Elsevier

International Journal of Plasticity

Volume 77, February 2016, Pages 174-191
International Journal of Plasticity

Orientation dependence of the deformation kink band formation behavior in Zn single crystal

https://doi.org/10.1016/j.ijplas.2015.10.005Get rights and content

Highlights

  • Developing behavior of the deformation band in Zn single crystal was examined.

  • Analysis method to distinguish the kink band and deformation twin was proposed.

  • Deformation bands were confirmed to be predominantly kink bands rather than twinning.

  • Crystallographic features of the kink band are varied with loading orientation.

  • The type of dislocation that forms the kink boundary varies with loading orientation.

Abstract

Variations in deformation kink band formation behavior with loading orientation were examined by the combination of experiment and computer simulation, using the Zn single crystal as a model material. Based on the results, the controlling factors for the formation behavior of deformation kink bands and its general features were discussed. Due to compression parallel to the basal plane, several deformation bands formed in the Zn single crystal. By the examination of the crystallographic nature of the deformation bands, they were found to exhibit three characteristic features: an ambiguous crystal rotation axis on the [0001] zone axis, an arbitrary rotation angle with a wide variation, and a variation in the crystal rotation angle within the deformation band boundary itself. In addition, an analysis protocol to classify the nature of the deformation bands via the observation on (0001) was newly proposed. As a result, the deformation bands formed in the Zn single crystal were confirmed to be predominantly deformation kink bands rather than deformation twining.

Among the abovementioned three crystallographic features, we first experimentally confirmed by using the single crystal that the variations in the rotation axis in deformation kink bands exhibit a strong dependence on loading orientation. Using computer simulation based on the crystal plasticity finite element analysis, the origin of the variation in rotation axis in deformation kink bands was clarified to be due to the initiation of different types of basal dislocations that construct the deformation kink band boundaries, which depends on the loading orientation. In addition, the variations in types of the dislocations owing to the internal stress were found to cause the significant waviness of the deformation band boundaries on (0001) specimen surface.

Introduction

Compared with slip and twining, “deformation kinking” is a less common deformation mode, but it is considered important for materials that exhibit strong plastic anisotropy. Deformation kinking in metallic materials was first discovered in Cd (Orowan, 1942), and then in Zn single crystals (Hess and Barrett, 1949) with a hexagonal close-packed (hcp) structure. Currently, the deformation kink band is believed to form in many types of anisotropic materials. These bands form not only in hcp metals but also in materials where only one slip system (shear deformation mode) is predominantly operative, such as: in Ti3SiC2 ceramics (Barcelo et al., 2009, Barsoum and El-Raghy, 1999, Barsoum et al., 1999, Farber et al., 1999, Murugaiah et al., 2004), mica (muscovite) (Basu et al., 2009, Misra and Burg, 2012), graphite (Barsoum et al., 2004), and hexagonal boron nitride (Turan and Knowles, 1995).

Recently, the long-period stacking ordered (LPSO) phase was discovered as a possible strengthening phase of Mg alloys (Kawamura et al., 2001). Since the Mg/LPSO two-phase alloy demonstrates superior mechanical properties when compared with conventional Mg alloys (Hagihara et al., 2010a, Hagihara et al., 2013, Itoi et al., 2008, Kawamura et al., 2001, Kawamura and Yamasaki, 2007, Oñorbe et al., 2012, Oñorbe et al., 2013, Shao et al., 2010, Wang et al., 2012, Yamasaki et al., 2005, Yamasaki et al., 2011, Yoshimoto et al., 2006), there are many possible practical applications for this material. The formation of deformation kink bands is proposed to follow the deformation mechanism of the LPSO phase along the direction parallel to the basal phase (Hagihara et al., 2010b, Hagihara et al., 2010c, Hagihara et al., 2011, Hagihara et al., 2010b, Yamasaki et al., 2013), since only the basal slip is predominantly operative in the LPSO phase, owing to its complicated crystal structure along the c-axis. Thus, understanding the nature of the deformation kink band and its accompanying properties is important to clarify the mechanical properties of these anisotropic materials, including the LPSO phase.

