Correlation between microstructure and mechanical properties of columnar crystals in the directionally solidifie Mg-Gd-Y-Er alloy

D.R.Fang ,S.S.Zhao ,X.P.Lin,* ,T.Chai ,Y.Kuo ,H.Sun ,Y.Dong

aSchool of Materials Science and Engineering,Northeastern University,No.11,Alley 3,Wenhua Road,Heping District,Shenyang,China

b School of Resources and Materials,Northeastern University at Qinhuangdao,Qinhuangdao 066004,China

Abstract The Mg-4.58Gd-0.45Y-0.01Er alloys with different volume fractions of columnar crystals in hard orientation (orientation factor of ＜a＞basal plane slip system is less than 0.2) were prepared by changing the pulling rate to regulate the crystal growth orientation.Tensile tests were performed on the Mg-4.58Gd-0.45Y-0.01Er alloy at room temperature,and the structure after deformation was investigated by electron backscatter diffraction (EBSD).Subsequently,the strengthening mechanism of columnar crystals in hard orientation was explored.The results show if orientation factors of ＜a＞basal plane slip system of columnar crystals are all greater than 0.4 (soft orientation),the alloy has low yield strength σs (64MPa),but great work hardening ability,and ultimate tensile strength σb and elongation δ are 114MPa and 37.3%,respectively.If orientation factors of ＜a＞basal plane slip system of columnar crystals are all less than 0.2 (hard orientation),the alloy has high strength (σs, 125MPa),but poor plasticity (δ,6.32%).If the “hard orientation” and the “soft orientation” columnar crystals are arranged alternately along the direction perpendicular to the crystal growth,the alloy has both superior strength (σs, 102MPa) and excellent plasticity(δ,22.5%) at room temperature.The improved comprehensive mechanical property can be attributed to two factors.On the one hand,the“hard orientation” columnar crystals can prevent the “soft orientation” crystals deforming,so the strength is improved.On the other hand,the “hard orientation” columnar crystals themselves can withstand a certain amount of deformation to retain appropriate plasticity.

Keywords: Directional solidification Mg-Gd-Y-Er alloy;Hard orientation;Mechanical properties.

1.Introduction

The development of high-strength cast magnesium alloys and tailoring of solidifie structures have become a hot topic at present [1,2].Studies have shown that the solidificatio structure,especially the grain morphology and crystal orientation,have a decisive influenc on mechanical properties and deformation behavior of magnesium alloys [3].In general,cast magnesium alloys often exhibit lower strength,especially poor plasticity at room temperature due to plenty of dendrites and coarse grains,as well as poor strain coordination of grain boundary [4].Therefore,tailoring the solidifica tion structure,designing and optimizing the grain morphology and orientation distribution,and improving the grain boundary strain coordination have become the key issues to be solved for developing cast magnesium alloys with high strength and toughness.

Directional solidificatio is a technology making the alloys grow along required direction during solidificatio to form columnar grains with a specifi crystal orientation [5].The columnar structure has similar geometric characteristics to bicrystals,and the constraint conditions for grain boundaries during deformation can be reduced from 5 to 3,compared with equiaxed crystals [6].Therefore,it is expected that the columnar structure with reduced grain boundary constraints will be more significan to improve the grain boundary strain coordination of HCP magnesium alloy with only two independent slip systems at room temperature.

