Kink-band formation in directionally solidifies Mg/Mg2Yb and Mg/Mg2Ca eutectic alloys with Mg/Laves-phase lamellar microstructure

Koji Hagihara ,Kosuke Miyoshi

a Division of Materials and Manufacturing Science,Graduate School of Engineering,Osaka University,2-1,Yamadaoka,Suita,Osaka 565-0871,Japan

b Department of Adaptive Machine Systems,Graduate School of Engineering,Osaka University,2-1 Yamadaoka,Suita,Osaka 565-0871,Japan

Abstract For the development of high-strength Mg alloys,active use of Laves phases such as C14-type Mg2Yb and Mg2Ca is strongly expected.However,the brittleness of the Laves phases is the biggest obstacle to it.We firs found that kink-band formation can be induced in directionally solidifies Mg/Mg2Yb and Mg/Mg2Ca eutectic lamellar alloys when a stress is applied parallel to the lamellar interface,leading to a high yield stress accompanied with ductility.That is,microstructural control can induce a new deformation mode that is not activated in the constituent phases,thereby inducing ductility.It was clarified that the geometric relationship between the operative slip plane in the constituent phases and the lamellar interface,and the microstructural features that provide kink-band nucleation sites are important factors for controlling kink-band formation.The obtained results show a possibility to open the new door for the development of novel high-strength structural material using the kink bands.

Keywords: Deformation kink band;Lamellar microstructure;Laves phase;Magnesium alloys;Mechanical properties.

1.Introduction

Improving the high-temperature strength of Mg alloys is very desirable to broaden their potential application in many fields Further,an increase in their modulus is required for their use as structural materials,e.g.,in automobiles [1].To achieve these improvements,active use of intermetallic compounds is expected.The Mg17Al12phase with the A12 structure [2,3] and several Laves phases;hexagonal C14-type Mg2Ca,Mg2Yb,etc.and C36-type (Mg,Al)2Ca are potential candidates [4-7].However,they exhibit brittle behavior during deformation at ambient temperatures [3,7],restricting their usage as strengthening components in Mg alloys.To overcome this,we recently proposed microstructural control,focusing on the lamellar microstructure.The brittle-to-ductile transition temperature of a Mg/Mg17Al12eutectic alloy can be decreased to 250°C [8],even though Mg17Al12cannot be plastically deformed below 300°C in its single-phase alloy[3].This is because controlling the lamellar microstructure can induce the formation of a “kink-band.” Kink bands form in materials in which only one slip system is predominantly operative,such as Zn [9].It was reported that when a stress is applied parallel to the slip plane of the predominately operative system,the avalanche generation of dislocations occurs in a restricted region,and their subsequent realignment along a direction perpendicular to the slip plane forms a kink band[9].

The use of kink bands for improving mechanical properties is an idea taken from studies on long-period stacking ordered (LPSO) phases,which have recently received attention as potential strengthening components in some Mg alloys containing Y and Zn [10-18].Notably,kink-band formation plays an exclusive role in increasing the strength and deformability of the LPSO phase [17].The crystal structure of the LPSO phase is constructed by the long-period stacking of close-packed planes (the basal plane in hexagonal structures) along thecaxis,and the Y/Zn atoms in the LPSO phase are periodically segregated on a specific close-packed plane where an fcc-like stacking fault exists [19].In other words,the crystal structure comprises the alternating stacking of a soft Mg layer and hard (Y,Zn)-containing layer,which is considered to be responsible for deformation kink-band formation [20-22].From this viewpoint,we have proposed that the development of lamellar-structured materials combining soft and hard phases,called a “mille-feuille material,” may have a possibility to induce deformation kink-band formation.This was indeed accomplished for a Mg/Mg17Al12eutectic alloy,resulting in an improved ductility [8].As other example,kink-band formation in the two-phase alloy was reported in Cu-Nb nanolaminate composites [23],and some eutectic alloys[24-27].However,the results are still lacking to establish a general criterion for inducing the kink band formation.

In this study,we focus on the deformation behavior of a Mg/Laves-phase two-phase alloy in the Mg-Yb and Mg-Ca systems.The Laves phase is expected to be better for improving the high-temperature strength than Mg17Al12[7],owing to its higher thermal stability.However,the brittleness of the Laves phases is the biggest obstacle to it until now.In this paper,the possibility of the kink-band formation in Mg/Laves-phase eutectic alloys and the controlling factors are discussed,for the establishment of a strategy for developing the novel high-strength structural materials.

