Skip to main content
SpringerLink
Log in

Dynamic hardening equation of the auto-body steel sheet with the variation of temperature

  • Published:
International Journal of Automotive Technology Aims and scope Submit manuscript

Abstract

This paper is concerned with the empirical hardening equation of steel sheets for an auto-body at intermediate strain rates with the variation of temperature. In order to identify the temperature dependence of the strain-rate sensitivity of steel sheets such as SPRC35R, SPRC45E and TRIP60, uniaxial tensile tests have been performed with the variation of the strain rate from 0.001/sec to 200/sec and the environmental temperature from −40°C to 200°C. The thermo-mechanical response at the quasi-static state is obtained from static tensile tests and that at the intermediate strain rate is obtained from high speed tensile tests. The effects of both the strain rate and the temperature on the flow stress and the fracture elongation are investigated with the experimental data. Experimental results provide the variation of the strain-rate sensitivity with respect to the temperature. They also show that as the strain rate increases, the variation of flow stress becomes sensitive to the temperature. A phenomenological constitutive model is newly proposed by modifying the well-known Khan-Huang-Liang model. Based on the experimental data, both the strain rate and the temperature dependent sensitivity of the flow stress are considered in the proposed model by coupling the strain, the strain rate and the temperature. In order to verify the accuracy of the proposed model quantitatively, the standard error between the experimental data and the fitted one is compared with other empirical constitutive models such as the Johnson-Cook and the Khan-Huang-Liang models. The comparison demonstrates that the model proposed gives relatively accurate description of the experimental data at the various strain rates and temperatures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abed, F. H. and Voyiadjis, G. Z. (2005). Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of bcc and fcc mechanism of metals. Int. J. Plasticity, 21, 1618–1639.

    Article  MATH  Google Scholar 

  • Campbell, J. D. and Ferguson, W. G. (1970). The temperature and strain-rate dependence of the shear strength of mild steel. Phil. Mag., 21, 63–82.

    Article  Google Scholar 

  • Costin, L. S., Crisman, E. E., Hawley, R. H. and Duffy, J. (1979). On the localization of plastic flow in mild steel tubes under dynamic torsional loading. In Mechanical Properties at High Rates of Strain, Edn J. Harding, Inst. Phys. Conf. Ser. No. 47, 90–100.

  • Cottrell, A. H. (1953). Dislocations and Plastic Flow in Crystals. Clarendon. Oxford.

    MATH  Google Scholar 

  • Cowper, G. R. and Symonds, P. S. (1957). Strain hardening and strain-rate effects in the impact loading of cantilever beams. Brown University Division of Applied Mathematics. Report No. 28.

  • Eleiche, A. M. (1981). Strain rate history and temperature effects on the torsional-shear behavior of a mild steel. Exp. Mech., 21, 285–294.

    Article  Google Scholar 

  • Follansbee, P. S. and Kocks, U. F. (1988). A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Metall., 36, 81–93.

    Article  Google Scholar 

  • Gilat, A. and Wu, X. (1997). Plastic deformation of 1020 steel over a wide range of strain rates and temperatures. Int. J. Plasticity, 13, 611–632.

    Article  Google Scholar 

  • Hoge, K. J. and Mukherjee, A. K. (1977). Temperature and strain rate dependence of the flow stress of tantalum. J. Mater. Sci. 12,8, 1666–1672.

    Article  Google Scholar 

  • Huh, H. and Kang, W. J. (2002). Crash-worthiness assessment of thin-walled structures with the highstrength steel sheet. Int. J. Vehicle Des., 30, 1–21.

    Article  Google Scholar 

  • Huh, H., Kang, W. J. and Han, S. S. (2002). A tension split Hopkinson bar for investigating the dynamic behavior of sheet metals. Exp. Mech., 42, 8–17.

    Article  Google Scholar 

  • Huh, H., Lim, J. H., Song, J. H., Lee, K. S., Lee, Y. W. and Han, S. S. (2003). Crashworthiness assessment of side impact of an auto-body with 60TRIP steel for side members. Int. J. Automotive Technology 4,3, 149–156.