The application of directional solidificatio technology to magnesium alloys is still in the exploratory stage relative to Ni alloys and Fe alloys.The research mainly focuses on two aspects.Grain morphology and mechanical properties at room temperature of directionally solidifie magnesium alloy.Mamoru Mabuchi et al.studied the properties of directionally solidifie AZ91 alloy [7] and found that the tensile strength(σb)and the elongation(δ)at room temperature were 290MPa and 10.4%,respectively,which were higher than those of the non-directionally solidifie alloy (199MPa and 5.0%).Liu et al.[8] reported the properties of directionally solidifie Mg-3.0Nd-1.5Gd alloy and found thatσbandδincreased from 78MPa and 8% to 138MPa and 12% (100μm/s),respectively.Wang et al.[9,10] investigated the structure evolution and mechanical properties of directionally solidifie MgxGd(x=1.38,2.35,4.38 wt.%)alloys,and the results showed that the temperature gradient (G),withdrawal rate (υ) and alloy composition could affect the grain morphology and the primary arm spacing,thus changing the mechanical properties of the alloy.Effects of process parameters on crystal orientation.Yang et al.[11] studied the effect of the withdrawal rate on the crystal growth orientation of Mg-14.61Gd alloy by experiments and finit element methods,and found that the growth orientation ofα-Mg changed from＜110＞and＜100＞to＜110＞whenυincreased from 10μm/s to 100μm/s.Pettersen et al.[12] studied the crystal growth orientation of directionally solidifie AZ91 alloys,they pointed out that the growth orientation was＜110＞at low G and highυ,and＜225＞at high G and lowυ.Du [13] reported that the growth orientation ofα-Mg changed from＜113＞to＜225＞with the increase of Al content and from＜113＞to＜225＞or＜112＞with the increase of Zn content for Mg-Al and Mg-Zn alloys.Shuai et al.[14] studied the directionally solidifie Mg-38% Zn alloy,they believed that the growth direction ofα-Mg grains was＜211＞,instead of the previously reported＜110＞and＜225＞[15,16].Salgado-Ordorica et al.[17]found that the growth orientation of directionally solidifie Mg-RE alloys were＜101＞and＜307＞.However,there are few reports on the relationship between crystal growth orientation and mechanical properties of directionally solidifie Mg alloys.Molodov [18,19] studied the mechanism of ductility and abnormal ductility of magnesium single crystal at room temperature,it was found that crystal growth orientation had a profound effect on the ductility,which was related to the deformation mechanism such as the twinning modes,the evolution of twin variants and dynamic recrystallization.

Mg-Gd alloys have attracted much attention due to excellent mechanical properties in the fiel of directional solidifi cation of magnesium alloys.Mg-Gd-Y alloy can be used to manufacture important aerospace equipments,such as cabin structure [20].In our previous research on the structure of directionally solidifie Mg-Gd-Y alloys,larger primary arm spacing of columnar crystals was observed [21].Therefore,a small amount of Er will be added to the Mg-Gd-Y alloy to refin the structure of the alloy,because Er is considered to be a beneficia element to improve the structure of magnesium alloys[22,23].In the present work,we try to further study the effect of directional solidificatio parameters on the structure and the crystal growth orientation of Mg-Gd-Y-Er alloys,as well as the correlation between the microstructure and tensile properties of the alloy.It is expected to reveal the mechanism improving the mechanical properties at room temperature,and help to provide theoretical basis and new technologies for the development of high-performance magnesium alloys.

2.Experimental

The alloy ingots were prepared from Mg-30Gd,Mg-30Y and Mg-10Er (wt.%) master alloy and pure Mg (purity 99.99%) using a self-made directional solidificatio furnace (vacuum degree:2.4×10-6Pa) with induction heating melting,pouring and pulling devices.In order to regulate the grain morphology and the crystal growth orientation of the alloy,the temperature gradient at the front edge of the solid/liquid interface was adjusted by altering pouring temperature (860～780°C) and cooling device temperature,and the solidificatio rate was controlled by the changing pulling rate,moreover,it’s also necessary to adjust Gd and Er content.After many experiments,the chemical composition of the alloy is determined to be 4.58% Gd,0.45% Y,0.01% Er and Mg balance (measured by ICAP6300 plasma spectrometry).Considering the parameters of the directional solidificatio equipment and the factors of high-temperature and volatile magnesium alloy melt,the temperature gradient is set at 100k/cm.Meanwhile,crystal orientation and primary arm spacing of the alloy was controlled by pulling rate.Pulling rate is 3mm/min,5mm/min,7mm/min,9mm/min and 11mm/min,respectively.

The specimens for tensile tests were cut along the longitudinal section of the directionally solidifie ingots by spark cutting technique.Their dimension is shown in Fig.1a(GB/T4338-2006).Uniaxial tensile tests was performed using a WWD3100 testing machine at a strain rate of 0.0001 s-1at room temperature,and the tensile stress was parallel to the crystal growth direction.

Microstructure of the Mg-Gd-Y-Er alloy was observed using an optical microscope (OM).The grain orientation was analyzed using a Smartlab X-ray diffraction (XRD),the angle range was 20°-80° and the scanning step was 0.02°.In addition,EBSD tests were carried out using the EDAX TSL(Mahwah,NJ) OIM EBSD system attached to a SUPRA-55 scanning electron microscope(SEM).EBSD samples were cut from different positions (see Fig.1b) away from the fracture of the tensile specimens after tensile tests,then mechanically ground on 800～5000# sandpapers,subsequently electrolytic polished in a solution of 30% nitric acid alcohol,followed by ion thinning.

