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Effect of grain boundary structures on grain boundary sliding in magnesium
Materials Letters 76 (2012) 32–35
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Effect of grain boundary structures on grain boundary sliding in magnesium Hidetoshi Somekawa a,⁎, Toshiji Mukai b a b
Research Center for Strategic Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047, Japan Department of Mechanical Engineering, Kobe University, 1-1 Rokkodai, Kobe, 657-8501, Japan
a r t i c l e
i n f o
Article history: Received 12 January 2012 Accepted 4 February 2012 Available online 16 February 2012 Keywords: Magnesium Grain boundary sliding Nanoindentation creep Grain boundary structure Grain boundary energy
a b s t r a c t The effect of grain boundary structures on the deformation behavior at the grain boundaries in magnesium was examined by the nanoindentation creep test. The results of the nanoindentation creep test showed that the dominant deformation mechanism around the grain boundary was grain boundary sliding; however, the occurrence of grain boundary sliding was closely related to the grain boundary energy. The grain boundary with high energy showed high strain rate sensitivity, which was the same tendency as that of the other metallic materials. Furthermore, the addition of aluminum atoms into magnesium tended to prevent the grain boundary sliding due to the decrease in grain boundary energy. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Understanding the characteristics and the deformation responses of the grain boundary in metallic materials is important, since the grain boundaries affect the mechanical properties such as strength and ductility. The effect of the grain boundary structures on the grain boundary strengthening [1,2] and the grain boundary migration [3,4] has been examined through various experiments, and the grain boundary energies [5,6] have also been obtained for many kinds of bicrystals with different boundary structures. The deformation behavior near the grain boundaries in magnesium and its alloys is quite unique compared to that of the other metallic materials. For example, the major slip system in magnesium at room temperature is only basal dislocation; however, not only basal—but also non-basal dislocations are activated at the grain boundaries during the plastic deformation due to the operation of a compatibility stress/strain at the grain boundary [7]. These activations can be observed near the grain boundaries in the deformed samples [7]. The grain boundary sliding has also occurred even at room temperature [8] because of the higher diffusion rate of the grain boundary in magnesium [9]. The polycrystalline magnesium with fine-grain structures showed a large strain rate dependence behavior at room temperature [10,11]. On the other hand, most of these results for magnesium and its alloys showed the deformation response not at the individual—but at all the grain boundaries. Our recent paper showed that a grain boundary was confirmed to obtain high strain rate sensitivity by the nanoindentation creep test
⁎ Corresponding author. Tel.: + 81 29 859 2473; fax: + 81 29 859 2601. E-mail address: [email protected] (H. Somekawa). 0167-577X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2012.02.010
[12]. However, there are no sufficient results to comprehend the deformation behavior at each of the grain boundaries in magnesium like that in other materials. Thus, the effect of the grain boundary structures on the deformation mechanism at the grain boundaries in magnesium is examined using the nanoindentation creep test, which is widely used for the investigation of mechanical properties and deformation behavior in small volumes of materials, in this study. The grain boundary energy is evaluated using the molecular dynamic (MD) simulation. The impact of additional elements, i.e., a conventional alloying element such as aluminum, will also be discussed. 2. Experimental procedure 2.1. Nanoindentation creep Pure magnesium with a purity of 99.94% and a Mg–1.0 at.