    Google Scholar 

  • Huh, H., Kim, S. B., Song, J. H. and Lim, J. H. (2008). Dynamic tensile characteristics of TRIP-type and DPtype steel sheets for an auto-body. Int. J. Mech. Sci., 50, 918–931.

    Article  MATH  Google Scholar 

  • Huh, H., Lim, J. H. and Park, S. H. (2009). High speed tensile test of steel sheets for the stress-strain curve at the intermediate strain rate. Int. J. Automotive Technology 10,2, 195–204.

    Article  Google Scholar 

  • Ishikawa, K. and Tanimura, S. (1992). Strain rate sensitivity of flow stress at low temperatures in 304N stainless steel. Int. J. Plasticity, 8, 947–958.

    Article  Google Scholar 

  • Johnson, G. R. and Cook, W. H. (1983). A constitutive model and data for metals subjected to large strain, high strain rates and high temperatures. Proc. 7th Int. Symp. Ballistics, The Hague, The Netherlands, 541–547.

  • Kang, W. J., Cho, S. S., Huh, H. and Chung, D. T. (1999). Modified Johnson-Cook model for vehicle body crashworthiness simulation. Int. J. Vehicle Des., 21, 424–435.

    Article  Google Scholar 

  • Khan, A. S. and Liang, R. (1999). Behaviors of three BCC metal over a wide range of strain rates and temperatures: Experiments and modeling. Int. J. Plasticity, 15, 1089–1109.

    Article  MATH  Google Scholar 

  • Khan, A. S. and Liang, R. (2000). Behaviors of three BCC metals during non-proportional multi-axial loadings: Experiments and modeling. Int. J. Plasticity, 16, 1443–1458.

    Article  MATH  Google Scholar 

  • Khan, A. S. and Huang, S. (1992). Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5–104 s−1. Int. J. Plasticity, 8, 397–424.

    Article  Google Scholar 

  • Khan, A. S., Suh, Y. S. and Kazmi, R. (2004). Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. Int. J. Plasticity, 20, 2233–2248.

    Article  MATH  Google Scholar 

  • Khan, A. S. and Zhang, H. (2000). Mechanically alloyed nanocrystalline iron and copper mixture: Behavior and constitutive modeling over a wide range of strain rates. Int. J. Plasticity, 16, 1477–1492.

    Article  MATH  Google Scholar 

  • Kim, J. S., Huh, H., Lee, K. W., Ha, D. Y., Yeo, T. J. and Park, S. J. (2006). Evaluation of dynamic tensile characteristics of polypropylene with temperature variation. Int. J. Automotive Technology 7,5, 571–577.

    Google Scholar 

  • Kim, K. P. and Huh, H. (2006). Dynamic limit analysis formulation for impact simulation of structural members. Int. J. Solids Struct., 43, 6488–6501.

    Article  MATH  Google Scholar 

  • Klepaczko, J. and Duffy, J. (1982). Strain rate history effects in body-centered-cubic metals. In Mechanical Testing for Deformation Model Development, Edn. R. W. Rhode and J. C. Swearengen, ASTM STP765, 251–268.

  • Kolsky, H. (1949). Stress Wave in Solids. Dover. New York.

    Google Scholar 

  • Lee, W.-S. and Liu, C.-Y. (2006). The effects of temperature and strain rate on the dynamic flow behavior of different steels. Mat. Sci. Eng. A, 426, 101–113.

    Article  Google Scholar 

  • Li, C. C. and Leslie, W. C. (1978). Effect of dynamic strain aging on the subsequent mechanical properties of carbon steels. Metall. Trans. A, 9, 1765–1775.

    Article  Google Scholar 

  • Liang, R. and Khan, A. S. (1999). A critical review of experimental results and constitutive models for BCC and FCC metals over a wide range of strain rates and temperatures. Int. J. Plasticity, 15, 963–980.

    Article  MATH  Google Scholar 

  • Mahadevan, K., McCoy, R., Schell, B. and Fekete, J. (1998). Strain-rate characterization of automotive steel and the effect of strain-rate in component crash analysis. SAE Paper No. 982392.

  • McCormick, P. G. (1978). Strain rate sensitivity prior to the onset of serrated yielding in a pressurized low carbon steel. Scripta Metall., 12, 197–208.

