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Hot deformation behavior of Mg2B2O5 whiskers reinforced AZ31B magnesium composite fabricated by stir-casting
Materials Science & Engineering A 573 (2013) 148–153
Contents lists available at SciVerse ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Hot deformation behavior of Mg2B2O5 whiskers reinforced AZ31B magnesium composite fabricated by stir-casting Yunpeng Zhu a, Peipeng Jin a,n, Peitang Zhao b, Jinhui Wang a, Li Han a, Weidong Fei a,b a b
Institute of Metal Research, Qinghai University, Xining 810016, PR China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 July 2012 Received in revised form 21 February 2013 Accepted 25 February 2013 Available online 6 March 2013
The hot deformation behavior of Mg2B2O5w/AZ31B composite was investigated by compression test at temperatures between 473 K and 673 K with the strain rates from 10 4 s 1 to 1 s 1. The constitutive equations were established by taking peak stresses as the function of temperatures and strain rates. It was found that the function of exponential and power law creep equations broke down at low and high stresses for the composite, respectively. The hyperbolic sine law creep equation was in good agreement with experimental results and can be applied to all flow stresses under the various deformation conditions. The composite possesses slightly higher activation energy values than that of lattice self-diffusion of pure Mg, and the stress exponent was calculated to be about 6.6. The plastic deformation mechanism of the composites at high temperature was mainly through the lattice diffusion controlled dislocation climb. Dynamic recrystallization took place during hot compression, and grains became coarser at lower strain rate and higher temperature. & 2013 Elsevier B.V. All rights reserved.
Keywords: Magnesium matrix composite Hot compression Constitutive equations Deformation
1. Introduction Discontinuously reinforced magnesium matrix composites (DRMMCs) have attracted great attention because of their low density, high properties [1] and good hot forming ability. However, the low temperature plastic forming ability of magnesium matrix composite is relatively poor plastic forming ability due to the hexagonal close-packed (HCP) crystal structure of magnesium matrix. The brittle ceramic discontinuous reinforcements in the composites further limit the plastic forming ability of DRMMCs. Therefore, the magnesium composites are normally deformed at higher temperature [2]. It is important to improve the formability of DRMMCs at low temperature for purpose of wide applications. Over the past decades, the hot deformation behavior of discontinuously reinforced metal matrix composites have been extensively investigated [1–4]. The constitutive equations which describe the relationship between flow stress and strain rate are very useful in conducting secondary processing for DRMMCs. Three typical constitutive equations, the power, the exponential, and the hyperbolic sine laws, have been used to describe the deformation behavior of metals and metal matrix composites (MMCs) during hot working, such as aluminum composites [5,6]. The power law relationship has been generally applied in hot deformed magnesium alloy at low stresses [3,7], while the exponential law was used in that at high stresses [8,9]. The hyperbolic sine law, in which both power and exponential equations are involved, can be applied at a wider stress range successfully [10,11].
n
Corresponding author. Tel.: þ86 971 536 3028; fax: þ 86 971 531 0440. E-mail address: [email protected] (P. Jin).
0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.02.051
Furthermore, the stress exponent, n, and the activation energy, Q, can be calculated by constitutive equations, which are key parameters related to the deformation mechanisms of the materials. It was found that the composites fabricated by powder metallurgy (PM) process have abnormally high stress exponent and activation energy. For example, Kim et al. [12,13] have reported that SiCp/2124Al composite fabricated by PM process possesses unusually high stress exponent and activation energy (about 390 kJ/mol). Han and Chan [14] have reported the activation energy of 774 kJ/mol for a 6061Al composite reinforced with 20 vol% SiC whisker, which is much higher than that of 142 kJ/mol for lattice self-diffusion of pure Al [15]. However, knowledge is still lack for magnesium matrix composites with low fraction of reinforcements, and their hot deformation behavior of this kind of materials is still not fully understood. The aim of present study is to investigate the hot deformation behavior of as-cast AZ31B magnesium matrix composite reinforced with low volume fraction of Mg2B2O5 whisker (Mg2B2O5w/ AZ31B) composite. The hot deformation constitutive equation is determined by the analysis of flow stress data. The deformation mechanism was discussed in terms of the calculated stress exponent and the activation energy. The microstructures of the hot deformed composites were examined, and their effects on the deformation behavior were discussed.
