1.Introduction

Grain refinement[1–3]an important method to improve the mechanical properties of Mg alloys.Previous studies have shown that the grain size has effect both on hardness(H)[4]and yield strength(σy)[5,6]of a material,and follow the Hall-Petch relationship which expresses as

and

where d is the mean grain size,H0,σ0,kH and ky are appropriate constants that were determined experimentally.The studies on the Mg alloys have shown that those Hall-Petch constants were strongly affected by crystal type[7]and solid solute atoms[8].Previous works on Mg–Gd[9]and Mg–Zn[10]solid solutions have shown that the solute atoms have stronger effect on ky.Compared with face-centered and body-centered cubic metals,theσ0 of Mg and its alloys with hexagonal structure can be related to the critical resolved shear stresses(CRSS)of basal and prism slip[11,12].However,few studies concern the influence of solutes on kH and H0 for Mg alloys.

（三）改善教学方法。对于高中生传统文化素养的培育，大多依赖于语文课课堂上教师对古诗词及文言文的讲授方式进行，受应试教育的影响，教师习惯在这一过程中落入翻译及要求背诵的教学模式中。

The addition of solid solution atoms is another way to adjust the microstructure and mechanical properties of material[12].The effect of atomic size and modulus misfits improved with increasing of solute content,which effects on the main slip systems and causes an increase in yield strength[13].On the other hand,the ky andσ0 should be related to main slip systems and CRSS are changed by solute atoms[14].The studies on Mg alloy with the alloying addition of Al[15],Zn[10],Y[16]and Gd[17]showed that the yield strength increased in proportion to cn,where c is the atom concentration of solute atoms and n=1/2 or 2/3[18,19].However,the effects of ky andσ0 values on the grain boundary strengthening were not clearly discussed in those studies.

Current applications of Mg alloys are still limited compared with Al or Fe alloys and improvements are always required[20–22].The addition of rare-earth elements(REs)has been found to improve the mechanical properties at ambient and elevated temperature of Mg alloys[23–25].Among all of the RE elements,Gd has the high solid solubility in Mg,with maximum solubility of 23.49 wt%at the eutectic temperature[26].The objective of this work is to study solid solution strengthening and the influence of grain size on the hardness and yield strength for polycrystalline Mg–Gd alloys with different amounts of Gd between 2 and 15 wt%.In order to investigate the influence of grain boundary strengthening and to obtain the Hall-Patch contents of Mg–Gd alloys,grains refined with 0.3 wt%Zr and hot extrusion were used to obtain fine and uniform grains for use in the analysis.

2.Experimental procedures

Fig.4(b)shows that the hardness of the extruded alloys increased monotonically with Gd content,which was similar to the T4-treated alloy.It can be seen that the data followed a similar trend except for the slope.The lines of best fit for the present data which indicate the hardness of parallel and perpendicular to the extrusion direction results,respectively,were as follow:

Hot extrusion was used to obtain fine grains.The billets of T4 treated pure Mg and Mg–Gd binary alloys were machined to 93 mm in diameter and 200 mm in length.The samples were heated up in an electromagnetic induction furnace at 440°C prior to extrusion.Indirect extrusion was carried out to produce round bars measuring 12 mm in diameter.The extrusion ratio was 1:60 and the extrusion rate(speed of the extruded bar at die exit)was set to 0.6 m/s at an extrusion temperature of 450°C.The extruded bars were cooled down using still air.

