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    Microstructure,mechanical and corrosion properties of Mg-2Dy-xZn (x=0,0.1,0.5 and 1 at.%)alloys

    2014-04-21 02:16:52
    Journal of Magnesium and Alloys 2014年1期

    State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals,Lanzhou University of Technology,Lanzhou 730050,China

    Microstructure,mechanical and corrosion properties of Mg-2Dy-xZn (x=0,0.1,0.5 and 1 at.%)alloys

    Guangli Bi*,Yuandong Li,Shijun Zang,Jianbin Zhang,Ying Ma,Yuan Hao

    State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals,Lanzhou University of Technology,Lanzhou 730050,China

    Microstructure,mechanical and corrosion properties of as-cast Mg-2Dy-xZn(x=0,0.1,0.5,and 1)(at.%)alloys were investigated.The microstructures of the as-cast Mg-2Dy and Mg-2Dy-0.1Zn alloys mainly consisted of α-Mg phase and Mg24Dy5eutectic phase.With 0.5 at.% Zn addition,Mg12ZnDy phase with 18R-type long period stacking ordered(LPSO)structure and Mg2Dy phase precipitated at the grain boundaries.When the content of Zn is 1 at.%,only the Mg3Zn3Dy2phase formed in the α-Mg matrix.The electrochemical measurements and immersion testing results indicated that the Mg-2Dy-0.1Zn alloy exhibited the best corrosion resistance.It revealed that the morphology,scale, amount and distribution of the second phase have a great effect on the corrosion resistance of alloy.Additionally,the tensile testing results showed that the Mg-2Dy-0.5Zn alloy exhibited the higher tensile strength and good elongation,especially at 200°C.The improvement of mechanical properties was mainly due to the strengthening of LPSO phase and grain ref i nement of α-Mg.

    Mg-Dy-Zn alloy;Microstructures;Mechanical properties;Corrosion behavior

    1.Introduction

    From the view of energy saving and environment protection,lightweight property of the metallic structural materials is becoming increasingly important.Thus,as the lightest structural metallic materials,magnesium alloys have received considerable interest in recent years due to their low density, high stiffness and high specif i c strength[1].However,the development of Mg alloys is limited to some extent because of their poor high-temperature strengths and low corrosion resistance.

    It is well known that addition of rare earth(RE)elements to Mg alloys can not only enhance effectively the heat resistance by precipitation strengthening[2-4]but also improve corrosion properties by forming the oxide layer containing RE elements[5,6].Moreover,it has been reported that the addition of Zn can further remarkably enhance mechanical properties of Mg-RE based alloys both at room and elevated temperatures,especially for those Mg based alloys containing one or more kinds of high content heavy RE elements(RE=Y,Gd, Ho,Dy and Y-rich misch meta etc.)[7-11].Besides β′phase, the different ratios of Zn and RE could lead to the formation of other strengthening phases,such as I phase[7],W phase[8] and long period stacking ordered(LPSO)phase[9-11],thus resulting in different mechanical behaviors.Nie et al.have [12]reported that addition of 1-2wt.%Zn to Mg-6Gd alloy can signif i cantly enhance the hardening response and creep strength of the alloy due to the uniform and dense distributionof basal precipitate plates.An increase of hardness for the Mg-6Gd-1Zn-0.6Zr alloy in the as-quenched condition is attributed to the co-segregation of Gd and Zn atoms[13]. Kawamura et al.[14]have demonstrated that the Mg-2(at.%) Y alloy containing 1 at.%Zn prepared by rapidly solidif i ed power metallurgy(RS P/M)process exhibits a high yield strength of ~600 MPa and an elongation of about 5%at room temperature.The excellent mechanical properties of the alloy are mainly due to f i ne grain size and the formation of LPSO phase.In addition,the similar role of ref i ning microstructure and strengthening mechanical properties by the Zn addition was also reported in other Mg-RE1-RE2alloys[10,15,16]. For example,Liu et al.[10,15]reported the effects of different Zn contents on microstructure and mechanical properties of extruded Mg-7Y-4Gd-0.4Zr and Mg-5Y-4Gd-0.4Zr alloys,respectively.The corresponding experimental results indicate that the peak-aged alloy exhibits the high tensile strength and good elongation,which results from the coprecipitation of β′phase and LPSO phase by the Zn addition.