2. Experimental Magnesium borate (Mg2B2O5w) whisker reinforced AZ31B magnesium matrix (Mg2B2O5w/AZ31B) composite were fabricated by
Y. Zhu et al. / Materials Science & Engineering A 573 (2013) 148–153
stir-casting with the 5 vol% of Mg2B2O5 whisker. The diameter and length of the whisker are in ranges of 0.2–2.0 mm and 20–50 mm, respectively. Cylindrical specimens, with the size of 10 mm in diameter and 15 mm in length, were machined from the composite ingot and tested compressively by Gleeble-1500 thermo-mechanical simulator. The uniaxial compression tests were carried out at temperatures ranging from 473 K to 673 K and various strain rates of 10 4 s 1, 10 3 s 1, 10 2 s 1, 10 1 s 1 and 1 s 1. Graphite was used to lubricate the die-workpiece interface. All specimens were heated up to the testing temperatures at a heating rate of 5 K/min, and then held at the temperature for 5 min before commencing the compression testing. The specimens were water quenched immediately after the compressive test. The microstructure of the deformed specimens was examined using Olympus-PMG3 optical microscopy (OM) and a TECNAIF30 transmission electron microscopy (TEM). The metallographic specimens were sectioned along the direction normal to the compression axis, and then was mounted, polished and etched by acetic–picric acid. TEM specimens were thinned by the ion milling.
0
The true stress–strain curves obtained at the strain rates of 10 s 1 and 0.1 s 1 and at different temperatures are shown in Fig. 1. Typically, the flow stress increases to a maximum initially due to the dominance of work hardening and then gradually until reach to a steady state. Such flow stress curve corresponds to the characteristic behavior of dynamic recrystallization (DRX) which overtakes initial work hardening [4,11,13]. Comparing flow curves in Fig. 1(a) with those in Fig. 1(b), it can be found that the flow curve exhibits lower peak stress (sp) and peak strain (ep) at low strain rate (10 3 s 1) than those at higher strain rate (0.1 s 1). Flow stress curves in Fig. 1 also illustrate the temperature effect on sp and ep, which decrease with the increase of temperature at two strain rates. 3
3.2. Constitutive equations Different constitutive equations have been used to describe the strain-stress flows of hot deformed alloys and composites [16–18]. The favorite equations are presented as follows: Q ð1Þ e_ ¼ AðsinhðasÞÞn exp RT
Q RT
e_ ¼ A00 expðbsÞexp
ð2Þ
Q RT
Q Z ¼ e_ exp RT
ð3Þ
ð4Þ
Q ¼R
! @ln s @lne_ e_ @ln s T @ 1=T
ð5Þ
Q ¼R
! @s @lne_ e_ @s T @ 1=T
ð6Þ
Q ¼R
! @lnðsinhðasÞÞ @lne_ e_ @lnðsinhðasÞÞ T @ 1=T
ð7Þ
3. Results and discussion 3.1. Flow stress–strain curves
e_ ¼ A0 sn exp
149
where A (A0 , A00 ), a ( ¼ b=n0 ), and b are constants of the material, n (n0 ) are stress exponent, Q is an apparent activation energy of the deformation, R is the gas constant. Z is the Zener–Hollomon parameter, also known as temperature compensated strain rate, which is determined by the strain rate e_ and temperature T. In previous studies three constitutive equations were employed to analyze the hot deformation behaviors of composite and monolithic alloys. It was found that different deformation mechanisms can be described by corresponding constitutive equations. However, it has not been clearly understood which constitutive equation can be used appropriately for the deformation of DRMMCs reinforced with relatively lower fraction of whisker. In present study, all constitutive equations mentioned above were tested and discussed in order to find a suitable equation which can properly describe the compressive deformation behavior of Mg2B2O5w/AZ31B composite. The values of A (A0 , A00 ), b, and n (n0 ) can be obtained from the plot of ln Z versus ln (sinh (as)), ln s, and s for different equations. However, the values of a and Q need to be determined first. In this study, the s was referred to the peak stress sp. The values of Q presented in Figs. 2–4 are determined by Eqs. (5)–(7), respectively. Constitutive equations are used to calculate hot
Fig. 1. True stress–strain curves for Mg2B2O5/AZ31B composites deformed at different temperatures (a) 10 3 s 1 and (b) 0.1 s 1.
150
Y. Zhu et al. / Materials Science & Engineering A 573 (2013) 148–153
Fig. 2. ln Z versus ln sp curve based on the power law (a) and comparison between calculated and measured sp values (b) for Mg2B2O5w/AZ31B composite.
Fig. 3. ln Z versus ln sp curve based on the exponent law (a) and comparison between calculated and measured sp values (b) for Mg2B2O5w/AZ31B composite.