Fig.1.Illustration of the tensile specimen (a) and the sample area for EBSD experiments (b).

Channel 5 software was used to obtain data such as crystal orientations,grain boundary misorientation,stress (strain)distribution,twins and low-angle grain boundaries during deformation,and to calculate the Schmid factor of the basal slip systems and twin type of various grains (grain boundary),further to study the correlation between the grain orientation,grain boundary misorientation and grain boundary strain coordination [24,25].Different grain boundaries are distinguished by colors during analyzing EBSD data.The blue lines represent low-angle grain boundaries with misorientation of 2°～15°,the red lines indicate {102} tensile twins with misorientation of 86°＜10＞,the yellow lines represent {101}compressive twins with misorientation of 56°＜110＞,the green lines indicate {101}-{102} double twins with misorientation of 38°＜110＞,and the black thin lines represent high-angle grain boundaries with misorientation greater than 15°.

3.Results and discussion

3.1.Effect of pulling rate on the microstructure of the Mg-Gd-Y-Er alloy

Fig.2 shows microstructure of the directionally solidifi cated Mg-Gd-Y-Er alloy at different pulling rate.It can be seen that the solidificatio structure is columnar polycrystal that grow along the direction of heat fl w,and longitudinal grain boundaries are relatively straight.The average primary dendrite arm spacing of the columnar crystals gradually decreases with increasing pulling rate,from 115μm and 105μm at 3mm/min and 5mm/min to 85μm and 70μm at 7mm/min and 11mm/min.According to the Hunt equation [26],when the temperature gradient is constant,the faster the pulling rate is,the faster the growth rate of the interface is,so the primary dendrite arm spacing is smaller.

Fig.2.Optical Microstructure images of the directionally solidificate Mg-Gd-Y-Er alloy at different pulling rate,(a) 3mm/min;(b) 5mm/min;(c) 7mm/min;(d) 11mm/min.

Fig.3.XRD patterns of directionally solidifie Mg-Gd-Y-Er samples prepared at different pulling rates.

3.2.Effect of pulling rate on preferred growth orientation of the Mg-Gd-Y-Er alloy

Fig.3 is XRD patterns of directionally solidifie Mg-Gd-Y-Er samples prepared at different pulling rates.The relative peak intensity ratio Im(m,different pulling rates) can be obtained from Fig.3,and Im/I0is listed in Table 1.(I0,the standard diffraction peak intensity of pure Mg powder in PDF cards).

Table 1 Im and Im/I0 of the Mg-Gd-Y-Er alloy.

According to Fig.3 and Table 1,it’s known that the preferred crystal growth plane of columnar crystals is mainly (102),then (103),when the pulling rate is 3mm/min and 5mm/min.It is mainly (103),then(102),when the pulling rate is 7mm/min.It’s only (1120)at 9mm/min and 11mm/min.In summary,the preferred growth crystal plane reveals a trend to change from(102)+(103)→(103)+(102)→(110) as the pulling rate increases.

Fig.4 shows Euler diagrams and corresponding inverse pole diagrams of the columnar crystals at pulling rate of 5mm/min,7mm/min and11mm/min,respectively.It can be seen from Fig.4a the angle between the c-axis of Mg crystal cells and the crystal growth direction (heat fl w direction) is about 35°～38° at a pulling rate of 5mm/min,and the growth orientation is highly consistent along the OX0direction,concentrated in＜313＞.By calculation,the Schmid factors(SF)of＜a＞basal slip system of the columnar crystals are greater than 0.4,which are all in soft orientation.That is,the arrangement rule of the columnar polycrystal along the direction perpendicular to the growth direction is “soft orientation/soft orientation/soft orientation”.It can be known from Fig.4b that the angle between the c-axis of Mg cell and the crystal growth direction (heat fl w direction) is 83°～88°,and the crystal growth direction is mainly concentrated in＜1210＞at a pulling rate of 11mm/min.By calculation,the Schmid factors of＜a＞basal slip system of the columnar crystals are less than 0.2,which are all in hard orientation.In other words,the arrangement rule of the columnar polycrystal along the direction perpendicular to the growth direction is “hard orientation/hard orientation/hard orientation”.According to Fig.4c,when the pulling rate is 7mm/min,the crystal growth orientation is mainly concentrated in two zones,i.e.the lines of [1210]-[0110] (soft orientation) and [0001]-[1210] (hard orientation).Therefore,the arrangement rule of the columnar polycrystal is “soft orientation/hard orientation/soft orientation/hard orientation”,i.e.the “soft orientation” and the“hard orientation” columnar crystals are arranged alternately perpendicular to the growth direction.