    As an important alloying element,Dy has a high solubility in Mg(25.3 wt.%).The solubility signif i cantly decreased with decreasing temperature,and the Mg24Dy5intermetallic phase has a high melting point(560°C)[17].Thus,the addition of Dy can effectively improve mechanical properties of Mg alloys at room and elevated temperatures by solid solution strengthening and precipitation strengthening.Recently,our previous investigation has indicated thatthe extruded Mg-2Dy-0.5Zn(at.%)alloy in peak-aged state(180°C, 90 h)exhibits high yield tensile strength(245 MPa)and ultimate tensile strength(260 MPa)at 300°C[18].Additionally, the previous work demonstrated that the Mg-Dy binary alloy exhibited a good combination of mechanical and bio-corrosion properties in medical application due to its good cytocompatibility and uniform corrosion behavior[19-21]. However,whether as structure or medical materials,the corrosion properties of the alloy were necessary to further improve to expand its application f i eld.The Zn addition could also improve corrosion resistant of Mg alloys by adjusting the morphology,distribution and volume fraction of the second phase.Yin et al.[22]have investigated the effect of Zn on corrosion property of extruded Mg-Zn-Mn alloy.They pointed out that the addition of 1%Zn make alloy exhibited the best corrosion resistance,which is mainly due to the formation of compact passive f i lm.Similarly,the corrosion property of Mg-10Gd alloys with 2-6%Zn has been studied by Srinivasan et al.[23].However,up to now,the effect of different Zn contents on the microstructure,mechanical and corrosion properties of the Mg-Dy alloy has not been reported.Therefore,in this paper,the as-cast Mg-2Dy-xZn (x=0,0.5,and 1at.%)alloys were prepared and the effect of Zn on the microstructure,mechanical property and corrosion behavior of the alloys was investigated.

    2.Experimental procedures

    The four alloy ingots with nominal compositions of Mg-2Dy (alloy A), Mg-2Dy-0.1Zn (alloy B), Mg-2Dy-0.5Zn(alloy C)and Mg-2Dy-1Zn(alloy D)(note that atomic percentage is used for all the alloy compositions in this paper)were prepared from commercially pure Mg,high pure Zn and Mg-20wt.%Dy(Dysprosium)master alloys. Melting was conducted by using a graphite crucible in an electric resistance furnace at about 750°C under the protection of antioxidant f l ux.The melts were homogenized at 720°C for 0.5 h,and then castinto a steelmold with sizeof 70 mm × 40 mm × 13 mm.

    The microstructures,phase structure and composition of the alloys were characterized using an Olym-pus optical microscope(OM)(GX71),X-ray diffraction(XRD)and transmission electronic microscopy(TEM)(JEM-2100F).The specimens for OM observation were prepared by the standard technology of grinding and polishing and etched by a solution of picric acid-ethanol-H2O.Thin foils for TEM observation were prepared using the Ion Polishing System(RES101). Tensile tests were carried out using an Instron-type tensile testing machine(Instron 1211)at room temperature(RT)and 200°C with a strain rate of 1 × 10-3s-1for all the specimens. The tensile specimens with a gage dimension of 16 mm in length,5 mm in width and 1.8 mm in thickness were cut from the as-cast ingots.

    For the immersion tests,the cubic samples size 10 × 10 × 10 mm3were ground on f i ner grades emery papers up to 800#,and polished with 0.5 mm Al2O3polishing pastes, supersonically cleaned and then dried with a hair drier.The corrosion surface area of samples after immersion test was observed under an optical microscope and then calculated using Image-Pro Plus.These samples were immersed in a NaCl aqueous solution(3.5 wt.%)at room temperature for 24 h.The weight loss of samples before and after experiments was measured using an analysis balance with a precision of 0.1 mg at room temperature,and the weight loss rate was calculated in g m-2h-1.Electrochemical polarization test were carried out in 3.5 wt.%NaCl solution at room temperature.A classical three electrode cell was used with a platinum plate as counter electrode,a saturated calomel electrode as reference electrode and the samples sealed by paraff i n with an exposed area of 1 cm2as working electrodes.Samples were immersed in the test solution and a polarization scan was carried out at a rate of 1 mV s-1.

