Numerical modeling of flow stress and grain evolution of an Mg AZ31B alloy based on hot compression tests

  • 33 Accesses


Magnesium alloys offer a wide range of applications in modern lightweight structures, although the correct forming parameters need to be found to reach a good combination of fine microstructure and the required mechanical properties. Several discrete and statistical methods have been proposed to simulate the dynamic recrystallization process and adopted to study microstructural evolution. However, the materials parameters necessary to develop these models are not widely available. Hence, industrial evaluation of these parameters is complex, unpractical for several types of material and time consuming for daily industrial applications. In that way, the thermomechanical behavior and grain size evolution modeling of the AZ31 alloy are proposed using isothermal compression data. Parameters to calculate coupled stress–strain–temperature parameters, dynamic recrystallization, volume fraction and grain size were obtained from the stress–strain curves. Then, the data were input in Deform-3D software to simulate the hot deformation process and verify with experimental data the consistency of the values obtained. Measured grains size agreed with the conducted modeling, showing the reliability of strain–stress and grain size data on predicting dynamic recrystallization phenomena.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. 1.

    Kumar DS, Sasanka CT, Ravindra K, Suman KNS (2015) Magnesium and its alloys in automotive applications—a review. Am J Mater Sci Technol.

  2. 2.

    Humphreys FJ, Hatherly M (2004) Hot deformation and dynamic restoration. In: Recrystallization and related annealing phenomena, 2nd edn. Elsevier, Amstredam, pp 415–450.

  3. 3.

    He Y, Ding H, Liu L, Shin K (2006) Computer simulation of 2D grain growth using a cellular automata model based on the lowest energy principle. Mater Sci Eng A 429:236–246.

  4. 4.

    Liu X, Li L, He F, Zhou J, Zhu B, Zhang L (2013) Simulation on dynamic recrystallization behavior of AZ31 magnesium alloy using cellular automaton method coupling Laasraoui–Jonas model. Trans Nonferrous Met Soc China 23:2692–2699.

  5. 5.

    Choi SH, Kim DW, Seong BS, Rollett AD (2011) 3-D simulation of spatial stress distribution in an AZ31 Mg alloy sheet under in-plane compression. Int J Plast 27:1702–1720.

  6. 6.

    Ryan ND, McQueen HJ (1990) Dynamic softening mechanisms in 304 austenitic stainless steel. Can Metall Q 29:147–162.

  7. 7.

    Poliak EI, Jonas JJ (1996) A one-parameter approach to determining the critical conditions for the initiation of dynamic recrystallization. Acta Mater 44:127–136.

  8. 8.

    Xu Y, Hu LX, Sun Y (2014) Dynamic recrystallization kinetics of as-cast AZ91D alloy. Trans Nonferrous Met Soc China 24:1683–1689. (english ed.)

  9. 9.

    Quan GZ, Mao YP, Li GS, Lv WQ, Wang Y, Zhou J (2012) A characterization for the dynamic recrystallization kinetics of as-extruded 7075 aluminum alloy based on true stress–strain curves. Comput Mater Sci 55:65–72.

  10. 10.

    Liu J, Cui Z, Ruan L (2011) A new kinetics model of dynamic recrystallization for magnesium alloy AZ31B. Mater Sci Eng A 529:300–310.

  11. 11.

    Sellars CM, McTegart WJ (1966) On the mechanism of hot deformation. Acta Metall 14:1136–1138.

  12. 12.

    Spigarelli S, El Mehtedi M, Cabibbo M, Evangelista E, Kaneko J, Jäger A, Gartnerova V (2007) Analysis of high-temperature deformation and microstructure of an AZ31 magnesium alloy. Mater Sci Eng A 462:197–201.

  13. 13.

    Liu J, Cui Z, Li C (2008) Modelling of flow stress characterizing dynamic recrystallization for magnesium alloy AZ31B. Comput Mater Sci 41:375–382.

  14. 14.

    Zimina M, Málek P, Bohlen J, Letzig D, Kurz G, Cieslar M (2015) Mechanical properties of homogenized twin-roll cast and conventionally cast AZ31 magnesium alloys. Mater Eng 22:8–15

  15. 15.

    Padilha F, Siciliano AF Jr (2005) Encruamento, recristalização, crescimento de grão e textura. ABM, São Paulo

  16. 16.