3.4 本研究意义及局限 本研究编制了综合医院护士工作满意度量表，共包含2个维度16个条目，并进行了信效度的检验。本量表的编制过程符合量表开发流程，并且经过初步的严格探索分析，验证该量表具有良好的信效度，可以全面反应护士工作满意度，对于推进护理管理工作的改革及降低离职率具有重要意义。由于条件所限，未进行验证性因子分析，对于维度分布情况有待进一步验证，今后在更多样本、更广范围上进一步验证其信效度，并建立全国常模。

Fig.5(a)presents the yield strength obtained from tensile and compression testing at room temperature.After T4 treatment,the tensile yield strength (TYS) increased significantly from 19 MPa to 107 MPa with Gd content increasing from 0 to 15 wt%.For Mg–Gd–Zr alloys,the TYS increased from 54 MPa to 120 MPa when Gd content increased from 2 to 15 wt%.The TYS of Mg–Gd–Zr alloys was higher than that of Mg–Gd alloy with same Gd content.Extrusion led to a significant improvement of the TYS for all alloys.The TYS of extruded Mg–Gd alloys increased from 76 MPa to 150 MPa with increasing Gd content from 0 to 15 wt%.The compression results follow a similar trend to those of tension.The compressive yield strength(CYS)enhanced with the increase of Gd content for all alloys in different conditions.After T4 treatment,the CYS of Mg–Gd binary reached 110 MPa for Mg–15Gd alloy,which was 90 MPa higher than that of pure Mg.The CYS was enhanced linearly with the increase of Gd content for Mg–Gd–Zr alloys.The CYS reached 120 MPa for Mg–15Gd–Zr alloy.After extrusion,CYS increased from 43 to 150 MPa with increasing Gd content from 0 to 15 wt%.With the same Gd content,the TYS and CYS in order from high to low was as follows:extruded Mg–Gd binary alloy,T4 state Mg–Zr–Gd alloys,and T4 state Mg–Gd binary alloy.

In order to investigate the influence of Gd content on the mechanical properties,Vickers hardness,tension and compression tests were measured on Mg–Gd and Mg–Gd–Zr alloys after T4 treatment and Mg–Gd extruded alloys.The specimens for hardness tests were prepared by grinding with silicon carbide emery paper up to 2500 grid.The hardness measurement was carried out using a Vickers hardness testing machine(KARL FRANK GMBH)with a load of 5 kg and a dwell time of 10 s[30].An average of 10 measurements was made for each specimen to ensure the reproducibility of results.Tension and compression tests were performed at room temperature using a Zwick 050 testing machine(Zwick GmbH&Co.,KG,Ulm,Germany)according to DIN EN ISO 6892-1[31]and DIN 50106[32],respectively.Tensile specimens had a 30 mm gauge length,6 mm diameter,and threaded heads.The compressive specimens were cylinders of height 16.5 mm and diameter 11 mm.Both tension and compression tests were done under a strain rate of 1×10-3 s-1.Three parallel specimens were taken for each group.

Table 1 Chemical composition and solution treatment conditions of alloys.

Alloys Gd(wt%)(at%) Zr(wt%) Solution Treatment Pure Mg 0.00[0.00] 0.00 530°C/6 h Mg–2Gd 2.00[0.31] 0.00 530°C/6 h Mg–5Gd 4.89[0.79] 0.00 530°C/6 h Mg–10Gd 9.26[1.55] 0.00 530°C/8 h Mg–15Gd 13.90[2.43] 0.00 530°C/8 h Mg–2Gd–Zr 2.02[0.32] 0.39 530°C/6 h Mg–5Gd–Zr 4.95[0.80] 0.20 530°C/6 h Mg–10Gd–Zr 10.04[1.70] 0.29 530°C/8 h Mg–15Gd–Zr 11.95[2.06] 0.22 530°C/8 h

3.Results

3.1.Microstructures

The chemical compositions of all studied alloys were listed in Table 1.According to the Mg–Gd phase diagram which was calculated using Pandat software(Fig.1),as-cast alloys with 15 wt%(2.62 at%)Gd had largest intermetallic phases which were easily observed(Fig.2(a)and(b)).A large amount of continuous equiaxed dendrites was present in the Mg matrix because of Gd segregation during the non-equilibrium solidification process in the alloys.Therefore,Mg–15Gd alloys are set as examples to explain that the Gd in studied alloys were full solid solute.From Fig.2(c)and(d),no second phases were observed in the alloys after T4 treatment,which was the case for all of the studied alloys after T4 treatment.The micrographs of the Mg–Gd alloys revealed that homogeneous and fine grains were produced and the microstructures both perpendicular and parallel to the extrusion direction were identical(Fig.2(e)and(f)),the crystal structure for all of the study materials was generally regular.