%Al alloy were prepared by casting, and then they were extruded in this study. The extruded alloys were annealed to reduce the dislocation density and to produce coarse-grained structures with an average grain size of about 50 μm. The nanoindentation creep tests were carried out to investigate the deformation behavior at the specific grain boundaries. An indentation load of 500 μN, a constant loading- and unloading-rate of 50 μN/s, and a holding period of 0.5 ks were used in all the nanoindentation creep tests using the Berkovich tip. Since the region around the grain boundary in magnesium had high strain rate sensitivity [12], the tip was indented about 1.0 μm away from the grain boundary, which consisted of misorientation angles of 23°, 44° and 78° in pure magnesium and 78° in the Mg–Al alloy. The indented grain interior had a Schmid factor of 0.25. A typical example of an indentation area observed by the electron back scatter diffraction method is shown in
H. Somekawa, T. Mukai / Materials Letters 76 (2012) 32–35
33
Fig. 1. The creep behaviors were measured at 20 or more points for each condition. The details of the experimental conditions in the nanoindentation creep test and the sample preparation for magnesium are reported elsewhere [12]. 2.2. MD simulation Magnesium bicrystals with three types of [1–100] symmetric tilt boundaries, which were Σ25 with the tilt angle of θ = 23°, Σ14 with θ = 44° and Σ10 with θ = 78° (hereafter denoted as, 23°-, 44°- and 78°-tilted boundaries, respectively), were modeled in this study. A typical tilt boundary model is shown in Fig. 1(d). The grain boundary energy, γgb, in the present models was evaluated at a temperature of 1 K with a NTP ensemble using the generalized EAM potential, which enables calculations for alloys containing magnesium and aluminum atoms. The grain boundary energy was obtained using the following equation: γ gb
U gb −U bulk ¼ 2Agb
ð1Þ
where Ugb and Ubulk are the internal energies with and without the grain boundary, respectively, and Agb is the grain boundary area. Magnesium atoms existing at the interfaces were also replaced by aluminum atoms, consisting of 4 atoms in each space, in the 78°-tilted boundary model (inset in Fig. 1(d)) to investigate the effect of the alloying element on the grain boundary energy. 3. Results and discussion The variation of indentation depth as a function of the time is shown in Fig. 2. This figure shows that the depth increases with the load holding segment, and the nanoindentation creep behavior affects the grain boundary structures. The maximum depth was obtained with a misorientation angle of 23°. The relationship between the stress, σ, (hardness; H) and the strain rate, ε̇, using the classical Tabor relationship during the creep behavior is given as follows; n ε_ ¼ Aσ ¼ A
n H α
ð2Þ
Fig. 2. The variation of indentation depth as a function of time in magnesium and Mg–Al alloy.
where A is a constant, α is the Tabor factor (=3.3 [13]) and n is the stress exponent (=1/m; m is the strain rate sensitivity exponent). The strain rate is defined as the instantaneous descent rate of the indenter divided by the displacement at a particular point in time, and the actual effective strain rate during the indentation, ε̇eff, is expressed as [14]:
ε_ eff ¼ C ε_ ¼ C
1 dh h dt
ð3Þ
where C is a constant of 0.1 [15,16]. A typical example for the variation of stress as a function of effective strain rate in nanoindentation creep is shown in Fig. 3. The m-value corresponded to the slope, and was obtained by the least square method from the stress (or hardness) and the strain rate curves of each indentation test. The average m-values for the grain boundary misorientation angles are listed in Table 1. The m-values of more than 0.3 were obtained in this study, and these values indicate that the dominant deformation mechanism around the grain boundaries is assumed to be grain boundary sliding. The present strain rate is found to be in a similar range as that for the initiation of grain boundary sliding, which was obtained from the uniaxial tensile tests [10]. On the other hand, the m-values are influenced by the grain boundary structures; the m-value for the
Fig. 1. Indentation area observed by the electron back scatter diffraction method and the grain boundary model in MD simulation; (A) misorientation angle of 23°, (B) 44°, (C) 78°, (D) [1–100] symmetric tilt boundary with the angle of 78°. Where the grain with the yellow color is a Schmid factor of 0.25, and the grain boundary with the white color is a specific misorientation angle of 23°, 44° or 78° in (A)–(C), respectively.