One of the first models to explain the formation of the deformation kink band in hcp crystals was proposed for Zn single crystals by Hess and Barrett (1949), shown in Fig. 1. In this model, cooperative initiation and/or operation followed by arrangements of basal dislocations to align perpendicular to the slip plane are believed to be the basic processes to form the deformation kink boundary. However, experimental observations and analysis of the deformation kink bands, i.e. the examination of the crystallographic natures of the deformation kink band, has not been sufficiently conducted. Actually, the crystallographic nature of the deformation kink band has not yet been sufficiently clarified not only in the anisotropic materials including the LPSO phase but even in the Zn single crystal in which the formation of kink band model was proposed (Barcelo et al., 2009, Hagihara et al., 2015a, Hagihara et al., 2015b, Yamasaki et al., 2013). In the LPSO phase, recently the conflicting opinion that denies the presence of the deformation kink band as the predominant deformation mode was also proposed, that attempts to explain the origin of the deformation bands by the formation of deformation twin (Kishida et al., 2014). Thus, clarifying the validity of the kink band model, shown in Fig. 1, and elucidating the formation mechanism is important for understanding the deformation behavior of the anisotropic materials that accompanies the formation of deformation bands.

In this study, we focused on the deformation behavior of Zn single crystals, in which the formation of deformation kink bands has been widely believed by many researchers (Bell and Cahn, 1957, Gilman, 1954, Gilman and Read, 1953, Hagihara et al., 2015b, Hagihara et al., 2015a, Hess and Barrett, 1949, Jillson, 1950, Mayama et al., 2015, Pieła, 1997, Pieła, 2006, Washburn and Parker, 1952, Wróbel and Pieła, 2010), as a model material. The purpose of this study is to clarify the variations in formation behavior and the crystallographic features of the deformation bands formed in the Zn single crystals with loading orientation, by using scanning electron microscopy with electron backscatter diffraction (SEM-EBSD) pattern analysis and so on. In addition, a computational analysis on the variations in crystal orientation by the formation of the deformation kink bands was conducted using the crystal plasticity finite element method. By combining these experimental and computational results, the general features are examined for deformation kink bands.

Section snippets

Compression tests of Zn single crystals

Zinc single crystals were grown using the Bridgman technique (NEV-DS2, Nisshin giken, Japan) with raw Zn ingots (99.99%) under an Ar-gas atmosphere in a carbon crucible. The crystal growth rate was set at 10.0 mm/h. The crystal orientation was determined for the single crystals by the back Laue X-ray diffraction method, with an accuracy of 1°. The deformation behavior of the single crystal was examined by compression tests. Rectangular specimens, that were approximately 2 × 2 × 5 mm3 in size,

Experimental results

Fig. 3(a–d) shows the typical stress–strain curves of Zn single crystals deformed at RT and 200 °C at the four different loading orientations. In addition, Fig. 3(e) shows the corresponding temperature dependence of the yield stress (defined as a 0.2% offset stress) at those loading orientations. The profiles of the stress–strain curve were largely varied depending on the loading orientation and temperature. At the D-orientation near [5 5 10¯ 8], the yield stress showed an extremely low value

Discussion

By the SEM-EBSD analysis, the deformation bands formed in the Zn single crystal were found to show three characteristic features on their crystallographic nature. The first is an ambiguous crystal rotation axis that varied on the [0001] zone axis from band to band. The second is an arbitrary crystal rotation angle that was not fixed and exhibited relatively wide distributions. The third is a variation in crystal rotation angle, even within a deformation band boundary itself. These features were

Conclusion

  • (1)

    In the deformation of a Zn single crystal at the [101¯0] and [8 3 11¯ 0] loading orientations, where the operation of basal slip was strongly hindered, significant formations of deformation bands were confirmed. At the [112¯0] orientation, the formation frequency of the deformation band was considerably lower than those at the [101¯0] and [8 3 11¯ 0] orientations, and the plastic deformation was predominantly occurred by the operation of the {112¯2} slip at RT. However, similar deformation

Acknowledgment

This work was supported by a grant-in-aid for Scientific Research on Innovative Areas (Project: “Materials Science on Synchronized LPSO Structure ∼ The Evolution of the Material Science for Innovative Development of the Next-generation Lightweight Structure Materials ∼”) from the Ministry of Education, Culture, Sports, Science and Technology of Japan (grant number: 23109001 and 23109008). This work was also partly supported by the Light Metals Educational Foundation of Japan, and by Council for

References (58)

  • G.A. Alers et al.

    The elastic constants of zinc between 4.2° and 670°K

    J. Phys. Chem. Solids

    (1958)
  • F. Barcelo et al.