2.Experimental procedure

Mother alloys with a nominal composition of Mg-10.7Yb(at%) and Mg-10.5Ca (at%) were fabricated by furnace melting.The alloy compositions correspond to the eutectic composition of Liquid→Mg+Mg2Yb/Mg2Ca Laves phases in their phase diagrams [28].Using the mother alloys,directional solidification treatments were conducted in a Bridgman furnace in an Ar gas atmosphere in a carbon crucible with a crystal growth rate of 10.0mm/h.The size of the obtained rod-like DS crystal wasφ12mm in diameter and～15cm in length.The melting of the mother alloys was conducted at 850°C,and the temperature gradient in directional solidification was～70°C/mm.

The constituent phases were examined using energy dispersive X-ray spectroscopy (EDS) in scanning electron microscopy (SEM).The crystal orientation relationship between phases was examined by electron backscatter diffraction (EBSD) in SEM.In the EBSD analyses,it was difficult to distinguish the Mg and Laves phases owing to their similarc/aratios (c/a=～1.62 in Mg [29],Mg2Yb [30],and Mg2Ca[31]).Thus,the EBSD analyses were conducted using only the Mg data,and the phases were classified with EDS.

The mechanical properties of the alloys were examined by compression tests.Rectangular specimens approximately 2×2×5mm3in size were cut using electrodischarge machining.Compression tests were conducted along two different loading axes aligned parallel to and inclined 45° with respect to the growth direction.Hereafter,these loading orientations are called the 0° and 45° orientations,respectively.Compression tests were performed at a nominal strain rate of 1.67×10-4s-1at temperatures ranging from room temperature (RT) to 400°C in vacuum.We especially focus on the results obtained for the Mg-Yb alloy in this paper,since the precise crystallographic analysis using EBSD was somewhat difficult for Mg-Ca alloys owing to severe surface oxidation.The details on Mg-Ca alloys will be described elsewhere.

3.Results

Fig.1(a) and (b) shows the microstructures of the directionally solidifies (DS)Mg/Mg2Yb eutectic alloy,observed on transverse and longitudinal sections with respect to the growth direction.An aligned lamellar microstructure whose interface is parallel to the growth direction developed.As shown in Fig.1(c) and (d),a similar lamellar microstructure developed in the DS Mg/Mg2Ca alloy.The average thicknesses of the lamellae were also similar:～2.1 and～2.8 μm in Mg-Yb and Mg-Ca,respectively.However,the details of these lamellar microstructures are slightly different.In the Mg/Mg2Ca alloy,the aligned lamellar microstructure almost fully covered the entire surface,while regions with different morphology coexisted in the Mg/Mg2Yb alloy with an interval of～50 μm,as indicated by arrows in Fig.1(a) and (b).At the narrow regions,the alignment of lamellae was locally collapsed as shown in Fig.2.

Fig.3(a)and(b)shows the typical crystal orientation maps obtained with SEM-EBSD on a transverse section in the Mg-Yb alloy.In addition,pole figure measured at Points A-D in Fig.3(a) and (b) are displayed in Fig.3(c) and (d),respectively.From the analyses,some crystal orientation relationships between Mg and Mg2Yb were identified in the lamellae as follows:

Case A was predominately observed in many lamellae,but lamellae with a different relationship (e.g.,Case B) were also confirmed with some frequency.

Fig.4 shows the temperature and loading orientation dependencies of the yield stress of Mg/Mg2Yb alloys.The yield stress and following plastic deformation behavior are strongly anisotropic owing to the lamellar microstructure.In the 0°orientation,all specimens fractured without exhibiting plastic strain below 200°C,and plastic deformation was only possible at and above 300°C.In the 45° orientation,plastic deformation was possible at and above 200°C with a lower yield stress.The yield stress monotonically decreased as the temperature increased,regardless of the loading orientation.For Mg/Mg2Ca alloys,plastic deformation was only possible at and above 400°C in the 0° orientation with a higher yield stress than that in Mg/Mg2Yb.

Fig.1.Microstructures of the DS (a,b) Mg/Mg2Yb and (c,d) Mg/Mg2Ca eutectic alloys observed on (a,c) transverse and (b,d) longitudinal sections with respect to the growth direction.Higher-magnification images are inserted at the left bottom corners in (b) and (d).

Fig.2.Higher magnification image of the microstructure in the DS Mg/Mg2Yb eutectic alloy observed on the longitudinal section.Aligned lamellar microstructure was locally collapsed as indicated by red arrows.