    3.Results and discussion

    3.1.Microstructure

    Fig.1.Optical microstructures of as-cast alloys:(a and e)alloy A,(b and f)alloy B,(c and g)alloy C,and(d and h)alloy D.

    Fig.1 shows optical microstructures of as-cast alloys.As can be seen from Fig.1(a)-(d),these alloys are mainly composed of α-Mg and secondary phases with different micrograph.The alloy A mainly consists of the spot-like eutectic phases with size of about 10 μm which mainly distribute at the grain boundaries(Fig.1(e)).The trace of Zn (0.1at.%)addition almost dissolves into the Mg matrix and no new phase is observed(Fig.1(f)).Moreover,it is found that the volume fraction of the eutectic phase seems to reduce because of the Zn addition,which may be related to the formation of atomic clusters containing Zn and Dy atoms in Mg matrix during solidif i cation.The similar atomic clusters consisted of Zn and Gd atoms also present in the as-quenched Mg-Gd-Zn alloy[13].Addition of 0.5at.%Zn leads to the formation of some coarse lamellar phases at the grain boundaries(Fig.1(g)).When the Zn content is 1 at.%,some discontinuous pocket compounds precipitate at the grain boundaries(Fig.1(h)).It is noted that a few cubic particles with size of 1-2 μm are present in alloy C and alloy D.In addition,the volume fraction ofthese second phases signif i cantly increases and the grain size of the alloy remarkably decreases with the addition of Zn.The grain sizes of the as-cast alloy A,alloy B,alloy C and alloy D are 260 μm, 130 μm,125 μm and 122 μm,respectively.

    Fig.2.XRD patterns of as-cast alloys.

    Fig.2 shows the X-ray diffraction patterns of as-cast alloys. The diffraction peaks of α-Mg and Mg24Dy5phase are indexed in alloy A and alloy B.Besides the two phases,the diffraction peaks of Mg12ZnDy phase and Mg3Zn3Dy2phase are observed in alloy C and alloy D,respectively.According to the XRD results and previous literature,the spot-like eutectic phase is Mg24Dy5in alloy A and alloy B[24],the lamellar phase is Mg12ZnDy in alloy C[18]and the pocket compound corresponds to Mg3Zn3Dy2in alloy D,which is similar to the Mg3Zn3Gd2phase in Mg-Gd-Zn alloys[25,26].The typical TEM images of the particles in alloy C and alloy D are shown in Fig.3.The SAED patterns taken from the lamellar phase and the pocket compound indicate 18R-type LPSO structure (hcp structure witha=0.321 nm andc=4.86 nm)[27,28] and Mg3Zn3Dy2(cubic witha=0.68 nm).Additionally,our previous investigation[29]has indicated that the cubic particle in alloy C is Mg2Dy phase.The phase is a non-equilibrium phase formed during solidif i cation process.Because of its small amount,this Mg2Dy phase was not detected in the XRD pattern.

    It reveals that the grain size of alloys and the formation of different kinds of secondary phases vary with Zn addition as shown in Fig.1.We consider that the reasons are mainly related to the following two aspects.Firstly,during solidif ication process,Dy atoms are aggregated at the solid/liquid interface due to their low solid solubility at low temperature. This enrichment hinders Zn atoms from diffusing to the Mg matrix,which results in the constitutional supercooling in the diffusion layer ahead of the advancing solid/liquid interface. The diffusion rate of the solute atoms is reduced.Therefore, the grain growth is restricted[30,31].In addition,constitutional supercooling is a major force for nucleation[32],which results in increasing the number of nuclei by activating the potential nuclei in the supercooling zone.On the other hand, the enrichment of Dy and Zn atoms leads to the formation of the LPSO phase and Mg3Zn3Dy2phase in alloy C and alloy D, respectively.The forming possibility of two ternary phases is considered to depend on the Zn(wt.%)/Dy(wt.%)ratio.Xu et al.[33]have reported that Mg3Zn6Y(I-phase)phase and Mg3Zn3Y2(W-phase)phase coexist in Mg-Zn-Yalloy when the ratio of Zn/Y is between 4.38 and 1.10,and when the ratio is lower than 1.10,the main second phase is W phase.For the present alloy C(Mg-11.92wt.%Dy-1.2wt.%Zn)and alloy D ((Mg-11.88wt.%Dy-2.38wt.%Zn)),the ratios of Zn/Dy are 0.1 and 0.2,respectively,which are all lower than 1.10.In addition,Dy could be easy to substitute by Y due to their similar atomic radius.Consequently,it can be concluded that Mg3Zn3Dy2phase could form alloy C and alloy D.However, in fact,the Mg3Zn3Dy2phase only precipitates in alloy D,but LPSO phase forms in alloy C.The previous literature[8,9] have demonstrated that the formation of the LPSO phase is related to alloy composition and types of rare earth elements. Abe et al.[34]have pointed out that the LPSO phase is not stacking ordered structure but also chemically ordered structure.The addition of small atomic percent of RE and Zn elements in Mg leads to the formation of LPSO phase due to the generation of long period chemical-ordered as well as stacking ordered structures[35].Therefore,the LPSO phase precipitates in alloy C due to the lower atomic percent of Zn and Dy(2.5at.%)than that(3at.%)of alloy D.As mentioned above,the decrease of grain size and the formation of the LPSO phase and Mg3Zn3Dy2compounds are mainly attributed to the addition of Zn.

