Effects of heat treatment on mechanical properties of an extruded Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr alloy and establishment of its Hall-Petch relation

Lei Liu ,Xiojie Zhou ,Shilun Yu ,Jin Zhng ,Xinzheng Lu ,Xin Shu ,Zijun Su

a Hunan Provincial Key Laboratory of Intelligent Manufacturing Technology for High-performance Mechanical Equipment,Changsha University of Science and Technology,Changsha 410114,China

b Hunan Xiangtou Goldsky Titanium Metal Co.,Ltd.,Changsha 410205,China

c Hunan Aerospace Tianlu Advanced Material Testing Co.,Ltd,Changsha 410600,China

d School of Mechanical Engineering,Hunan University of Technology,Zhuzhou 412007,China

Abstract The effects of T4,T5,and T6 treatment on the microstructure and mechanical properties of the extruded Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr(wt.%) alloy with a relatively low RE content (7.5wt.%) were investigated.T4 treatment at 450-500 °C induces a gradual grain growth of α-Mg but an obvious transition of texture component from ＜0001＞⊥ED to ＜0001＞ED.Interdendritic LPSO phases are highly stable against annealing while intragranular ones experience dissolution and re-precipitation.After peak-ageing at 200 °C,the elongation of as-extruded and T4 samples is just slightly reduced or even increased due to the weak ageing hardening response.T5 sample exhibits an attractive combination of strength and ductility,with a tensile yield strength (TYS) of 303MPa and elongation of 20.0%.The Hall-Petch relation for the alloys with or without ageing treatment has been estimated.Grain boundary strengthening rather than precipitation strengthening has the dominant contribution to TYS,and a modified equation is developed to predict grain boundary strengthening values for Mg-Gd-Y-Zn-Zr alloys which contain different Schmid factors for basal slip.

Keywords: Magnesium alloys;Heat treatment;Hall-Petch;Mechanical properties;Strengthening mechanism.

1.Introduction

Magnesium alloys have been extensively investigated recently because of their potential to be utilized in the fields of load bearing,energy storage,and biomedical application due to their high specific strength [1-4],large hydrogen storage capacity [5-8],and good biocompatibility [9-11] etc.Therein,Mg-Gd-Y-Zn-Zr alloys,which contain high content of RE elements and exhibit high performance[12-17],probably become rivals to some Al alloys or even steel structural materials in areas where weight saving is urgently needed.

For instance,Xu et al.[12] fabricated a T5-treated Mg-8.2Gd-3.8Y-1.0Zn-0.4Zr (wt.%,similarly hereinafter) extruded alloy,showing an ultimate tensile strength (UTS) of 520MPa,tensile yield strength (TYS) of 462MPa,and elongation of 10.6%.A much higher hardness than any other reported Mg-based alloys was achieved via high pressure torsion (HPT) and peak-ageing for the same alloy [13].Homma et al.[14] fabricated a high-strength Mg-10Gd-6Y-1.6Zn-0.6Zr alloy by hot extrusion and ageing,exhibiting an UTS of 542MPa,TYS of 473MPa,and elongation of 8.0%.Moreover,Yu et al.[15] successfully prepared a high-strength Mg-11Gd-4.5Y-1Nd-1.5Zn-0.5Zr alloy with an UTS of 547MPa,TYS of 473MPa,and elongation of 2.6%,via the combination of hot extrusion,cold rolling,and ageing.The high strength of the above alloys were mainly attributed to the nanoscale ageing precipitates (derived from the high RE content,＞12wt.%),fin grains,and/or strong basal texture,etc.

For sake of obtaining the extraordinarily high strength for Mg alloys,the combination of high RE content and T5 treatment (peak-ageing immediately after hot deformation without solution treatment or annealing) was considered as a feasible way at the partial expense of elongation.However,high content of RE elements increases the cost and limits the utilization of these alloys especially in large volume components[18,19].Recently,researchers have tried to develop Mg alloys containing less RE or even RE-free alloys with relatively high mechanical properties to overcome the economic drawback[20-25].Moreover,although T5 treatment possesses the advantage of avoiding grain growth due to free of annealing and therefore ensuring high strength,the annealing treatment (T4)prior ageing could change the texture and grain size to modify the ductility.The effects of ageing after annealing (T6)on the mechanical properties of Mg-RE-Zn alloys are also scarcely investigated while deserving attention.

