Skip to main content
SpringerLink
Log in

A new integration algorithm for finite deformation of thermo-elasto-viscoplastic single crystals

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

An algorithmfor integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic deformation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on thermal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evolution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.

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

  1. Zener, C., Hollomon, J.H.: Effect of strain rate upon plastic flow of steel. J. Appl. Phys. 15, 22–32 (1944)

    Article  Google Scholar 

  2. Johnson, G.R., 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 541–547 (1983)

    Google Scholar 

  3. Tong, L., Stahel, S., Hora, P.: Modeling for the FE-simulation of warm metal forming processes. AIP Conf. Proc. 778, 625 (2005)

    Article  Google Scholar 

  4. Sung, J.H., Kim, J.H., Wagoner, R.H.: A plastic constitutive equation incorporating strain, strain-rate, and temperature. Int. J. Plasticity 26, 1746–1771 (2010)

    Article  MATH  Google Scholar 

  5. Kocks, U.F., Argon, A.S., Ashby, M.F.: Thermodynamics and kinetics of slip. Prog. Mater. Sci 19, 1–127 (1975)

    Article  Google Scholar 

  6. Frost, H.J., Ashby, M.F.: Deformation Mechanism Maps: The Plasticity and Creep of Metals and Ceramics. Pergamon Press, New York (1982)

    Google Scholar 

  7. Zerilli, F.J., Armstrong, R.W.: Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys. 61, 1816–1825 (1987)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Nemat-Nasser, S., Guo, W., Liu, M.: Experimentally-based micromechanical modeling of dynamic response of molybdenum. Scripta Mater. 40, 859–872 (1999)

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Voyiadjis, G.Z., Almasri, A.H.: A physically based constitutive model for fcc metals with applications to dynamic hardness. Mech. Mater. 40, 549–563 (2008)

    Article  Google Scholar 

  12. Cai, M.C., Niu, L.S., Ma, X.F., et al.: A constitutive description of the strain rate and temperature effects on the mechanical behavior of materials. Mech. Mater. 42, 774–781 (2010)

    Article  Google Scholar 

  13. Gao, C.Y., Zhang, L.C.: A constitutive model for dynamic plasticity of FCC metals. Mater. Sci. Eng. A 527, 3138–3143 (2010)

    Article  Google Scholar 

  14. Rusinek, A., Rodriguez-Martinez, J.A., Arias, A.: A thermoviscoplastic constitutive model for FCCmetals with application to OFHC copper. Int. J. Mech. Sci. 52, 120–135 (2010)

    Article  Google Scholar 

  15. Rodríuez-Martíez, J.A., Rodríuez-Millán, M., Rusinek, A., et al.: A dislocation-based constitutive description for modeling the behaviour of FCC metals within wide ranges of strain rate and temperature. Mech. Mater. 43, 901–912 (2011)

    Article  Google Scholar 

  16. Lallit, A.: Constitutive equations for hot-working of metals. Int. J. Plasticity 1, 213–231 (1985)

    Article  MATH  Google Scholar 

  17. Rashid, M.M., Nemat-Nasser, S.: A constitutive algorithm for rate-dependent crystal plasticity. Comput. Method. Appl. M. 94, 201–228 (1992)

    Article  MATH  Google Scholar 

  18. Ganapathysubramanian, S., Zabaras, N.: Modeling the thermoelastic-viscoplastic response of polycrystals using a continuum representation over the orientation space. Int. J. Plasticity 21, 119–144 (2005)

    Article  MATH  Google Scholar 

  19. Yalcinkaya, T., Brekelmans, W., Geers, M.: BCC single crystal plasticity modeling and its experimental identification. Model. Simul. Mater. Sc. 16, 1–16 (2008)

    Google Scholar 

  20. Peirce, D., Asaro, R.J., Needleman, A.: Material rate dependence and localized deformation in crystalline solids. Acta Metallurgica 31, 1951–1976 (1983)

    Article  Google Scholar 

  21. Kalidindi, S.R., Bronkhorst, C.A., Anand, L.: Crystallographic texture evolution in bulk deformation processing of FCC metals. J. Mech. Phys. Solids 40, 537–569 (1992)

