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Strain Rate-Dependent Tensile and Fracture Properties of Low-Carbon Ferritic Low-Density Steels

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The study investigated the tensile properties of two low-carbon ferritic low-density steels at strain rates of 1 × 10−4 s−1, 1 × 10−3 s−1, and 1 × 10−2 s−1. These steels underwent cold and warm rolling as well as annealing. Various tensile properties were evaluated, including yield strength, ultimate tensile strength, strain hardening exponent, energy absorption up to 10 pct engineering strain, and strain rate sensitivity. The results showed that higher strain rates increased yield strength, ultimate tensile strength, and energy absorption in both steels. The strain hardening exponent was determined using the Hollomon and differential Crussard–Jaoul analysis. The electron backscattered diffraction (EBSD) and transmission electron microscopy (TEM) technique were employed to explain the strain hardening response in both steels. Both steels exhibited two distinct stages of deformation, describing their strain hardening behavior. The study observed a decrease in strain rate sensitivity with increasing true strain in both steels. Steel 1 displayed higher strain rate sensitivity than Steel 2, resulting in a delayed necking tendency and higher total elongation. Micrographs of fracture surfaces revealed the presence of quasi-cleavage facets and secondary cracks at strain rates of 1 × 10−3 s−1 and 1 × 10−2 s−1 in both steels. At a lower strain rate of 1 × 10−4 s−1, Steel 1 exhibited a dimple fracture due to its lower strength and higher total elongation, while Steel 2 displayed a quasi-cleavage fracture. The progression of voids in Steel 1 at a strain rate of 1 × 10−4 s−1 was characterized by establishing a relationship between actual thickness strain and the quantity of voids. This analysis provided insights into the steels void formation and growth mechanisms under specific conditions.

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Body centered cubic


Rolling direction


Transverse direction


Normal direction


Cold rolling


Warm rolling


Finish rolling temperature




Yield strength


Ultimate tensile strength


Uniform elongation


Total elongation


Yield ratio


Product of UTS and UE


Yield point elongation


Vickers Pyramid Number


Strain rate sensitivity



\(\sigma_{t}\) :

True stress

\(\varepsilon_{t}\) :

True strain

\(n_{H}\) :

Hollomon strain hardening exponent

n L :

Ludwik strain hardening exponent

K H :

Hollomon material strength coefficient

\(K_{L}\) :

Ludwik material strength coefficient

\(U_{T}\) :

Total energy absorbed up to fracture

\(\sigma_{u}\) :

Ultimate tensile strength

\(\varepsilon_{T}\) :

Engineering strain up to fracture

\(C_{p}\) :

Material constant

\(\dot{\varepsilon }_{t}\) :

True strain rate

\(m\) :

Strain rate sensitivity


  1. G. Frommeyer, E.J. Drewes, and B. Engl: Rev. Métallurgie, 2000, vol. 97, pp. 1245–53.

    Article  CAS  Google Scholar 

  2. S.Y. Han, S.Y. Shin, B.J. Lee, S. Lee, N.J. Kim, and J.H. Kwak: Metall. Mater. Trans. A, 2013, vol. 44A, pp. 235–47.

    Article  Google Scholar 

  3. R.G. Baligidad, U. Prakash, A. Radhakrishna, V. Ramakrishna Rao, P.K. Rao, and N.B. Ballal: Scr. Mater., 1997, vol. 36, pp. 667–71.

