Effect of consolidation parameters on mechanical properties of Cu-based bulk amorphous alloy consolidated by hot pressing
来源期刊:中国有色金属学报(英文版)2012年第8期
论文作者:蔡安辉 熊翔 刘咏 安伟科 周果君 罗云 李铁林 李小松
文章页码:2032 - 2040
关键词:热压; 铜基非晶合金; 应变极限; 固结;力学性能
Key words:hot pressing; Cu-based amorphous alloy; strain limit; consolidation; mechanical property
摘 要:采用雾化法制备Cu50Zr40Ti10非晶合金粉末,在大气环境下将其热压成型为块体非晶合金,并基于L9(34)正交实验对热压成型条件进行优化。固结成型的Cu50Zr40Ti10块体非晶合金的抗压强度和应变极限值分别达到1090.4 MPa和11.9 %。固结压力显著影响块体非晶合金的应变极限和抗压强度,但是固结温度的影响不显著。初始成形力对块体非晶合金的抗压强度的影响不显著而对应变极限的影响很显著。Cu50Zr40Ti10非晶合金粉末的最优热压成型工艺条件为:首先在150 MPa压力下进行预成型,然后在380 ℃和450 MPa条件下进行热压。
Abstract: Cu50Zr40Ti10 bulk amorphous alloys were fabricated by hot pressing gas-atomized Cu50Zr40Ti10 amorphous powder under different consolidation conditions without vacuum and inert gas protection. The consolidation conditions of the Cu50Zr40Ti10 amorphous powder were investigated based on an L9(34) orthogonal design. The compression strength and strain limit of the Cu50Zr40Ti10 bulk amorphous alloys can reach up to 1090.4 MPa and 11.9 %, respectively. The consolidation pressure significantly influences the strain limit and compression strength of the compact. But the mechanical properties are not significantly influenced by the consolidation temperature. In addition, the preforming pressure significantly influences not the compression strength but the strain limit. The optimum consolidation condition for the Cu50Zr40Ti10 amorphous powder is first precompacted under the pressure of 150 MPa, and then consolidated under the pressure of 450 MPa and the temperature of 380 ℃.
Trans. Nonferrous Met. Soc. China 22(2012) 2032-2040
CAI An-hui1, XIONG Xiang2, LIU Yong 2, AN Wei-ke1, ZHOU Guo-jun1, LUO Yun1, LI Tie-lin1, LI Xiao-song1
1. College of Mechanical Engineering, Hunan Institute of Science and Technology, Yueyang 414006, China;
2. State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China
Received 7 August 2011; accepted 5 April 2012
Abstract: Cu50Zr40Ti10 bulk amorphous alloys were fabricated by hot pressing gas-atomized Cu50Zr40Ti10 amorphous powder under different consolidation conditions without vacuum and inert gas protection. The consolidation conditions of the Cu50Zr40Ti10 amorphous powder were investigated based on an L9(34) orthogonal design. The compression strength and strain limit of the Cu50Zr40Ti10 bulk amorphous alloys can reach up to 1090.4 MPa and 11.9 %, respectively. The consolidation pressure significantly influences the strain limit and compression strength of the compact. But the mechanical properties are not significantly influenced by the consolidation temperature. In addition, the preforming pressure significantly influences not the compression strength but the strain limit. The optimum consolidation condition for the Cu50Zr40Ti10 amorphous powder is first precompacted under the pressure of 150 MPa, and then consolidated under the pressure of 450 MPa and the temperature of 380 ℃.
Key words: hot pressing; Cu-based amorphous alloy; strain limit; consolidation; mechanical property
1 Introduction
Bulk amorphous alloys have attracted considerable attention both in fundamental research and engineering application due to their many unique properties, such as excellent corrosion resistance, remarkably high strength and hardness, and large elastic deformation limit [1,2]. Most of bulk amorphous alloys are fabricated by casting methods, and their shape and size are seriously limited in the case of the alloys having relatively low glass forming ability, which also limits the range of their applications [3,4]. Powder metallurgy method can produce good amorphous microstructures, and has an advantage of fabricating larger bulk amorphous alloy products in variety of shapes than casting methods [5].
