Skip to main content
Log in

Analysis of the twin variant selection in polycrystalline cobalt

  • Metals & corrosion
  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

The samples of polycrystalline cobalt were strained in tension in the second stage of work hardening in order to activate twinning. The identification of twins and their orientation was analyzed using electron backscatter diffraction. The study of twin variant selection was carried out based on two parameters, namely the Schmid factor (SF) and the geometric compatibility factor (m'). The results indicate that the grains contained the \(\left\{ {10\overline{1}2} \right\}\) extension twins in most cases while the \(\left\{ {11\overline{2}1} \right\}\) extension twin mode was present in few cases, as well. In the grains containing only one twin variant, the SF analysis correctly predicted the activated twins in most cases. In the grains with variant pairs in para-position, nearly half of the studied twins had the highest SF of all possible variants, which means that they followed the Schmid law. On the other hand, for twin pairs in meta- or ortho-position, a different behavior was observed. Twins in these configurations were selected rather by the strain compatibility criterion than by the Schmid law, as SF values of the activated twins were significantly lower than those of the twins in para-position. Of these two configurations, the ortho-position one is highly preferred. The combined analysis using SF and m' parameter, predicted the occurrence of specific twin modes and variants only partially. A local analysis considering the effect of neighboring grains should be developed to account for the cases where the two parameters fail to explain the occurrence of particular twins, which seems to be related to the presence of a high fraction of high-angle grain boundaries.

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.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

Similar content being viewed by others

References

  1. Yoshinaga H, Horiuchi R (1963) Deformation mechanisms in magnesium single crystals compressed in the direction parallel to hexagonal axis. Trans JIM 4:4–8. https://doi.org/10.2320/matertrans1960.4.1

    Article  Google Scholar 

  2. Zhang XY, Zhu YT, Liu Q (2010) Deformation twinning in polycrystalline Co during room temperature dynamic plastic deformation. Scripta Mater 63:387–390

    Article  CAS  Google Scholar 

  3. Martinez M, Fleurier G, Chmelík F, Knapek M, Viguier B, Hug E (2017) TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension. Mater Charact 134:76–83. https://doi.org/10.1016/j.matchar.2017.09.038

    Article  CAS  Google Scholar 

  4. Chino Y, Kimura K, Hakamada M, Mabuchi M (2008) Mechanical anisotropy due to twinning in an extruded AZ31 Mg alloy. Mater Sci Eng A 485:311–317. https://doi.org/10.1016/j.msea.2007.07.076

    Article  CAS  Google Scholar 

  5. Bozzolo N, Chan L, Rollett AD (2010) Misorientations induced by deformation twinning in titanium. J Appl Crystallogr 43:596–602

    Article  CAS  Google Scholar 

  6. Xu S, Toth LS, Schuman C, Lecomte JS, Barnett MR (2017) Dislocation mediated variant selection for secondary twinning in compression of pure titanium. Acta Mater 124:59–70. https://doi.org/10.1016/j.actamat.2016.10.063

    Article  CAS  Google Scholar 

  7. Kumar MA, Wroński M, McCabe RJ, Capolungo L, Wierzbanowski K, Tomé CN (2018) Role of microstructure on twin nucleation and growth in HCP titanium: a statistical study. Acta Mater 148:123–132. https://doi.org/10.1016/j.actamat.2018.01.041

    Article  CAS  Google Scholar 

  8. Bingert JR, Mason TA, Kaschner GC, Gray GT, Maudlin PJ (2002) Deformation twinning in polycrystalline Zr: insights from electron backscattered diffraction characterization. Metall Mater Trans A 33:955–963. https://doi.org/10.1007/s11661-002-0165-7

    Article  Google Scholar 

  9. Partridge PG (1967) The crystallography and deformation modes of hexagonal close-packed metals. Metall Rev 12:169–194. https://doi.org/10.1179/mtlr.1967.12.1.169

    Article  CAS  Google Scholar 

  10. Martinez M, Hug E (2019) Characterization of deformation twinning in polycrystalline cobalt: a quantitative analysis. Materialia 7:100420

    Article  Google Scholar 

  11. Beyerlein IJ, Capolungo L, Marshall PE, McCabe RJ, Tomé CN (2010) Statistical analyses of deformation twinning in magnesium. Philos Mag 90:2161–2190

    Article  CAS  Google Scholar 

  12. Capolungo L, Marshall PE, McCabe RJ, Beyerlein IJ, Tomé CN (2009) Nucleation and growth of twins in Zr: a statistical study. Acta Mater 57:6047–6056. https://doi.org/10.1016/j.actamat.2009.08.030

    Article  CAS  Google Scholar 

  13. Zhu YT, Zhang XY, Liu Q (2011) Observation of twins in polycrystalline cobalt containing face-center-cubic and hexagonal-close-packed phases. Mater Sci Eng A 528:8145–8149. https://doi.org/10.1016/j.msea.2011.07.062

