damage parameters

\(D\) :

Damage variable

\(e_{u}\) :

Elongation

\(E\) :

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

References

  1. 1.

    Mohr, D., Henn, S.: Calibration of stress-triaxiality dependent crack formation criteria: a new hybrid experimental–numerical method. Exp. Mech. 47(6), 805–820 (2007)

    Article  Google Scholar 

  2. 2.

    Lemaitre, J.: A Course on Damage Mechanics. Springer, Berlin (1996)

    Google Scholar 

  3. 3.

    Gurson, A.L.: Continuum theory of ductile rupture by void nucleation and growth: part I- yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15 (1977)

    Article  Google Scholar 

  4. 4.

    Chu, C., Needleman, A.: Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Technol. 102, 249–256 (1980)

    Article  Google Scholar 

  5. 5.

    Needleman, A., Tvergaard, V.: An analysis of ductile rupture in notched bars. J. Mech. Phys. Solids 32(6), 461–490 (1984)

    Article  Google Scholar 

  6. 6.

    Gologanu, M., Leblond, J.B., Devaux, J.: Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41(11), 1723–1754 (1993)

    Article  Google Scholar 

  7. 7.

    Garajeu, M., Michel, J., Suquet, P.: A micromechanical approach of damage in viscoplastic materials by evolution in size, shape and distribution of voids. Comput. Methods Appl. Mech. Eng. 183(3–4), 223–246 (2000)

    Article  Google Scholar 

  8. 8.

    Pardoen, T., Hutchinson, J.: An extended model for void growth and coalescence. J. Mech. Phys. Solids 48(12), 2467–2512 (2000)

    Article  Google Scholar 

  9. 9.

    Benzerga, A., Besson, J., Pineau, A.: Anisotropic ductile fracture: part II: theory. Acta Mater. 52(15), 4639–4650 (2004)

    Article  Google Scholar 

  10. 10.

    Ruzicka, J., Spaniel, M., Prantl, A., Dzugan, J., Kuzelka, J., Moravec, M.: Identification of ductile damage parameters in the Abaqus. Bull. Appl. Mech. 8, 89–92 (2012)

    Google Scholar 

  11. 11.

    McClintock, F.A.: A criterion for ductile fracture by the growth of holes. J. Appl. Mech. 35(2), 363–371 (1968)

    Article  Google Scholar 

  12. 12.

    Rice, J.R., Tracey, D.M.: On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 17(3), 201–217 (1969)

    Article  Google Scholar 

  13. 13.

    Cockcroft, M., Latham, D.: Ductility and the workability of metals. J. Inst. Met. 96(1), 33–39 (1968)

    Google Scholar 

  14. 14.

    Brozzo, P., Deluca, B., Rendina, R.: A new method for the prediction of formability limits in metal sheets. Sheet Metal Forming and Formability. In: Proceedings of the 7th Biennial Conference of the International Deep Drawing Research Group (1972)

  15. 15.

    Clift, S.E., Hartley, P., Sturgess, C., Rowe, G.: Fracture prediction in plastic deformation processes. Int. J. Mech. Sci. 32(1), 1–17 (1990)

    Article  Google Scholar 

  16. 16.

    Lemaitre, J.: A continuous damage mechanics model for ductile fracture. J. Eng. Mater. Technol. 107, 83–89 (1985)

    Article  Google Scholar 

  17. 17.

    Johnson, G.R., Cook, W.H.: Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. 21(1), 31–48 (1985)

    Article  Google Scholar 

  18. 18.

    Hooputra, H., Gese, H., Dell, H., Werner, H.: A comprehensive failure model for crashworthiness simulation of aluminium extrusions. Int. J. Crashworth. 9(5), 449–464 (2004)

    Article  Google Scholar 

  19. 19.

    Haji Aboutalebi, F., Banihashemi, A.: Numerical estimation and practical validation of Hooputra’s ductile damage parameters. Int. J. Adv. Manuf. Technol. 75(9–12), 1701–1710 (2014)

    Article  Google Scholar 

  20. 20.

    Bao, Y., Wierzbicki, T.: On fracture locus in the equivalent strain and stress triaxiality space. Int. J. Mech. Sci. 46(1), 81–98 (2004)

    Article  Google Scholar 

  21. 21.

    Bao, Y., Wierzbicki, T.: On the cut-off value of negative triaxiality for fracture. Eng. Fract. Mech. 72(7), 1049–1069 (2005)

    Article  Google Scholar 

  22. 22.

    Bao, Y., Wierzbicki, T.: Determination of fracture locus for the 2024T351 aluminum. Impact and Crashworthiness Laboratory, Report No. 81 (2002)

  23. 23.

    Bao, Y., Bai, Y., Wierzbicki, T.: Calibration of A710 steel for fracture. Massachusetts Institute of Technology, Impact and Crashworthiness Laboratory Report No. 135 (2004)

  24. 24.