    Article  CAS  Google Scholar 

  4. I. Gutierrez-Urrutia: ISIJ Int., 2021, vol. 61, pp. 16–25.

    Article  CAS  Google Scholar 

  5. V.K. Singh, R. Rana, S.B. Singh, and A. Kundu: ISIJ Int., 2023, vol. 63, pp. 930–40.

    Article  CAS  Google Scholar 

  6. V.V. SatyaPrasad, S. Khaple, and R.G. Baligidad: Jom, 2014, vol. 66, pp. 1785–93.

    Article  CAS  Google Scholar 

  7. U. Brüx, G. Frommeyer, and J. Jimenez: Steel Res., 2002, vol. 73, pp. 543–48.

    Article  Google Scholar 

  8. H. Helms and U.L. Lambrecht: Int. J. Life Cycle Assess., 2007, vol. 12, pp. 58–64.

    CAS  Google Scholar 

  9. R. Rana, C. Lahaye, and R.K. Ray: Jom, 2014, vol. 66, pp. 1734–46.

    Article  Google Scholar 

  10. H. Kim, D.W. Suh, and N.J. Kim: Sci. Technol. Adv. Mater., 2013, vol. 14, p. 11.

    Article  Google Scholar 

  11. S. Khaple, B.R. Golla, and V.V.S. Prasad: Def. Technol., 2022, vol. 26, pp. 1–22.

    Google Scholar 

  12. A. Kundu and P.C. Chakraborti: J. Mater. Sci., 2010, vol. 45, pp. 5482–89.

    Article  CAS  Google Scholar 

  13. G. Mirone, R. Barbagallo, M.M. Tedesco, D. De Caro, and M. Ferrea: Metals, 2022, vol. 12, p. 960.

    Article  CAS  Google Scholar 

  14. W. Wang, Y. Ma, M. Yang, P. Jiang, F. Yuan, and X. Wu: Metals, 2018, vol. 8, p. 11.

    Article  Google Scholar 

  15. P. Rawat, U. Prakash, and V.V.S. Prasad: J. Mater. Eng. Perform., 2021, vol. 30, pp. 6297–6308.

    Article  CAS  Google Scholar 

  16. K.M. Chang and J.W. Morris: Metall. Trans. A, 1979, vol. 10, pp. 1377–87.

    Article  Google Scholar 

  17. S. Khaple, V.V. SatyaPrasad, and B.R. Golla: Trans. Indian Inst. Met., 2018, vol. 71, pp. 2713–16.

    Article  CAS  Google Scholar 

  18. R. Chen, P. Chen, and X.W. Li: Mater. Sci. Eng. A, 2023, vol. 862, 144475.

    Article  CAS  Google Scholar 

  19. D. Han, H. Ding, D. Liu, B. Rolfe, and H. Beladi: Mater. Sci. Eng. A, 2020, vol. 785, 139286.

    Article  CAS  Google Scholar 

  20. S. Khaple, R.G. Baligidad, M. Sankar, and V.V. Satya Prasad: Mater. Sci. Eng. A, 2010, vol. 527, pp. 7452–56.

    Article  Google Scholar 

  21. J. Herrmann, G. Inden, and G. Sauthoff: Acta Mater., 2003, vol. 51, pp. 3233–42.

    Article  CAS  Google Scholar 

  22. C. Castan, F. Montheillet, and A. Perlade: Scr. Mater., 2013, vol. 68, pp. 360–64.

    Article  CAS  Google Scholar 

  23. A. Zargaran, H.S. Kim, J.H. Kwak, and N.J. Kim: Scr. Mater., 2014, vol. 89, pp. 37–40.

    Article  CAS  Google Scholar 

  24. D.G. Morris, M.A. Muñoz-Morris, and L.M. Requejo: Mater. Sci. Eng. A, 2007, vol. 460–461, pp. 163–73.

    Article  Google Scholar 

  25. L. Falat, A. Schneider, G. Sauthoff, and G. Frommeyer: Intermetallics, 2005, vol. 13, pp. 1256–62.

    Article  CAS  Google Scholar 

  26. S. Mohapatra, S. Kumar, S. Das, and K. Das: Mater. Lett., 2022, vol. 330, 133243.

    Article  Google Scholar 

  27. J.T. Benzing, W.E. Luecke, S.P. Mates, D. Ponge, D. Raabe, and J.E. Wittig: Mater. Sci. Eng. A, 2021, vol. 803, 140469.

    Article  CAS  Google Scholar 

  28. J. Du, P. Chen, X. Guan, Q. Peng, C. Lin, and X. Li: Metals, 2022, vol. 12, p. 1374.

    Article  CAS  Google Scholar 

  29. A. Mohamadizadeh, A. Zarei-Hanzaki, H.R. Abedi, S. Mehtonen, and D. Porter: Mater. Charact., 2015, vol. 107, pp. 293–301.

    Article  CAS  Google Scholar 

  30. H.R. Abedi, A. Zarei Hanzaki, K.L. Ou, and C.H. Yu: Mater. Des., 2017, vol. 116, pp. 472–80.

    Article  CAS  Google Scholar 

  31. N. Zhou, R. Song, W. Huo, and Z. Zhang: Steel Res. Int., 2021, vol. 92, pp. 1–9.

    Google Scholar 

  32. Y.G. Yang, W.Z. Mu, X.Q. Li, H.T. Jiang, M. Wang, Z.L. Mi, and X.P. Mao: J. Iron Steel Res. Int., 2022, vol. 29, pp. 316–26.