compression stresses at various rates and temperatures. The calculated peak stresses from constitutive equations were compared with the measured stresses from compression tests. Fig. 2(a) shows the relationship of ln Z versus lnsp corresponding to the power law and the values of A0 and n0 are obtained according to the plot. Fig. 2(b) illustrates the comparison between calculated and measured peak stresses, sp. It can be seen that the deviation between the predicted value and measured value is significant at high stresses (sp 4140 MPa), and the maximum relative error is 54.3% at T¼673 K with higher strain rate e_ ¼ 1 s1 . These results indicate the breakdown of power law at high compressive stresses, which has been reported by McQueen and Galiyev [5,9]. According to the exponential law, the relationship of ln Z versus sp is shown in Fig. 3(a), and the values of A00 and b can be calculated. Although the correlation coefficient (R2) of ln Z versus sp is 0.99, the deviation between the predicted value and measured value is high at low stresses level (sp o40 MPa), as shown in Fig. 3(b). The maximum relative error is 93.8% at T¼673 K and strain rate e_ ¼ 104 s1 , which suggests the
breakdown of the exponent law at low stresses. This result is consistent with results reported by Galiyev and Ryan [9,19]. The good linear relationship of ln Z versus ln (sinh (asp)) was observed in Fig. 4(a) when the hyperbolic sine law was applied. The values of A and n were determined as 2.38 1012 and 6.6, respectively. From Fig. 4(b) shows the comparison between calculated and measured values of sp. It can be seen that the predicted values fit the measured value very well. The maximum relative error is 10.2% at T¼473 K and strain rate e_ ¼ 1s1 , and other relative errors are below 5%. Based on results in Fig. 4, the hyperbolic sine law can be applied over entire stress range for the composite tested in this study. 3.3. Microstructures Fig. 5(a) shows the microstructure of as-cast Mg2B2O5w/AZ31B composites. It can be seen that the Mg2B2O5 whisker located at the grain boundaries mostly and the mean grain size is about 200 mm. The higher magnification of Fig. 5(a) illustrates that the aspect ratio (length to diameter) of the whisker is in the range of
Y. Zhu et al. / Materials Science & Engineering A 573 (2013) 148–153
151
Fig. 4. ln Z versus ln sp curve based on the hyperbolic sine law (a) and comparison between calculated and measured sp values (b) for Mg2B2O5w/AZ31B composite.
10–50. The microstructures of specimens deformed under different deformation conditions are displayed in Fig. 5(b)–(f). Many twins were observed at such a high Z parameter which is similar to AZ serial alloy [20] in Fig. 5(b), due to the high activation energy and lack of easily activated independent slip systems of magnesium at low temperature. The strain is partially accommodated by twinning which are often in multiple parallel groups with some intersecting ones. As the temperature rises to 573 K, there was no twin observed. Instead, fine grains formed as the result of DRX appeared, as shown in Fig. 5(d). More detailed examination revealed that finer DRX grains mainly formed in the vicinity of Mg2B2O5 whiskers. This may indicate that the nucleation of DRX can be promoted by the reinforcement [1]. At 673 K, DRX grains grew larger overriding these as-cast coarse grains and twin boundaries have been invisible in Fig. 5(f). Microstructures of samples deformed at 673 K under different strain rates are presented in Fig. 5(c), (e), and (f). Their average grain sizes are about 11 mm, 9 mm and 5 mm, respectively. The results indicate that grain size increases with the decrease of strain rate and rise of temperature, which is similar to the results reported by AlSamman and Gottstein [21]. Fig. 6(a) and (b) shows the typical TEM micrographs of Mg2B2O5w/AZ31B composites compressed at different conditions. At low temperature 473 K, a number of deformation twins appeared and distributed uniformly as shown in Fig. 6(a). The occurrence of twinning at low temperature resulted in high compression stress. It can be seen that twins are parallel and end with sharp points at locations close to the grain boundary, which is similar to that observed by Myshlyaev et al. [22]. In Fig. 5(c)–(f), many equiaxed grains formed in specimens, indicating the occurrence of DRX during the compression. Typical dynamic recrystallized microstructure of the specimen compressed at 673 K and strain rate of 10 2 s 1 is shown in Fig. 6(b). Fine DRX grains in the matrix can be seen clearly, and there is nearly no visible dislocation. 3.4. Discussion Nieh et al. [23] have discussed main creep mechanisms of metals and composites, and they have suggested that the stress exponents predicted by theoretical models are dependent on the creep mechanism: n ¼1 for diffusional creep, n¼2 for grain boundary sliding, n ¼3 for glide controlled creep, n¼ 4–5 for
dislocation climb controlled creep, n48 for dispersion strengthened alloys. According to Fig. 4(a), the value of n ¼6.6 gave the best linear fitting at the entire temperature range. However, no deformation mechanism associated with n ¼6.6 has been proposed in literature. It has been reported that the stress exponent is not an integer [5,13]. In this study, the stress exponent is between 5 and 8. Therefore, the hot deformation mechanism of Mg2B2O5w/AZ31B composite may be dislocation climb creep or dispersion strengthened or the combination of both modes. In dispersion strengthened materials (n 48), the existence of the threshold stress (s0) can apparently causes an extremely high stress exponent [24]. One simple approach to confirm that if the value of stress exponent is reasonable or not (which suggests the deformation mode of the materials following either dislocation climb creep or dispersion strengthened) is to find the threshold stress. The threshold stress is estimated using the standard linear extrapolation method [3,16,25]. In order to determine the stress exponent reasonably, the stress was replaced by the effective stress se (se ¼ s s0) [26], in which s was replaced by sp in this study. Fig. 7 shows plots of the e_ 1=8 versus sp in double linear scales. Then, the threshold stress at each temperature was determined by extrapolating the linear plot to the point of zero strain rates. It can be seen in Fig. 7 that the correlation coefficients of linear plots of e_ 1=8 versus sp at low temperature are very high (R2 ¼0.937 at 473 K; R2 ¼0.959 at 523 K). Furthermore, the extrapolated threshold value at 673 K is a negative (i.e., s0 ¼ 3.62 MPa). Based on these facts, n ¼8 is unlikely the appropriate value for the present composite studied. From above discussion, it is rational to suggest that the deformation mechanism Mg2B2O5w/AZ31B composite at elevated temperature is mainly in the mode of dislocation climb creep. Then, the value of Q is found to be 164 kJ/mol for the composite studied, which is slightly higher than QL (¼135 kJ/mol) of Mg with the lattice self-diffusion [15]. However, it is very close to the value of Q¼158.7 kJ/mol of AZ31B magnesium alloy reported by Liu et al. [11]. Taking both parameters of n and Q into consideration, it is reasonable to conclude that the deformation mechanism of the current composite is lattice diffusion controlled dislocation climb. At low temperature, many twins were observed due to the lack of activated slip systems. DRX is associated with low stacking fault energy. The addition of reinforcements likely improved the nucleation of DRX during hot deformation by increasing dislocation density in the matrix [1].
