Abstract
When plastic deformation in hexagonal metals with lower symmetry than in cubic metals cannot support the external load, the crystal can break along a certain plane. Using a simple criterion based on the surface energy, Young modulus and interplanar separation, the anisotropy of fracture is discussed for three typical hexagonal metals, magnesium, titanium and zinc. The obtained results are generally in agreement with the experimental observations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ando S, Sakamoto T, Ikejiri Y et al (2006) Crack orientation dependence of fatigue behavior in titanium single crystals by thin sheet plain bending. Key Eng Mater 326–328:967–970
Ando S, Tsushida M, Kitahara H (2010) Deformation behavior of magnesium single crystal in c-axis compression and a-axis tension. Mater Sci Forum 654–656:699–702
Ando S, Kitahara H, Tsushida M (2011) Fatigue behavior of pure titanium single crystals by bending method. Proc Eng 10:1384–1389. https://doi.org/10.1016/j.proeng.2011.04.230
Bullen FP (1963) Cleavage of zinc single crystals. Trans Met Soc AIME 227:1069–1077
Christian JW, Mahajan S (1995) Deformation twinning. Prog Mater Sci 39:1–157. https://doi.org/10.1016/0079-6425(94)_00007-7
Deruyttere AE, Greenough GB (1953) Cleavage fracture of zinc single crystals. Nature 172:170–171. https://doi.org/10.1038/172170a0
Deruyttere AE, Greenough GB (1956) The criterion for the cleavage fracture of zinc single crystals. J Inst Met 84:337–345
Gandhi C, Ashby MF (1979) Fracture-mechanism maps for materials which cleave: f.c.c., b.c.c. and h.c.p. metals and ceramics. Acta Metal 27:1565–1602
Kaushik YV, Narasimhan R, Mishra RK (2014) Experimental study of fracture behavior of magnesium single crystals. Mater Sci Eng A 590:174–185. https://doi.org/10.1016/j.msea.2013.10.018
Luo Y, Qin R (2014) Surface energy and its anisotropy of hexagonal close-packed metals. Surf Sci 630:195–201. https://doi.org/10.1016/j.susc.2014.08.013
Macmillan NH, Kelly A (1972) On the relationship between ideal tensile strength and surface energy. Mater Sci Eng A 10:139–143. https://doi.org/10.1016/0025-5416(72)_90078-X
Mine Y, Ando S, Takashima K (2011) Crystallographic fatigue crack growth in titanium single crystals. Mater Sci Eng A 528:7570–7578. https://doi.org/10.1016/j.msea.2011.06.079
Paidar V, Čapek J, Ostapovets A (2018) Secondary twinning in zinc. Philos Mag Lett 98:437–445. https://doi.org/10.1080/09500839.2019.1566799
Tang Y, El-Awady JA (2014) Formation and slip of pyramidal dislocations in hexagonal close packed magnesium single crystals. Acta Mater 71:319–332. https://doi.org/10.1016/j.actamat.2014.03.022
Tromans D (2011) Elastic anisotropy of hcp metal crystals and polycrystrals. Int J Rec Res Appl Stud 61:452–483
Wang J, Beyerlein IJ, Tome CN (2010) An atomic and probabilistic perspective on twin nucleation in Mg. Scripta Mater 63:741–746. https://doi.org/10.1016/j.scriptamat.2010.01.047
Wu Z, Curtin WA (2015) Brittle and ductile crack-tip behavior in magnesium. Acta Mater 88:1–12. https://doi.org/10.1016/j.actamat.2015.01.023
Wu Z, Curtin WA (2016) Intrinsic structural transitions of the pyramidal I \(< {\rm c}+{\rm a}>\) dislocation in magnesium. Scripta Mater. 116:104–107. https://doi.org/10.1016/j.scriptamat.2016.01.041
Yoo MH (1981) Slip, twinning, and fracture in hexagonal close-packed metals. Metal Trans 12A:409–418
Yoo MH, Wei CT (1967) Slip modes of hexagonal-close-packed metals. J Appl Phys 38:4317. https://doi.org/10.1063/1.1709121
Acknowledgements
The authors gratefully acknowledge the financial support of the Czech Science Foundation [Projects No. 18-06110S] and the Operational Programme Research, Development and Education financed by European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports [Project No. SOLID21].
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Paidar, V., Čapek, J. Anisotropy of fracture in hexagonal metals. Int J Fract 225, 123–127 (2020). https://doi.org/10.1007/s10704-020-00472-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-020-00472-0