Fig.5 shows the typical stress-strain curves of Mg/Mg2Yb alloys compressed at various temperatures.In the 0° orientation,some specimens could be deformed at 300°C but fractured just after yielding with～0.3% plastic strain.However,significant plastic deformation was possible at 400°C.In contrast,greater than 5% deformation was possible at 300°C in the 45° orientation.The shape of the stress-strain curve was different depending on the loading orientation.The flow stress drastically decreased just after yielding;that is,a yield drop occurred,and a plateau region for the flow stress with a low work-softening rate followed in the 0° orientation.Yield drop was observed also in the 45° orientation,but the decrease in the flow stress was rather small in the 45° orientation.In Fig.5,the stress-strain curves for Mg/Mg2Ca alloys deformed at 400°C are displayed for comparison.In Mg/Mg2Ca alloys,the yield drop in the 0° orientation was more significant in appearance than that in Mg/Mg2Yb.

Fig.3.(a,b) Typical crystal orientation maps analyzed using SEM-EBSD in the transverse section of the DS Mg/Mg2Yb alloy.(c,d) Pole figure measured at positions (c) A and B and (d) C and D,as indicated in (a) and (b).The distinction of the phases was conducted with the help of EDS analysis.

Fig.4.Temperature and loading orientation dependencies of the yield stress of the DS Mg/Mg2Yb and Mg/Mg2Ca alloys.

Fig.6(a)and(b)shows the deformation markings observed in Mg/Mg2Yb specimens deformed to～5% plastic strain at 400°C along the 45° and 0° orientations,respectively.In the 45°-oriented specimen,shear deformation occurred nearly parallel to the lamellar interface.Shear deformation occurred locally in some specific lamellar grains,resulting in several large steps on the side surface of the specimen,as indicated with arrows.In contrast,many beak-like deformation bands were introduced nearly perpendicular to the lamellar interface in the 0°-oriented specimen.As confirmed in the high magnification image of the deformation microstructure shown in Fig.6(c),the lamellar interface was observed to have a large amount of bending in the deformation bands.The formation of deformation bands was confirmed also in the Mg/Mg2Ca eutectic alloy in the 0°orientation as shown in Fig.6(e).However,their sizes were significantly different.In the Mg/Mg2Ca specimens,only a few large deformation bands formed at the end edges of the specimens,while small beak-like deformation bands were abundantly and homogeneously introduced in the Mg/Mg2Yb specimens.

Fig.5.Typical stress-strain curves for the Mg/Mg2Yb alloys deformed in the 0° and 45° orientations at various temperatures.The stress-strain curves for the Mg/Mg2Ca alloys deformed at 400°C are also displayed for comparison.

Fig.6.OM images showing the deformation markings in the deformed(a-c)Mg/Mg2Yb and(d-f)Mg/Mg2Ca alloys to～5%plastic strain at 400°C,deformed in the (a,d) 45° and (b,e) 0° orientations.(c,f) Higher-magnification images of the deformation bands introduced during deformation in the 0° orientation.

The deformed Mg/Mg2Yb specimen was further analyzed using SEM-EBSD to examine the crystallographic features of the deformation bands.Fig.7(a) shows typical crystal orientation maps showing the deformed region.Introduction of many deformation bands can be recognized by the bending of lamellae,as indicated by black arrows.The examination of the deformation bands was conducted in some specimens deformed under the same condition;at 400°C to～5% plastic strain.As the summary,Fig.7(b) shows the distribution of the crystal rotation angle with respect to the matrix(undeformed region) in the deformation bands.The rotation angle is define as shown in the schematic in the graph.As shown in Fig.7(b),the crystal rotation angle has a wide distribution ranging from～5° to～70°.This feature is different from that observed in the deformation twin,in which the crystal rotation angle is fixed because they possess a definite crystal orientation relationship with respect to the matrix.The results in Fig.7(b) demonstrate that the deformation bands are not deformation twins but are the deformation kink bands,similarly to those observed in the Mg/Mg17Al12eutectic alloy[8].

Fig.7(c) and (d) shows crystal orientation maps of typical deformation kink bands.The colony grains in Fig.7(c)and (d) correspond to those shown in Fig.3(a) and (b),respectively.That is,the lamellae in Fig.7(c) and (d) satisfied the “Case A” and “Case B” orientation relationships,respectively.It is to note that kink bands formed when a stress was applied parallel to the lamellar interface,regardless of the difference in the crystal orientation relationship between Mg and Mg2Yb,as shown in Fig.7(c) and (d).In Fig.7(c)and (d),the loading orientation and the crystal rotation axis in the kink band with respect to the undeformed region were measured between the points indicated by black circles in the Mg and Mg2Yb phases.