    Lee, Y., Wierzbicki, T.: Quick fracture calibration for industrial use, Report No: 115. Impact and crashworthiness laboratory, Massachusetts Institute of Technology (2004)

  25. 25.

    Jeong, D., Yu, H., Gordon, J., Tang, Y.: Finite element analysis of unnotched Charpy impact tests. In: Proceedings of the Materials Science and Technology 2008 Conference and Exhibition (2008)

  26. 26.

    Kacem, A., Krichen, A., Manach, P.-Y., Thuillier, S., Yoon, J.W.: Failure prediction in the hole-flanging process of aluminium alloys. Eng. Fract. Mech. 99, 251–265 (2013)

    Article  Google Scholar 

  27. 27.

    Yu, H., Jeong, D.: Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens. Theor. Appl. Fract. Mech. 54(1), 54–62 (2010)

    Article  Google Scholar 

  28. 28.

    Haji Aboutalebi, F., Poursina, M., Nejatbakhsh, H., Khataei, M.: Numerical simulations and experimental validations of a proposed ductile damage model for DIN1623 St12 steel. Engineering Fracture Mechanics, vol. 192, pp. 276–289 (2018)

  29. 29.

    Brunig, M., Gerke, S., Schmidt, M.: Damage and failure at negative stress triaxialities: experiments, modeling and numerical simulations. Int. J. Plast. 102, 70–82 (2018)

    Article  Google Scholar 

  30. 30.

    Gerke, S., Zistl, M., Bhardwaj, A., Brunig, M.: Experiments with the X0-specimen on the effect of non-proportional loading paths on damage and fracture mechanisms in aluminum alloys. Int. J. Solids Struct. 163, 157–169 (2019)

    Article  Google Scholar 

  31. 31.

    Pimenov, A., Abramov, A., Traino, A., Efremov, N.: Reduction in strip tearing during stopping and starting of a continuous cold-rolling mill. Metallurgist 31(4), 94–95 (1987)

    Article  Google Scholar 

  32. 32.

    Mashayekhi, M., Torabian, N., Poursina, M.: Continuum damage mechanics analysis of strip tearing in a tandem cold rolling process. Simul. Model. Pract. Theory 19(2), 612–625 (2011)

    Article  Google Scholar 

  33. 33.

    Poursina, M., Dehkordi, N.T., Fattahi, A., Mirmohammadi, H.: Application of genetic algorithms to optimization of rolling schedules based on damage mechanics. Simul. Model. Pract. Theory 22, 61–73 (2012)

    Article  Google Scholar 

  34. 34.

    Sun, Q., Zan, D.Q., Pan, H.L., Chen, J.J.: On the utilization of shear modified GTN damage model in cold rolling. Appl. Mech. Mater. 750, 47–50 (2015)

    Article  Google Scholar 

  35. 35.

    Wierzbicki, T., Bao, Y., Lee, Y.-W., Bai, Y.: Calibration and evaluation of seven fracture models. Int. J. Mech. Sci. 47(4–5), 719–743 (2005)

    Article  Google Scholar 

  36. 36.

    Bai, Y., Wierzbicki, T.: A new model of metal plasticity and fracture with pressure and Lode dependence. Int. J. Plast. 24(6), 1071–1096 (2008)

    Article  Google Scholar 

  37. 37.

    Bai, Y., Wierzbicki, T.: Application of extended Mohr–Coulomb criterion to ductile fracture. Int. J. Fract. 161(1), 1 (2010)

    Article  Google Scholar 

  38. 38.

    Bai, Y., Bao, Y., Wierzbicki, T.: Fracture of prismatic aluminum tubes under reverse straining. Int. J. Impact Eng. 32(5), 671–701 (2006)

    Article  Google Scholar 

  39. 39.

    Bai, Y., Teng, X., Wierzbicki, T.: On the application of stress triaxiality formula for plane strain fracture testing. J. Eng. Mater. Technol. 131(2), 1–10 (2009)

    Article  Google Scholar 

  40. 40.

    Mae, H., Teng, X., Bai, Y., Wierzbicki, T.: Calibration of ductile fracture properties of a cast aluminum alloy. Mater. Sci. Eng. A 459(1–2), 156–166 (2007)

    Article  Google Scholar 

  41. 41.

    ISO/IEC 17025 standard, general requirements for the competence of testing and calibration laboratories (2017)

  42. 42.

    Earl, J.C., Brown, D.K.: Distributions of stress and plastic strain in circumferentially notched tension specimens. Eng. Fract. Mech. 8(4), 599–611 (1976)

    Article  Google Scholar 

  43. 43.

    Isfahan Mobarakeh Steel Company Internal Reports—No. 48246991-1 (2009)

  44. 44.

    ibaAnalyzer Analysis Software Manual, issue 6.3, iba AG., Germany (2014)

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to F. Haji Aboutalebi.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Keywords

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