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Fig. 5. Optical micrographs of Mg2B2O5w/AZ31B composites: (a) as-cast; (b) T¼ 473 K, e_ ¼ 0:1 s1 , (Z ¼1.29 1017); (c) T ¼673 K, e_ ¼ 103 s1 , (Z¼ 5.3 109); (d) T¼ 573 K, e_ ¼ 0:1 s1 , (Z ¼8.9 1013); (e) T¼673 K, e_ ¼ 102 s1 , (Z ¼5.3 1010); (f) T¼ 673 K, e_ ¼ 0:1 s1 , (Z¼5.3 1011).
Fig. 6. TEM micrographs of compressed Mg2B2O5w/AZ31B composites at: (a) T¼ 473 K and e_ ¼ 0:1 s1 , and (b) T ¼673 K and e_ ¼ 102 s1 .
4. Conclusions The peak stresses were used in the creep equations. It was found that the hyperbolic sine law can be applied at generally
over entire stress range. While, the exponential and power laws broke down at low and high stress levels, respectively. The constitutive equation for flow stress of hot deformed 5 vol% whiskers reinforced magnesium composite can be described by
Y. Zhu et al. / Materials Science & Engineering A 573 (2013) 148–153
153
Acknowledgment The authors would like to express their sincere thanks to Dr. Tianping Zhu, research associate of The University of Auckland for his helpful discussions. This work was financially supported by National Fundamental Research Program of China (Grant no. 2011CB612200). References [1] [2] [3] [4] [5] [6] [7] [8]
Fig. 7. Linear plots of sp versus e_ 1=n for n ¼8.
[9] [10] [11] [12] [13]
the hyperbolic sine law, and the parameters are as follows:
A ¼ 2:38 1012 s1 , n ¼ 6:6, a ¼ 0:0139 MPa1 , Q ¼ 164 kJ=mol
1. The value of stress exponent is estimated to be 6.6, and the activation energy is slightly higher than the value for lattice self-diffusion of pure magnesium. It is suggested that the deformation mechanism of Mg2B2O5w/AZ31B composite follows the mode of lattice diffusion controlled dislocation climb. 2. Dynamic recrystallization (DRX) took place during hot compression, and DRX grains grew larger when the strain rate decreases and temperature rises. Twins disappeared gradually with the increase of deforming temperature. The addition reinforcement of Mg2B2O5 whiskers likely promotes the DRX nucleation and leads to finer grains in the vicinity of whiskers.