The powder metallurgy methods for consolidating amorphous alloy powders include hot/cold pressing [6-9], extrusion [10,11], rolling [12], spark plasma sintering [13-16], pulsed current sintering [17], microwave induced sintering [18], and so on. However, these consolidation methods require a vacuum condition, resulting in the limit of their engineering applications. Some investigations on the powder consolidation have been conducted without vacuum protection. KIM et al [8] investigated the magnetic properties of Fe-Si-B amorphous powder cores prepared by cold pressing using phenol resin as a binder under the pressure of 18 t/cm2. Although the glassy powder cores exhibited stable permeability in the high frequency of 10 MHz, their mechanical properties were undoubtedly worse due to the addition of the binder. ANDO et al [19] consolidated Nd-Fe-B amorphous powders using explosive compaction. Although the highly dense compact (>95% relative density) without cracks was obtained under an optimum condition, a very thin melted layer was observed at the interface of powder particles. DROZDZ et al [20] produced a bulk amorphous cast iron by powder compaction at a high pressure (7.7 GPa), and found that the samples pressed at room temperature exhibit big, well seen porosity. KIM et al [21] investigated the microstructure and mechanical properties of powder injection molded product of Cu-based amorphous powder, and found that the specimens sintered at 470 ℃ between Tg and Tx showed powders just stuck together, and the injection molded Cu-based amorphous powders were hardly sintered even at temperatures just below the melting temperature as most of amorphous phases were replaced by crystalline phases. These attempts indicate that it is difficult for obtaining ideal compacts that consolidated the amorphous powder without high temperature between Tg and Tx. Among all mentioned consolidation methods, hot pressing is simple in the equipment and technology. Therefore, how to obtain ideal bulk amorphous alloys using hot pressing between Tg and Tx without vacuum protection and degassing procedure is a challenge for speeding up engineering application of bulk amorphous alloys.
On the other hand, the main factors influencing the consolidation effect are the pressure, time, and temperature, respectively. KIM et al [13] investigated the effects of consolidation temperature (between Tg and Tx) and pressure (80 MPa and 300 MPa) on microstructures and mechanical properties of Cu-based bulk amorphous alloys consolidated by spark plasma sintering. They found that the density and compression strength increased with increasing the temperature at the pressure of 80 MPa and with the same consolidation time. The density and compression strength increased with increasing the consolidation time at the pressure of 80 MPa and at the same temperature. In addition, the compression strength increased with increasing the consolidation time at the pressure of 300 MPa and at the same temperature, inverse for the hardness. DROZDZ et al [20] investigated the consolidation behavior of as-milled Fe-based amorphous powder at high pressure (7.7 GPa) and at the elevated temperature below Tx using hot pressing. They found that the density increased with increasing the temperature, and the compaction processed at temperature up to 520 ℃ (approximately at Tx) enabled the production of bulk amorphous alloys. However, the significance of these factors on the properties of bulk amorphous alloys has scarcely been investigated. Thus it is important for further investigating the effect of these factors on the properties of bulk amorphous alloys fabricated by powder metallurgy without vacuum protection and degassing procedure.
It is well known that Cu-Zr-Ti alloy system is a good glass former whose critical dimension forming amorphous state can reach up to 5 mm [22]. The high ΔTx (66.7 K [23]) of Cu50Zr40Ti10 amorphous alloy indicates its high thermal stability, which is possible for investigating the effect of the consolidation temperature on its property. In addition, the hardness of Cu50Zr40Ti10 alloy was the lowest in Cu(50+x)Zr(40-x)Ti10 alloy system [24], which would be a good condition for the hot pressing.
In the present work, Cu50Zr40Ti10 bulk amorphous alloys were obtained by the consolidation of gas-atomized amorphous alloy powder by using hot pressing technique based on an L9(34) orthogonal test. Its strain limit and compression strength were investigated.
2 Experimental
2.1 Experimental plan
For the elaboration of experimental plan, the orthogonal method for three factors at three levels was adopted. The studied factors and the assignment of the corresponding levels are listed in Table 1. The chosen array is the L9(34) which has nine rows corresponding to the number of tests (8 degrees of freedom) with three columns at three levels, as listed in Table 2. The factors are assigned to the columns. The plan of experiments is made of nine tests (array rows), in which the first column is assigned to the preforming pressure (A), the second column to the consolidation pressure (B), the third column to the consolidation temperature (C), and the forth column to the error (D), respectively.