Taking the above factors into consideration,in this work a Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr alloy which contains relatively low RE elements (7.5wt.%) but exhibits good combination of strength and ductility was fabricated by hot extrusion.The effects of T4,T5,and T6 treatment on the microstructure and mechanical properties of the as-extruded alloy were systematically investigated.The Hall-Petch relation was established as well as other strengthening mechanisms.In addition,a reliable equation to predict grain boundary strengthening effect was established for this alloy of any texture of interest.This paper hopes to provide useful information for the fabrication of high-performance Mg alloys with low RE content.

2.Materials and methods

2.1.Material preparation

An ingot with a size ofΦ130mm×1500mm was produced via the direct chill casting technology.Pure Mg and Zn,Mg-25Gd,Mg-25Y,Mg-25Zr (wt.%) master alloys were melted at 780 °C and casted at 680 °C under the protection atmosphere of CO2and Ar.The composition was examined to be Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr (wt.%) by an inductively coupled plasma (ICP) analyser.After homogenization at 510 °C for 36h,a cylindrical billet with a size ofΦ115mm×300mm machined from the ingot was extruded toΦ20mm through an extrusion container ofΦ120mm(namely with an extrusion ratio of 36),at 380 °C and a ram speed of 0.3mm/s.

T4 treatment was conducted at 450,475,and 500 °C for 0-16h.The ageing schedule in both the T5 and T6 treatment was fixed at 200 °C for 0-68h.Samples were quenched into water immediately after heat treatment.

2.2.Microstructure characterization

Microstructure was characterized by optical microscopy(OM,Leica DMIL) and scanning electron microscopy (SEM,FEI Sirion 200,operated at 20kV).Specimens for both OM and SEM observation were ground and polished,followed by etching in a solution of 6g picric acid,40ml acetic acid,40ml water,and 100ml ethanol.Electron back-scatter diffraction (EBSD) was conducted on a Helios Nanolab 600i SEM equipped with the HKL EBSD system,with the scanning step ranging from 1/10 to 1/5 of the average grain size of each sample.Inverse pole figure (IPF) colouring maps,pole figures average Schmid factor,etc.were derived from the EBSD data.In IPF colouring maps,high-angle grain boundaries (HAGB,＞15° misorientation) were indicated as black lines while low-angle grain boundaries (LAGB,2-15° misorientation)were indicated as white lines.EBSD specimens were electro-polished at -40 °C,using a solution of 15ml perchloric acid and 285ml ethyl alcohol.The average grain size ofα-Mg was measured based on low magnification OM or IPF colouring images using Image-Pro-Plus 6.0 software,and at least 300 randomly selected grains (include both DRXed and un-DRXed ones) were counted for each case to ensure the accuracy of obtained values.

2.3.Mechanical property tests

Age-hardening response was determined by Vickers hardness tests which were conducted with a load of 4.9N and dwelling time of 15s,and 10 indentations were measured for each sample.Tensile tests were conducted on an Instron 3369 machine at a crosshead speed of 1mm/min at room temperature.The tensile axis was parallel to the extrusion direction(ED).The 0.2% proof strength was applied as the tensile yield strength.More than three specimens,with a gauge length of 25mm and a diameter of 5mm,were tested for each state to ensure the reliability of the results.

