Skip to main content
Log in

A new constitutive analysis of hexagonal close-packed metal in equal channel angular pressing by crystal plasticity finite element method

  • Original Article
  • Published:
Continuum Mechanics and Thermodynamics Aims and scope Submit manuscript

Abstract

Most of hexagonal close-packed (HCP) metals are lightweight metals. With the increasing application of light metal products, the production of light metal is increasingly attracting the attentions of researchers worldwide. To obtain a better understanding of the deformation mechanism of HCP metals (especially for Mg and its alloys), a new constitutive analysis was carried out based on previous research. In this study, combining the theories of strain gradient and continuum mechanics, the equal channel angular pressing process is analyzed and a HCP crystal plasticity constitutive model is developed especially for Mg and its alloys. The influence of elevated temperature on the deformation mechanism of the Mg alloy (slip and twin) is novelly introduced into a crystal plasticity constitutive model. The solution for the new developed constitutive model is established on the basis of the Lagrangian iterations and Newton Raphson simplification.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Staiger, M.P., Pietak, A.M., Huadmai, J., Dias, G.: Magnesium and its alloys as orthopedic biomaterials: a review. Biomateiral 27, 1728–1734 (2006)

    Article  Google Scholar 

  2. Yuan, G.Y., Zhang, X.B., Niu, J.L., Tao, H.R., Chen, D.Y., He, Y.H., Jiang, Y., Ding, W.J.: Research progress of new type of degradable biomedical magnesium alloys JDBM. Chin. J. Nonferrous Met. 21(10), 2476–2488 (2011)

    Google Scholar 

  3. Aghion, E., Bronfin, B.: Magnesium alloys development towards the 21st century. Mater. Sci. Forum 350–351, 19–30 (2000)

    Article  Google Scholar 

  4. MroDIKE, B.L., Ebert, T.: Magnesium: Properties—applications—potential. Mater. Sci. Eng. A 302, 37–45 (2001)

    Article  Google Scholar 

  5. Hirsch, J., Al-Samman, T.: Superior light metals by texture engineering: optimized aluminum and magnesium alloys for automotive applications. Acta Mater. 61, 818–843 (2013)

    Article  Google Scholar 

  6. Mayama, T., Noda, M., Chiba, R., Kuroda, M.: Crystal plasticity analysis of texture development in magnesium alloy during extrusion. In. J. Plast. 27, 1916–1935 (2011)

    Article  MATH  Google Scholar 

  7. Friedrich, H.E., Mordike, B.L.: Magnesium Technology. Springer, New York (2006)

    Google Scholar 

  8. Czerwinski, F.: Magnesium Injection Molding. Springer, New York (2008)

    Book  Google Scholar 

  9. Fernandez, A., Perez-Prado, M.T., Wei, Y., Jerusalem, A.: Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation. Int. J. Plast. 27, 1739–1757 (2011)

    Article  MATH  Google Scholar 

  10. Couling, S.L., Pashak, J.F., Sturkey, L.: Unique deformation and aging characteristic of certain magnesium-base alloys. Trans. Am. Soc. Met. 51, 94–107 (1959)

    Google Scholar 

  11. Kocks, U.F., Westlake, D.G.: The importance of twinning for the ductility of CPH polycrystals. Trans. Metall. Soc. AIME 239, 1107–1109 (1967)

    Google Scholar 

  12. Chin, G.Y., Mammel, W.L.: Competition among basal, prism, and pyramidal slip modes in hcp metals. Metall. Trans. 1, 357–361 (1970)

    Article  Google Scholar 

  13. Vagaralia, S.S., Langdon, T.G.: Deformation mechanisms in h.c.p. metals at elevated temperatures—I. Creep behavior of magnesium. Acta Metall. 29(12), 1969–1982 (1981)