[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
C.Y. Wang, K. Wu, M.Y. Zheng, Mater. Sci. Eng. A 487 (2008) 495–498. Z.J. Li, W.D. Fei, L.D. Wang, Mater. Sci. Eng. A 432 (2006) 275–280. S.C. Tjong, Z.Y. Ma, Compos. Sci. Technol. 59 (1999) 1117–1125. T.G. Nieh, J. Wadsworth, Scr. Mater. 32 (1995) 1133–1137. H.J. McQueen, N.D. Ryan, Mater. Sci. Eng. A 322 (2002) 43–46. P. Zhang, F.G. Li, Q. Wan, J. Mater. Eng. Perform. 19 (2010) 1290–1297. R.S. Mishra, T.R. Bieler, A.K. Mukherjee, Acta Mater. 45 (1997) 561–568. H. Takuda, H. Fujimoto, N. Hatta, J. Mater. Process. Technol. 80–81 (1998) 513–516. A. Galiyev, R. Kaibyshev, G. Gottstein, Acta Mater. 49 (2001) 1199–1207. A. Mwembela, E.B. Konopleva, H.J. McQueen, Scr. Mater. 37 (1997) 1789–1795. J. Liu, Z.S. Cui, C.X. Li, Comput. Mater. Sci. 41 (2008) 375–382. W.J. Kim, Scr. Mater. 41 (1999) 1131–1136. W.J. Kim, J.H. Yeon, D.H. Shin, S.H. Hong, Mater. Sci. Eng. A 269 (1999) 142–151. B.Q. Han, K.C. Chan, Scr. Mater. 36 (1997) 593–598. H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps, Pergamon, Oxford, 1982. Y. Li, T.G. Langdon, Acta Mater. 46 (1998) 3937–3948. Q. Guo, H.G. Yan, H. Zhang, Z.H. Chen, Z.F. Wang, Mater. Sci. Technol. 21 (2005) 1349–1354. K. Yu, W.X. Li, J. Zhao, Z.Q. Ma, R.C. Wang, Scr. Mater. 48 (2003) 1319–1323. N.D. Ryan, H.J. McQueen, J. Mech. Work. Technol. 12 (1986) 279–296. T. Al-Sammana, X. Li, S.G. Chowdhuryb., Mater. Sci. Eng. A 527 (2010) 3450–3463. T. Al-Samman, G. Gottstein., Mater. Sci. Eng. A 490 (2008) 411–420. M.M. Myshlyaev, H.J. McQueen, A. Mwembela, E. Konopleva., Mater. Sci. Eng. A 337 (2002) 121–133. T.G. Nieh, J. Wadsworth, O.D. Sherby, Superplasticity in Metals and Ceramics, Cambridge University Press, New York, 1997. H. Watanabe, T. Mukai, M. Mabuchi, K. Higashi, Acta Mater. 49 (2001) 2027–2037. H. Dieringa, Y.D. Huang, P. Maier, N. Hort, K.U. Kainer, Mater. Sci. Eng. A 410–411 (2005) 85–88. Z.Y. Ma, S.C. Tjong, Compos. Sci. Technol. 61 (2001) 771–786.
Contents lists available at SciVerse ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Hot deformation behavior of Mg2B2O5 whiskers reinforced AZ31B magnesium composite fabricated by stir-casting Yunpeng Zhu a, Peipeng Jin a,n, Peitang Zhao b, Jinhui Wang a, Li Han a, Weidong Fei a,b a b
Institute of Metal Research, Qinghai University, Xining 810016, PR China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 July 2012 Received in revised form 21 February 2013 Accepted 25 February 2013 Available online 6 March 2013
The hot deformation behavior of Mg2B2O5w/AZ31B composite was investigated by compression test at temperatures between 473 K and 673 K with the strain rates from 10 4 s 1 to 1 s 1. The constitutive equations were established by taking peak stresses as the function of temperatures and strain rates. It was found that the function of exponential and power law creep equations broke down at low and high stresses for the composite, respectively. The hyperbolic sine law creep equation was in good agreement with experimental results and can be applied to all flow stresses under the various deformation conditions. The composite possesses slightly higher activation energy values than that of lattice self-diffusion of pure Mg, and the stress exponent was calculated to be about 6.6. The plastic deformation mechanism of the composites at high temperature was mainly through the lattice diffusion controlled dislocation climb. Dynamic recrystallization took place during hot compression, and grains became coarser at lower strain rate and higher temperature. & 2013 Elsevier B.V. All rights reserved.
Keywords: Magnesium matrix composite Hot compression Constitutive equations Deformation
1. Introduction Discontinuously reinforced magnesium matrix composites (DRMMCs) have attracted great attention because of their low density, high properties [1] and good hot forming ability. However, the low temperature plastic forming ability of magnesium matrix composite is relatively poor plastic forming ability due to the hexagonal close-packed (HCP) crystal structure of magnesium matrix. The brittle ceramic discontinuous reinforcements in the composites further limit the plastic forming ability of DRMMCs. Therefore, the magnesium composites are normally deformed at higher temperature [2]. It is important to improve the formability of DRMMCs at low temperature for purpose of wide applications. Over the past decades, the hot deformation behavior of discontinuously reinforced metal matrix composites have been extensively investigated [1–4]. The constitutive equations which describe the relationship between flow stress and strain rate are very useful in conducting secondary processing for DRMMCs. Three typical constitutive equations, the power, the exponential, and the hyperbolic sine laws, have been used to describe the deformation behavior of metals and metal matrix composites (MMCs) during hot working, such as aluminum composites [5,6]. The power law relationship has been generally applied in hot deformed magnesium alloy at low stresses [3,7], while the exponential law was used in that at high stresses [8,9]. The hyperbolic sine law, in which both power and exponential equations are involved, can be applied at a wider stress range successfully [10,11].
n
Corresponding author. Tel.: þ86 971 536 3028; fax: þ 86 971 531 0440. E-mail address: [email protected] (P. Jin).