Fig.7.(a) Typical crystal orientation maps measured in the Mg/Mg2Yb specimen deformed to～5% plastic strain at 400°C in the 0° orientation using SEM-EBSD.(b) Distribution of the crystal rotation angle in the deformation bands with respect to the matrix (undeformed region).(c,d) Higher-magnification crystal orientation maps showing the typical deformation bands.The colony grains in (c) and (d) correspond to those shown in Fig.3(a) [Case A] and Fig.3(b) [Case B],respectively.

The measurement results are plotted in the stereographic projections in Fig.8(a) and (b).The results demonstrate that the rotation axis in the kink band varied depending on the crystal orientation relationship of lamellae.For the kink band shown in Fig.7(c),the crystal rotation axes are～＜0001＞and＜1100＞in Mg and Mg2Yb,respectively.On the other hand,they are～＜1100＞and～＜110＞in Mg and Mg2Yb,respectively,in the kink band shown in Fig.7(d).It must be emphasized that in both kink bands,the crystal rotation axis was located almost perpendicular to the loading orientation and the normal of the lamellar interface in both phases,regardless of the difference in the crystal orientation relationship of lamellae.

4.Discussion

In this study,we firs found that kink-band formation can be induced in directionally solidifies Mg/Mg2Yb and Mg/Mg2Ca eutectic lamellar alloys when a stress is applied parallel to the lamellar interface.This gives the large ductility to the alloy accompanied by a high yield stress;nevertheless the brittleness of the Mg2Yb and Mg2Ca Laves phases is a serious concern until now.

Regarding the formation mechanism of the kink band,Yamasaki et al.previously reported in their study used the LPSO phase and Zn that the crystal rotation axis in a deformation kink band is geometrically determined as the direction perpendicular to the shear direction and the slip plane normal of the dislocations that form the kink-band boundary [32,33].The measured results are in good agreement with this,assuming that only dislocations whose slip plane is parallel to the lamellar interface can be operative owing to the constraint of the lamellar interface during deformation in the 0° orientation and that they form the kink band.In this situation,the crystal rotation axis must be perpendicular to the loading orientation and the normal of the lamellar interface in the kink band.

Fig.8.(a,b) Stereographic projections showing the geometric relations of the loading axis,lamellar interface,and rotation axis in the deformation kink bands shown in Fig.7(c) and (d),respectively.The crystal rotation axes were measured between the points indicated by the black circles in Fig.7(c) and (d),i.e.,between A-B and B-C in Fig.7(c) and between D-E and E-F in Fig.7(d).

The operative slip systems in Mg are well studied;(0001)＜110＞ basal,{1100}＜110＞ prismatic,and{112}＜11＞ and {1011}＜11＞ pyramidal slips are plausible [34,35].In the kink band shown in Fig.7(c),assuming the operation of (1100)[110] prismatic slip whose slip plane is parallel to the lamellar interface,the formation of a kink band with a [0001] rotation axis can be explained since the crystal rotation axis is perpendicular to both the slip plane normal and shear direction [left projection in Fig.8(a)].On the other hand,for the kink band shown in Fig.7(d),assuming (112)[11] pyramidal slip whose slip plane is parallel to the lamellar interface,the formation of kink band with a [1100] rotation axis can be explained [left projection in Fig.8(b)].

Compared to Mg,there are few studies on the operative deformation modes of the C14 Laves phase.For bulk C14-MgZn2single crystals,the operative deformation mode in this phase is predominantly (0001)＜110＞basal slip [36].However,Zehnder et al.reported other plausible operative deformation modes in C14-Mg2Ca from micropillar compression tests:{1100}＜110＞prismatic,{1011}＜110＞pyramidal,and {112}＜113＞pyramidal slip systems in addition to (0001)＜110＞basal slip [7].Even if the operation of these slip systems is assumed,however,the crystal rotation axes measured in the kink bands in Mg2Yb shown in Fig.8(a) and (b) cannot be explained.This implies that kink-band formation in Mg/Mg2Yb eutectic alloys is predominantly governed by soft Mg,and a complicated accommodation process may follow in Mg2Yb.However,we suppose that this is not derived from the fact that Mg is softer than Mg2Yb but ascribed to the crystallographic features of the lamellar interface.This is because the conclusion obtained in this study is different from that for the Mg/Mg17Al12alloy,for which hard Mg17Al12governs kink-band formation[8].In the Mg/Mg17Al12eutectic alloy,the {110} slip plane in Mg17Al12is parallel to the lamellar interface but is not in Mg.Our results suggest that the mechanisms controlling kink-band formation significantly vary depending on the geometric relationship between the operative slip plane and the lamellar interface.To prove this conclusion,further studies on kink-band formation in other alloys are required.