The average grain sizes of the solid solute Mg–Gd(–Zr)alloys are shown in Fig.3.Before extrusion,the largest grain size was obtained from Mg–2Gd alloy(from several millimeters to centimeters),which is higher than that of pure Mg.A definite decrease in grain size with increasing of Gd content is apparent.For the Mg–Gd–Zr alloys,the average grain size of Mg–Gd–Zr was about 350µm with low Gd content,and it decreased to 130 and 100µm for Mg–10Gd–Zr and Mg–15Gd–Zr alloys.Compared with the Mg–Gd binary alloys,the grain size of the alloys with Zr dropped drastically.Extrusion is another efficient method to achieve grain refinement.Extrusion refined the average grain size of Mg–Gd alloy to approximately 30µm and from 650 to 55µm of pure Mg.

式中：Q为风机所需风量（m3/h）；K为风管和除尘器的漏风系数，取 1.15；Q1为系统风量（m3/h）.

3.2.Hardness testing

Fig.1.Mg–rich side of Mg–Gd phase diagram.

Fig.2.Microstructures of(a)as-cast Mg–15Gd alloy,(b)as-cast Mg–15Gd–Zr alloy,(c)Mg–15Gd alloy,(b)Mg–15Gd–Zr alloy after T4 treatment,(c)extruded Mg–15Gd alloy parallel to extrusion axis,and(d)extruded Mg–15Gd alloy perpendicular to extrusion axis.

Fig.3.Average grain size of Mg–Gd–(Zr)alloys.

The hardness test results of the Mg–Gd(–Zr)alloys after T4 treatment and extrusion are shown in Fig.4.As shown in Fig.4(a),the hardness of the experimental alloys increased monotonically with Gd content,and the Mg–Gd alloys with or without Zr had a similar linear relationship.The hardness(Hv5)had a relationship with the Gd content(c)according to the following equations for alloys without and with Zr,respectively:

A range of Mg–Gd(–Zr)(up to 15 wt%)was prepared by permanent mold direct chill casting[27].High-purity Mg(MEL,UK,99.94 wt%)was molten in a mild steel crucible(1.0044,EU Grade)under a protective atmosphere(Ar+2%SF6).Pure Gd(Grirem,China,99.5 wt%)was added at the melt temperature of 750°C.Zr,in the form of Mg–33.3 wt%Zr master alloy was used as a grain refiner for some of the alloys.The melt was stirred at 200 rpm for 20 min,after which the melt was cast using a directly chilled permanent mold casting method.The size of the cylindric mold was 110 mm in bottom external diameter,230 mm in height and 5 mm in mold wall thickness.First,the melt was poured into a mold that was preheated at 500°C,and the filled mold was held at 670°C for 30 min under a protective gas atmosphere.Then,the whole steel crucible with the melt was lowered into cooling water at a rate of 10 mm/s.When the bottom of the steel crucible touched the water,it stopped for 1 s.When the melt was fully immersed,the solidification had completed.Previously study shown that the intermetallic compounds in Mg–15Gd could completely dissolve into the matrix after 6 h solid solution treatment[28].For alloys with low Gd content(0–5 wt%),the T4 solution treatment was conducted at 530°C for 6 h to prevent from grain growth.The T4 treatment for 8 h were applied on the Mg–xGd(–Zr)(x=10,15)alloys due to the high Gd concentration.