0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.02.051
Furthermore, the stress exponent, n, and the activation energy, Q, can be calculated by constitutive equations, which are key parameters related to the deformation mechanisms of the materials. It was found that the composites fabricated by powder metallurgy (PM) process have abnormally high stress exponent and activation energy. For example, Kim et al. [12,13] have reported that SiCp/2124Al composite fabricated by PM process possesses unusually high stress exponent and activation energy (about 390 kJ/mol). Han and Chan [14] have reported the activation energy of 774 kJ/mol for a 6061Al composite reinforced with 20 vol% SiC whisker, which is much higher than that of 142 kJ/mol for lattice self-diffusion of pure Al [15]. However, knowledge is still lack for magnesium matrix composites with low fraction of reinforcements, and their hot deformation behavior of this kind of materials is still not fully understood. The aim of present study is to investigate the hot deformation behavior of as-cast AZ31B magnesium matrix composite reinforced with low volume fraction of Mg2B2O5 whisker (Mg2B2O5w/ AZ31B) composite. The hot deformation constitutive equation is determined by the analysis of flow stress data. The deformation mechanism was discussed in terms of the calculated stress exponent and the activation energy. The microstructures of the hot deformed composites were examined, and their effects on the deformation behavior were discussed.
2. Experimental Magnesium borate (Mg2B2O5w) whisker reinforced AZ31B magnesium matrix (Mg2B2O5w/AZ31B) composite were fabricated by
Y. Zhu et al. / Materials Science & Engineering A 573 (2013) 148–153
stir-casting with the 5 vol% of Mg2B2O5 whisker. The diameter and length of the whisker are in ranges of 0.2–2.0 mm and 20–50 mm, respectively. Cylindrical specimens, with the size of 10 mm in diameter and 15 mm in length, were machined from the composite ingot and tested compressively by Gleeble-1500 thermo-mechanical simulator. The uniaxial compression tests were carried out at temperatures ranging from 473 K to 673 K and various strain rates of 10 4 s 1, 10 3 s 1, 10 2 s 1, 10 1 s 1 and 1 s 1. Graphite was used to lubricate the die-workpiece interface. All specimens were heated up to the testing temperatures at a heating rate of 5 K/min, and then held at the temperature for 5 min before commencing the compression testing. The specimens were water quenched immediately after the compressive test. The microstructure of the deformed specimens was examined using Olympus-PMG3 optical microscopy (OM) and a TECNAIF30 transmission electron microscopy (TEM). The metallographic specimens were sectioned along the direction normal to the compression axis, and then was mounted, polished and etched by acetic–picric acid. TEM specimens were thinned by the ion milling.
0
The true stress–strain curves obtained at the strain rates of 10 s 1 and 0.1 s 1 and at different temperatures are shown in Fig. 1. Typically, the flow stress increases to a maximum initially due to the dominance of work hardening and then gradually until reach to a steady state. Such flow stress curve corresponds to the characteristic behavior of dynamic recrystallization (DRX) which overtakes initial work hardening [4,11,13]. Comparing flow curves in Fig. 1(a) with those in Fig. 1(b), it can be found that the flow curve exhibits lower peak stress (sp) and peak strain (ep) at low strain rate (10 3 s 1) than those at higher strain rate (0.1 s 1). Flow stress curves in Fig. 1 also illustrate the temperature effect on sp and ep, which decrease with the increase of temperature at two strain rates. 3
3.2. Constitutive equations Different constitutive equations have been used to describe the strain-stress flows of hot deformed alloys and composites [16–18]. The favorite equations are presented as follows: Q ð1Þ e_ ¼ AðsinhðasÞÞn exp RT
Q RT
e_ ¼ A00 expðbsÞexp
ð2Þ
Q RT
Q Z ¼ e_ exp RT
ð3Þ
ð4Þ
Q ¼R
! @ln s @lne_ e_ @ln s T @ 1=T
ð5Þ
Q ¼R
! @s @lne_ e_ @s T @ 1=T
ð6Þ
Q ¼R
! @lnðsinhðasÞÞ @lne_ e_ @lnðsinhðasÞÞ T @ 1=T
ð7Þ
3. Results and discussion 3.1. Flow stress–strain curves
e_ ¼ A0 sn exp
149
where A (A0 , A00 ), a ( ¼ b=n0 ), and b are constants of the material, n (n0 ) are stress exponent, Q is an apparent activation energy of the deformation, R is the gas constant. Z is the Zener–Hollomon parameter, also known as temperature compensated strain rate, which is determined by the strain rate e_ and temperature T. In previous studies three constitutive equations were employed to analyze the hot deformation behaviors of composite and monolithic alloys. It was found that different deformation mechanisms can be described by corresponding constitutive equations. However, it has not been clearly understood which constitutive equation can be used appropriately for the deformation of DRMMCs reinforced with relatively lower fraction of whisker. In present study, all constitutive equations mentioned above were tested and discussed in order to find a suitable equation which can properly describe the compressive deformation behavior of Mg2B2O5w/AZ31B composite. The values of A (A0 , A00 ), b, and n (n0 ) can be obtained from the plot of ln Z versus ln (sinh (as)), ln s, and s for different equations. However, the values of a and Q need to be determined first. In this study, the s was referred to the peak stress sp. The values of Q presented in Figs. 2–4 are determined by Eqs. (5)–(7), respectively. Constitutive equations are used to calculate hot
Fig. 1. True stress–strain curves for Mg2B2O5/AZ31B composites deformed at different temperatures (a) 10 3 s 1 and (b) 0.1 s 1.
