View source for Localized Twin Bands in Sheet Bending of a Magnesium Alloy

Authors: J.C. Baird<sup>*</sup>, B. Li<sup>*</sup>, S. Yazdan Parast<sup>*</sup>, S.J. Horstemeyer<sup>*</sup>, L.G. Hector Jr.<sup>**</sup>, P.T. Wang<sup>*</sup>, M.F. Horstemeyer<sup>* ***</sup> 

<table>
<tr><td><sup>*</sup></td><td>Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS 39759, USA</td></tr>
<tr><td><sup>**</sup></td><td>General Motors R&D Center, 30500 Mound Road, Warren, MI 48090, USA</td></tr>
<tr><td><sup>***</sup></td><td>Department of Mechanical Engineering, Mississippi State University, Starkville, MS 39762, USA</td></tr>
</table>

Corresponding author: [mailto:binli@cavs.msstate.edu Bin Li]



=== Abstract ===
''Three-point bending tests were performed at room temperature on Mg-Al-Zn magnesium sheet material (~8.0 µm initial grain size). In-situ electron backscatter diffraction (EBSD) and optical microscopy examinations revealed a highly localized twinning pattern during bending. In the compression zone,   twins were localized in bands, each band comprising high density twins, but twins were absent between the bands. As the bending angle increased, the twin bands grew across the center line. Possible mechanisms for such localized twin bands are discussed.''

Key words: Twinning; Magnesium; Bending; Plastic deformation;

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=== Introduction ===

Wrought Mg alloys have attracted substantial attention as potential light weight replacement materials for heavier aluminum and steel alloys in ground transportation vehicles. Broader application of Mg alloys has been hampered, however, by their poor ductility and fracture toughness at room temperature (RT) despite their high strength-to-weight ratios. In contrast to the high ductility of the cubic lattice of ferrous alloys, the low ductility of Mg alloys results from a lack of slip systems inherent to their hexagonal-close packed (HCP) lattices. The stress required to plastically deform Mg along its (easy) basal slip plane is two-orders-of-magnitude lower that the (hard) prismatic plane at RT. The five independent slip systems required by the von Mises criterion<ref name="ref1"></ref> for sufficient ductility are simultaneously activated only at temperatures near 300 °C. Moreover, the nearly ideal c/a ratio promotes twinning, rather than basal or prismatic slip at RT. Twinning-dominated deformation gives rise to unique mechanical properties in Mg alloys, such as “sigmoidal” hardening in plastic flow, tension-compression asymmetry, and anisotropy in plastic deformation<ref name="ref2"></ref><ref name="ref3"></ref><ref name="ref4"></ref>.

While conventional forming processes (e.g. stamping) of wrought Mg alloys are problematic at RT, high-temperature forming facilitates the manufacture of near-net shapes from Mg alloy sheets. To reduce energy consumption and manufacturing costs, it is desirable to reduce the processing temperatures of Mg sheet forming. Hence, understanding the deformation mechanisms which drive microstructural and texture evolution of Mg alloys during forming rather than post-forming is crucial to achieve optimized processing and end products. Moreover, development of physically-realistic constitutive models for Mg sheet is critical for finite element simulations of formability. The mechanical properties of AZ31 Mg sheet metals have been studied extensively <ref name="ref5"></ref><ref name="ref6"></ref><ref name="ref7"></ref>; however, little attention has been given to their microstructural evolution during forming. 

Because bending is significant in many sheet stamping processes, the purpose of the present study is to examine the microstructural evolution of AZ31 Mg during three-point bending at RT. We applied in-situ electron backscatter diffraction (EBSD) and optical microscopy to investigate twinning. We found the formation of localized twin bands in the compression zone of the sheet which extend to the tension zone with increase bending angle. Possible mechanisms responsible for the formation of localized twin bands are reviewed.

=== Experimental Procedure ===

The material chosen for the current study is a twin-roll cast sheet of AZ31 Mg alloy with a 1.0 mm thickness<ref name="ref8"></ref>.  The initial grain size was ~8.0 µm. The as-received sheet was annealed at 300°C for 2 hours in an Argon atmosphere. Strips with a dimension 60×7×1 mm3 were cut for subsequent three-point bending tests. The through-thickness cross sections of the strips were metallographically polished and then electropolished using a Struers electropolisher and the standard C1 Struers electrolyte (160 mg sodium thiocyanate, 800 ml ethanol, 80 ml ethylene glycol monobutyl ether, and 20 ml distilled water). 