    Article  MathSciNet  Google Scholar 

  • Meyers, A. (1994). Dynamic Behavior of Materials. John Wiley & Sons. New York.

    Book  MATH  Google Scholar 

  • Miura, K., Takagi, S., Obara, T. and Tanimura, S. (1996). Dynamic deformation behavior of steel sheet for automobile. SAE Paper No. 960019.

  • Nemat-Nasser, S. and Guo, W.-G. (2001). Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures. J. Mech. Phys. Solids, 35, 1823–1846.

    Article  Google Scholar 

  • Nemat-Nasser, S. and Guo, W.-G. (2003). Thermomechanical response of DH-36 structural steel over a wide range of strain rates and temperatures. Mech. Mater., 35, 1023–1047.

    Article  Google Scholar 

  • Nemat-Nasser, S., Guo, W. G. and Kihl, D. P. (2001). Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures. J. Mech. Phys. Solids, 49, 1823–1846.

    Article  MATH  Google Scholar 

  • Nemat-Nasser, S. and Isaacs, J. B. (1996). Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and Ta-W alloys. Acta Mater., 45, 907–919.

    Article  Google Scholar 

  • Porsche Engineering Service Inc. (2001). ULSAB-AVC Engineering Report.

  • Robert, A. A. (1983). Thermal gradients, strain rate and ductility in sheet steel tensile specimens. Metall. Trans. A, 16, 37–43.

    Google Scholar 

  • Robinson, J. M. and Shaw, M. P. (1994). Microstructural and mechanical influences on dynamic strain aging phenomena. Int. Mater. Rev., 39, 113–122.

    Google Scholar 

  • Shi, N. F. and Meuleman, D. J. (1992). Strain rate sensitivity of automotive steels. SAE Paper No. 922045.

  • Song, J. H., Huh, H., Kim, H. G. and Park, S. H. (2006). Evaluation of the finite element modeling of a spot welded region for crash analysis. Int. J. Automotive Technology 7,3, 329–336.

    MATH  Google Scholar 

  • Stevenson, R. (1982). Inferring microscopic deformation behavior from the form of constitutive equation for lowcarbon steel and 5182-0 aluminum. Edn R. W. Rhode and J. C. Swearengen, ASTM STP765, 366–381.

  • Tateno, H., Hishida, Y. and Shibata, K. (1998). New materials technology for achieving both crashworthiness and weight reduction using energy-absorbing steel with higher strain-rate sensitivity. SAE Paper No. 980953.

  • Uenishi, A. and Teodosiu, C. (2004). Constitutive modeling of the high strain rate behavior of interstitialfree steel. Int. J. Plasticity, 20, 915–936.

    Article  MATH  Google Scholar 

  • Yasuki, T. (2000). An investigation on vehicle crash analysis accuracy. Proc. EUROPAM 2000, Nantes, France, 1–5.

  • Zener, C. and Holloman, J. H. (1944). Effect of strain rate upon plastic flow of steel. J. Appl. Phys., 15, 22–32.

    Article  Google Scholar 

  • Zerilli, F. J. and Armstrong, R. W. (1987). Dislocationmechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys., 61, 1816–1825.

    Article  Google Scholar 

  • Zukas, J. A., Nicholas, T., Swift, H. F., Greszczuk, L. B. and Curran, D. R. (1982). Impact Dynamics. John Wiley & Sons. New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical, Aerospace and Systems Engineering, KAIST, Daejeon, 305-701, Korea

    H. Huh

  2. Structure Research Departments, Hyundai Heavy Industries Co., Jeonha-dong, Dong-gu, Ulsan, 682-792, Korea

    H. J. Lee

  3. Department of Manufacturing Convergence Technology, Korea Institute of Industrial Technology, 1271-18 Sa-3 dong, Sangrok-gu, Ansan-si, Gyeonggi, 426-173, Korea

    J. H. Song

Authors
  1. H. Huh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. J. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. H. Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Huh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huh, H., Lee, H.J. & Song, J.H. Dynamic hardening equation of the auto-body steel sheet with the variation of temperature. Int.J Automot. Technol. 13, 43–60 (2012). https://doi.org/10.1007/s12239-012-0005-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12239-012-0005-8

Key Words

Search

Navigation