Characterization of Staggered Twin Formation in HCP Magnesium

  • M. Arul KumarEmail author
  • B. Leu
  • P. Rottmann
  • I. J. Beyerlein
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


Twins in hexagonal close-packed polycrystals, most often nucleate at grain-boundaries (GBs), propagate into the grain and terminate at opposing GBs. Regularly, multiple parallel twins of the same variant form inside the same grain. When twins terminate inside the grains, rather than the grain boundary, they tend to form a staggered structure. Whether a staggered twin structure or the more common grain spanning twin structure forms can greatly affect mechanical behavior. In this work, the underlying mechanism for the formation of staggered twins is studied using an elasto-visco-plastic fast Fourier transform model, which quantifies the local stresses associated with \( \left\{ {10\overline{1} 2} \right\} \)-type staggered twins in magnesium for different configurations. The model results suggest that when a twin tip is close to the lateral side of another twin, the driving force for twin propagation is significantly reduced. As a result, the staggered twin structure forms.


Deformation twins Staggered structure Local stresses Crystal plasticity Magnesium 



This work is fully funded by the US Department of Energy, Office of Basic Energy Sciences Project FWP 06SCPE401. I.J.B. acknowledges financial support from the National Science Foundation (NSF CMMI-1729887). BL acknowledges financial support from the National Defense Science and Engineering Graduate (NDSEG) Fellowship. The authors thank Luoning Ma (Johns Hopkins University) for the preparation of TEM specimen.