34
H. Somekawa, T. Mukai / Materials Letters 76 (2012) 32–35
Fig. 3. The variation of stress as a function of effective strain rate in nanoindentation creep test.
misorientation angle of 23° is the highest among the three kinds of misorientation angles. The experimental results using bicrystals have shown that the grain boundary sliding in the low-angle grain boundaries and the coincidence site lattice (CSL) boundaries is smaller than that in the high-angle grain boundaries [3]. In addition, when the dominant deformation mechanism is the grain boundary sliding, the superplastic behavior in the high-angle grain boundaries is superior to that in the low-angle grain boundaries and CSL boundaries [17–19]. The difference in grain boundary sliding resulted from the disordered structures and/ or the fraction of free volume at the grain boundaries. MD simulations have indicated that the kite structures affect the grain boundary sliding, and the existence of pore structures is important for the occurrence of grain boundary sliding [20–22]. The present 78°-tilted boundary model is constructed from a similar type of kite structure, shown in the inset in Fig. 1(d). The other tilted models in this study include the same structures, AAAEAAAE in the 23°-tilted boundary model and AAEAAE in the 44°-tilted boundary model, although each model contains a different fraction of this kite structure. The grain boundary sliding is also known to have a close relation to the grain boundary energy [23–25], i.e., the grain boundaries with high energy tend to enhance the grain boundary sliding. The calculated grain boundary energies using the MD simulation are listed in Table 1. This table includes the previously reported results, which were obtained using the tight biding potential [26]. The present grain boundary energies are higher than the previous ones due to the difference in using a potential; however, they show the same tendency, where the grain boundary energy; 23° > 44° > 78°-tilted boundaries. This table shows that the grain boundary with high energy is found to have a higher m-value. One of the inherent factors for the occurrence of grain boundary sliding in magnesium is the grain boundary energy, which is the same as that in the other metallic materials. The influence of the alloying element on the deformation behavior at the interface is discussed hereafter. Typical results of the nanoindentation creep tests in the Mg–Al alloy are plotted in Figs. 2 and 3, and the average m-value for the Mg–Al alloy is included in Table 1. These figures show that the m-value of the misorientation angle of Table 1 The results of nanoindentation creep tests and MD simulations.
4. Summary The deformation behavior around three kinds of grain boundary structures in magnesium was investigated using nanoindentation creep tests. The following results were obtained. (1) The dominant deformation mechanism near the grain boundary was the grain boundary sliding even at room temperature. The grain boundary structure affected the strain rate sensitivity, i.e., m-value. (2) The grain boundary energy was one of the factors to influence the m-value. The grain boundary with a high energy, which was obtained using the MD simulation, showed a high m-value. (3) The m-value and grain boundary energy in the Mg–Al alloy were lower than those in pure magnesium. The addition of aluminum atoms into magnesium had the role of decreasing the grain boundary energy and suppressing the grain boundary sliding. Acknowledgments One of the authors (HS) is grateful to Ms. M. Isaki (National Institute for Materials Science) for her technical help. This work was supported by the JSPS Grant-in-Aid for Young Scientists (B) No. 21760564 and 23760675. References [1] [2] [3] [4] [5]
angle, degree
m-value
γgb, J/m2
γgb, J/m2 [26]
23 44 78 78
0.50 ± 0.15 0.43 ± 0.13 0.39 ± 0.14 0.30 ± 0.15
1.25 0.56 0.40 0.32
0.91 0.43 0.33 –
(magnesium) (magnesium) (magnesium) (Mg–Al)
78° for the Mg–Al alloy is found to be lower than that for pure magnesium. Using Eq. (1), the grain boundary energy is obtained to be 0.32 J/m 2 in the 78°-tilted boundary of the Mg–Al alloy, which is also lower than that in pure magnesium (0.40 J/m 2), shown in Table 1. The detailed electric distribution analysis using the first principle calculation is necessary to understand the mechanism for the decrease in the grain boundary energy in the future; however, a recent MD simulation shows that the aluminum atoms provide stability to the magnesium atoms due to the strong bonding between the aluminum and magnesium atoms [27]. Thus, one of the reasons for the lower m-value in the Mg–Al alloy is the reduction in grain boundary energy by the addition of aluminum atoms. Recent experimental studies have shown that the elongation-tofailure in the fine-grained pure magnesium exceeds ~ 50% at room temperature [28], while the typical magnesium alloys, i.e., Mg–3Al– 1Zn (AZ31) alloys, show an elongation of up to 20–30% despite their similar grain size [29]. Watanabe et al. also examined the effect of alloying elements on the superplastic behavior in fine-grained magnesium with a grain size of 2 μm through the damping capacity [30]. They reported that the addition of aluminum atoms was effective for suppressing the grain boundary sliding, which corresponds to the present result. Therefore, the addition of aluminum atoms into magnesium enhances the strength due to well known solid solution strengthening; however, the ductility tends to decrease due to the prevention of grain boundary sliding.