    Article  CAS  Google Scholar 

  14. Zhang XY, Li B, Wu XL, Zhu YT, Ma Q, Liu Q, Wang PT, Horstemeyer MF (2012) Twin boundaries showing very large deviations from the twinning plane. Scripta Mater 67:862–865. https://doi.org/10.1016/j.scriptamat.2012.08.012

    Article  CAS  Google Scholar 

  15. Sun Q, Zhang XY, Yin RS, Ren Y, Tan L (2015) Structural characterization of 10–13 twin boundaries in deformed Cobalt. Scripta Mater 108:109–112

    Article  CAS  Google Scholar 

  16. Sun Q, Zhang XY, Wang YC, Ren Y, Tan L, Liu Q (2016) Structural characterization of 10–11 twin boundaries in deformed cobalt. Mater Charact 116:44–47

    Article  CAS  Google Scholar 

  17. Seeger A, Kronmuller H, Boser O, Rapp M (1963) Plastische verformung von kobalteinkristallen. Phys Stat Sol 3:1107–1125

    Article  CAS  Google Scholar 

  18. Beyerlein IJ, Wanf J, Barnett MR, Tomé CN (2012) Double twinning mechanisms in magnesium alloys via dissociation of lattice dislocations. Proc R Soc A 468:1496–1520. https://doi.org/10.1098/rspa.2011.0731

    Article  CAS  Google Scholar 

  19. Mu S, Jonas JJ, Gottstein G (2012) Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy. Acta Mater 60:2043–2053. https://doi.org/10.1016/j.actamat.2012.01.014

    Article  CAS  Google Scholar 

  20. Koike J, Sato Y, Ando D (2008) Origin of the anomalous 10–12 twinning during tensile deformation of mg alloy sheet. Mater Trans 49:2792–2800. https://doi.org/10.2320/matertrans.MRA2008283

    Article  CAS  Google Scholar 

  21. Wang S, Zhang Y, Schuman C, Lecomte JS, Zhao X, Zuo L, Philippe MJ, Esling C (2015) Study of twinning/detwinning behaviors of Ti by interrupted in situ tensile tests. Acta Mater 82:424–436. https://doi.org/10.1016/j.actamat.2014.09.038

    Article  CAS  Google Scholar 

  22. Shi ZZ, Zhang Y, Wagner F, Juan PA, Berbenni S, Capolungo L, Lecomte JS, Richeton T (2015) On the selection of extension twin variants with low Schmid factors in a deformed Mg alloy. Acta Mater 83:17–28. https://doi.org/10.1016/j.actamat.2014.10.004

    Article  CAS  Google Scholar 

  23. Jonas JJ, Mu S, Al-Samman T, Gottstein G, Jiang L, Martin E (2011) The role of strain accommodation during the variant selection of primary twins in magnesium. Acta Mater 59:2046–2056. https://doi.org/10.1016/j.actamat.2010.12.005

    Article  CAS  Google Scholar 

  24. Guo C, Xin R, Xu J, Song B, Liu Q (2015) Strain compatibility effect on the variant selection of connected twins in magnesium. Mater Des 76:71–76. https://doi.org/10.1016/j.matdes.2015.03.041

    Article  CAS  Google Scholar 

  25. Guo C, Xin R, Ding C, Song B, Liu Q (2014) Understanding of variant selection and twin patterns in compressed Mg alloy sheets via combined analysis of Schmid factor and strain compatibility factor. Mater Sci Eng A 609:92–101. https://doi.org/10.1016/j.msea.2014.04.103

    Article  CAS  Google Scholar 

  26. Wang L, Eisenlohr P, Yang Y, Bieler TR, Crimp MA (2010) Nucleation of paired twins at grain boundaries in titanium. Scripta Mater 63:827–830. https://doi.org/10.1016/j.scriptamat.2010.06.027

    Article  CAS  Google Scholar 

  27. Luster J, Morris MA (1995) Compatibility of dependence on deformation in two-phase ti-ai alloys: microstructure and orientation relationships. Metall Mater Trans A 26:1745–1756. https://doi.org/10.1007/BF02670762

    Article  Google Scholar 

  28. Xin R, Liang Y, Ding C, Guo C, Wang B, Liu Q (2015) Geometrical compatibility factor analysis of paired extension twins in extruded Mg–3Al–1Zn alloys. Mater Des 86:656–663. https://doi.org/10.1016/j.matdes.2015.07.130

    Article  CAS  Google Scholar 

  29. Bouquet G, Dubois B (1978) Influence of the f.c.c. phase retained at room temperature on the mechanical properties of cobalt. Scripta Metall 12:1079–1081. https://doi.org/10.1016/0036-9748(78)90078-9