    Article  Google Scholar 

  14. Christian, J.W., Mahajan, S.: Deformation twinning. Prog. Mater. Sci. 39(1–2), 1–157 (1995)

    Article  Google Scholar 

  15. Agnew, S.R., Yoo, M.H., Tome, C.N.: Application of texture simulation to understanding mechanical behavior of Mg and solid solution alloys containing Li or Y. Atca Mater. 49(20), 4277–4289 (2001)

    Google Scholar 

  16. Agnew, S.R., Duygulu, O.: Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B. Int. J. Plast. 21(6), 1161–1193 (2005)

    Article  MATH  Google Scholar 

  17. Chapuis, A., Driver, J.H.: Temperature dependency of slip and twinning in plane strain compressed magnesium single crystals. Acta Mater. 59, 1986–1994 (2011)

    Article  Google Scholar 

  18. Garcia-Grajales, J.A., Fernandez, A., Leary, D., Jerusalem, A.: A new strain rate dependent continuum framework for Mg alloys. Comput. Mater. Sci. 115, 41–50 (2016)

    Article  Google Scholar 

  19. Koike, J., Kobayashi, T., Mukai, T., Watanabe, H., Suzuki, M., Maruyama, K., Higashi, K.: The activity of non-basal slip systems and dynamic recovery at room temperature in fine-grained AZ31B magnesium alloys. Acta Mater. 51(7), 2055–2206 (2003)

    Article  Google Scholar 

  20. Keshavarz, Z., Barnett, M.R.: EBSD analysis of deformation modes in Mg–3Al–1Zn. Scr. Mater. 55(10), 915–918 (2006)

    Article  Google Scholar 

  21. Armstrong, R.W., Walley, S.M.: High strain rate properties of metals and alloys. Int. Mater. Rev. 53(3), 105–128 (2008)

    Article  Google Scholar 

  22. Serra, A., Bacon, D.J.: Modelling the motion of 11-22 twinning dislocations in the HCP metals. Mater. Sci. Eng. A400–401, 496–498 (2005)

    Article  Google Scholar 

  23. Bilby, B.A., Crocker, A.G.: The theory of the crystallography of deformation twinning. Proc. R. Soc. 288, 240–255 (1965)

    Article  ADS  Google Scholar 

  24. Fernandez, A., Jerusalem, A., Gutierrez-Urrutia, I., Perez-Prado, M.T.: Three-dimensional investigation of grain boundary–twin interactions in a Mg AZ31 alloy by electron backscatter diffraction and continuum modeling. Acta Mater. 61, 7679–7692 (2013)

    Article  Google Scholar 

  25. Staroselsky, A.V.L.: Crystal plasticity due to slip and twining. Ph.D. Thesis, Massachusetts Institute of Technology (1998)

  26. Staroselsky, A.V., Anand, L.: A constitutive model for hcp materials deforming by slip and twining: application to magnesium alloys AZ31B. Int. J. Plast. 19(10), 1843–1864 (2003)

    Article  MATH  Google Scholar 

  27. levesque, J., Inal, K., Neale, K.W., Mishra, R.K.: Numerical modeling of formability of extruded magnesium alloy tubes. Int. J. Plast. 26, 65–83 (2010)

    Article  Google Scholar 

  28. Herrerz-Solaza, V., LLorca, J., Dogan, E., Karaman, I., Segurado, J.: An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: Application to AZ31 Mg alloy. Int. J. Plast. 57, 1–15 (2014)

    Article  Google Scholar 

  29. Juan, P.A., Berbenni, S., Barnett, M.R., Tome, C.N., Capolungo, L.: A double inclusion homogenization scheme for polycrystals with hierarchal topologies: application to twinning in Mg alloys. Int. J. Plast. 60, 182–196 (2014)

    Article  Google Scholar 

  30. Gehrmann, R., Frommert, M.M., Gottstein, G.: Texture effects on plastic deformation of magnesium. Mater. Sci. Eng. A 395(1–2), 338–349 (2005)

    Article  Google Scholar 

  31. Al-samman, T., Gottstein, G.: Room temperature formability of a magnesium AZ31 alloy: examining the role of texture on the deformation mechanisms. Mater. Eng. A 488(1–2), 406–414 (2008)