It follows that the preferred growth crystal plane and orientation change with increasing pulling rate when the alloy composition and temperature gradient are constant.When the pulling rate is less than or equal to 5mm/min,the preferred growth crystal plane is mainly (1012),then (1013),and the preferred growth orientation is＜313＞.When the pull rate is greater or equal to 11mm/min,the preferred growth crystal plane is (110) and the preferred growth orientation is＜1210＞.When the pulling rate is 7mm/min,the preferred growth crystal plane is mainly (1013),then (1012),and the preferred growth orientation is distributed in two orientation regions on the lines of [1210]-[0110] and [0001]-[1210].

3.3.Effect of the pulling rate on room temperature mechanical properties of the Mg-Gd-Y-Er alloy

Fig.4.EBSD orientation images and the corresponding inverse pole diagrams of the directionally solidifie Mg-Gd-Y-Er alloy,(a) pulling rate:5mm/min,(b) pulling rate:11mm/min,(c) inverse pole diagrams (OX direction).

Fig.5.Tensile properties of the Mg-Gd-Y-Er specimens at different pulling rates at room temperature,(a)tensile engineering stress-strain curves,(b)dependence of strength and plasticity on the pulling rate.

Fig.5 shows the tensile properties of the Mg-Gd-Y-Er specimens at different pulling rates at room temperature.As can be seen,when orientation factors of＜a＞basal plane slip system of column crystals are all greater than 0.4,the yield strength(σs)of the alloy is relatively low,but the curve shows a long uniform plastic deformation stage after yield.Theσsandσbof the alloy prepared at a pulling rate of 5mm/min are 65MPa and 114MPa,respectively,and the elongation (δ)is 37.3%,it’s clear that the alloy has great room temperature plasticity,good work hardening ability and sufficien tensile strength.In contrast,when orientation factors of＜a＞basal plane slip system of column crystals are all less than 0.2 theσsof the alloy is 125MPa at a pulling rate of 11mm/min,but the alloy specimen breaks after a short deformation stage after the yield point andδis only 6.32%.Moreover,the alloy’sσbis only 15MPa higher than itsσs.When the columnar crystal with orientation factor＞0.4 and the columnar crystal with orientation factor＜0.2 are arranged alternately (pulling rate:7mm/min),theσsof the alloy is 100MPa,53.8% higher than that of the alloy prepared at a pulling rate of 5mm/min.However,the strain hardening rate of the alloy (7mm/min) is lower than that of the alloy (5mm/min).The ultimate tensile strengthσbof the alloy (7mm/min) reaches 122MPa,andδis maintained at 22.50%,which is better than the currently reported cast magnesium alloys [2,27].It is evident that the“soft orientation/hard orientation/soft orientation/hard orientation” alloy has excellent comprehensive mechanical properties.

Fig.6.EBSD diagrams of the sample cut from the arc area of the tensile specimen (pulling rate:5mm/min),(a) Euler diagram,(b) twin type diagram,(c)misorientation distribution (inset is inverse pole diagram),(d) Kernel Average Misorientation (KAM) figure

In conclusion,the crystal orientation and microstructure greatly affect the room temperature tensile properties of directionally solidifie alloys.Therefore,EBSD technology was used to further study the tensile deformation structure of the columnar polycrystalline alloy and explore its deformation mechanism.

3.4.Columnar crystal structure and tensile deformation structure

3.4.1.Tensile deformation structure of the “soft orientation/soft orientation/soft orientation” alloy

Fig.6 shows the diagrams from the EBSD experiment on the sample cut from the arc area of the tensile specimen(pulling rate:5mm/min).It can be calculated that the Euler angles (φ1,φ,φ2) of the columnar crystals A,B and C shown in Fig.6a are (52.0,91.5,40.5),(111.2,122.9,22.1)and (127.7,84.4,40.6),respectively.The angles between the c-axis of the Mg crystal cell and the tensile stress axis are 38.0°,38.5° and 38.1°,respectively,and the orientations are[314],[314] and [225],respectively,as shown in Fig.6c.Table 2 shows Schmid factors of two independent basal slip systems according to Euler angles of grains A,B and C,and yield strength calculated by formula (1) [28] (external stress corresponding to critical shear stress).

Table 2 Schmid factors of basal slip systems and yield strength [29].