3.Results and discussion

3.1.Microstructure of the as-homogenized and as-extruded alloy

Fig.1a shows the microstructure of the as-homogenized alloy.Block-like interdendritic LPSO phases surroundα-Mg grains which possess an average diameter of 76.8μm and are fille with intragranular thin-platelet LPSO phases.Thinplatelet phases in each individual grain are aligned parallel with each other while have no preferential orientation relationship with those in neighbouring grains,which indicates a randomized texture of the as-homogenized sample.Both the interdendritic and intragranular LPSO phases should be 14H type which is the stable structure in as-homogenized Mg-Gd-Y-Zn-Zr alloys as reported previously [26,27].And they tend to be crushed and aligned along ED after extrusion (Figs.1b,c,and d),indicating the formation of basal fibr texture which will be confirmed subsequenly.Sufficien dynamic recrystallization (DRX) occurs due to the large extrusion ratio of 36,and a fine average grain size of 2.6μm is achieved.The average volume fraction of LPSO phases,measured from low magnification SEM images,is 5.2%.

Fig.1.Microstructure of the (a) as-homogenized and (b,c,d) as-extruded Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr alloys:(a,b) optical micrographs,(c,d) SEM images((d) is the high magnification of the box in (c)).

Energy dispersive spectrometer (EDS) results (Table 1) reveal that,in spite of different sizes,the phases marked A,B,C in Fig.1d possess the same atomic ratio of RE/Zn ( 1:1),agreeing with the previously reported examination of LPSO phases [28].The total content of RE and Zn elements decreases when the phase size reduces,since the EDS chemistry measurements would become inaccurate for small particles due to the interference of the surrounding matrix.The brighter phases like that marked D should be Zr-rich clusters which acted as the grain refine during solidification [29] and were aligned along ED during extrusion.

Table 1EDS results of the test points marked in Fig.1d.

Fig.2.(a) IPF colouring map with respect to TD and (b) EBSD-derived pole figure of the as-extruded alloy.

Fig.3.Optical micrographs of the samples annealed at 450 °C for different durations.

Fig.2a shows the IPF colouring map of the as-extruded alloy.The black regions mainly represent the LPSO phases which cannot be indexed due to the lack of phase parameters.A microstructure containing colourful and equiaxial grains can be detected,which reveals the sufficiently DRXed microstructure with a relatively randomized texture.However,the pole figure shown in Fig.2b still indicates the existence of a typical basal fibr texture (i.e.the basal planes ofα-Mg grains tend to be parallel with ED) despite the weak intensity of 3.6.

3.2.Microstructure and mechanical properties of the T4-treated samples

To study the effects of T4 treatment on the microstructure and mechanical properties,the as-extruded sample was annealed at 450,475,and 500 °C for 0-16h.As shown in Figs.3-6,theα-Mg grain size exhibits a gradual increase during annealing at 450 °C.When annealed at 475 and 500°C,although the grain growth rate still keeps gradual during holding from 2 to 16h,dramatical grain growth already occurs after annealing for a short time of 2h,with the average grain size increasing to 9.8 and 15.0μm for 475 and 500 °C,respectively.It is reasonable to deduce that the annealing temperature rather than time determines the grain size level during annealing.The gradual grain growth at the late stage of annealing should be mainly attributed to the following reasons:1) the limited driving force for grain growth due to the high extrusion temperature and sufficiently DRXed microstructure (i.e.lack of the stored energy),and 2) the resistance to grain boundaries migration during grain growth induced by the fine and dispersed interdendritic LPSO phases.

Actually,unlike theα-Mg matrix,the interdendritic LPSO phases are highly stable against annealing.Little change involving both the length decrease and diameter increase can be detected,which differs from the phenomenon observed in a long-time (168h) annealed Mg-6.9Y-1.4Zn (wt.%) alloy [30].The limited annealing time in the present work fails to disturb the aligned interdendritic LPSO phases which show an average length of～19.2μm and diameter of～5.4μm.

It is noteworthy that intragranular LPSO phases in theα-Mg grains are dissolved into the matrix during annealing at the lower temperatures of 450 and 475 °C (Figs.3 and 4).And the high magnification SEM image of Fig.7b further confirm this phenomenon,showing highly reduced thin-platelet LPSO phases compared to the as-extruded alloy(Fig.1d).It means that intragranular LPSO phases are less thermostable than interdendritic ones.Actually,these thinplatelet LPSO phases could begin to be dissolved during hot deformation process (extrusion in this work) accompanied by the occurrence of DRX like that reported in [31-33],since DRXed grain boundaries may provide pressure (or energy)on precipitates for this endothermic reaction of dissolution[32,34].And the annealing process can further promote this reaction because the diffusion rate and solid solubility rises due to the increase of temperature from extrusion to annealing.