  1. 1.
    P.G. Partridge (1967) The crystallography and deformation modes of hexagonal close-packed metals. Metallurgical Reviews 12: 169–194.CrossRefGoogle Scholar
  2. 2.
    M.H. Yoo (1981) Slip, Twinning, and Fracture in Hexagonal Close-Packed Metals. Metall Trans A 12(3): 409–418.CrossRefGoogle Scholar
  3. 3.
    M.H. Yoo, J.K. Lee (1991) Deformation Twinning in Hcp Metals and Alloys. Philos Mag A 63(5): 987–1000.Google Scholar
  4. 4.
    I.J. Beyerlein, L. Capolungo, P.E. Marshall, R.J. McCabe, C.N. Tome (2010) Statistical analyses of deformation twinning in magnesium (vol 90, pg 2161, 2010). Philos Mag 90(30): 4073–4074.CrossRefGoogle Scholar
  5. 5.
    L. Capolungo, P.E. Marshall, R.J. McCabe, I.J. Beyerlein, C.N. Tome (2009) Nucleation and growth of twins in Zr: A statistical study. Acta Mater 57(20): 6047–6056.CrossRefGoogle Scholar
  6. 6.
    M.A. Kumar, M. Wroński, R.J. McCabe, L. Capolungo, K. Wierzbanowski, C.N. Tomé (2018) Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study. Acta Mater 148: 123–132.Google Scholar
  7. 7.
    R.J. McCabe, G. Proust, E.K. Cerreta, A. Misra (2009) Quantitative analysis of deformation twinning in zirconium. Int J Plasticity 25(3): 454–472.CrossRefGoogle Scholar
  8. 8.
    B.M. Morrow, R.J. Mccabe, E.K. Cerreta, C.N. Tome (2014) In-Situ TEM Observation of Twinning and Detwinning During Cyclic Loading in Mg. Metall Mater Trans A 45a(1): 36–40.CrossRefGoogle Scholar
  9. 9.
    J. Wang, I.J. Beyerlein, C.N. Tome (2010) An atomic and probabilistic perspective on twin nucleation in Mg. Scripta Mater 63(7): 741–746.CrossRefGoogle Scholar
  10. 10.
    J. Wang, J.P. Hirth, C.N. Tome (2009) ((1)over-bar0 1 2) Twinning nucleation mechanisms in hexagonal-close-packed crystals. Acta Mater 57(18): 5521–5530.Google Scholar
  11. 11.
    M.A. Kumar, I.J. Beyerlein, R.J. McCabe, C.N. Tome (2016) Grain neighbour effects on twin transmission in hexagonal close-packed materials. Nat Commun 7.Google Scholar
  12. 12.
    M.A. Kumar, I.J. Beyerlein, C.N. Tome (2016) Effect of local stress fields on twin characteristics in HCP metals. Acta Mater 116: 143–154.Google Scholar
  13. 13.
    G.C. Kaschner, C.N. Tome, I.J. Beyerlein, S.C. Vogel, D.W. Brown, R.J. McCabe (2006) Role of twinning in the hardening response of zirconium during temperature reloads. Acta Mater 54(11): 2887–2896.CrossRefGoogle Scholar
  14. 14.
    G. Proust, C.N. Tome, G.C. Kaschner (2007) Modeling texture, twinning and hardening evolution during deformation of hexagonal materials. Acta Mater 55(6): 2137–2148.CrossRefGoogle Scholar
  15. 15.
    Q. Yu, J. Wang, Y.Y. Jiang, R.J. McCabe, N. Li, C.N. Tome (2014) Twin-twin interactions in magnesium. Acta Mater 77: 28–42.CrossRefGoogle Scholar
  16. 16.
    Q. Yu, J. Zhang, Y. Jiang (2011) Fatigue damage development in pure polycrystalline magnesium under cyclic tension–compression loading. Materials Science and Engineering: A 528(25–26): 7816–7826.CrossRefGoogle Scholar
  17. 17.
    N.P. Daphalapurkar, J.W. Wilkerson, T.W. Wright, K.T. Ramesh (2014) Kinetics of a fast moving twin boundary in nickel. Acta Mater 68: 82–92.CrossRefGoogle Scholar
  18. 18.
    E. Faran, D. Shilo (2010) Twin Motion Faster Than the Speed of Sound. Phys Rev Lett 104(15).Google Scholar
  19. 19.
    M.A. Kumar, A.K. Kanjarla, S.R. Niezgoda, R.A. Lebensohn, C.N. Tome (2015) Numerical study of the stress state of a deformation twin in magnesium. Acta Mater 84: 349–358.Google Scholar
  20. 20.
    J. Michel, H. Moulinec, P. Suquet (2000) A computational method based on augmented Lagrangians and fast Fourier Transforms for composites with high contrast. CMES-Computer Modeling in Engineering & Sciences 1(2): 79–88.Google Scholar
  21. 21.
    H. Moulinec, P. Suquet (1994) A fast numerical method for computing the linear and nonlinear mechanical properties of composites. Comptes Rendus De L Academie Des Sciences Serie Ii 318(11): 1417–1423.Google Scholar
  22. 22.
    R.A. Lebensohn (2001) N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform. Acta Mater 49(14): 2723–2737.Google Scholar
  23. 23.
    R. Brenner, R.A. Lebensohn, O. Castelnau (2009) Elastic anisotropy and yield surface estimates of polycrystals. Int J Solids Struct 46(16): 3018–3026.CrossRefGoogle Scholar
  24. 24.
    R.A. Lebensohn, R. Brenner, O. Castelnau, A.D. Rollett (2008) Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper. Acta Mater 56(15): 3914–3926.CrossRefGoogle Scholar