    Article  Google Scholar 

  32. Li, H.J., Öchsner, A., Ni, G.W., Wei, D.B., Jiang, Z.Y.: Analysis of surface asperity flattening based on two different methods. Contin. Mech. Thermodyn. 28(6), 1623–1634 (2016)

    Article  ADS  Google Scholar 

  33. Jens, C.W.: Equal channel angular pressing (ECAP) of AA6082: mechanical properties, texture and microstructural development. Ph.D. Thesis, Norwegian University of Science and Technology (NTNU), 17 (2004)

  34. Azushima, A., Kopp, R., Korhonen, A., Yang, D.Y., Micari, F., Lahoti, G.D., Groche, P., Yanagimoto, J., Rosochowski, N., YAnangida, A.: Severe plastic deformation (SPD) processes for metals. CIRP Manuf. Technol. 57, 716–735 (2008)

    Article  Google Scholar 

  35. Alexander, M.L., Alexander, V.P., Panayiotis, A.K., Konstantinos, N.A., Yuri, A.E.: 8th International conference on research and development in mechanical industry, pp. 236–240. Uzice, Serbia (2008)

  36. Alexander, M.L., Alexander, V.P., Panayiotis, A.K.: International conference on computational plasticity, pp. 1–4. Barcelona, Spain (2009)

  37. Melicher, R.: Numerical simulation of plastic deformation of aluminium workpiece induced by ECAP technology. Appl. Comput. Mech. 3, 319–330 (2009)

    Google Scholar 

  38. Melicher, R., Handrik, M.: Analysis of shape parameters of tool for ECAP technology. Acta Mechanica Slovaca, 3-C/2008, Kosice, 273-284. (in Slovak) (2008)

  39. Melicher, R.: Finite element method simulation of equal channel angular pressing. In: Transcom 2009. Zilina (2009), pp. 91–94

  40. Iwahashi, Y., Wang, J., Horita, Z., et al.: Principle of equal-channel angular pressing for the processing of ultra-fine grained materials. Scr. Mater. 3, 143 (1996)

    Article  Google Scholar 

  41. Melicher, R. Appl. Comput. Mech. 3, 319–330 (2009) Finite element analysis of plastic deformation of aluminium specimen by ECAP process. In: Nekonvenčné technológie 2008, 21/235, pp. 1–12. (in Slovak)

  42. Shaeri, M.H., Shaeri, M., Ebrahimi, M., Salehi, M.T., Seyyedein, S.H.: Effect of ECAP temperature on microstructure and mechanical properties of Al–Zn–Mg–Cu alloy. Prog. Nat. Sci. Mater. Int. 26, 182–191 (2016)

    Article  Google Scholar 

  43. Kroner, E.: On the plastic deformation of polycrystals. Acta Mater. 9, 155–161 (1961)

    Article  Google Scholar 

  44. Kroner, E.: Kontinuumstheorie der Versetzungen und Eigenspannungen. Springer, Berlin (1958). (in German)

    Book  MATH  Google Scholar 

  45. Kroner, E.: Physics of Defects. North-Holland Publishing Company, Amsterdam (1981)

    MATH  Google Scholar 

  46. Kroner, E.: Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Ration. Mech. Anal. 4, 273–334 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  47. Lee, E.H., Liu, D.T.: Finite-strain elastic–plastic theory with application to plane-wave analysis. J. Appl. Phys. 38, 19–27 (1967)

    Article  ADS  Google Scholar 

  48. Malvern, L.: Introduction to the Mechanics of a Continuum Medium. Prentice-Hall, Englewood Cliffs (1969)

    Google Scholar 

  49. Barret, C.R., Ardell, A.J., Sherby, O.D.: Influence of modulus on temperature dependence of activation energy for creep at high temperatures. Trans. AIME 230, 200 (1964)