Fig.4.Optical micrographs of the samples annealed at 475 °C for different durations.

Fig.5.Optical micrographs of the samples annealed at 500 °C for different durations.

Interestingly,at 500 °C,the dissolved thin-platelet LPSO phases appear again after annealing for more than 12h(Figs.5e and f).Chun et al.[31] found that LPSO phases,which were dissolved during rolling,re-precipitated from the DRXed regions during annealing,because DRXed grains were enriched in solute atoms after dissolution of the particles and this higher concentration formed new precipitates behind the recrystallization front.Moreover,the dissolution and precipitation of LPSO phases were also reported in an undeformed Mg-6.9Gd-3.2Y-1.5Zn-0.5Zr alloy during solution treatment at 510 °C [26],which were attributed to the content of solute atoms and their current solid solubility in the matrix.And it was founded that the initial alloy states played an important role in evolution of intragranular LPSO phases,which could be mainly attributed to the segregation of solute atoms and stacking faults withinα-Mg grains [35].In the present paper,the dissolution of intragranular LPSO phases and their re-precipitation at high temperature of 500 °C should also derive from the pressure of DRXed grain boundaries on these particles and the subsequent re-segregation of solute atoms to the form of a more stable state (LPSO).It is rationalized to infer that re-precipitation would also occur during annealing at 450 or 475 °C if there is enough annealing time to achieve the equilibrium state.

Fig.8 shows the hardness variation as a function of annealing temperature and time.The hardness of as-extruded alloy significantly drops after being annealed for 0.5h at all temperatures, which probably results from the obvious grain growth accompanied by the annihilation of dislocations.Subsequently, the hardness decrease tendency becomes more gradual, in accordance with the gradual grain growth shown in Fig.6.Based on the curves shown in Fig.8, the samples annealed at 450 °C for 15h, 475 °C for 9h, and 500 °C for 6.5h (designated as 450T4, 475T4, 500T4 hereafter) were selected to analyse their texture and mechanical properties,because these representatives possess the superior hardness amongst the adequately annealed (6h as a threshold assumed in this paper) samples.

Fig.6.Variation of the average grain size as a function of annealing temperature and time.

Fig.7.SEM images of the sample annealed at 450 °C for 15 h: (a) low magnification, (b) high magnification of the box in (a).

Fig.8.Variation of hardness of the annealed samples as a function of annealing temperature and time.

IPF colouring maps and pole figures of the T4 representatives are shown in Fig.9.The average grain size of each sample is 9.2, 13.4, and 18.9μm, respectively.Pole figures reveal that the basal fibre texture component remains in the 450T4 and 475T4 samples, while the new texture component of0001direction (i.e.c axis of α-Mg) parallel to ED appears in all the three samples.In particular, the 500T4 sample exhibits a stronger texture intensity (5.5) than that of the as-extruded one.Although the larger grain size and smaller grain number may cause the larger texture intensity due to the reduction of statistical data, it can not disturb the conclusion that the transition of <0001>⊥ED texture component to <0001>ED occurs during annealing, which should result from the preferential grain growth of certain crystallographic orientations.Unlike the AZ31 extruded alloy in which the<0001>⊥ED and<0001>ED texture components show equal thermal stability [36], in the present work, the boundary migration ability of the <0001>ED component seems higher, and the consumption of the <0001>⊥ED texture by the <0001>ED texture with the advance of grain growth could lead to the domination of the <0001>ED texture component.However, this supposition and related mechanism calls for systematic investigations in the future.Despite the difference in texture component, the Schmid factor for basal slip (SFB) along ED of the as-extruded and T4 samples is still approaching (0.27–0.29, as listed in Table 2) due to the relatively weak texture intensity.