Table 1 Assignment of levels to factors
Table 2 Orthogonal array L9(34), compression strength σc, and strain limit of bulk amorphous alloys
2.2 Experimental procedures
Master ingots of the Cu50Zr40Ti10 alloy (composition is given in nominal mole fraction) were prepared by arc melting a mixture of high purity Cu, Zr and Ti in a Ti-gettered argon atmosphere. The glassy alloy powders were produced by a high pressure argon gas atomization method. Atomization of the Cu50Zr40Ti10 alloy was carried out in a close coupled nozzle atomizing system. The master alloy was induction heated at 1200 K in an alumina crucible under a vacuum of 10-2 Pa. The melt was teemed through a guide tube, and atomized by a jet of Ar at 4.0 MPa. The Cu50Zr40Ti10 powder was collected and sieved in a closed system filled with inert gas. A uniaxial pressing method was conducted with top and bottom stainless steel punches. In order to alleviate the oxidation of the powders, the powders were precompacted at pressure between 75 and 225 MPa before hot pressing. The powders were put into a stainless steel mold, heated by a heating buff at a heating rate of 10 K/min, and then hot pressed at pressure between 300 and 600 MPa and temperature between 360 and 400 ℃ for 30 s. The detailed hot pressing parameters are shown in Table 1. The hot pressed specimens are in a cylindrical shape with a diameter of 10 mm and a height of about 15 mm.
2.3 Testing methods
The amorphous structure of the powder and the compact was examined by X-ray diffractometry (XRD) in reflection with a monochromatic Cu Kα radiation. The thermal stability of the amorphous powders was examined by differential scanning calorimetry (DSC) at a heating rate of 0.5 K/s. The density of the specimens was determined by the Archimedean method. Mechanical properties under uniaxial compression were measured using a mechanical testing machine at a constant crosshead speed which corresponds to the initial strain rate of 5×10-2 s-1. The microstructure was characterized by scanning electron microscopy (SEM) and optical microscopy (OM). The experimental results of the compression strength and strain limit are shown in Table 2.
3 Results
3.1 SEM image of gas-atomized powder
The SEM image of the gas-atomized Cu50Zr40Ti10 powder is shown in Fig.1. The size of the gas-atomized powder is less than 50 μm. In addition, most of the gas-atomized powders are in spherical form and this can be suitable for the consolidation of powder by hot pressing.
3.2 XRD analysis
The formation of amorphous phase of the gas-atomized Cu50Zr40Ti10 powder was confirmed by X-ray diffraction. The XRD pattern of the gas-atomized powder less than 50 μm is shown in Fig. 2. As can be seen in Fig. 2, fully amorphous phase of the gas- atomized powder without any crystallinity is formed in the particle size less than 50 μm. Therefore, the Cu50Zr40Ti10 amorphous powders with a particle size less than 50 μm were used for subsequent consolidation in this study.
Fig. 1 SEM image of gas-atomized Cu50Zr40Ti10 powder
Fig. 2 X-ray diffraction pattern of gas-atomized powder less than 50 μm
3.3 DSC analysis
The thermal stability and crystallization behavior of the Cu50Zr40Ti10 amorphous powders were examined by DSC measurement. Figure 3 shows the DSC curve of the Cu50Zr40Ti10 amorphous powder with a particle size less than 50 μm at a constant heating rate of 0.5 K/s. As shown in Fig. 3, the onset temperature of crystallization Tx is 693.2 K. Below the onset of crystallization, the glass transition Tg, which is shown as an endothermic reaction in the DSC curve, occurs at ~629.5 K. Thus a fairly large supercooled liquid region ?Tx of ~63.7 K exists in gas-atomized Cu50Zr40Ti10 amorphous powder, indicating that the studied amorphous powder can be used to investigate the effect of the consolidation temperature on the properties of the consolidated sample. However, the ?Tx of the studied amorphous alloy powder is slightly lower than the literature data measured with melt spun Cu50Zr40Ti10 amorphous ribbons [23].