  25. 25.
    R.A. Lebensohn, M.I. Idiart, P.P. Castaneda, P.G. Vincent (2011) Dilatational viscoplasticity of polycrystalline solids with intergranular cavities. Philos Mag 91(22): 3038–3067.CrossRefGoogle Scholar
  26. 26.
    A.K. Kanjarla, R.A. Lebensohn, L. Balogh, C.N. Tome (2012) Study of internal lattice strain distributions in stainless steel using a full-field elasto-viscoplastic formulation based on fast Fourier transforms. Acta Mater 60(6–7): 3094–3106.CrossRefGoogle Scholar
  27. 27.
    R.A. Lebensohn, A.K. Kanjarla, P. Eisenlohr (2012) An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int J Plasticity 32–33: 59–69.CrossRefGoogle Scholar
  28. 28.
    P. Eisenlohr, M. Diehl, R.A. Lebensohn, F. Roters (2013) A spectral method solution to crystal elasto-viscoplasticity at finite strains. Int J Plasticity 46: 37–53.CrossRefGoogle Scholar
  29. 29.
    M.A. Kumar, I.J. Beyerlein, R.A. Lebensohn, C.N. Tome (2017) Modeling the effect of neighboring grains on twin growth in HCP polycrystals. Model Simul Mater Sc 25(6).CrossRefGoogle Scholar
  30. 30.
    M.A. Kumar, I.J. Beyerlein, R.A. Lebensohn, C.N. Tome (2017) Role of alloying elements on twin growth and twin transmission in magnesium alloys. Mat Sci Eng a-Struct 706: 295–303.Google Scholar
  31. 31.
    M.A. Kumar, I.J. Beyerlein, C.N. Tome (2016) Grain size constraints on twin expansion in hexagonal close packed crystals. J Appl Phys 120(15).Google Scholar
  32. 32.
    I.J. Beyerlein, R.J. McCabe, C.N. Tome (2011) Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study. J Mech Phys Solids 59(5): 988–1003.CrossRefGoogle Scholar
  33. 33.
    R.F.S. Hearmon (1946) The Elastic Constants of Anisotropic Materials. Rev Mod Phys 18(3): 409–440.CrossRefGoogle Scholar
  34. 34.
    G. Simmons, H. Wang (year) Single crystal elastic constants and calculated aggregate properties: A Handbook. MIT Press.Google Scholar
  35. 35.
    H. Abdolvand, A.J. Wilkinson (2016) Assessment of residual stress fields at deformation twin tips and the surrounding environments. Acta Mater 105: 219–231.CrossRefGoogle Scholar
  36. 36.
    L. Balogh, S.R. Niezgoda, A.K. Kanjarla, D.W. Brown, B. Clausen, W. Liu, C.N. Tome (2013) Spatially resolved in situ strain measurements from an interior twinned grain in bulk polycrystalline AZ31 alloy. Acta Mater 61(10): 3612–3620.CrossRefGoogle Scholar
  37. 37.
    I. Basu, H. Fidder, V. Ocelik, J.T.M. de Hosson (2018) Local Stress States and Microstructural Damage Response Associated with Deformation Twins in Hexagonal Close Packed Metals. Crystals 8(1).CrossRefGoogle Scholar
  38. 38.
    Q. Sun, X. Zhang, Y. Ren, L. Tan, J. Tu (2015) Observations on the intersection between 101̅2 twin variants sharing the same zone axis in deformed magnesium alloy. Mater Charact 109: 160–163.Google Scholar
  39. 39.
    Q. Sun, X.Y. Zhang, J. Tu, Y. Ren, H. Qin, Q. Liu (2015) Characterization of basal-prismatic interface of \( \left\{ {10\overline{1} 2} \right\} \) twin in deformed titanium by high-resolution transmission electron microscopy. Phil Mag Lett 95(3): 145–151.Google Scholar
  40. 40.
    F. Wang, K. Hazeli, K.D. Molodov, C.D. Barrett, T. Al-Samman, D.A. Molodov, A. Kontsos, K.T. Ramesh, H. El Kadiri, S.R. Agnew (2018) Characteristic dislocation substructure in \( \left\{ {10\overline{1} 2} \right\} \) twins in hexagonal metals. Scripta Mater 143: 81–85.Google Scholar
  41. 41.
    Y. Liu, N. Li, M.A. Kumar, S. Pathak, J. Wang, R.J. McCabe, N.A. Mara, C.N. Tome (2017) Experimentally quantifying critical stresses associated with basal slip and twinning in magnesium using micropillars. Acta Mater 135: 411–421.CrossRefGoogle Scholar
  42. 42.
    J. Jeong, M. Alfreider, R. Konetschnik, D. Kiener, S. Oh (2018) In-situ TEM observation of {1012} twin-dominated deformation of Mg pillars: Twinning mechanism, size effects and rate dependency. Acta Mater 158: 407–421.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  • M. Arul Kumar
    • 1
    Email author
  • B. Leu
    • 2
  • P. Rottmann
    • 2
  • I. J. Beyerlein
    • 2
    • 3
  1. 1.Los Alamos National LaboratoryMaterials Science and Technology DivisionLos AlamosUSA
  2. 2.Materials DepartmentUniversity of California at Santa BarbaraSanta BarbaraUSA
  3. 3.Mechanical Engineering DepartmentUniversity of California at Santa BarbaraSanta BarbaraUSA

Personalised recommendations