Fig.10 shows the typical engineering stress and engineering strain curves of the as-extruded and T4 samples, and Table 2 lists the corresponding mechanical properties and average grain size.The as-extruded alloy exhibits an UTS of 331MPa, TYS of 279MPa, and elongation of 20.5%.For T4 samples alone, both the UTS and TYS decrease with the augment of average grain size, and their strength is much lower than that of as-extruded alloy.As shown in Fig.11, dimples and tear ridges are the main fracture feathers in both the as-extruded and T4 samples, indicating that the fracture char-

Table 2Average tensile properties of Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr alloys of different states (standard deviation is given in parentheses) as well as the average grain size (dAVG) and Schmid factors for basal slip (SFB).

Fig.9.(a,b,c) IPF colouring maps and (d,e,f) EBSD-derived pole figure of the T4 samples annealed at (a,d) 450 °C for 15h,(b,e) 475 °C for 9h,and(c,f) 500 °C for 6.5h,respectively.

Fig.10.Typical engineering stress and engineering strain curves of the asextruded (EX) and T4 samples.

Fig.10 shows the typical engineering stress and engineering strain curves of the as-extruded and T4 samples,and Table 2 lists the corresponding mechanical properties and average grain size.The as-extruded alloy exhibits an UTS of 331MPa,TYS of 279MPa,and elongation of 20.5%.For T4 samples alone,both the UTS and TYS decrease with the augment of average grain size,and their strength is much lower than that of as-extruded alloy.As shown in Fig.11,dimples and tear ridges are the main fracture feathers in both the as-extruded and T4 samples,indicating that the fracture characteristics remain plastic after annealing which keeps in accordance with the holistic high level of elongation(＞18.5%).In spite of this,the larger grain size may simultaneously endow the T4 samples with the lower strength as well as the slightly reduced ductility.On one hand,the grain boundary strengthening effect decreases with the increase of grain size according to the well-known Hall-Petch relation [37].On the other hand,fine grains can induce a more homogeneous deformation which contributes to maintain the ductility [38].Although the texture type and intensity vary among the asextruded and T4 samples,they obtain the comparativeSFB(basal slip dominates during tensile tests at room temperature).Thus the texture should has little effect on the discrepancy of strength and elongation.The Hall-Petch relation and other strengthening mechanisms will be discussed in detail inSection 3.4.

3.3.Microstructure and mechanical properties of the T5/T6-treated samples

In order to further improve the mechanical properties,the as-extruded and T4 samples were aged at 200 °C,after which the T5 and T6 samples were obtained respectively.Fig.12a shows the aging hardening response of the as-extruded and T4 samples.The hardness of the as-extruded alloy just slightly increases by 2.8% (from 86.8 to 89.3 HV0.5) after peak ageing for 52h.Although the time to reach peak (listed in Table 2) decreases for T4 samples,their rates of hardness increase remain low (9.7%,8.6%,and 9.1% for 450T4,475T4,and 500T4 samples respectively).The reduced RE content accounts for the weak aging hardening response,since there are no sufficient solute atoms for the formation of extensive ageing precipitates which are considered as a dominative strengthening factor for Mg-RE and Mg-RE-Zn alloys [12,13,39,40].The optical micrographs of the T6 samples (Figs.12b, c, and d) exhibit a slight change of contrast compared with the T4 ones (Figs.3, 4, and 5), indicating the limited phase transition during ageing.Meanwhile, there is only slight change of average grain size, since the grain growth already tends to be gradual during annealing at higher temperatures.

Fig.11.SEM images showing fracture surfaces of some tensile tested specimens:(a) as-extruded,(b) 450T4,(c) 500T4,and (d) 450T6.

Fig.12.(a) Aging hardening response of the as-extruded and T4 samples at 200 °C,and optical micrographs of the peak-aged samples:(b) 450T6,(c) 475T6,(d) 500T6.