第四，由于不同国家或地区的政治、经济、文化和社会制度不同，其人口、资源和环境禀赋也存在较大的差异，各国所处的发展阶段不同，所选择的经济增长模式和发展路径各异，因此，其经济发展和生态环境保护的关系必定存在较大的差异。世界各国应根据自身的特点选择合适的经济增长模式和发展路径，在保持经济发展的同时，更加注重生态环境保护，通过共同努力和相互合作，构建人类命运共同体，实现人类的可持续发展。我国应认真践行习近平生态文明思想，从中华民族长远利益考虑，探索出一条生态优先、绿色发展的新路子。

Fig.4.Effect of Gd content on the hardness of Mg–Gd alloys.(a)The different of influence from adding Zr;(b)the different of influence from extrusion direction.

3.3.Tensile/compression testing

The chemical compositions of these alloys measured by an X-ray fluorescence(XRF)analyzer(Bruker AXS S4 Explorer,Germany)for Gd,and spark optical emission spectroscopy(OES,Spectrolab M9 Kleve,Germany)for Zr.The metallographic specimens for microstructural observations were etched at room temperature in a solution of 8 g picric acid,5 ml acetic acid,10 ml distilled water and 100 ml ethanol after mechanical polishing. Microstructures were characterized using an optical light microscope(Reichert-Jung MeF3)with a digital camera attachment. Grain sizes were determined using the line intercept method described in ASTM standard E 112-13[29]

Fig.5(b)shows the yield strength ratios(TYS/CYS)for extruded Mg–Gd alloys.When the asymmetry ratios decreased from 1.77 to 1,the alloys with 5–15 wt%Gd had very similar yield strength to those obtained from both tensile and compression tests.This indicates that adding Gd element is an effective method for reducing the t/c yield asymmetry of extruded Mg alloy.

4.Discussion

4.1.Solid solution effects on hardness

其中河北镇和漫水河站采用实测雨量过程，其余3站采用人工分配雨量。降雨主要集中在两个时段，一是12：00至15：00共3个小时，河北镇降雨127.4 mm，漫水河降雨98mm；二是 16：00至 22：00共 6 个小时，河北镇降雨369 mm，漫水河降雨279 m，雨量和雨强均达到极端天气情况。

Lee et al.[4]found that H followed the Hall-Petch relationships(Eq.(1)).However,in this case grain size has little effect on hardness of Mg–Gd alloys.As shown in Fig.6,the hardness of Mg–Gd alloy exhibits grain size independence according to Eq.(1),and kH value is given in Table 2.Comparison with the kH value of Al–Mg alloy(10.0–50.9 kg mm-3/2)[35]shows that the effect of grain size on Mg–Gd alloy is significantly lower than that of Al-Mg alloy.

4.2.The Hall-Petch constants for yield strength

Fig.5.(a)Yield strength of Mg–Gd alloys.The solid line denotes the tensile test,and the dash line denotes the compressive test;(b)t/c asymmetry in yield behavior of extruded Mg–Gd alloys.

Fig.6.Variation in Vickers hardness with d-1/2 for Mg–Gd alloy.

Table 2 Hall-Petch constant for hardness of Mg–Gd alloys.

Alloy kH(kg mm-3/2)Mg–2 wt%Gd -1.00 Mg–5 wt%Gd 1.98 Mg–10 wt%Gd 0.13 Mg–15 wt%Gd -0.23

Fig.7.Hall-Petch content calculation,using TYS and CYS data for Mg–Gd.The block diagrams and solid lines denote tensile data;the circle dots and dashed lines denote compression.

The strengthening effects in the Mg–Gd alloys originate from solid solution and grain boundary strengthening effects.Previous work[9]has shown that Gd in solution has stronger effects on ky value.The Hall-Petch relation(Eq.(2))of studied Mg–Gd alloys was calculated by yield strength and average grain diameter,as shown in Fig.7.The results of Hall-Petch constants are given in Table 3.In this study,since the pure Mg only had two different grain sizes(T4 state and extruded),the values for ky for pure Mg in Table 3 are from Ref.[9].