Three-point bending was performed with a specially designed, in-house test fixture that enabled in-situ electron backscatter diffraction (EBSD) and metallography. In contrast to conventional EBSD scans, where test specimens are unloaded after deformation, the test fixture used in the present study makes it possible to scan the specimens in-situ, i.e., without being unloaded, to examine the microstructure and texture evolution (further details of our design will be described elsewhere). This capability circumvents the problem of detwinning<ref name="ref9"></ref><ref name="ref10"></ref><ref name="ref11"></ref> after a deformed specimen is unloaded. Detwinning is common in deformation of Mg and Mg alloys and leads to the loss of microstructure and texture information. Moreover, continuous observations of microstructure and texture evolution without unloading are preferable for understanding deformation mechanisms during bending. The EBSD scans were performed through the thickness of the sheet using a Zeiss Supra 40 Field Emission Gun (FEG) Scanning Electron Microscope (SEM) equipped with an EDAX Hikari Electron Backscatter Diffraction (EBSD) detection system. After data collection, all data sets were rotated 90° about the transverse direction (TD) so that data analysis could be performed along the normal direction (ND). All EBSD scans were preformed with the load still on the specimen. Specimens undergoing bending were also examined by optical microscopy with differential interference contrast (DIC) illumination. 

During three-point bending, the stress state varies continuously from compression on the top edge under the indenter to tension on the bottom edge. At the neutral axis, the strain reverses signs<ref name="ref12"></ref>. These stress states provide an ideal scenario for in-situ study by EBSD of twinning-detwinning and other important issues related to material deformation. For rolled Mg sheets with a strong basal texture, the compression zone of the specimen provides a preferred loading condition for the   extension twins which, in turn, generate an elongation along the <c> axis that is nearly parallel to the normal direction of the sheet. In the tension zone, however, the stress state disfavors the  twinning.

=== Results ===
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Figure 1 displays the inverse pole figure (IPF) map that corresponds to the initial texture and microstructure of the Mg AZ31 rolled sheet. The pole figure is shown as well. The initial texture is typical of rolled materials exhibiting a strong basal (0001) pole, i.e., fiber texture. 

Electron backscatter diffraction scans during bending were conducted in different locations in the compression zone, near the neutral axis, and in the tension zone. These locations were pre-selected from a background image comprising the entire cross-section. Figure 2 shows the IPF map of a region in the compression zone. As expected, twinning occurred in this zone during bending. The twins are localized in a band with a width that is much larger than the grain size. The band runs roughly 45° from top to bottom. Away from this twin band, no twins are observed. Misorientation analysis shows that the twins are indeed   extension twins. The compressive stress creates an elongation along the <c> axis of the highly textured microstructure. Notably, the twin variants are aligned in two nearly perpendicular directions. Most of the twin variants run through whole grain, with the twins in the neighboring grains being connected at the grain boundary. The pole figure confirms that the   twinning indeed took place, as two new intensity spots appear nearly 90° away from the rod intensity, a definitive signature of the extension twins.

Figure 2 shows only one twin band; however, multiple twin bands are formed in the compression zone of the sheet, as shown in Figure 3. This EBSD scan was taken near the geometrical center line which is in the middle of the image. Twin patterns similar to Figure 2 can be observed. Multiple twins connect at the grain boundaries of neighboring grains. As the bending angle increases, the twin bands continue to grow across the center line. A similar pole figure was also captured, typical of the   twinning. It was found that the farther the scans were taken from the maximum compression, thus closer to the maximum tension, the more the intensity spot from twinning was reduced.

In addition to the in-situ EBSD scans in local regions of compression and tension, metallography observations were also made on another specimen during three-point bending. To better reveal the localized twin bands, the differential interference contrast (DIC) illumination technique was used. Figure 4(a) shows multiple, highly localized twin bands. The width of the bands narrows as they propagate toward the tension zone, and the length of the individual bands decreases as the distance to the indenter increases. 