Fig.13.Typical engineering stress and engineering strain curves of the T5 and T6 samples.

Fig.13 shows the typical engineering stress and engineering strain curves of the T5 and T6 samples, and the corresponding mechanical properties are listed in Table 2.Both the TYS and UTS are just slightly improved (16–24MPa for TYS, 11–20MPa for UTS) after ageing due to the weak ageing strengthening effect.However, the T5 sample still exhibits the satisfactory comprehensive mechanical properties given the low RE content, with the TYS of 303MPa, UTS of 351MPa, and elongation of 20.0%.

It is worth noting that the elongation of some samples(450T6, 475T6) is even increased rather than decreased after peak-ageing treatment, which goes against the general conclusion that the strength could be improved by the ageing strengthening effect at the expense of elongation.In this work,the dominant microstructural evolution during ageing is precipitation,since the grain size,texture,and dislocation density should basically remain unchanged due to the low ageing temperature of 200 °C after the adequate annealing.The authors conjecture that a spot of aging precipitates may be beneficial to the ductility, since these precipitates could pin the movement of a few dislocations in the grain interior and therefore relieve the stress concentration near the grain boundaries especially the interface of interdendtritic LPSO phases andα-Mg matrix where microcracks frequently appear [41,42].And the more homogeneous tensile deformation and slightly higher elongation to fracture could therefore be achieved in a portion of T6 samples.The fracture characteristics of the 450T6 sample (Fig.11d) remain plastic (dimples and tear ridges),similar to those of T4 samples (Figs.11b and c).

Fig.14.Relation between TYS (σy) and the inverse of the square root of grain size (d?1/2), the so-called Hall–Petch plot, of the Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr alloy before and after ageing treatment.

3.4.Analyses of strengthening mechanisms and Hall–Petch relation

It is clarified in Fig.14 that the variations in TYS (σy)of the alloys with or without ageing treatment are governed by the Hall–Petch relation.The intercept constant (σ0)and slope coefficient (kvalue) in each Hall–Petch relationσy=σ0+kd?1/2is established to be 100.4, 109.5MPa and 288.5, 323.3MPa μm?1/2, respectively.Thus the equations ofσy=100.4+288.5d?1/2for T4 and as-extruded alloys, andσy=109.5+323.3d?1/2for T6 and T5 alloys can be obtained.Although the number of experimental points are limited for each line,their location indicates an obvious correlation which can be supported by the high fitting quality (R2=0.99).However, except for the grain boundary strengthening effect, the above equations involve many other strengthening mechanisms which may be independent of grain size (for instance,solid solution strengthening,dislocation strengthening,precipitation strengthening, and strengthening by LPSO, etc.), making these equations unable to accurately evaluate the contribution ofα-Mg grain refinement to theσyand fail to adapt the changes of other factors like LPSO volume, dislocations,and precipitation density, etc.The above analysis suggests the need for calculation of each strengthening factor that influences the TYS (Fig.15).

3.4.1.Solid solution strengthening

It was reported that RE atoms obtain a significant solid solution strengthening effect due to their large atomic size mismatch with Mg atoms, and the solid solution strengthening(σss) is proportional to c2/3, where c is the atomic concentration [43].He et al.[44] calculated theσssfor a Mg-Gd-Y-Zr alloy with 0.6 at.%(Gd+Y)to be ～38MPa,assuming that Gd and Y atoms possess the equal effect.For the present alloy,the atomic concentration of Gd, Y, and Zn element is 0.72,0.94, and 0.48 at.%, respectively.Assuming that all Zn atoms react with RE atoms to form LPSO phases with the RE/Zn ratio of 1:1 (suggested by Table 1), therefore the residual RE content is about 1.2 at.% and all dissolved inα-Mg matrix of the as-extruded sample due to the high extrusion temper-ature (380 °C).Then theσssis calculated to be ～59.7MPa according to the rate of c2/3.

Table 3Strengthening contributions to TYS of as-extruded and T4 alloys at ambient temperature.