Fig. 3 DSC curve of Cu50Zr40Ti10 amorphous powder with particle size less than 50 μm at constant heating rate of 0.5 K/s
3.4 Range and variance analysis
The gas-atomized Cu50Zr40Ti10 amorphous powder was consolidated by a hot pressing apparatus without vacuum protection and by degassing procedure, and the bulk amorphous alloy compacts were prepared in the form of cylinder with a diameter of 10 mm and a height of ~15 mm. The preforming pressure, consolidation pressure and consolidation temperature were varied with parameters on processing the consolidation of amorphous powder. An L9(34) orthogonal test was adopted to investigate the effect of three consolidation parameters on the compression strength and strain limit of the compacts, respectively. The parameters and their corresponding values are shown in Table 1. The compressive stress—strain curves for the compacts are shown in Fig. 4. The measured compression strength and strain limit of the compacts are listed in Table 2. An analysis of variance of the data was done with the compression strength and strain limit for analyzing the effect of the preforming pressure, consolidation pressure, and consolidation temperature on the total variance of the results, respectively. In order to analyze the significance of three factors on the compression strength and strain limit of the compacts, the fourth column (D) in L9(34) orthogonal array is assigned to the error. Table 3 and Table 4 show the results of the analysis of variance for the strain limit and compression strength, respectively. As shown in Table 3, the deviation of the consolidation temperature (C) is less than that of the error (D). This indicates that the consolidation temperature does not influence the strain limit of the compact, thus the sum of the deviation of C and D is chosen as the deviation of the error. After being done so, it is clearly from Table 3 that the preforming pressure and consolidation pressure both significantly influence the strain limit of the compact. As shown in Table 4, the deviation of the preforming pressure (A) and consolidation temperature (C) is less than that of the error (D). This indicates that the preforming pressure and consolidation temperature do not influence the compression strength of the compact, so the sum of the deviation of A, C and D is chosen as the deviation of the error. One can find from Table 4 that the consolidation pressure significantly influences the compression strength of the compact.
Fig. 4 Compressive stress—strain curves of compacts at strain rate of 5×10-2 s-1 (Numbers 1-9 are test number shown in Table 2)
Table 3 Variance analysis for strain limit
Table 4 Variance analysis for compression strength
In addition, the range analysis was also performed on the strain limit and compression strength in order to obtain the optimal consolidation condition for the compacts (see Table 3 and Table 4), respectively. As shown in Table 3, the ascending sequence of the range of three factors for the strain limit is the consolidation temperature, preforming pressure, and consolidation pressure, respectively. As shown in Table 4, the ascending sequence of the range of the factors for the compression strength is the preforming pressure, consolidation temperature, and consolidation pressure, respectively. These results indicate that the influence degree of three factors on the compression strength and strain limit increases according to the ascending sequence of the range, which is also coherent with the results of the analysis of variance.
On the other hand, the averaged values of the strain limit and compression strength for each factor at different levels are plotted in Fig. 5 in order to analyze the relationships between three factors and the mechanical properties, and to obtain the optimal consolidation conditions for the fabrication of the compacts. As shown in Fig. 5, the strain limit and compression strength first both increase and then decrease with the increase of three factors. The strain limit and compression strength both reach up to a maximum at the second level of three factors, respectively. This indicates that the optimum combinations of three factors for the strain limit and compression strength both are A2B2C2. Thus the optimum consolidation condition for the Cu50Zr40Ti10 amorphous powder is first precompacted under the pressure of 150 MPa, and then consolidated under the pressure of 450 MPa at the temperature of 380 ℃, respectively, at the strain limit and compression strength point of view. In addition, the theoretical optimum values for the strain limit and compression strength are both calculated according to the orthogonal theory. The optimal theoretical values are 12.1 % for the strain limit and 1180.7 MPa for the compression strength, respectively, which are slightly higher than the practical optimum values shown in Table 2.
Fig. 5 Averaged values of strain limit and compression strength for each factor at different levels: (a) Consolidation temperature; (b) Preforming pressure; (c) Consolidation pressure
3.5 Microstructure and fractography of compacts
In order to investigate the bonding between the amorphous alloy powders, the polished cross sections of the compacts were examined by using an OM. Figure 6 presents the OM microstructures of the polished cross sections of the compacts consolidated under different consolidation temperatures and consolidation pressures at the preforming pressure of 75 MPa. It is noted that there are the same results for the compacts preformed at other pressures. As shown in Fig. 6, there are many pores (dark parts) resulted from the original pores before the consolidation and the pores resulted from the pull-out of the powder during polishing, indicating that the fully densification compact cannot be obtained under the studied conditions. In addition, the density of the compacts first increases with increasing consolidation temperature and pressure and then decreases when the consolidation temperature and the consolidation pressure exceed 380 ℃ and 450 MPa, respectively. The powder boundary is more and clearer when the consolidation temperature and the consolidation pressure reach up to 380 ℃ and 450 MPa, respectively.