Where cosφcosλis Schmid factor,andτis critical resolved shear stress (CRSS).According to Table 2,the SFs of＜a＞basal plane slip systems of the A,B and C are 0.480,0.474 and 0.485,respectively.However,it can be seen from Fig.6c that the crystal orientation of A and C deviates little from the OX axis,while the crystal orientation of B deviates much from the OX axis.During the deformation,in order to meet the mutual coordination and cooperation of the grains,two independent basal plane slip systems in grain B are activated,in addition,the {1012} tensile twin in grain B are also activated,as shown in Fig.6a and b.Furthermore,it can be known from Fig.6c that the misorientation between the twin and the matrix is 86±3°＜110＞.The calculation by the misorientation method show that the external force required to activate tensile twin variants (marked with Tb1,red lines in the Fig.6b) with only orientation ((1012) [1011]) is about 8.26Mpa.Further observations reveal that the number of twin variants in the grain boundary affecting zone of grain B (as shown by arrow B in the Fig.6b) is more than that in the crystal,and some twin variants have merged and expanded.The extended tensile twin grain boundaries are interwoven with the piled low-angle grain boundaries (blue lines) to form new high-angle grain boundaries nearly parallel to the original longitudinal grain boundaries (arrow B in Fig.6b),and the stress or the strain is also concentrated in the grain boundary affecting zone (Fig.6d).As a result of inhomogeneous deformation between adjacent grains,stress concentration makes the adjacent grains shearing along the grain boundary (grain boundary affecting zone).It’s believed that shearing of grain boundaries directly contributes to the deformation.

Fig.7.EBSD diagrams of the sample cut from the uniform plastic deformation area of the tensile specimen (pulling rate:5mm/min),(a) Euler diagram,(b)twin type diagram,(c) distribution map showing Schmid factor of basal slip,(d) KAM diagram.

No tensile twin variant are found in grain A and only low density low-angle grain boundaries are observed in the grains and at grain boundaries (Fig.6b),indicating that it only takes two independent basal slip systems to coordinate the grain boundary strain.However,a small amount of tensile twins variants are activated near the grain boundary of grain C to coordinate the grain boundary strain.

Hence one can see that＜a＞basal slip and tensile twins are the main deformation mechanisms for the columnar polycrystalline “soft orientation/soft orientation/soft orientation”alloy in the initial deformation.As a result of the lower CRSS of basal slip and tensile twin,less activating force is required.Moreover,owing to small misorientation between adjacent columnar crystals,the tensile twin variant only with one orientation can overcome the grain boundary obstruction and coordinate strain together with two independent basal slip systems.Accordingly,it has low yield strength.

Fig.7 shows the diagrams from the EBSD experiment on the sample cut from the uniform plastic deformation area of the tensile specimen (pulling rate:5mm/min).According to Fig.7a,the Euler angles (φ1,φ,φ2) of grains A,B and C during the uniform plastic deformation stage are (133.5,36.3,7.3),(83.9,138.7,52.1) and (32.1,81.4,54.9),respectively.The angles between the c-axis of the Mg crystal cell and the tensile stress axis are 64.6°,49.0° and 58.3°,respectively.And SFs of the＜a＞basal slip systems are 0.387,0.495 and 0.388,respectively.The deformation of grain B with higher SF is restricted by grains A and C with relatively lower SF.The {1012} tensile twin variants in grain B have merged and expanded,and extended twin boundaries forms zigzag longitudinal grain boundaries similar to high-angle grain boundaries,which will divide the matrix and changes the matrix’s orientation.As shown by arrow A in Fig.7c,SFs of the basal slip systems skimmed by the tensile twin boundary are lower than 0.193.The density of low-angle grain boundary piled up in columnar grains and longitudinal grain boundaries (A/B,B/C) increases significantl and there are twin boundary variants coordinating strain in the grain boundary affecting zone.Furthermore,it’s shown by arrow A in Fig.7a that the angle between the c-axis of Mg cell and the tensile stress axis turns to 85°in the grain boundary affecting zone of grian C at the B/C grain boundary after being engulfed by tensile twin boundaries.The basal slip system is in hard orientation (arrow B in Fig.7c),and the {1011} compression twinning and{1011}-{1012} double twinning are activated to coordinate grain boundary strain (arrow A in Fig.7b).Twin boundaries interweaves with the piled low-angle grain boundaries,resulting in stress or strain concentration,as shown in Fig.7d.The stress or strain is concentrated in the grain boundary affecting zone (arrow A in Fig.7d) and the area where the expanded tensile twin boundary interweaves with the piled low-angle grain boundaries (arrow B in Fig.7d).