The effects of Gd onσ0 and ky are shown in Fig.8.The Gd has strong effects on both tension and compressive notional Friction stress.For pure Mg,theσ0 shows a big difference between tension and compression;on the contrary,Mg–Gd alloys show no tension/compression asymmetry in theσ0.The ky-values obtained from tensile and compressive tests for Mg–2Gd alloy were 0.27 and 0.16 MPa m1/2,respectively.The t/c asymmetry of extruded Mg–2Gd alloys was 1.2,which means texture still affects the mechanical properties of the alloy,and caused the different ky-values for tension and compression[36].Similarto the notional friction stress, there was no tension/compression asymmetry in the ky value,which increased from 0.19 to 0.30 MPa m1/2 with Gd content increasing.

Table 3 Hall-Petch Constants.

Alloy ky(MPa m1/2) σ0(MPa)Tension Compression Tension Compression Pure Mg 0.23±0.02 0.25±0.02 10.06 10.75 Mg–2 wt%Gd 0.27±0.02 0.16±0.03 38.38±1.88 41.72±3.44 Mg–5 wt%Gd 0.19±0.01 0.19±0.02 67.77±0.67 66.03±1.89 Mg–10 wt%Gd 0.26±0.02 0.24±0.01 81.21±1.88 85.61±1.74 Mg–15 wt%Gd 0.29±0.02 0.31±0.05 92.45±2.73 92.50±2.43

4.3.The yield strength of Mg–Gd polycrystalline alloys

The results of tensile and compression tests(Fig.5(a))clearly show that strain hardening occurs in all the studied alloys.Combined with hardness test results,the mechanical properties Mg–Gd alloys can be enhanced by increasing the amount of alloy solute atoms.

Fig.4 summarizes the results of hardness tests on Mg–Gd alloys under different treatments,which indicates near linear increases of hardness with solute concentration(≈25 kg mm-2/at%Gd)for both T4 treated and extruded alloys.These values are dramatically higher than those reported for Mg–Al(≈3.3 kg mm-2/at%Al)[15],Mg–Zn(≈9 kg mm-2/at%Zn)[33],Mg–Y(≈13.23 kg mm-2/at%Y)[16],and Mg–Sn alloys(≈6.88 kg mm-2/at%Sn)[34],and even much higher than for the Mg–Gd alloys(≈14 kg mm-2/at%Gd)which reported by Gao et al.[17].

Fleischer[18]and Labusch[19]reported that the strength in metallic materials was related to the concentration of solute atoms at room temperature.The relationship between yield strength and solute concentration is given by the following equations:

我和他们是不一样的，我自己这么坚信。那个时候的我满脑子都是尝试雷蒙德·卡弗的极简小说和品钦为代表的极繁小说（或名“歇斯底里现实主义”、“精雕细琢后现代派”）的冲动。我坐在地板上，靠着床沿坐着，身边的冰可乐冷凝出来的水把宽松的裤子打湿了一块。我那时觉得，我的小说里应该有一只流浪猫。

whereσ0.2 is the 0.2%yield strength andσm is the strength contributed from the matrix.In this case,theσm value is the same asσ0(Mg)for pure Mg in Table 3.The calculatedσ0(MgGd)value for Mg–Gd alloys is as follows

The effect of solid solution strengtheningσys can be calculated as follows:

Fig.9 presents the relative contribution of individual strengthening mechanisms in Eq.(7)to the yield strength of Mg–Gd alloy.The yield stress contributes from solid solute Gd was calculated with Eq.(9).The solid solution strengthening shows remarkable effect on yield strength of Mg–Gd alloy in the Fig.9.