    Article  CAS  Google Scholar 

  33. V. Tarigopula, O.S. Hopperstad, M. Langseth, A.H. Clausen, and F. Hild: Int. J. Solids Struct., 2007, vol. 45, pp. 601–19.

    Article  Google Scholar 

  34. H. Huh, S.B. Kim, J.H. Song, and J.H. Lim: Int. J. Mech. Sci., 2008, vol. 50, pp. 918–31.

    Article  Google Scholar 

  35. S. Xu, D. Ruan, J.H. Beynon, and Y. Rong: Mater. Sci. Eng. A, 2013, vol. 573, pp. 132–40.

    Article  CAS  Google Scholar 

  36. D.Q. Zou, S.H. Li, and J. He: Mater. Sci. Eng. A, 2016, vol. 680, pp. 54–63.

    Article  CAS  Google Scholar 

  37. K. Li, B. Yu, R.D.K. Misra, G. Han, Y.T. Tsai, C.W. Shao, C.J. Shang, J.R. Yang, and Z.F. Zhang: Mater. Sci. Eng. A, 2019, vol. 742, pp. 116–23.

    Article  CAS  Google Scholar 

  38. J.T. Benzing, W.A. Poling, D.T. Pierce, J. Bentley, K.O. Findley, D. Raabe, and J.E. Wittig: Mater. Sci. Eng. A, 2018, vol. 711, pp. 78–92.

    Article  CAS  Google Scholar 

  39. Y. Jiang, T. Zou, M. Liu, Y. Cai, Q. Wang, Y. Wang, Y. Pei, H. Zhang, Y. Liu, and Q. Wang: J. Iron. Steel Res. Int., 2022, vol. 29, pp. 316–26.

    Article  Google Scholar 

  40. Y.H. Liu, Y.Q. Ning, X.M. Yang, Z.K. Yao, and H.Z. Guo: Mater. Des., 2016, vol. 95, pp. 669–76.

    Article  CAS  Google Scholar 

  41. H. Pan, X. Li, S. Zhang, W. Zhou, Z. Wu, and L. Liu: Mater. Sci. Eng. A, 2023, vol. 879, 145241.

    Article  CAS  Google Scholar 

  42. P.J. Szabó, D.P. Field, B. Jóni, J. Horky, and T. Ungár: Metall. Mater. Trans. A, 2015, vol. 46A, pp. 1948–57.

    Article  Google Scholar 

  43. M. Najafi, H. Mirzadeh, and M. Alibeyki: J. Mater. Eng. Perform., 2019, vol. 28, pp. 5409–14.

    Article  CAS  Google Scholar 

  44. R. Saha and R.K. Ray: Mater. Sci. Eng. A, 2010, vol. 527, pp. 1882–90.

    Article  Google Scholar 

  45. H. Bhadeshia and R. Honeycombe: Butterworth-Heinemann, 2017.

  46. B.K. Choudhary, E.I. Samuel, G. Sainath, J. Christopher, and M.D. Mathew: Metall. Mater. Trans. A, 2013, vol. 44A, pp. 4979–92.