Fig.8.EBSD diagrams of the sample cut from the area near the fracture of the tensile specimen (pulling rate:5mm/min),(a) Euler diagram,(b) twin type diagram,(c) distribution map showing Schmid factor of basal slip,(d) KAM diagram.

Therefore,during the deformation,plenty of slip initiates and proliferates,and dislocations are piled up near the longitudinal grain boundaries and twin boundaries,they are also interwoven and interact on each other.Extended twin boundaries forms zigzag grain boundaries similar to high-angle grain boundaries,which will divide the columnar crystal matrix.The orientation of the matrix engulfed by the tensile twins gradually turns to "hard orientation",and compression twin with high CRSS (76～153MPa) is activated to coordinate strain.In addition,the SF of＜a＞basal slip systems of some grains gradually decreases to reduce the resolved shear stress on the slip plane.Grain boundary hardening caused by the elastic incongruity of grain boundaries and the interaction between dislocations and grain boundaries during plastic deformation gradually increases the strain hardening rate of the alloy,that is,work hardening occurs.

Fig.8 shows the diagrams from the EBSD experiment on the sample cut from the area near the fracture of the tensile specimen (pulling rate:5mm/min).The tensile twin boundaries continue to merge and expand,finall disappear after engulfin the matrix,the basal slip systems of the matrix engulfed by the tensile twins is in hard orientation (Fig.8c).The c-axis of Mg cell of grain B is nearly perpendicular to the direction of tensile stress (89.8°),forming plenty of intersecting compression twin bands,as shown by the arrows in Fig.8b.High-density low-angle grain boundaries accumulate near the twin boundaries and they interact on each other,so the matrix is divided into multiple grains with different orientations,resulting in plenty of transverse grain boundaries which can damage the continuity of columnar crystal structure,and the stress and strain are concentrated in the area(as shown in Fig.8d).Eventually,microcracks emerge under tensile stress,until the alloy breaks.The angles between the c-axis of the Mg cells of the gains A and C matrix and the tensile stress axis are 59.9° and 59.8°,respectively,and the SF of the＜a＞basal slip systems is 0.43,and cracks initiate from hard-orientation grain B.This also shows that deformation of the columnar crystals is inhomogeneous under tensile load.

In addition,it is also observed that the orientation of the columnar crystal rotates with the increase of the strain during uniaxial tension,as shown in Fig.9.The angle (φ) between the c-axis of Mg cells of columnar crystals and the tensile stress axis at the initial stage of deformation is between 38.0°and 38.5° (Fig.9a).With the increase of strain,the angle (φ)increases gradually.In the stage of uniform plastic deformation,theφis between 49° and 65° (Fig.9b).However,Theφof the columnar crystals with microcracks is close to 90°.That is,from less than 45° to 45° and then to 90°.

Fig.9.The angle (φ) between the c-axis of Mg cells of columnar crystals and the tensile stress axis,(a) initial deformation stage,(b) uniform plastic deformation stage,(c) columnar crystals with microcracks.

This can be attributed to two reasons.On the one hand,The normal and shear stress of the external force perpendicular to the slip plane constitute a force couple,which makes the slip plane turning toward the external force axis,then the crystal also rotates.The angle between the Mg cells of columnar crystals and the tensile stress axis gradually turns from 36° to 45°,and then turns to 90.That is,the shear stress on the slip plane gradually increases to the maximum,then decrease.Thus,the slip will become difficult finall the alloy breaks.On the other hand,to coordinate the deformation of the grains,the grains not only slip along the single slip system with the most advantageous orientation but also slip by way of two independent basal slip systems,even twinning occurs,thus the deformation can change accordingly.Mutual restraint and promotion of adjacent grains cause a force couple,resulting in rotation of grains,which make the deformed grains continue deforming.

3.4.2.Tensile deformation structure of the “hardorientation/hard orientation/hard orientation” alloy

Fig.10 shows the diagrams from the EBSD experiment on the sample cut from the arc area of the tensile specimen(pulling rate:11mm/min).It can be calculated that the Euler angles (φ1,φ,φ2) of grains D,E and F matrix shown in Fig.10a are (6.8,65.2,22.8),(159.1,25.0,45.3) and (178.7,73.5,40.5),respectively.The angles between the c-axis of the Mg crystal cells and the tensile stress axis are 83.8°,81.3°and 88.8°,respectively.The growth orientations are [110],[221] and [210],respectively,lying at [1210] in the X0inverse pole diagram,as shown in Fig.10d.