Fig.15.Relation between grain boundary strengthening contributions (σgb)and the inverse of the square root of grain size(d?1/2)for the samples without ageing.

It is noteworthy that, compared with the as-extruded sample, the solid solution strengthening effect in T4 samples should be higher since the annealing process promotes the dissolution of intragranular LPSO into the matrix as revealed by Fig.7.Once the extreme case is taken into consideration(i.e.all RE atoms are dissolved into the matrix), the total RE content of ～1.66 at.% corresponds to theσssof ～74.1MPa(then～14.4MPa, compared to the as-extruded sample)based on the rate of c2/3.In fact, the volume fraction of the dissolved intragranular LPSO phases is much lower than that of stable interdendritic ones or the whole LPSO,and therefore the increase ofσssinduced by the dissolution of intragranular LPSO phases, which fails to be accurately evaluated, should be limited.If a discount of 20% is assumed here and the increase ofσssis estimated as ～0.2(～2.9MPa), which might be negligible.For making the subsequent calculation feasible,theσssvalue of the as-extruded alloy(59.7MPa)was utilized to represent theσssvalue of T4 samples as listed in Table 3.

3.4.2.Strengthening by LPSO

Load-bearing strengthening of LPSO:For the present alloy,the load-bearing strengthening effect mainly derives from the reinforcement phases of interdendritic LPSO (the intragranular ones are ignored here due to their small volume fraction as well as their ‘symbiotic’ and coherent relationship withα-Mg matrix).According to the shear-lag theory, the load transfer happens at the interface between LPSO phases andα-Mg matrix by shear stresses which can be expressed as Eq.(1) [45]:

whereσmis the strength of matrix,VpandVmare the volume fraction of LPSO phases (5.2%) and matrix (94.8%), respectively,andsis the average aspect ratio of the length and diameter of LPSO phases (～3.56).Considering thatVp+Vm=1,the strength caused by LPSO phases via the load bearing mechanism can be expressed as:=1.78Vpσm≈0.093σm=σy=0.085σy.By substituting into the respective TYS, the TYS improvement owning to the loadbearing strengthening is thus obtained.

Particle strengthening of LPSO:The increase of TYS caused by particle strengthening that arises from the resistance of LPSO phases to the movement of dislocations,,can be estimated using Eq.(2) [46–48]:

wheredpis the average particle size (equivalent diameter by conversion of area, which is 11.5μm in the present paper)of the LPSO phases, andλis the interparticle spacing which can be estimated using Eq.(3) [46–48]:

Theλvalue is calculated to be 12.9μm, and then≈ 0.5MPa.Therefore the strengthening by LPSO can be calculated by the equation ofσLPSO=+=0.5+0.085σy, and the result of each sample is listed in Tables 3 and 4.

Table 4Strengthening contributions to TYS of T5 and T6 alloys at ambient temperature.

3.4.3.Dislocation strengthening

Dislocation strengtheningσdislcaused by the dislocation density ofα-Mg grains (the DRXed grains are ignored due to their much lower dislocation density compared with un-DRXed grains) can be calculated using the Eq.(4) [48]:

whereαis a constant (0.2 for Mg [49]),Gis the shear modulus (16.6GPa for Mg [50]),bis the Burger’s vector(3.21×10?10m for Mg [50]),MunDRXis the Taylor factor for un-DRXed regions (3.5 for Mg with a strong texture [49]),ρunDRXis the dislocation density in un-DRXed regions (a typical value of 1×1014m?2for deformed Mg alloys [48]),andfunDRXmeans the volume fraction of un-DRXed regions.By analysing the EBSD data, the volume fraction of the un-DRXed regions (funDRX) in the as-extruded alloy is confirmed as 15.5%.Then theσdislvalue is calculated to be 5.8MPa for as-extruded alloys, which contributes little to the TYS.Thus theσdislin T4, T5, and T6 alloys could be ignored since the annealing or ageing treatment probably further eliminates those limited dislocations.