The bands roughly point in the same direction, about 45° with the loading direction. Interestingly, the tip of the longest band (indicated by the arrow) extends across the center line (also shown in Figure 3), indicative of movement of the neutral axis<ref name="ref12"></ref><ref name="ref13"></ref> (the position of which was not measured in this study). Figure 4(b) shows that as the bending angle increases, the twin bands widen laterally. Meanwhile, more twin bands appear in the direction nearly perpendicular to the original twin bands (indicated by the arrow).

How the neutral axis moves in Mg bending is somewhat controversial. According to Avedesian and Baker<ref name="ref13"></ref>, Mg alloys shorten in bending because the neutral axis shifts slightly toward the tension zone. This is in stark contrast to FCC and BCC metals. Alternatively, Ben-Artzy et al.<ref name="ref12"></ref> measured the movement of the neutral axis in four-point bending of Mg extrusion alloys using a state-of-the-art digital image correlation technique and a miniature bending stage. By tracking the line of zero strain through the cross-section of Mg bend specimens at regular intervals established by the framing rate of a digital camera, they found that the neutral axis does not coincide with the geometrical center line for Mg alloys. Rather, it shifts toward the compression zone, but the shift is sensitive to alloy type and the accumulated plastic strain. An ancillary study of three-point bending of these alloys would be required to determine whether or not this behavior is related to the type of bending test since the observation of Avedesian and Baker<ref name="ref13"></ref> presumably pertains to three point bending. Nevertheless, the crossing of the extension twins over the center line in the present study appears to be consistent with the Avedesian and Baker<ref name="ref13"></ref> observation.

Additional three-point bending tests were conducted on non-annealed Mg AZ31 sheet specimens and we found that the occurrence of the localized twin bands are repeatable. To the best of our knowledge, such highly localized twin bands in Mg sheet bending have not been previously reported. Shear bands formed during sheet forming such as cold/warm rolling of AZ31 Mg sheets have been reported in<ref name="ref5"></ref><ref name="ref6"></ref>, but these bands are different from what we observed in the AZ31 Mg sheet bending. Several important questions are raised by our observations (Figure 2 to 4). For example: (a) How do the localized twin bands nucleate and grow during sheet bending or sheet forming? (b) How do the bands affect Mg sheet formability, especially at RT? (c) How do temperature and strain rate influence the formation of the twin band nucleation and growth? To answer these questions, more systematic investigations are required. Here we briefly discuss mechanisms that may be responsible for the localized twin bands. 

As the EBSD and metallography images demonstrate, highly localized twinning occurred in three-point bending despite the relatively fine grain structure of the Mg AZ31 sheet. Our close examinations of the twins in the individual grains revealed that for those grains in the twin bands, one twin variant runs through an entire grain, i.e. from one side of the grain boundary to the opposite side. At the location where this twin variant stops, another twin variant nucleates and propagates into the neighboring grain, approximately in the same direction. Such nucleation and growth of the twin variants in the neighboring grains cascades until the stress state of the sheet disfavors   twinning. The majority of the twin variants connect at the grain boundaries and form a continuous band. This unusual twinning pattern suggests that the twin variants in the neighboring grains cannot be completely independent of each other. Deformation twins in HCP metals are preferentially nucleated at grain boundaries<ref name="ref14"></ref>, dislocations with a <c> component<ref name="ref15"></ref>; a twin/matrix interface where twin/slip interactions are present<ref name="ref16"></ref>. Wang and Beyerlein et al.<ref name="ref14"></ref> simulated nucleation of a   twin at a grain boundary in Mg. Their results show that grain boundaries with low misorientation angles are preferred nucleation sites. The connected twins observed in this work differ from paired nucleation at low angle grain boundaries because the twin bands cross a number of grains with high angle grain boundaries. Paired   twin variants (butterflies) at grain boundaries in HCP metals were observed and reported previously<ref name="ref17"></ref><ref name="ref18"></ref>. Two twin variants are located on both sides but connect at a grain boundary. Wang and Eisenlohr et al.<ref name="ref17"></ref> investigated the formation of paired twin variants that formed during four-point bending in titanium in terms of Schmid factors, c-axis misalignment, and the alignment of twinning systems between the neighboring grains. They found that these conditions are insufficient to account for the number of paired twins observed in their experiments, and hence there should be unidentified factors that affect the formation of paired twins at the grain boundaries. Beyerlein and Capolungo et al.<ref name="ref18"></ref>suggested that grain boundary misorientation angle strongly influences twin nucleation and growth, and defect structures at grain boundaries should be taken into account for the formation of paired twins.