Table 2 shows the activated＜a＞basal slip system,SF and the external force activating slip,calculated according to the Euler angles of grains D,E and F.It can be seen from Table 2 that SFs of the basal slip system of D,E and F are 0.11,0.15 and 0.02,respectively.The maximum external force activating the basal slip system is as high as 81MPa,dozens of times as many as that of “soft orientation” crystals.Since the angle between the c-axis of the Mg cell and the tensile stress axis is close to 90°,the {1011} compression twin initiates to coordinate strain.As shown in Fig.10b and Fig.10c,there are {1011} compression twins with misorientation of 56°＜110＞and 38°＜110＞relative to the matrix,{1011}-{1012} double twin variants and {1012} tensile twins in the matrix.Calculated according to Fig.10c,the proportion of compression twins(double twins)and tensile twins are 51.9%and 35.0%,respectively.

Fig.11 shows the diagrams from the EBSD experiment on the sample cut from the uniform plastic deformation area of the tensile specimen (pulling rate:11mm/min).During the continuous deformation,plenty of compression twin bands form in columnar crystals (see arrows in Fig.11a),and slip dislocations are accumulated(blue low-angle grain boundaries in Fig.11b) near the compression twin bands (Fig.11b)and they interact on each other,giving rise to form a lot of transverse grain boundaries similar to high-angle grain boundary(Fig.11c),which damages the continuity of the columnar crystals,thus generating a large area where the stress or strain concentrates in the crystal.As shown by the arrows in Fig.11d,the stress and strain concentration is even severe than that of the grain boundaries in the area where the highdensity low angle grain boundaries interweave with twin boundaries,and the area will be the source of microcracks under tensile stress.So the elongation of the “hard orientation/hard orientation/hard orientation” alloy is only 6.32%.

Fig.10.EBSD diagrams of the sample cut from the arc area of the tensile specimen (pulling rate:11mm/min),(a) Euler diagram,(b) twin type diagram,(c)misorientation distribution map,(d) inverse pole diagram,(e) KAM diagram.

Fig.11.EBSD diagrams of the sample cut from the uniform plastic deformation area of the tensile specimen (pulling rate:11mm/min),(a) Euler diagram,(b)twin type (low-angle grain boundary),(c) high-angle boundary,(d) KAM diagram.

Fig.12.EBSD diagrams of the sample cut from the uniform plastic deformation area of the tensile specimen (pulling rate:7mm/min),(a) Euler diagram,(b)twin type diagram,(c) KAM diagram,(d) Strain Contouring.

3.4.3.Tensile deformation structure of the “soft orientation/hard orientation/soft orientation/hard orientation” alloy

Fig.12 shows the diagrams from the EBSD experiment on the sample cut from the uniform plastic deformation area of the “soft orientation/hard orientation/soft orientation/hard orientation” tensile specimen (7mm/min).For the alloy specimen,the columnar crystal with orientation factor＞0.4(soft orientation) and the columnar crystal with orientation factor＜0.2 (hard orientation) are arranged alternately.It can be seen that there are plenty of {1012} tensile twins (red)and high-density low angle grain boundaries (blue) in the“soft orientation” grains A and C.Instead of merging and expanding as shown in Fig.7,the tensile twin boundaries fragment,twines and interweaves with high-density low angle grain boundaries.In the “hard orientation” grains B and D,there are high-density compression twin bands (yellow lines in Fig.12b),low-angle grain boundaries (blue lines),and tensile twin boundaries (red lines),and the compression twin bands are parallel (arrow A in Fig.12b) or crossed(arrow B in Fig.12b).It is shown that the “hard orientation”columnar crystals strongly restrict the deformation of the“soft orientation” columnar crystals.According to Fig.12c,the stress concentration mostly exists in the area where the twin boundaries interweave with low-angle grain boundaries in the “soft orientation” columnar crystals.The “hard orientation” columnar crystals also coordinate and cooperate deformation.It can also be seen from the Strain Contouring(CS) in Fig.12d that the dislocation distribution in the “hard orientation” grain B is relatively uniform,while that in the“soft orientation” grains A and C is not very uniform.The dislocation density at the position corresponding to the red area (stress or strain concentration) in Fig.12c is very high,even higher than that at grain boundaries.