    3.2.Mechanical properties

    Fig.3.TEM images of the lamellar phase(a)and pocket compound(b)in alloy C and alloy D,and the corresponding SAED patterns of the two particles.

    Fig.4.Tensile properties of as-cast alloys at room temperature and 200°C.

    Fig.4 shows the mechanical properties of as-cast alloys at room temperature(RT)and 200°C and the corresponding tensile data are also listed in Table 1.It can be seen from Fig.4 and Table 1 that the yield strength(σ0.2)and ultimate tensile strength(σb)of the alloys decrease,while the elongation(ε) increases with increasing temperature.The alloy C exhibits the highest tensile properties among four alloys.The σ0.2and σbof the alloy are 100 MPa and 145 MPa at RT,142 MPa and 90 MPa at 200°C,which increase by 11%and 21.4%at RT, 22.2% and 28.2%at 200°C comparing with alloy A, respectively.In addition,it is noted that the tensile properties of alloy C almost decrease with increasing temperature.It suggests that the 0.5 at.%Zn addition signif i cantly improves the tensile properties of Mg-2Dy alloy at elevated temperature.The good room temperature strength and non-decreasing elevated temperature tensile properties of the alloy C are mainly attributed to grain ref i nement and strengthening of LPSO phase.

    The difference of tensile properties of as-cast alloys is mainly related to their various microstructures.The grain size of the alloys decreases with Zn addition as shown in Fig.1. According to the Hall-patch relationship [30] (σy= σ0+kyd-1/2,where σyis the yield strength, σ0andkyare constants for a given polycrystalline material),the yield strength of alloy increases with decreasing grain size.In addition,the role of solution strengthening of Zn in Mg matrix gradually increases with increasing Zn content.When the Zn contentexceeds0.1at.%,someMg12ZnDy phasesand Mg3Zn3Dy2compounds precipitated in the alloy C and alloy D,respectively.This also suggests that the solubility of Zn in Mg reaches a maximum value for the alloy C and alloy D. Besides the grain ref i nement and solution strengthening,theprecipitation strengthening of second phase plays an important role in improving the tensile properties of Mg-Dy alloy with Zn addition.

    Table 1Tensile property of as-cast alloys at room temperature and 200°C.

