Acta Mechanica Solida Sinica

, Volume 27, Issue 6, pp 579–587 | Cite as

Numerical Simulation of Deformation Behavior of 22MnB5 Boron Steel at Elevated Temperatures and Experimental Verification

  • Dan Zhao
  • Yiguo Zhu
  • Liang Ying
  • Ping Hu
  • Ying Chang
  • Wanxi Zhang


The effects of strain, strain rate and temperature on the mechanical behavior of 22MnB5 boron steel deformed isothermally under uniaxial tension tests and the experimental characterization of 22MnB5 boron steel in the austenitic region have been investigated. Based on the crystal plasticity theory and thermal kinematics, an improved integration model is presented. In this model, the elastic deformation gradient is the integration variable of the governing equation, which contains not only the elastic deformation but also the thermal effects. In the coupled thermo-mechanical process, this model can reveal the evolution of microstructures such as the rotation of a single crystal and the slip systems in each of them. The plastic behavior of the boron steel can be well described by the presented model.

Key Words

crystal plasticity integration model 22MnB5 boron steel high temperature deformation 


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  1. 1.
    Naderi, M., Durrenberger, L., Molinari, A. and Bleck, W., Constitutive relationships for 22MnB5 boron steel deformed isothermally at high temperatures. Materials Science and Engineering: A, 2008, 478(1–2): 130–139.CrossRefGoogle Scholar
  2. 2.
    Nikravesh, M., Naderi, M. and Akbari, G.H., Influence of hot plastic deformation and cooling rate on martensite and bainite start temperatures in 22MnB5 steel. Materials Science and Engineering: A, 2012, 540: 24–29.CrossRefGoogle Scholar
  3. 3.
    Abbasi, M., Saeed-Akbari, A. and Naderi, M., The effect of strain rate and deformation temperature on the characteristics of isothermally hot compressed boron-alloyed steel. Materials Science and Engineering: A, 2012, 538: 356–363.CrossRefGoogle Scholar
  4. 4.
    Johnson, G.R. and Cook, W.H., A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: The 7th International Symposium on Ballistic. 1983: 541–547.Google Scholar
  5. 5.
    Khan, A.S. and Huang, S., Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5–104 s−1. International Journal of Plasticity, 1992, 8(4): 397–424.CrossRefGoogle Scholar
  6. 6.
    Sung, J.H., Kim, J.H. and Wagoner, R.H., A plastic constitutive equation incorporating strain, strain-rate, and temperature. International Journal of Plasticity, 2010, 26(12): 1746–1771.CrossRefGoogle Scholar
  7. 7.
    Zerilli, F.J. and Armstrong, R.W., Dislocation-mechanics-based constitutive relations for material dynamics calculations. Journal of Applied Physics, 1987, 61(5): 1816–1825.CrossRefGoogle Scholar
  8. 8.
    Rusinek, A., Rodriguez-Martinez, J.A. and Arias, A., A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper. International Journal of Mechanical Sciences, 2010, 52(2): 120–135.CrossRefGoogle Scholar
  9. 9.
    Rodríguez-Martínez, J.A., Rodríguez-Millán, M., Rusinek, A. and Arias, A., A dislocation-based constitutive description for modeling the behaviour of FCC metals within wide ranges of strain rate and temperature. Mechanics of Materials, 2011, 43(12): 901–912.CrossRefGoogle Scholar
  10. 10.
    Anand, L., Constitutive equations for hot-working of metals. International Journal of Plasticity, 1985, 1(3): 213–231.CrossRefGoogle Scholar
  11. 11.
    Rashid, M.M. and Nemat-Nasser, S., A constitutive algorithm for rate-dependent crystal plasticity. Computer Methods in Applied Mechanics and Engineering, 1992, 94(2): 201–228.CrossRefGoogle Scholar
  12. 12.
    Ganapathysubramanian, S. and Zabaras, N., Modeling the thermoelastic-viscoplastic response of polycrystals using a continuum representation over the orientation space. International Journal of Plasticity, 2005, 21(1): 119–144.CrossRefGoogle Scholar
  13. 13.
    Roters, F., Eisenlohr, P., Hantcherli, L., Tjahjanto, D.D., Bieler, T.R. and Raabe, D., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Materialia, 2010, 58(4): 1152–1211.CrossRefGoogle Scholar
  14. 14.
    Peirce, D., Shear band bifurcations in ductile single crystals. Journal of the Mechanics and Physics of Solids, 1983, 31(2): 133–153.CrossRefGoogle Scholar
  15. 15.
    Kalidindi, S.R., Bronkhorst, C.A. and Anand, L., Crystallographic texture evolution in bulk deformation processing of FCC metals. Journal of the Mechanics and Physics of Solids, 1992, 40(3): 537–569.CrossRefGoogle Scholar
  16. 16.
    Sarma, G. and Zacharia, T., Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials. Journal of the Mechanics and Physics of Solids, 1999, 47(6): 1219–1238.CrossRefGoogle Scholar
  17. 17.
    Maniatty, A.M., Dawson, P.R. and Lee, Y.S., A time integration algorithm for elasto-viscoplastic cubic crystals applied to modelling polycrystalline deformation. International Journal for Numerical Methods in Engineering, 1992, 35(8): 1565–1588.CrossRefGoogle Scholar
  18. 18.
    Ganapathysubramanian, S. and Zabaras, N., A continuum sensitivity method for finite thermo-inelastic deformations with applications to the design of hot forming processes. International Journal for Numerical Methods in Engineering, 2002, 55(12): 1391–1437.CrossRefGoogle Scholar
  19. 19.
    Meissonnier, F.T., Busso, E.P. and O’Dowd, N.P., Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains. International Journal of Plasticity, 2001, 17(4): 601–640.CrossRefGoogle Scholar
  20. 20.
    Hutchinson, J.W., Bounds and self-consistent estimates for creep of polycrystalline materials. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1976, 348(1652): 101–127.CrossRefGoogle Scholar
  21. 21.
    Pan, J. and Rice, J.R., Rate sensitivity of plastic flow and implications for yield-surface vertices. International Journal of Solids and Structures, 1983, 19(11): 973–987.CrossRefGoogle Scholar
  22. 22.
    Mathur, K.K. and Dawson, P.R., On modeling the development of crystallographic texture in bulk forming processes. International Journal of Plasticity, 1989, 5(1): 67–94.CrossRefGoogle Scholar
  23. 23.
    Hu, P., Ma, N., Liu, L. and Zhu, Y., Theories, Methods and Numerical Technology of Sheet Metal Cold and Hot Forming: Analysis, Simulation and Engineering Applications. Springer Press, 2012: 101–103.Google Scholar
  24. 24.
    Zhao, D., Zhu, Y.G., Hu, P. and Zhang, W.X., Constitutive model of single crystal thermal finite deformation. Acta Mechanica Solida Sinica, 2013, 3: 266–271 (in Chinese).CrossRefGoogle Scholar
  25. 25.
    Taylor, G.I., Plasticity strain in metals. Journal of Institute of Metals, 1938, 62: 307–324.Google Scholar
  26. 26.
    Sachs, G., Zur ableitung einer fliessbedingung. Zeitschrift Vereines Deutscher Ingenieure, 1928, 72(103): 734–736.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  • Dan Zhao
    • 1
  • Yiguo Zhu
    • 1
  • Liang Ying
    • 1
  • Ping Hu
    • 1
  • Ying Chang
    • 1
  • Wanxi Zhang
    • 1
  1. 1.State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and MechanicsDalian University of TechnologyDalianChina

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