Fig. 6 OM microstructures of polished cross-sections of compacts consolidated under different consolidation temperatures and pressures at preforming pressure of 75 MPa: (a) 300 MPa, 360 ℃, ρ=6.67 g/cm3; (b) 450 MPa, 380 ℃, ρ=7.03 g/cm3; (c) 600 MPa, 400 ℃, ρ=6.81 g/cm3
In addition, SEM imaging was conducted on the fracture surface of the test samples in order to investigate the mechanical response of the compacts. The typical SEM fractography of the compacts is shown in Fig. 7. The fracture surface shows the classic vein-like and smooth cleavage fracture patterns as well as the fracture along the particle boundaries. In addition, there are many pores between the amorphous alloy powders and the cracks initiate and propagate along the particle boundaries.
Fig. 7 Typical SEM image of compression specimen fabricated under performing pressure of 75 MPa, consolidation pressure of 450 MPa and consolidation temperature of 380 ℃
4 Discussion
It is well known that the mechanical property of the compact depends on the pore, inclusion, amount of particle boundary, and so on. As shown in Fig. 5(a), the compression strength and strain limit of the compacts both first increase with increasing consolidation temperature and then decrease when the consolidation temperature exceeds 380 ℃. As indicated in Refs. [25,26], the viscosity of the amorphous alloy decreases with increasing temperature in the supercooled liquid region, thus the deformation capacity of amorphous alloy increases with increasing temperature. It should result in the increase of mechanical property of the compact with increasing consolidation temperature, which is coherent with the results of Ref. [13]. However, the Cu50Zr40Ti10 amorphous powders would be oxidized by the residual air in the pores of the precompacts due to without degassing and vacuum protection during heating [27]. Thus the hardness and strength of the amorphous powder are too high to be deformed at ambient temperature even at very high pressure [8,20]. As shown in Fig. 6, the density of the compacts is not improved and the powder boundary is clearer and more when the consolidation temperature reaches up to 400 ℃. Thus the effective load area decreases due to the decrease of the density of the compact and the position of the initiation of the cracks increases due to the increase of the magnitude of the powder boundary when the consolidation temperature reaches up to 400 ℃. This indicates that the mechanical property of the compact will decrease when the consolidation temperature reaches up to 400 ℃. In order to further clarify this fact, XRD analyses were performed on the compacts consolidated under different consolidation temperatures in Fig. 8. It is clearly seen from Fig. 8 that the compacts are partially oxidized and the oxides are composed of CuO and ZrO2. The oxidization of the amorphous powder is more and more serious with increasing consolidation temperature. These hard and brittle oxides will deteriorate the consolidation capacity of the powders, but these oxides could play a reinforce role in the compact when the content of these oxides is less than a critical content. The comprehensive effects of two factors would result in the increase of the mechanical properties of the compacts. However, when the content of the oxides increases up to a critical value, the oxides could play not a reinforce role but a deteriorate role. It would result in the decrease of the mechanical properties.
Fig. 8 X-ray diffraction patterns of compacts consolidated at different consolidation temperatures
As shown in Fig. 5(b), the compression strength and strain limit of the compact both increase when the preforming pressure is less than 150 MPa. It would be due to the increase of the densification of the precompact with increasing preforming pressure, resulting in the alleviation of oxidation of the powders. Thus the mechanical properties of the compact are improved. However, the mechanical properties of the compacts decrease when the preforming pressure exceeds 150 MPa. It would be resulted from the formation of the microcracks due to the cracking of the air oxides on the surface of the gas-atomized powder in the precompact under high preforming pressure, resulting in the increase of the air content in the precompact which leads to more serious oxidization of the amorphous powders. Thus the powders are more difficultly consolidated, resulting in the increase in the defects, inclusions and amount of particle boundaries. In fact, YAN et al [27] investigated the surface structure of Cu-based gas-atomized amorphous powders, and found that amorphous powders were enveloped by a thick (30 nm) oxide ceramic. YAMASAKI et al [28] also found the same phenomenon during investigation of vacuum degassing behavior of Zr-, Ni-, and Cu-based amorphous alloy powders. Therefore, the mechanical properties of the compacts are deteriorated.