    Article  Google Scholar 

  22. Maniatty, A.M., Dawson, P.R., Lee, Y.S.: A time integration algorithm for elasto-viscoplastic cubic crystals applied to modelling polycrystalline deformation. Int. J. Numer. Meth. Eng. 35, 1565–1588 (1992)

    Article  MATH  Google Scholar 

  23. Sarma, G., Zacharia, T.: Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials. J. Mech. Phys. Solids 47, 1219–1238 (1999)

    Article  MATH  Google Scholar 

  24. Meissonnier, F.T., Busso, E.P., O’Dowd, N.P.: Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains. Int. J. Plasticity 17, 601–640 (2001)

    Article  MATH  Google Scholar 

  25. Ganapathysubramanian, S., Zabaras, N.: A continuum sensitivity method for finite ther mo-inelastic deformations with applications to the design of hot forming processes. Int. J. Numer. Meth. Eng. 55, 1391–1437 (2002)

    Article  MATH  Google Scholar 

  26. Hutchinson, J.W.: Bounds and self-consistent estimates for creep of polycrystalline materials. Proceedings of the Royal Society of London. A. Math. Phys. Sci. 348, 101 (1976)

    Article  MATH  Google Scholar 

  27. Pan, J., Rice, J.R.: Rate sensitivity of plastic flow and implications for yield-surface vertices. Int. J. Solids Struct. 19, 973–987 (1983)

    Article  MATH  Google Scholar 

  28. Mathur, K.K., Dawson, P.R.: On modeling the development of crystallographic texture in bulk forming processes. Int. J. Plasticity 5, 67–94 (1989)

    Article  Google Scholar 

  29. Balasubramanian, S., Anand, L.: Elasto-viscoplastic constitutive equations for polycrystalline fcc materials at low homologous temperatures. J. Mech. Phys. Solids 50, 101–126 (2002)

    Article  MATH  Google Scholar 

  30. Sarma, G.B., Radhakrishnan, B.: Modeling microstructural effects on the evolution of cube texture during hot deformation of aluminum. Mater. Sci. Eng. A 385, 91–104 (2004)

    Article  Google Scholar 

  31. Hockett, J.E.: On relating the flow stress of aluminum to strain, strain rate, and temperature. Transactions Of the Metallurgical Society of AIME 239, 969–976 (1967)

    Google Scholar 

  32. Ling, X., Horstemeyer, M.F., Potirniche, G.P.: On the numerical implementation of 3D rate-dependent single crystal plasticity formulations. Int. J. Numer. Meth. Eng. 63, 548–568 (2005)

    Article  MATH  Google Scholar 

  33. Grujicic, M., Batchu, S.: Crystal plasticity analysis of earing in deep-drawn OFHC copper cups. J. Mater. Sci. 37, 753–764 (2002)

    Article  Google Scholar 

  34. Li, D., Ghosh, A.: Tensile deformation behavior of aluminum alloys at warm forming temperatures. Mater. Sci. Eng. A 352, 279–286 (2003)

    Article  Google Scholar 

  35. Field, J.E., Walley, S.M., Proud, W.G., et al.: Review of experimental techniques for high rate deformation and shock studies. Int. J. Impact Eng. 30, 725–775 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, 116023, Dalian, China

    Dan Zhao, Yi-Guo Zhu, Ping Hu & Wan-Xi Zhang

Authors
  1. Dan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi-Guo Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ping Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wan-Xi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping Hu.

Additional information

The project was supported by the Key Project of the National Natural Science Foundation of China (10932003), Project of Chinese National Programs for Fundamental Research and Development (2012CB619603 and 2010CB832700), and “04” Great Project of Ministry of Industrialization and Information of China (2011ZX04001-21).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, D., Zhu, YG., Hu, P. et al. A new integration algorithm for finite deformation of thermo-elasto-viscoplastic single crystals. Acta Mech Sin 29, 709–717 (2013). https://doi.org/10.1007/s10409-013-0072-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-013-0072-8

Keywords

Search

Navigation