150
Y. Zhu et al. / Materials Science & Engineering A 573 (2013) 148–153
Fig. 2. ln Z versus ln sp curve based on the power law (a) and comparison between calculated and measured sp values (b) for Mg2B2O5w/AZ31B composite.
Fig. 3. ln Z versus ln sp curve based on the exponent law (a) and comparison between calculated and measured sp values (b) for Mg2B2O5w/AZ31B composite.
compression stresses at various rates and temperatures. The calculated peak stresses from constitutive equations were compared with the measured stresses from compression tests. Fig. 2(a) shows the relationship of ln Z versus lnsp corresponding to the power law and the values of A0 and n0 are obtained according to the plot. Fig. 2(b) illustrates the comparison between calculated and measured peak stresses, sp. It can be seen that the deviation between the predicted value and measured value is significant at high stresses (sp 4140 MPa), and the maximum relative error is 54.3% at T¼673 K with higher strain rate e_ ¼ 1 s1 . These results indicate the breakdown of power law at high compressive stresses, which has been reported by McQueen and Galiyev [5,9]. According to the exponential law, the relationship of ln Z versus sp is shown in Fig. 3(a), and the values of A00 and b can be calculated. Although the correlation coefficient (R2) of ln Z versus sp is 0.99, the deviation between the predicted value and measured value is high at low stresses level (sp o40 MPa), as shown in Fig. 3(b). The maximum relative error is 93.8% at T¼673 K and strain rate e_ ¼ 104 s1 , which suggests the
breakdown of the exponent law at low stresses. This result is consistent with results reported by Galiyev and Ryan [9,19]. The good linear relationship of ln Z versus ln (sinh (asp)) was observed in Fig. 4(a) when the hyperbolic sine law was applied. The values of A and n were determined as 2.38 1012 and 6.6, respectively. From Fig. 4(b) shows the comparison between calculated and measured values of sp. It can be seen that the predicted values fit the measured value very well. The maximum relative error is 10.2% at T¼473 K and strain rate e_ ¼ 1s1 , and other relative errors are below 5%. Based on results in Fig. 4, the hyperbolic sine law can be applied over entire stress range for the composite tested in this study. 3.3. Microstructures Fig. 5(a) shows the microstructure of as-cast Mg2B2O5w/AZ31B composites. It can be seen that the Mg2B2O5 whisker located at the grain boundaries mostly and the mean grain size is about 200 mm. The higher magnification of Fig. 5(a) illustrates that the aspect ratio (length to diameter) of the whisker is in the range of
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Fig. 4. ln Z versus ln sp curve based on the hyperbolic sine law (a) and comparison between calculated and measured sp values (b) for Mg2B2O5w/AZ31B composite.
10–50. The microstructures of specimens deformed under different deformation conditions are displayed in Fig. 5(b)–(f). Many twins were observed at such a high Z parameter which is similar to AZ serial alloy [20] in Fig. 5(b), due to the high activation energy and lack of easily activated independent slip systems of magnesium at low temperature. The strain is partially accommodated by twinning which are often in multiple parallel groups with some intersecting ones. As the temperature rises to 573 K, there was no twin observed. Instead, fine grains formed as the result of DRX appeared, as shown in Fig. 5(d). More detailed examination revealed that finer DRX grains mainly formed in the vicinity of Mg2B2O5 whiskers. This may indicate that the nucleation of DRX can be promoted by the reinforcement [1]. At 673 K, DRX grains grew larger overriding these as-cast coarse grains and twin boundaries have been invisible in Fig. 5(f). Microstructures of samples deformed at 673 K under different strain rates are presented in Fig. 5(c), (e), and (f). Their average grain sizes are about 11 mm, 9 mm and 5 mm, respectively. The results indicate that grain size increases with the decrease of strain rate and rise of temperature, which is similar to the results reported by AlSamman and Gottstein [21]. Fig. 6(a) and (b) shows the typical TEM micrographs of Mg2B2O5w/AZ31B composites compressed at different conditions. At low temperature 473 K, a number of deformation twins appeared and distributed uniformly as shown in Fig. 6(a). The occurrence of twinning at low temperature resulted in high compression stress. It can be seen that twins are parallel and end with sharp points at locations close to the grain boundary, which is similar to that observed by Myshlyaev et al. [22]. In Fig. 5(c)–(f), many equiaxed grains formed in specimens, indicating the occurrence of DRX during the compression. Typical dynamic recrystallized microstructure of the specimen compressed at 673 K and strain rate of 10 2 s 1 is shown in Fig. 6(b). Fine DRX grains in the matrix can be seen clearly, and there is nearly no visible dislocation. 3.4. Discussion Nieh et al. [23] have discussed main creep mechanisms of metals and composites, and they have suggested that the stress exponents predicted by theoretical models are dependent on the creep mechanism: n ¼1 for diffusional creep, n¼2 for grain boundary sliding, n ¼3 for glide controlled creep, n¼ 4–5 for