    Article  CAS  Google Scholar 

  30. Dubos PA, Fajoui J, Iskounen N, Coret M, Kabra S, Kelleher J, Girault B, Gloaguen D (2020) Temperature effect on strain-induced phase transformation of cobalt. Mater Lette 281:128812. https://doi.org/10.1016/j.matlet.2020.128812

    Article  CAS  Google Scholar 

  31. Čapek J, Máthis K, Clausen B, Stráská J, Beran P, Lukáš P (2014) Study of the loading mode dependence of the twinning in random textured cast magnesium by acoustic emission and neutrondiffraction methods. Mater Sci Eng A 602:25–32. https://doi.org/10.1016/j.msea.2014.02.051

    Article  CAS  Google Scholar 

  32. Fleurier G, Hug E, Martinez M, Dubos PA, Keller C (2015) Size effects and Hall-Petch relation in polycrystalline cobalt. Philos Mag Lett 95:122–130. https://doi.org/10.1080/09500839.2015.1020351

    Article  CAS  Google Scholar 

  33. Bachmann F, Hielscher R, Schaeben H (2010) Texture analysis with MTEX – free and open source software toolbox. Solid State Phenom 160:63–68. https://doi.org/10.4028/www.scientific.net/ssp.160.63

  34. Standford N (2008) Observation of 1121 twinning in a Mg-based alloy. Phil Mag Lett 88:379–386. https://doi.org/10.1080/09500830802070793

    Article  CAS  Google Scholar 

  35. Sabisch JEC, Minor AM (2018) Microstructural evolution of rhenium Part I: Compression. Mater Sci Eng A 732:251–258. https://doi.org/10.1016/j.msea.2018.06.057

    Article  CAS  Google Scholar 

  36. Kacher J, Minor AM (2014) Twin boundary interactions with grain boundaries investigated in pure rhenium. Acta Mater 81:1–8. https://doi.org/10.1016/j.actamat.2014.08.013

    Article  CAS  Google Scholar 

  37. Jeffery R, Smith E (1966) Deformation twinning in rhenium single crystals. Philos Mag 13:1163–1168. https://doi.org/10.1080/14786436608213532

    Article  CAS  Google Scholar 

  38. Kumar MA, Beyerlein IJ, McCabe RJ, Tomé CN (2016) Grain neighbour effects on twin transmission in hexagonal close-packed materials. Nat Commun 7:13826. https://doi.org/10.1038/ncomms13826

    Article  CAS  Google Scholar 

  39. Ecob N, Ralph B (1983) The effect of grain size on deformation twinning in a textured zinc alloy. J Mater Sci 18:2419–2429. https://doi.org/10.1007/BF00541848

    Article  CAS  Google Scholar 

  40. Khosravani A, Fullwood DT, Adams BL, Rampton TM, Miles MP, Mishra RK (2015) Nucleation and propagation of 10–12 twins in AZ31 magnesium alloy. Acta Mater 100:202–214

    Article  CAS  Google Scholar 

  41. Couret A, Caillard D (1985) An in situ study of prismatic glide in magnesium-I. The rate controlling mechanism. Acta Metall 33:1447–1454

    Article  CAS  Google Scholar 

  42. Koike J (2005) Enhanced deformation mechanisms by anisotropic plasticity in polycrystalline Mg alloys at room temperature. Metall Mater Trans A 36:1689–1696

    Article  Google Scholar 

  43. Máthis K, Nyilas K, Axt A, Dragomir-Cernatescu I, Ungár T, Lukáč P (2004) The evolution of non-basal dislocations as a function of deformation temperature in pure magnesium determined by X-ray diffraction. Acta Mater 52:2889–2894

    Article  Google Scholar 

  44. Agnew SR, Horton JA, Yoo MH (2002) Transmission electron microscopy investigation of <c+a> dislocations in Mg and α-solid solution Mg-Li alloys. Metall Mater Trans A 33:851–858

    Article  Google Scholar 

  45. Fernandez A, Jerusalem A, Gutierrez-Urrutia I, Perez-Prado MT (2013) 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. https://doi.org/10.1016/j.actamat.2013.09.005

    Article  CAS  Google Scholar 

  46. Korner K, Karnthaler HP (2006) Weak-beam study of glide dislocations in h.c.p. cobalt. Philos Mag 48:469–477

    Article  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the Czech Science Foundation under the grant No. 19-22604S. M.K. and P.D. gratefully acknowledge financial support from OP RDE, MEYS, grant No. CZ.02.1.01/0.0/0.0/16_013/0001794. PM. acknowledges partial financial support by ERDF, project No. CZ.02.1.01/0.0/0.0/15_003/0000485.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mayerling Martinez Celis.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Handling Editor: Sophie Primig.

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Martinez Celis, M., Minárik, P., Hug, E. et al. Analysis of the twin variant selection in polycrystalline cobalt. J Mater Sci 56, 7740–7752 (2021). https://doi.org/10.1007/s10853-020-05718-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10853-020-05718-9

Navigation