3.4.4.Grain boundary strengthening

Here we define the grain boundary strengtheningσgbas the contribution merely fromα-Mg grain boundary and grain orientation to TYS, which can be calculated by the equation ofσgb=σy?σss?σLPSO?σdislfor the as-extruded and T4 samples (results are listed in Table 3).And a liner fitted equationσgb=36.0+248.1d?1/2(R2=0.99) can be obtained to predict theσgbfor Mg-Gd-Y-Zn-Zr alloys with the averageSFBof 0.28 (see Table 2).Theσgbvalues for T5 and T6 alloys (as listed in Table 4) are calculated by this equation according to the corresponding grain size shown in Table 2, assuming thatSFBdoes not change during the ageing treatment.

Furthermore,Kwak et al.[48]proposed that when the TYS of Mg alloys with different textures were multiplied by their ownSFBand then divided by aSFBassociated with a specific texture of interest, the Hall–Petch relation can be modified.Therefore, the equation to roughly predict theσgbfor Mg-Gd-Y-Zn-Zr alloys with other textures can be obtained as follows by blending in theSFB:

3.4.5.Precipitation strengthening

Precipitation strengtheningσpptexists in the T5 and T6 samples, which can be calculated by the equation ofσppt=σy?σss?σLPSO?σgb.Therein, the values ofσy,σLPSO, andσgbhave been obtained based on the previous calculation.And theσssfor T5 and T6 samples can be evaluated according to the discussion inSection 3.4.1.The solubility of(Gd+Y) in solid Mg is close to (0.6 at.%) at 200 °C, and theσssis therefore calculated to be ～38MPa [44].Finally, theσpptvalue for each sample can be calculated and the results are listed in Table 4.

According to the above analysis on various strengthening mechanisms, it can be concluded that the grain boundary strengthening is the predominant strengthening mechanism for this Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr alloy with the relatively low RE content.The contribution of precipitation strengthening to TYS for peak-aged (T5 and T6) alloys is limited to ～20%.Therefore, in order to further improve the strength for this alloy, it is crucial to find methods to simultaneously obtain the ultra-fine grains and strong basal texture,deserving researches in the future.

4.Conclusions

The effects of heat treatment(involving T4,T5,and T6)on microstructure and mechanical properties of an extruded Mg-4.3Gd-3.2Y-1.2Zn-0.5Zr (wt.%) alloy have been investigated.The contribution of various strengthening mechanisms to the tensile yield strength has also been estimated and compared.The main conclusions are presented as follows.

(1) Theα-Mg grains of the as-extruded alloy exhibit a gradual grain growth at the middle and late stage of annealing (T4) at 450–500 °C for 0–16h, accompanied by their texture component transforming from<0001>⊥ED to<0001>ED.Interdendritic LPSO phases are highly stable against annealing since their size keeps almost unchanged, while intragranular ones are firstly dissolved at all annealing temperatures but re-precipitate after annealing at 500 °C for above 12h.

(2) After peak-ageing at 200 °C (T5 or T6), the elongation of the as-extruded and T4 samples is just slightly decreased or even improved, with their TYS increased by 16–24MPa.The T5 sample exhibits a satisfactory combination of strength and ductility, with the TYS of 303MPa,UTS of 351MPa, and elongation of 20.0%.

(3) The alloys without aging treatment share a Hall–Petch relation ofσy=100.4+288.5d?1/2while the aged samples possess a Hall–Petch relation ofσy=109.5+323.3d?1/2.Grain boundary strengthening rather than precipitation strengthening has the dominant contribution to the TYS for this alloy due to the relatively low RE content.And a modified equation ofσgb=is established to predict the grain boundary strengthening contribution for Mg-Gd-Y-Zn-Zr alloys with any texture of interest.

Declaration of Competing Interest

None.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos.51904036 and 51874049),the Hunan Provincial Natural Science Foundation of China (Nos.2020JJ5600 and 2018JJ2365),the Hunan Education Department Outstanding Youth Project of China (No.17B069),and the Scientifi Research Project of Hunan Education Department (No.20C0088).