    It is noted that a great number of Mg12ZnDy phases with 18R LPSO structure precipitate in the dendrite grain boundaries.The phase has a same crystal structure with Mg12ZnY phase due to the similar atomic radius of Y and Dy.The previous literature have demonstrated that the LPSO phase has a good thermal stability and a higher hardness than the α-Mg matrix[36,37].Furthermore,the kinking of the LPSO phase during deformation could effectively impede the dislocation movement and enhance tensile properties of the alloy at both room and elevated temperatures[38].Also,the LPSO phase itself also acts as a strong reinforcement in LPSO/Mg twophase alloy to strengthen the Mg matrix[39].So,it can be deduced that the strengthening role of Mg12ZnDy phase in our investigated alloy should be similar as that of Mg12ZnY phase in Mg-Zn-Yalloy.In addition,our previous investigation has conf i rmed that presence of a large number of f i ne and dispersive LPSO phases signif i cantly improves the elevated temperature tensile strength of extruded Mg-2Dy-0.5Zn (at.%)alloy[18].Compared with the Mg24Dy5phase in alloy A and alloy B,the Mg12ZnDy phase with LPSO structure in alloy C has the higher thermal ability,better interface stability and larger volume fraction.Thus,the role of the precipitation strengthening of second phase is dominant in the alloy C.In contrast,although the pocket Mg3Zn3Dy2compound in the alloy D has a smaller particle size and larger fraction volume than Mg12ZnDy phase in the alloy C,it has an incoherent interface with Mg matrix due to a bcc crystal structure of the phase.Additionally,most of the phases mainly distribute at the grain boundaries(see Fig.1(h)),where the stress concentration often occurs during deformation.Under this condition,the weak interface between the Mg3Zn3Dy2compound and Mg matrix could provide the opening site of a microcrack[25,26], which declines the tensile strength and elongation of the alloy, especially at elevated temperature.For the present alloys, because the alloy C has the f i ner grain size and a large number of LPSO phases having high thermal stability,it exhibits the highest tensile strength at room temperature and 200°C.

    3.3.Corrosion behavior

    Fig.5.Weight loss rate of the as-cast alloys in 3.5 wt.%NaCl solution for 2 h.

    The corrosion resistant of the alloys varies with the change in the microstructures due to Zn addition.Fig.5 shows the weight loss rates of the alloys in 3.5 wt.%NaCl solution for 2 h.The data indicate the corrosion rate of the alloy f i rstly decreases and then greatly increases with the Zn addition.The alloy B exhibits the lowest weight loss rate among four alloys. The value of weight loss rate of alloy B is only 2.27 mg/cm2/d, which is far less than that of alloy D(49.41 mg/cm2/d).This reveals that the alloy B exhibits the better corrosion resistant. Moreover,it can be seen that the surfaces of the four alloys have different features after 2 h immersion test in 3.5 wt.% NaCl solution as shown in Fig.6.For the alloy A,the whole surface of specimens has lost metal luster and some corrosion pits form and develop from the surface into inside of the alloy. The similar corrosion surface feature is also observed in the alloy B,alloy C and alloy D.In addition,the corrosion surface area(CSA)of alloy A is about 50%,it f i rstly decreases and then increases with Zn addition.For the alloy B,the value of CSA is only about 10%,and it further rapidly increases to 70% for the alloy C and f i nally reaches 100%for the alloy D.The optical surface observation results of the immersion specimens indicate that the alloy B exhibits an excellent corrosion resistant in the same test condition as compared to other three alloys.The surface features of corrosion specimen are in good agreement with weight loss rate in Fig.5.The polarization curves of the alloys in 3.5 wt.%NaCl solution in Fig.7 indicate that the corrosion potential increases f i rstly then decreases,but the corrosion current represents an opposite trend with Zn addition.The effect of Zn addition on corrosion resistance of the alloy is shown in Fig.8.It can be seen that the alloy B exhibits the highest polarization potential(-1.566 V) and the lowest corrosion current(19.32 μA/cm2).This reveals that alloy B has a higher corrosion resistance than the other three alloys,which coincides with the experimental results of immersion tests.

    Fig.6.Optical surface micrographs of as-cast alloys after 2 h immersion test in 3.5 wt.%NaCl solution.

    Fig.7.Polarization curves of as-cast alloys in 3.5 wt.%NaCl solution.

    Fig.8.Effect of Zn content on corrosion potential and corrosion current density of as-cast alloys.