Where γgb is the grain boundary energy and the m-value is obtained from the nanoindentation creep test.
[6] [7] [8] [9] [10] [11] [12]
Su JQ, Demura M, Hirano T. Philos Mag 2002;A82:1541. Hauser JJ, Chalmers B. Acta Metall 1961;9:802. Kokawa H, Watanabe T, Karashima S. Philos Mag 1981;A44:1239. Matsunaga K, Nishimura H, Muto H, Yamamoto T, Ikuhara Y. Appl Phys Lett 2003;82:1179. Yoshida H, Yokoyama K, Shibata N, Ikuhara Y, Sakuma T. Acta Mater 2004;52: 2349. Tsurekawa S, Tanaka T, Yoshinaga H. Mater Sci Eng 1994;A176:341. Koike J, Kobayashi T, Mukai T, Watanabe H, Suzuki M, Maruyama K, et al. Acta Mater 2003;51:2055. Koike J, Ohyama R, Kobayashi T, Suzuki M, Maruyama K. Mater Trans 2003;44: 445. Frost HJ, Ashby MF. Deformation-mechanism map. Oxford: Pergamon Press; 1982. Wang CL, Mukai T, Nieh TG. J Mater Res 2009;24:1615. Chua BW, Lu L, Lai MO. Mater Res Bull 2006;41:2102. Somekawa H, Mukai T. Philos Mag Lett 2010;90:883.
H. Somekawa, T. Mukai / Materials Letters 76 (2012) 32–35 [13] [14] [15] [16] [17] [18] [19] [20] [21]
Tabor DS. The hardness of metals. Oxford: Clarendon Press; 1951. Mayo MJ, Nix WD. Acta Metall 1988;36:2183. Wang CL, Lai YH, Huang JC, Nieh TG. Scr Mater 2010;62:175. Alkorta J, Martinez-Esnaola JM, Sevillano JG. Acta Mater 2008;56:884. Kaibyshev R, Goloborodko A, Musin F, Nikulin I, Sakai T. Mater Trans 2002;43: 2408. Hirata T, Osa T, Hosokawa H, Higashi K. Mater Trans 2002;43:2385. Valiev RZ, Langdon TG. Prog Mater Sci 2006;51:881. Sansoz F, Molinari JF. Acta Mater 2005;53:1931. Yuasa M, Nakazawa T, Mabuchi M. Mater Sci Eng 2010;A527:2629.
[22] [23] [24] [25] [26] [27] [28] [29] [30]
35
Millett PC, Selvam RP, Saxena A. Mater Sci Eng 2006;A431:92. Qi Y, Krajewski PE. Acta Mater 2007;55:1555. Namilae S, Chandra N, Nieh TG. Scr Mater 2002;46:49. McLean D. Grain boundaries in metals. Oxford: Oxford Univ. Press; 1957. Chou JT, Ikeda K, Nakashima H. J Jpn Inst Met 2005;69:303. Du N, Qi Y, Krajewski PE, Bower AF. Metall Mater Trans 2011;42A:651. Chapman JA, Wilson DV. J Inst Met 1961;91:39. Somekawa H, Kim HS, Singh A, Mukai T. J Mater Res 2007;22:2598. Watanabe H, Owashi A, Uesugi T, Takigawa Y, Higashi K. Philos Mag 2011;91: 4158.