dislocation climb controlled creep, n48 for dispersion strengthened alloys. According to Fig. 4(a), the value of n ¼6.6 gave the best linear fitting at the entire temperature range. However, no deformation mechanism associated with n ¼6.6 has been proposed in literature. It has been reported that the stress exponent is not an integer [5,13]. In this study, the stress exponent is between 5 and 8. Therefore, the hot deformation mechanism of Mg2B2O5w/AZ31B composite may be dislocation climb creep or dispersion strengthened or the combination of both modes. In dispersion strengthened materials (n 48), the existence of the threshold stress (s0) can apparently causes an extremely high stress exponent [24]. One simple approach to confirm that if the value of stress exponent is reasonable or not (which suggests the deformation mode of the materials following either dislocation climb creep or dispersion strengthened) is to find the threshold stress. The threshold stress is estimated using the standard linear extrapolation method [3,16,25]. In order to determine the stress exponent reasonably, the stress was replaced by the effective stress se (se ¼ s s0) [26], in which s was replaced by sp in this study. Fig. 7 shows plots of the e_ 1=8 versus sp in double linear scales. Then, the threshold stress at each temperature was determined by extrapolating the linear plot to the point of zero strain rates. It can be seen in Fig. 7 that the correlation coefficients of linear plots of e_ 1=8 versus sp at low temperature are very high (R2 ¼0.937 at 473 K; R2 ¼0.959 at 523 K). Furthermore, the extrapolated threshold value at 673 K is a negative (i.e., s0 ¼ 3.62 MPa). Based on these facts, n ¼8 is unlikely the appropriate value for the present composite studied. From above discussion, it is rational to suggest that the deformation mechanism Mg2B2O5w/AZ31B composite at elevated temperature is mainly in the mode of dislocation climb creep. Then, the value of Q is found to be 164 kJ/mol for the composite studied, which is slightly higher than QL (¼135 kJ/mol) of Mg with the lattice self-diffusion [15]. However, it is very close to the value of Q¼158.7 kJ/mol of AZ31B magnesium alloy reported by Liu et al. [11]. Taking both parameters of n and Q into consideration, it is reasonable to conclude that the deformation mechanism of the current composite is lattice diffusion controlled dislocation climb. At low temperature, many twins were observed due to the lack of activated slip systems. DRX is associated with low stacking fault energy. The addition of reinforcements likely improved the nucleation of DRX during hot deformation by increasing dislocation density in the matrix [1].
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Fig. 5. Optical micrographs of Mg2B2O5w/AZ31B composites: (a) as-cast; (b) T¼ 473 K, e_ ¼ 0:1 s1 , (Z ¼1.29 1017); (c) T ¼673 K, e_ ¼ 103 s1 , (Z¼ 5.3 109); (d) T¼ 573 K, e_ ¼ 0:1 s1 , (Z ¼8.9 1013); (e) T¼673 K, e_ ¼ 102 s1 , (Z ¼5.3 1010); (f) T¼ 673 K, e_ ¼ 0:1 s1 , (Z¼5.3 1011).
Fig. 6. TEM micrographs of compressed Mg2B2O5w/AZ31B composites at: (a) T¼ 473 K and e_ ¼ 0:1 s1 , and (b) T ¼673 K and e_ ¼ 102 s1 .
4. Conclusions The peak stresses were used in the creep equations. It was found that the hyperbolic sine law can be applied at generally
over entire stress range. While, the exponential and power laws broke down at low and high stress levels, respectively. The constitutive equation for flow stress of hot deformed 5 vol% whiskers reinforced magnesium composite can be described by
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Acknowledgment The authors would like to express their sincere thanks to Dr. Tianping Zhu, research associate of The University of Auckland for his helpful discussions. This work was financially supported by National Fundamental Research Program of China (Grant no. 2011CB612200). References [1] [2] [3] [4] [5] [6] [7] [8]
Fig. 7. Linear plots of sp versus e_ 1=n for n ¼8.
[9] [10] [11] [12] [13]
the hyperbolic sine law, and the parameters are as follows:
A ¼ 2:38 1012 s1 , n ¼ 6:6, a ¼ 0:0139 MPa1 , Q ¼ 164 kJ=mol
1. The value of stress exponent is estimated to be 6.6, and the activation energy is slightly higher than the value for lattice self-diffusion of pure magnesium. It is suggested that the deformation mechanism of Mg2B2O5w/AZ31B composite follows the mode of lattice diffusion controlled dislocation climb. 2. Dynamic recrystallization (DRX) took place during hot compression, and DRX grains grew larger when the strain rate decreases and temperature rises. Twins disappeared gradually with the increase of deforming temperature. The addition reinforcement of Mg2B2O5 whiskers likely promotes the DRX nucleation and leads to finer grains in the vicinity of whiskers.
[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
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