Another notable feature is the large variation in the kinkband morphology among alloys.Only a few large kink bands formed in Mg/Mg2Ca,while many small kink bands homogeneously formed in Mg/Mg2Yb.This variation in kink-band morphology is considered to be derived from the difference in the microstructures of the DS alloys.As indicated in Fig.1(c)and (d),an aligned lamellar microstructure almost perfectly develops in Mg/Mg2Ca,but regions where the alignment of lamellae is disturbed coexist with an interval of～50 μm in the Mg/Mg2Yb alloy,as indicated by the arrows in Fig.1(a) and (b).These regions may act as nucleation sites for kink-band formation via stress concentration and assist with the homogeneous formation of small kink bands.Related results were previously reported in Mg/Mg17Al12alloys[8].In the alloys,only a few large kink bands form in a fully lamellar-microstructured alloy,but the introduction of primary Mg17Al12grains enables the homogeneous formation of small kink bands,enhancing ductility.The partly disturbed lamellar microstructures may play the same role as the primary grains in Mg/Mg17Al12.Homogeneous small-kink-band formation induces plastic deformation without the formation of microcracks [Fig.6(c)],leading to a decrease in the possible deformation temperature in Mg/Mg2Yb (300°C) relative to that in Mg/Mg2Ca (400°C).

Our results demonstrate that the formation of kink bands can occur in some metallic materials in which an aligned lamellar microstructure exists,even though the constituent phase is the brittle intermetallic phase.The sandwich of brittle phase by softer phase (in this case Mg) effectively prevents the catastrophic fracture of the brittle phase.Then,the harder brittle phase prevents the easy propagation of shear strain across the lamellar interface and restricts the deformation only parallel to the lamellar interface,which induces the kink-band formation.Thus,the“mille-feuille microstructure control”approach has a potential to drastically increase the strength of alloys with keeping a ductility,via the kink-band formation.It is especially effective for high-temperature strengthening,where other hardening mechanisms such as precipitation hardening and grain-refinement hardening etc.lose their effects,as shown in Fig.4.

On the other hand,the present results indicate that the large plastic deformation of Mg/Laves-phase composite along the direction parallel to the lamellar interface is possible only at temperatures above 300°C,and the room-temperature ductility is not obtained by the kink-band formation.This is a different feature that observed in LPSO phases [20-22].The reason of this must be clarified and it must be improved in future research for realizing the practical application of this material.

It was clarified in this study that the kink-band formation behavior shows strong orientation dependence.Thus,the fabrication of textured materials is strongly required for practical application of the mille-feuille materials to bring out the superior mechanical properties.However,it is also necessary to study the effect of kink-band formation on the deformation behavior of random-textured polycrystalline materials in future research,in order to expand the practical field.

As the strategy to control kink-band formation behavior in mille-feuille materials,the present study demonstrated that a microstructure that provides nucleation sites for kink-band formation is important.The studies to clarify the further details on the formation criteria of the kink band;for example,in what kind of combination of phases the kink-band formation occurs or not,are strongly required to develop millefeuille materials with superior mechanical properties.

5.Conclusion

(1) In the deformation of directionally solidifies Mg/Mg2Yb and Mg/Mg2Ca eutectic lamellar alloys,kink-band formation can be induced when a stress is applied parallel to the lamellar interface.This leads to a high yield stress accompanied with ductility;nevertheless the brittleness of the Mg2Yb/Mg2Ca C14-type Laves phases is a serious concern until now.

(2) Kink-band formation in Mg/Mg2Yb eutectic alloys is predominantly governed by soft Mg.This is not derived from the fact that Mg is softer than Mg2Yb,but is ascribed to the crystallographic features of the lamellar interface.The slip plane in Mg is parallel to the lamellar interface but is not in Mg2Yb in the lamellar microstructure.

(3) The existence of partly disturbed lamellar microstructures in Mg/Mg2Yb plays an effective role for inducing the homogeneous small-kink-band formation in the alloy.This enables the plastic deformation without the formation of microcracks,leading to a decrease in the possible deformation temperature in Mg/Mg2Yb(300°C) relative to that in Mg/Mg2Ca (400°C).

Declaration of Competing Interest

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.

CRediT authorship contribution statement

Koji Hagihara:Conceptualization,Investigation,Methodology,Validation,Writing -original draft.Kosuke Miyoshi:Investigation,Writing -review &editing.

Acknowledgments

This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI for Scientifi Research on Innovative Areas "MFS Materials Science" (Grant Numbers:JP18H05478 and JP18H05475).This work was also partly supported by the Light Metals Educational Foundation of Japan.

Data availability

The raw/processed data required to reproduce these find ings cannot be shared at this time as the data also forms part of an ongoing study.