    Xu Y, Hu L, Sun Y (2013) Deformation behaviour and dynamic recrystallization of AZ61 magnesium alloy. J Alloys Compd 580:262–269.

  17. 17.

    Aliakbari Sani S, Ebrahimi GR, Kiani Rashid AR (2016) Hot deformation behavior and dynamic recrystallization kinetics of AZ61 and AZ61 + Sr magnesium alloys. J Magnes Alloy 4:104–114.

  18. 18.

    Liao C, Wu H, Wu C, Zhu F, Lee S (2014) Hot deformation behavior and flow stress modeling of annealed AZ61 Mg alloys. Prog Nat Sci Mater Int 24:253–265.

  19. 19.

    Nourollahi GA, Farahani M, Babakhani A, Mirjavadi SS (2013) Compressive deformation behavior modeling of AZ31 magnesium alloy at elevated temperature considering the strain effect. Mater Res 16:1309–1314.

  20. 20.

    Bhattacharya R, Lan YJ, Wynne BP, Davis B, Rainforth WM (2014) Constitutive equations of flow stress of magnesium AZ31 under dynamically recrystallizing conditions. J Mater Process Technol 214:1408–1417.

  21. 21.

    Ion SE, Humphreys FJ, White SH (1982) Dynamic recrystallisation and the development of microstructure during the high temperature deformation of magnesium. Acta Metall 30:1909–1919.

  22. 22.

    Shaban M, Eghbali B (2010) Determination of critical conditions for dynamic recrystallization of a microalloyed steel. Mater Sci Eng A 527:4320–4325.

  23. 23.

    Quan GZ, Shi Y, Wang YX, Kang BS, Ku TW, Song WJ (2011) Constitutive modeling for the dynamic recrystallization evolution of AZ80 magnesium alloy based on stress–strain data. Mater Sci Eng A 528:8051–8059.

  24. 24.

    Sellars CM, Whiteman JA (1978) Recrystallization and grain growth in hot rolling. Met Sci 13:187–194.

  25. 25.

    Mcqueen HJ, Jonas JJ (1984) Recent advances in hot working: fundamental dynamic softening mechanisms. J Appl Metalwork 3:233–241.

  26. 26.

    Lv B-J, Peng J, Shi D-W, Tang A-T, Pan F-S (2013) Constitutive modeling of dynamic recrystallization kinetics and processing maps of Mg–2.0Zn–0.3Zr alloy based on true stress–strain curves. Mater Sci Eng A 560:727–733.

  27. 27.

    He Y, Pan Q, Chen Q, Zhang Z, Liu X, Li W (2012) Modeling of strain hardening and dynamic recrystallization of ZK60 magnesium alloy during hot deformation. Trans Nonferrous Met Soc China 22:246–254.

  28. 28.

    Bergström Y (1970) A dislocation model for the stress–strain behaviour of polycrystalline α-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations. Mater Sci Eng 5:193–200.

  29. 29.

    Guo-Zheng Q, Yang W, Ying-Ying L, Jie Z (2013) Effect of temperatures and strain rates on the average size of grains refined by dynamic recrystallization for as-extruded 42CrMo steel. Mater Res 16:1092–1105.

  30. 30.

    Fatemi-Varzaneh SM, Zarei-Hanzaki A, Beladi H (2007) Dynamic recrystallization in AZ31 magnesium alloy. Mater Sci Eng A 456:52–57.

  31. 31.

    ASTM Standard (2012) E112–12: standard test methods for determining average grain size. ASTM Int E112–12:1–27.

  32. 32.

    Lee BH, Reddy NS, Yeom JT, Lee CS (2007) Flow softening behavior during high temperature deformation of AZ31 Mg alloy. J Mater Process Technol 187–188:766–769.

Download references


The authors thank LNNano and Villares Metals for technical support.

Author information

Correspondence to J. A. Avila.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Technical Editor: João Marciano Laredo dos Reis.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Giorjao, R.A.R., Monlevade, E.F., Avila, J.A. et al. Numerical modeling of flow stress and grain evolution of an Mg AZ31B alloy based on hot compression tests. J Braz. Soc. Mech. Sci. Eng. 42, 57 (2020) doi:10.1007/s40430-019-2146-4

Download citation


  • AZ31B
  • Isothermal compression
  • Dynamic recrystallization
  • Finite element modeling
  • Gleeble simulation