The blunt ends where the twin variants connect at the grain boundaries (Figure 2 and 3) suggest that the repulsive force between twinning dislocations is negligible. Paired twins were also observed by Li et al.<ref name="ref19"></ref> in their transmission electron microscopy studies. It was observed that twin variants were able to penetrate grain boundaries and extend into a neighboring grain, retaining the initial crystallographic orientation, but the extended region does not necessarily satisfy the twin orientation relationship with the neighboring grain. These observations call into question the controlling mechanism of this particular twinning mode. According to classical twinning theory<ref name="ref20"></ref><ref name="ref21"></ref>, atomic shuffling is required for most of the twinning modes in low symmetry HCP structures because a homogeneous shear is unable to carry the parent lattice to the twin lattice. Atomic shuffling was confirmed by Li et al.<ref name="ref22"></ref><ref name="ref23"></ref><ref name="ref24"></ref> in their atomistic simulations. For   twinning, the magnitude of the theoretical elementary twinning dislocation equals 0.024 nm for Mg<ref name="ref25"></ref>, which is much smaller than the magnitude of the shuffles<ref name="ref22"></ref>. During twinning, localized stresses are generated at twin tips due to strain accommodation and such stress localization catalyzes twin nucleation in neighboring grains. Due to the shuffling dominated twin growth, connection of the twin variants in the neighboring grains at grain boundaries is permissible because of negligible repulsive forces between twinning dislocations. Such a multiplication of twins in neighboring grains propagates in the highly textured initial microstructure of the Mg AZ31 rolled sheet, and this could be one of the contributing factors for the localized twin bands observed in this study.
In summary, three-point bending was performed on an AZ31 Mg sheet. Highly localized twin bands were observed through in-situ EBSD and optical metallography. Each twin band was comprised of high density   twins, whereas between the twin bands, no twins were present. Possible mechanisms for such localized twin bands are briefly discussed. Additional study is required to understand the mechanism responsible for twin band formation during bending and the impact on AZ31 Mg sheet formability and material model development for finite element simulations.
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[[Image:AZ31RolledSheetInitial.jpg|500px]]<br/>
Figure 1. The initial microstructure and texture of the AZ31 rolled sheet. The texture is typical of the (0001) rod texture. The average grain size is about 8.0 µm. (click on image to enlarge)

[[Image:Az31RolledSheetEBSD.jpg|500px]]<br/>
Figure 2.  Electron backscatter diffraction (EBSD) shows a high density of twins in the sheet deformed in three-point bending. The twinning is highly localized. Away from the twin band, almost no twins can be observed. It can be seen from the pole figure that the twins are   extension twins. The scan was taken near the top of the cross-section in the compression zone of the specimen.  (click on image to enlarge)

[[Image:AZ31RolledSheetMultipleTwinBands.jpg|500px]]<br/>
Figure 3. Multiple twin bands were observed that span both the compression and the tension zones near the center line of the specimen (indicated by a dash-dotted line in the middle). The twin bands grow across the center line, indicative of a shift of the neutral axis<ref name="ref12"></ref><ref name="ref13"></ref>. (click on image to enlarge)

Figure 4a is missing

[[Image:AZ31RolledSheetOpticalMicroscopy.jpg|500px]]<br>
Figure 4. Through-thickness (1.0 mm) optical microscopy with the differential interference contrast (DIC) illumination during three-point bending. The load remained on the specimen when the images were taken. (a) Alternating twin bands can be clearly observed. From the indenter toward both ends of the strip, the length and width of the twin bands decreases because the plastic strain decreases. The longest twin band (indicated by the dark arrow) passes the center line. (b) As the bending angle increases, the twin bands widen by lateral growth. Meanwhile, new bands (indicated by the arrow) that are nearly perpendicular to the original bands are formed. (click on image to enlarge)
</td>
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</table>

=== Acknowledgements ===

J.C. Baird, B. Li, S. Yazdan Parast, S.J. Horstemeyer, P.T. Wang and M.F. Horstemeyer are grateful for the support from the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University. Thanks are extended to Dr. H. El Kadiri for his valuable discussions and H.R. Wainwright for her assistance with the preparation of the manuscript.

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[[Category: Research Paper]]
[[Category: Magnesium]]