Contents lists available at SciVerse ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/matlet
Effect of grain boundary structures on grain boundary sliding in magnesium Hidetoshi Somekawa a,⁎, Toshiji Mukai b a b
Research Center for Strategic Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki, 305-0047, Japan Department of Mechanical Engineering, Kobe University, 1-1 Rokkodai, Kobe, 657-8501, Japan
a r t i c l e
i n f o
Article history: Received 12 January 2012 Accepted 4 February 2012 Available online 16 February 2012 Keywords: Magnesium Grain boundary sliding Nanoindentation creep Grain boundary structure Grain boundary energy
a b s t r a c t The effect of grain boundary structures on the deformation behavior at the grain boundaries in magnesium was examined by the nanoindentation creep test. The results of the nanoindentation creep test showed that the dominant deformation mechanism around the grain boundary was grain boundary sliding; however, the occurrence of grain boundary sliding was closely related to the grain boundary energy. The grain boundary with high energy showed high strain rate sensitivity, which was the same tendency as that of the other metallic materials. Furthermore, the addition of aluminum atoms into magnesium tended to prevent the grain boundary sliding due to the decrease in grain boundary energy. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Understanding the characteristics and the deformation responses of the grain boundary in metallic materials is important, since the grain boundaries affect the mechanical properties such as strength and ductility. The effect of the grain boundary structures on the grain boundary strengthening [1,2] and the grain boundary migration [3,4] has been examined through various experiments, and the grain boundary energies [5,6] have also been obtained for many kinds of bicrystals with different boundary structures. The deformation behavior near the grain boundaries in magnesium and its alloys is quite unique compared to that of the other metallic materials. For example, the major slip system in magnesium at room temperature is only basal dislocation; however, not only basal—but also non-basal dislocations are activated at the grain boundaries during the plastic deformation due to the operation of a compatibility stress/strain at the grain boundary [7]. These activations can be observed near the grain boundaries in the deformed samples [7]. The grain boundary sliding has also occurred even at room temperature [8] because of the higher diffusion rate of the grain boundary in magnesium [9]. The polycrystalline magnesium with fine-grain structures showed a large strain rate dependence behavior at room temperature [10,11]. On the other hand, most of these results for magnesium and its alloys showed the deformation response not at the individual—but at all the grain boundaries. Our recent paper showed that a grain boundary was confirmed to obtain high strain rate sensitivity by the nanoindentation creep test
⁎ Corresponding author. Tel.: + 81 29 859 2473; fax: + 81 29 859 2601. E-mail address: [email protected] (H. Somekawa). 0167-577X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.matlet.2012.02.010
[12]. However, there are no sufficient results to comprehend the deformation behavior at each of the grain boundaries in magnesium like that in other materials. Thus, the effect of the grain boundary structures on the deformation mechanism at the grain boundaries in magnesium is examined using the nanoindentation creep test, which is widely used for the investigation of mechanical properties and deformation behavior in small volumes of materials, in this study. The grain boundary energy is evaluated using the molecular dynamic (MD) simulation. The impact of additional elements, i.e., a conventional alloying element such as aluminum, will also be discussed. 2. Experimental procedure 2.1. Nanoindentation creep Pure magnesium with a purity of 99.94% and a Mg–1.0 at.%Al alloy were prepared by casting, and then they were extruded in this study. The extruded alloys were annealed to reduce the dislocation density and to produce coarse-grained structures with an average grain size of about 50 μm. The nanoindentation creep tests were carried out to investigate the deformation behavior at the specific grain boundaries. An indentation load of 500 μN, a constant loading- and unloading-rate of 50 μN/s, and a holding period of 0.5 ks were used in all the nanoindentation creep tests using the Berkovich tip. Since the region around the grain boundary in magnesium had high strain rate sensitivity [12], the tip was indented about 1.0 μm away from the grain boundary, which consisted of misorientation angles of 23°, 44° and 78° in pure magnesium and 78° in the Mg–Al alloy. The indented grain interior had a Schmid factor of 0.25. A typical example of an indentation area observed by the electron back scatter diffraction method is shown in