As shown in Fig. 5(c), the compression strength and strain limit of the compacts increase with increasing consolidation pressure when the consolidation pressure is less than 450 MPa. It is well known that the densification of the compact increases with increasing consolidation pressure [13], resulting in the increase of the mechanical properties of the compacts. However, the mechanical properties of the compacts decrease when the consolidation pressure exceeds 450 MPa. It would result from not only the formation of the cracks due to the abruption of the oxide film on the surface of the powder but also the increase of the position of the initiation of the cracks due to the increase of the magnitude of the powder boundaries, leading to the decrease of the mechanical properties of the compact under high consolidation pressure. These results are coherent with the results observed from Fig. 6.
As shown in Table 2, the fracture strength of the compact is significantly lower than that of the corresponding amorphous ribbon [23]. The reason would be due to the fact that the structure of the Cu50Zr40Ti10 amorphous ribbon is more homogeneous than that of the compact. As shown in Fig. 6 and Fig. 7, many holes emerge in the compacts, which results in the decrease of the effective load area. At the same time, many powder boundaries can be observed on the polished cross section of the compact in Fig. 6. It is advantageous of the initiation and propagation of the cracks in Fig. 7. These results would lead to the remarkably decrease of the compression strength of the compact. However, the strain limit of the compact is significantly more than that of the Cu50Zr40Ti10 amorphous ribbon [23].
In addition, the compacts exhibit a high strain limit in Fig. 4. As mentioned above, the compact can be considered a porous amorphous/oxide composite. These phenomena are also in agreement with the results of the porous amorphous alloys [29,30] and the amorphous/ crystalline composites [31]. The compacts can be largely deformed under low load due to the existence of the holes during initial deformation. With increasing deformation, the sample is gradually densified due to the close of the holes during the compression, and the load area gradually increases. Thus the compacts exhibit the large strain limit.
5 Conclusions
1) The size of the gas-atomized Cu50Zr40Ti10 amorphous powders is less than 50 μm. The glass transition temperature (Tg), the crystallization temperature (Tx), and the supercooled liquid region (?Tx) of the gas-atomized Cu50Zr40Ti10 amorphous powders are 629.5, 693.2, and 63.7 K, respectively.
2) The consolidation pressure significantly influences the strain limit and compression strength of the compact. But the mechanical properties are not significantly influenced by the consolidation temperature. In addition, the preforming pressure significantly influences not the compression strength but the strain limit.
3) The optimum consolidation condition for the Cu50Zr40Ti10 amorphous powder is first precompacted under the pressure of 150 MPa, and then consolidated under the pressure of 450 MPa and the temperature of 380 ℃.
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蔡安辉1,熊 翔2,刘 咏2,安伟科1,周果君1,罗 云1,李铁林1,李小松1
1. 湖南理工学院 机械工程学院,岳阳 414006;
2. 中南大学 粉末冶金国家重点实验室,长沙 410083
摘 要:采用雾化法制备Cu50Zr40Ti10非晶合金粉末,在大气环境下将其热压成型为块体非晶合金,并基于L9(34)正交实验对热压成型条件进行优化。固结成型的Cu50Zr40Ti10块体非晶合金的抗压强度和应变极限值分别达到1090.4 MPa和11.9 %。固结压力显著影响块体非晶合金的应变极限和抗压强度,但是固结温度的影响不显著。初始成形力对块体非晶合金的抗压强度的影响不显著而对应变极限的影响很显著。Cu50Zr40Ti10非晶合金粉末的最优热压成型工艺条件为:首先在150 MPa压力下进行预成型,然后在380 ℃和450 MPa条件下进行热压。
关键词:热压; 铜基非晶合金; 应变极限; 固结;力学性能
(Edited by LI Xiang-qun)
Foundation item: Project (50874045) supported by the National Natural Science Foundation of China; Projects (200902472, 20080431021) supported by the China Postdoctoral Science Foundation; Project (10A044) supported by the Research Foundation of Education Bureau of Hunan Province of China
Corresponding author: CAI An-hui; Tel: +86-730-8648848; E-mail: cah1970@sohu.com
DOI: 10.1016/S1003-6326(11)61425-8