According to the above calculation,the external force activating basal slip and tensile twins in“soft orientation”columnar crystals are less than 2MPa and 10MPa,respectively,while the external force activating basal slip system in “hard orientation” columnar crystals is 81MPa,and the external force activating compression twins is 300MPa.“Hard orientation” columnar crystals and “soft orientation” columnar crystals are arranged alternately to form a "two-phase" alloy with a layered structure similar to pearlite,and the “hard orientation” columnar crystals are equivalent to “second phase”strengthening the alloy.

When the "two-phase" alloy is subjected to tension,the slip occurs firstl in the “soft orientation” columnar crystals.The deformation of “soft orientation” columnar crystals is restricted by the adjacent “hard orientation” columnar crystals and must be coordinated with the deformation of the adjacent grains.On the one hand,the dislocation movement is restricted between the two “hard orientation” columnar crystals because the deformation of “soft orientation” columnar crystals is hampered.Thus plenty of tensile twin variants are activated in order to coordinate strain.subsequently,numerous dislocations and twin boundaries are intertwined,and it is very difficul to continue deformation,so the strength is improved.On the other hand,the “hard orientation” columnar crystals themselves can withstand a certain amount of deformation,and compression twins,double twins and tensile twins are activated to coordinate strain,so the alloy can still retain appropriate plasticity.

It follows that the plastic deformation of the "two-phase"alloy depends on the volume fraction of the“hard orientation”columnar crystals.It is assumed that the stain of the “soft orientation” columnar crystals is equal to that of the “hard orientation” columnar crystals,then mean fl w stress () of the alloy [30] at a given strain is

Wheref1andf2are the volume fraction of “soft orientation” and “hard orientation” columnar crystals,respectively,andf1+f2=1.σ1andσ2are fl w stress of “soft orientation”and “hard orientation” columnar crystals at a given strain,respectively.The mean fl w stress of the alloy will increase linearly with increasingf2.

For the “soft orientation/soft orientation/soft orientation”columnar polycrystalline alloy,f2is about zero,and the alloy has low yield strength (64MPa),but excellent plasticity (δ,37%).With the increase of f2,the yield strength of the alloy increases,but the plasticity decreases.When f2is about 50%and the “soft orientation” and “hard orientation” columnar crystals are arranged alternately,the alloy has superior yield strength (102MPa) and good room temperature plasticity (δ,22%).When f2rises to more than 90%,the alloy has high yield strength,but low plasticity (δ,6%).

Conclusions

(1) The directional solidificatio structure of the Mg-4.58Gd-0.45Y-0.01Er alloy is columnar polycrystal that grows along the direction of heat fl w,and their longitudinal grain boundaries are relatively straight.The average primary dendrite arm spacing of columnar crystals gradually decreases with increasing pulling rate.When the pulling rate is not more than 5mm/min,the preferred crystal growth plane is mainly (1012),and the preferential growth orientation is highly concentrated in＜313＞.When the pulling rate is greater than 9mm/min,the referred crystal growth plane is (110),and the preferential growth orientation is concentrated in [1210].When the pulling rate is 7mm/min,the preferred crystal growth plane is mainly (1013),and the growth orientation is distributed in two regions on the lines of [1210]-[0110] and [0001]-[1210].

(2) The yield strength of the “two-phase” alloy composed of “soft orientation” and “hard orientation” columnar crystals is related to the volume fraction of “hard orientation” columnar crystals (f2).Iff2is about zero(5mm/min),the alloy has low yield strength (σs,64MPa),but great work hardening ability,andσbandδare 114MPa and 37.3% respectively.Iff2is greater than 90% (11mm/min),the alloy has high strength(σs,125MPa),but poor plasticity (δ,6.32%).Iff2is about 50% (7mm/min),the alloy has both superiorσs(102MPa) and excellent plasticity (δ,22.50%).

(3) When the "two-phase" “soft orientation/hard orientation/soft orientation/hard orientation” alloy is subjected to tension,the “soft orientation” columnar crystals firs deform,but the deformation is hampered and dislocation movement is restricted between the two “hard orientation” columnar crystals.Thus plenty of tensile twin variants are activated in order to coordinate strain.Subsequently,numerous dislocations and twin boundaries are interwoven,and it is very difficul to continue deformation,so the strength is improved.In addition,the “hard orientation” columnar crystals themselves can withstand a certain amount of deformation,so that the alloy can still retain appropriate plasticity.Therefore,the columnar polycrystalline Mg alloy has both superior strength and excellent plasticity.

Declaration of Competing Interest

None.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos.51775099 and 51675092)and the Natural Science Foundation of Hebei Province(E2018501032 and E2018501033).