    Electron-backscattered diffraction and transmission electron microscopy study of post-creep Ti3SiC2

    J. Alloys Comp.

    (2009)
  • M.W. Barsoum et al.

    Room-temperature ductile carbides

    Met. Mater. Trans. A

    (1999)
  • M.W. Barsoum et al.

    Dislocations, kink bands, and room-temperature plasticity of Ti3SiC2

    Met. Mater. Trans. A

    (1999)
  • M.W. Barsoum et al.

    Kink bands, nonlinear elasticity and nanoindentations in graphite

    Carbon

    (2004)
  • M.W. Barsoum et al.

    Microscale modeling of kinking nonlinear elastic solids

    Phys. Rev. B

    (2005)
  • S. Basu et al.

    On spherical nanoindentations, kinking nonlinear elasticity of mica single crystals and their geological implications

    J. Struct. Geol.

    (2009)
  • R.L. Bell et al.

    The dynamics of twinning and the interrelation of slip and twinning in zinc crystals

    Proc. Roy. Soc. A

    (1957)
  • I.J. Beyerlein et al.

    A dislocation-based constitutive law for pure Zr including temperature effects

    Int. J. Plast.

    (2008)
  • J. Cheng et al.

    A crystal plasticity FE model for deformation with twin nucleation in magnesium alloys

    Int. J. Plast.

    (2015)
  • D. Egusa et al.

    Micro-kinking of the long-period stacking/order (LPSO) phase in a hot-extruded Mg97Zn1Y2 alloy

    Mater. Trans.

    (2013)
  • L. Farber et al.

    High-resolution transmission electron microscopy study of a low-angle boundary in plastically deformed Ti3SiC2

    Phil. Mag. Lett.

    (1999)
  • J.J. Gilman

    Mechanism of ortho kink-band formation in compressed zinc monocrystals

    Trans. AIME

    (1954)
  • J.J. Gilman et al.

    Bend-plane phenomena in the deformation of zinc monocrystals

    Trans. AIME

    (1953)
  • S. Graff et al.

    Yielding of magnesium: from single crystal to polycrystalline aggregates

    Int. J. Plast.

    (2007)
  • K. Hagihara et al.

    In-situ observation on the formation behavior of the deformation kink bands in Zn single crystal and LPSO phase

    Mater. Trans.

    (2015)
  • K. Hagihara et al.

    High-temperature compressive deformation behavior of Mg97Zn1Y2 extruded alloy containing a long-period stacking ordered (LPSO) phase

    Mater. Sci. Eng. A

    (2013)
  • K. Hagihara et al.

    Effect of long-period stacking ordered phase on mechanical properties of Mg97Zn1Y2 extruded alloy

    Acta Mater

    (2010)
  • K. Hagihara et al.

    Plastic deformation behavior of Mg89Zn4Y7 extruded alloy composed of long-period stacking ordered phas

    Intermetallics

    (2010)
  • K. Hagihara et al.

    Plastic deformation behavior of Mg12ZnY LPSO-phase with 14H-typed structure

    Mater. Trans.

    (2011)
  • K. Hagihara et al.

    Crystallographic nature of deformation bands shown in Zn and Mg-based long-period stacking ordered (LPSO) phase

    Phil. Mag.

    (2015)
  • K. Hagihara et al.

    Plastic deformation behavior of Mg12YZn with 18R long-period stacking ordered structure

    Intermetallics

    (2010)
  • T. Hama et al.

    Crystal-plasticity finite-element analysis of inelastic behavior during unloading in a magnesium alloy sheet

    Int. J. Plast.

    (2011)
  • V. Herrera-Solaz et al.

    An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: application to AZ31 Mg alloy

    Int. J. Plast.

    (2014)
  • J.B. Hess et al.

    Structure and nature of kink bands in zinc

    Met. Trans.

    (1949)
  • T. Itoi et al.

    A high-strength Mg–Ni–Y alloy sheet with a long-period ordered phase prepared by hot-rolling

    Scr. Mater.

    (2008)
  • D.C. Jillson

    An experimental survey of deformation and annealing processes in zinc

    Trans. AIME

    (1950)
  • Y. Kawamura et al.

    Rapidly solidified powder metallurgy Mg97Zn1Y2 alloys with excellent tensile yield strength above 600 MPa

    Mater. Trans.

    (2001)
  • Y. Kawamura et al.

    Formation and mechanical properties of Mg97Zn1RE2 alloys with long-period stacking ordered structure

    Mater. Trans.

    (2007)
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