    Article  Google Scholar 

  47. S. Sevsek, C. Haase, and W. Bleck: Metals, 2019, vol. 18, p. 344.

    Article  Google Scholar 

  48. H.J. Kleemola and M.A. Nieminen: Met. Trans., 1974, vol. 5, pp. 1863–66.

    Article  CAS  Google Scholar 

  49. George Ellwood Dieter: Mechanical Metallurgy, 2nd ed. McGraw-Hill Book Co., London, 1988, pp. 103–272.

    Google Scholar 

  50. R. Rana: High-Performance Ferrous Alloys, Springer, New York, 2021, pp. 240–42.

    Book  Google Scholar 

  51. H.K. Yang, Z.J. Zhang, Y.Z. Tian, and Z.F. Zhang: Mater. Sci. Eng. A, 2017, vol. 690, pp. 146–57.

    Article  CAS  Google Scholar 

  52. P. Larour, A. Bäumer, K. Dahmen, and W. Bleck: Steel Res. Int., 2013, vol. 84, pp. 426–42.

    Article  CAS  Google Scholar 

  53. J. Speer, R. Rana, D. Matlock, A. Glover, G. Thomas, and E. De Moor: Metals, 2019, vol. 9, pp. 1–9.

    Article  CAS  Google Scholar 

  54. A.H. Cottrell and B.A. Bilby: Proc. Phys. Soc. Sect. A, 1949, vol. 62, pp. 49–62.

    Article  Google Scholar 

  55. Y. Chen, Z. Wu, G. Wu, N. Wang, Q. Zhao, and J. Luo: Mater. Sci. Eng. A, 2021, vol. 802, 140657.

    Article  CAS  Google Scholar 

  56. S. Pramanik and S. Suwas: Jom, 2014, vol. 66(9), pp. 1868–76.

    Article  CAS  Google Scholar 

  57. C. Edwards, D. Phillips, and H. Jones: J. Iron Steel Inst., 1940, vol. 142, pp. 199–236.

    Google Scholar 

  58. S.M. Hasan, A. Mandal, S.B. Singh, and D. Chakrabarti: Mater. Sci. Eng. A, 2019, vol. 751, pp. 142–53.

    Article  CAS  Google Scholar 

  59. M. Umemoto, K. Tsuchiya, Z.G. Liu, and S. Sugimoto: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 1785–94.

    Article  CAS  Google Scholar 

  60. S. Sankaran, S. Sangal, and K.A. Padmanabhan: Mater. Sci. Technol., 2005, vol. 21, pp. 1152–60.

    Article  CAS  Google Scholar 

  61. J.T. Benzing, A. Kwiatkowski da Silva, L. Morsdorf, J. Bentley, D. Ponge, A. Dutta, J. Han, J.R. McBride, B. Van Leer, B. Gault, D. Raabe, and J.E. Wittig: Acta Mater., 2019, vol. 166, pp. 512–30.

    Article  CAS  Google Scholar 

  62. A. Kundu, D.P. Field, and P.C. Chakraborti: Mater. Sci. Eng. A, 2020, vol. 773, p. 138854.

    Article  CAS  Google Scholar 

  63. A.H. Jahanara, Y. Mazaheri, and M. Sheikhi: Mater. Sci. Eng. A, 2019, vol. 764, p. 138206.

    Article  CAS  Google Scholar 

  64. S. Sinha, A. Pukenas, A. Ghosh, A. Singh, W. Skrotzki, and N.P. Gurao: Philos. Mag., 2017, vol. 97, pp. 775–97.

    Article  CAS  Google Scholar 

  65. I.D. Choi, D.M. Bruce, S.J. Kim, C.G. Lee, D.K. Matlock, and J.G. Speer: vol. 42, 2002, pp. 1483–89.

  66. C.A.R. Saleh, M.K. Jain, and D.S. Wilkinson: Metall. Mater. Trans. A, 2009, vol. 40A, pp. 3117–27.

    Google Scholar 

  67. H. Choi, S. Lee, J. Lee, F. Barlat, and B.C. De Cooman: Mater. Sci. Eng. A, 2017, vol. 687, pp. 200–10.

    Article  CAS  Google Scholar 

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The financial support of the work has been received from Science and Engineering Research Board, Department of Science and technology, Government of India (file no.: CRG/2020/001511) under core research grant. One of the authors (AK) is thankful to Professor P. C. Chakraborti, Metallurgical and Material Engineering Department, Jadavpur University, Kolkata-700032, India, for useful discussion and for the provision of the research facilities at Metallurgical and Material Engineering Department, Jadavpur University, Kolkata-700032, India and Centre of Excellence in Phase Transformation and Product Characterisation, Jadavpur University, Kolkata-700032, India, for the Thermo-Calc facility. The authors would also like to thank Central Research Facility, Department of Metallurgical and Materials Engineering and Steel Technology Centre of Indian Institute of Technology, Kharagpur for providing research facility.

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Vinit Kumar Singh: Conceptualization, Methodology, Software Validation, Formal analysis, Investigation, Data curation, Writing—original draft, Visualization. Radhakanta Rana: Formal analysis, Investigation, Resources, Review & editing, Data curation. Shiv Brat Singh: Investigation, Visualization, Supervision, Review & editing, Data curation, Project administration, Funding acquisition. Amrita Kundu: Conceptualisation, Methodology, Validation, Formal analysis, Writing—original draft, Review & editing, Supervision, Project administration, Funding acquisition.

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Singh, V.K., Rana, R., Singh, S.B. et al. Strain Rate-Dependent Tensile and Fracture Properties of Low-Carbon Ferritic Low-Density Steels. Metall Mater Trans A 55, 2990–3010 (2024).

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