随着当前信息技术的快速发展，微信、微博以及各类交友软件都在不断的涌现，这些新媒体传播方式的出现，让原本信息接受能力相对较强，且对于外界各种新鲜事物都充满了好奇心的大学生极容易受到诱导。可以说，在现如今的新媒体环境下，其在给高校学生心理健康教育工作带来便利的同时，也带来了较大冲击力，因此，高校只有不断加强对于心理健康教育工作的重视度，将心理健康教育和新媒体环境进行有效的结合，才能够更好的推进高校学生心理健康教育事业的发展。

For full solid solution alloy,the yield strength of its polycrystals can be represented by the following equation:

其中可研阶段东线泵站抽水电价为0.5元/kWh。考虑到近几年各地电价水平已多次调整，建议按目前江苏、山东两省普通工业实际电价水平进行测算。

whereσy0 is the yield stress of pure magnesium;ZF and ZL are constants;ξF and ξL are different linear combinations of the size misfit parameter and shear modulus misfit parameter,respectively;G is the shear modulus of pure magnesium;and c is the atomic concentration of solute.

在线诊断开始之前要有一定量的原始正常样本和原始故障样本，分别对正常样本抗体库和故障样本抗体库进行初始化，再开始在线故障诊断。

The data points in Fig.10 have been plotted following Fleischer and Labusch´s equations with n= 1/2 and 2/3.The best fitting lines through the origin show that the alloys follow Eqs.(10)and(11)well.The slopes of fitting lines for TYS of Mg–Gd alloys are 523 and 926 for n= 1/2 and 2/3(R 2= 0.97 and 0.97), respectively. Compared with the strengthening rates of Al(118 and 196)[15],Zn(578 and 905)[33]and Y(737 and 1249)[16],Gd shows much higher solution strengthening ability than Al,and similar ability with Zn,but lower than Y.The solid solution strengthening rate of Gd in this study is lower than that in Gao's report(683 and 1168)[17].In Gao's study,only a single value of σ0(46.5 MPa)and ky(0.19 MPa m1/2)for all Mg–Gd alloys were used to calculated the grain size effect,which might cause the different result.

Fig.8.Effect of Gd content on Hall-Patch constants.(a)Notional friction stress;(b)stress intensity factor.

Fig.9.Relative contribution of individual strengthening mechanisms to the(a)tensile and(b)compressive yield strength of Mg–Gd alloys.

Fig.10.Δσs of Mg–Gd alloys which calculated with(a)tensile and(b)compressive test result as a function of cn for given values of n.

Gao[17]has calculated the interaction parameter(ε)which defined as a combined effect of atomic size(δ)and shear modulus(G).According to the result,the solid solution strengthening rate should have the sequence as Zn>Al>Y>Gd.The investigation on the effect of those alloying elements on the chemical bonding of solid solute Mg alloy suggested that Gd is not only significantly enhancing the bond energy between Gd and Mg but also between Mg atoms.Compared with Al and Zn,the covalent bond give rise to higher solution strengthening ability,even Gd has lower size/modulus misfits with Mg[37].Additionally,the slopes of fitting lines for CYS are 524 and 927 for n= 1/2 and 2/3(R =2 0.97 and 0.99),respectively,which is similar as those of tension data.

5.Summary

Solid solution effects on the hardness and yield stress were investigated for Mg–Gd and Mg–Gd–Zr alloys with Gd contents between 2 and 15 wt%.The hardness linearly increases with increasing Gd content with a slope of ≈25 kg mm-2/at%Gd for alloys without and with Zr addition.Grain size has little effect on hardness of Mg–Gd alloy.Hall-Petch constants have been calculated with tensile and compressive data.For the tensile test,with the stress intensity factor,ky,strength data firstly decreases from 0.27 MPa m1/2 for Mg–2 wt%Gd alloy to 0.19 MPa m1/2 for Mg–5 wt%Gd alloy,then increases to 0.29 MPa m1/2 for Mg–15 wt%Gd alloy.However,ky is nearly linear increased form 0.16–0.31 MPa for compressive test.After correcting for grain size strengthening,the yield strengths of tension and compression both increase linearly with cn,where c is the atom concentration of Gd,and n=1/2 or 2/3.

Acknowledgments

The present work was co-supported by the China Scholarship Council,China,Grant ID:201406890032.

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