    The difference in the corrosion resistance of alloys is mainly related to their various microstructures.As far as we know,the galvanic corrosion caused by the potential difference between α-Mg and second phase generally occurs in Mg matrix in the vicinity of second phase.The morphology,scale, amount and distribution of the second phase mainly inf l uence the corrosion properties of the alloy.Song et al.[40,41]have demonstrated that the β (Mg17Al12)phase in AZ91 alloys could act as either a corrosion barrier or a galvanic cathode accelerating corrosion.Which role dominates the corrosion process mainly depends on the distribution and volume faction of the β phase.The f i nely and continuously distributed β phase is former,while the coarsening and uncontinuously distributed one is later.The effect of second phase on corrosion resistance in the investigated alloys is similar to that of β phase in AZ91 alloy.For the present alloys,the microstructure of the alloy varies with Zn addition as shown in Fig.1.A great number of second phases precipitate in the alloy with Zn addition.By comparing the alloy A,the trace addition of Zn(0.1at.%) seems to promote the dissolution of Dy in Mg matrix during solidif i cation,which reduces the precipitation of Mg24Dy5phase in Mg matrix and decreases the volume fraction of the phase in the alloy B.Thus,the alloy B exhibits a much better corrosion resistance than alloy A.In addition,the trace Zn addition could also reduce the effects of Fe,Ni elements and improve the corrosion resistance of Mg alloys[22].In contrast,the Zn content reaches 0.5%and 1%,the ternary Mg12DyZn phase and Mg3Zn3Dy2phase precipitate at the grain boundaries and are much nobler than α-Mg matrix. These second phases can act as micro-cathodes during corrosion process and accelerate the corrosion of α-Mg matrix adjacent to these second phases due to the galvanic couple effect[40].Moreover,the higher volume fraction and larger particle size of second phases in alloy C and alloy D than that in alloy B are also two important factors to accelerate galvanic corrosion.The large corrosion area and deep corrosion pit in the surface of the samples after immersion reveal the inferior corrosion resistance of the two alloys as shown in Fig.6.Thus, alloy B exhibits the best corrosion resistance among the four alloys.

    4.Conclusions

    Microstructure,mechanical and corrosion properties of ascast Mg-2Dy-xZn(x=0,0.1,0.5 and 1)(at.%)alloys have been investigated.The following conclusions can be drawn.

    (1)The microstructures of as-cast alloy A and alloy B consist of α-Mg and some Mg24Dy5eutectic phases.With the 0.5at.%Zn addition,the Mg12ZnDy phase with 18R-type LPSO structure and Mg2Dy phase precipitate in the dendrite boundaries of alloy C,respectively.When the Zn content is 1 at.%,the Mg3Zn3Dy2phase is observed at the grain boundaries of alloy D.In addition,the grain size of as-cast alloys signif i cantly decreases from 260 μm of alloy A to 122 μm of alloy D with Zn addition.

    (2)The tensile testing results indicate that the alloy C exhibits the highest tensile strength,yield strength and elongation at room temperature and 200°C.The yield strength and tensile strength of the alloy are 100 MPa and 145 MPa at RT,142 MPa and 90 MPa at 200°C.The improvement of mechanical properties of the alloy is mainly attributed to grain ref i nement of α-Mg and strengthening of LPSO phase.

    (3)The electrochemical measurements and immersion testing results indicated that the alloy B exhibited the best corrosion resistance.The value of weight loss rate of the alloy B is only 2.27 mg/cm2/d,which is far less than that of alloy D(49.41 mg/cm2/d).Simultaneously,the alloy B exhibits the highest polarization potential and the lowest corrosion current among four alloys.The good corrosion resistance of the alloy is related to the f i ne and humongous distribution of Mg24Dy5phases with a low volume fraction.

    Acknowledgments

    This work was f i nancially supported by National Natural Science Foundation of China(51301082,51301083).

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    [38]X.H.Shao,Z.Q.Yang,X.L.Ma,Acta Mater.58(2010)4760-4771.

    [39]K.Hagihara,A.Kinoshita,Y.Sugino,M.Yamasaki,Y.Kawamura, H.Y.Yasuda,Y.Umakoshi,Acta Mater.58(2010)6282-6293.

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    [41]G.Song,A.Atrens,M.Dargusch,Corros.Sci.41(1998)249-273.

    Received 8 January 2014;revised 25 February 2014;accepted 10 March 2014 Available online 18 April 2014

    *Corresponding author.Tel./fax:+86 931 2973564.

    E-mail address:glbi@163.com(G.Bi).

    Peer review under responsibility of National Engineering Research Center for Magnesium Alloys of China,Chongqing University

    Production and hosting by Elsevier

    http://dx.doi.org/10.1016/j.jma.2014.03.002.

    2213-9567/Copyright 2014,National Engineering Research Center for Magnesium Alloys of China,Chongqing University.Production and hosting by Elsevier B.V.All rights reserved.

    Copyright 2014,National Engineering Research Center for Magnesium Alloys of China,Chongqing University.Production and hosting by Elsevier B.V.All rights reserved.

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