    Google Scholar 

  50. Ishikawa, K., Watanabe, H.: High temperature compressive properties over a wide range of strain rates in an AZ31 magnesium alloy. J. Mater. Sci. 40, 1577–1582 (2005)

    Article  ADS  Google Scholar 

  51. Robinson, S.L., Sherby, O.D.: Mechanical behavior of polycrystalline tungsten at elevated temperature. ibid 17, 109 (1969)

    Google Scholar 

  52. Ruano, O.A., Wadsworth, J., Sherby, O.D.: Deformation mechanisms in an austenitic stainless steel (25Cr–20Ni) at elevated temperature. J. Mater. Sci. 20, 3735 (1985)

    Article  ADS  Google Scholar 

  53. Reed-Hill, R.E., Robertson, W.D.: Additional modes of deformation twinning in magnesium. Acta Metall. 5(12), 717–727 (1957)

    Article  Google Scholar 

  54. Reed-Hill, R.E., Robertson, W.D.: The crystallographic characteristics of fracture in magnesium single crystals. Acta Metall. 5(12), 728–737 (1957)

    Article  Google Scholar 

  55. Yoshinaga, H., Obara, T., Morozumi, S.: Twinning deformation in magnesium compressed along the C-Axis. Mater. Sci. Eng. 12(5–6), 255–264 (1973)

    Article  Google Scholar 

  56. Simmons, G., Wang, H.: Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook. MIT Press, Cambridge (1971)

    Google Scholar 

  57. Choi, S.H., Kim, D.H., Park, S.S., You, B.S.: Simulation of stress concentration in Mg alloys using the crystal plasticity finite element method. Acta Mater. 58, 320–329 (2010)

    Article  Google Scholar 

  58. Hutchinson, J.W.: Bounds and self-consistent estimates for creep of polycrystalline materials. Proc. R. Soc. Lond. 348, 101–127 (1976)

    Article  ADS  MATH  Google Scholar 

  59. Asaro, R.J., Needleman, A.: Texture development and strain hardening in rate dependent polycrystals. Acta Metall. 33, 923–953 (1985)

    Article  Google Scholar 

  60. Cuitino, A.M., Ortiz, M.: Computational modelling of single crystals. Model. Simul. Mater. Sci. Eng. 1, 225–263 (1992)

    Article  ADS  Google Scholar 

  61. Zhao, Z., Kuchnicki, S.N., Radovitzky, R.A., Cuitino, A.M.C.: Influence of in-grain mesh resolution on the prediction of deformation textures in fcc polycrystals by crystal plasticity FEM. Acta Mater. 55, 2361–2373 (2007)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  63. Mcginty, R.D., Mcdowell, D.L.: A semi-implicit integration scheme for rate independent finite crystal plasticity. Int. J. Plast. 22, 996–1025 (2006)

    Article  MATH  Google Scholar 

  64. Press, W.H.: Numerical Recipes for Fortran 77. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  65. Li, H.J.: Surface roughness in metal forming. Ph.D. Thesis, University of Wollongong (2012)

  66. Hibbitt, Karlsson and Sorensen: ABAQUS/Standard User’s Manual. Hibbitt, Karlsson & Sorensen Inc, Providence (2002)

  67. Dassauh Systèmes Simulia Corp: ABAQUS GUI Toolkit Reference Manual [M]. ABAQUS, Inc, Pawtucket, USA (2008)

  68. Zhuang, Z., Zhang, F., Cen, S.: Analysis and Examples of ABAQUS Nonlinear Finite Element. Science Press, Beijing (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hejie Li.

Additional information

Communicated by Andreas Öchsner.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, H., Öchsner, A., Yarlagadda, P.K.D.V. et al. A new constitutive analysis of hexagonal close-packed metal in equal channel angular pressing by crystal plasticity finite element method. Continuum Mech. Thermodyn. 30, 69–82 (2018). https://doi.org/10.1007/s00161-017-0583-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00161-017-0583-9

Keywords

Navigation