H. Somekawa, T. Mukai / Materials Letters 76 (2012) 32–35
33
Fig. 1. The creep behaviors were measured at 20 or more points for each condition. The details of the experimental conditions in the nanoindentation creep test and the sample preparation for magnesium are reported elsewhere [12]. 2.2. MD simulation Magnesium bicrystals with three types of [1–100] symmetric tilt boundaries, which were Σ25 with the tilt angle of θ = 23°, Σ14 with θ = 44° and Σ10 with θ = 78° (hereafter denoted as, 23°-, 44°- and 78°-tilted boundaries, respectively), were modeled in this study. A typical tilt boundary model is shown in Fig. 1(d). The grain boundary energy, γgb, in the present models was evaluated at a temperature of 1 K with a NTP ensemble using the generalized EAM potential, which enables calculations for alloys containing magnesium and aluminum atoms. The grain boundary energy was obtained using the following equation: γ gb
U gb −U bulk ¼ 2Agb
ð1Þ
where Ugb and Ubulk are the internal energies with and without the grain boundary, respectively, and Agb is the grain boundary area. Magnesium atoms existing at the interfaces were also replaced by aluminum atoms, consisting of 4 atoms in each space, in the 78°-tilted boundary model (inset in Fig. 1(d)) to investigate the effect of the alloying element on the grain boundary energy. 3. Results and discussion The variation of indentation depth as a function of the time is shown in Fig. 2. This figure shows that the depth increases with the load holding segment, and the nanoindentation creep behavior affects the grain boundary structures. The maximum depth was obtained with a misorientation angle of 23°. The relationship between the stress, σ, (hardness; H) and the strain rate, ε̇, using the classical Tabor relationship during the creep behavior is given as follows; n ε_ ¼ Aσ ¼ A
n H α
ð2Þ
Fig. 2. The variation of indentation depth as a function of time in magnesium and Mg–Al alloy.
where A is a constant, α is the Tabor factor (=3.3 [13]) and n is the stress exponent (=1/m; m is the strain rate sensitivity exponent). The strain rate is defined as the instantaneous descent rate of the indenter divided by the displacement at a particular point in time, and the actual effective strain rate during the indentation, ε̇eff, is expressed as [14]:
ε_ eff ¼ C ε_ ¼ C
1 dh h dt
ð3Þ
where C is a constant of 0.1 [15,16]. A typical example for the variation of stress as a function of effective strain rate in nanoindentation creep is shown in Fig. 3. The m-value corresponded to the slope, and was obtained by the least square method from the stress (or hardness) and the strain rate curves of each indentation test. The average m-values for the grain boundary misorientation angles are listed in Table 1. The m-values of more than 0.3 were obtained in this study, and these values indicate that the dominant deformation mechanism around the grain boundaries is assumed to be grain boundary sliding. The present strain rate is found to be in a similar range as that for the initiation of grain boundary sliding, which was obtained from the uniaxial tensile tests [10]. On the other hand, the m-values are influenced by the grain boundary structures; the m-value for the
Fig. 1. Indentation area observed by the electron back scatter diffraction method and the grain boundary model in MD simulation; (A) misorientation angle of 23°, (B) 44°, (C) 78°, (D) [1–100] symmetric tilt boundary with the angle of 78°. Where the grain with the yellow color is a Schmid factor of 0.25, and the grain boundary with the white color is a specific misorientation angle of 23°, 44° or 78° in (A)–(C), respectively.
34
H. Somekawa, T. Mukai / Materials Letters 76 (2012) 32–35
Fig. 3. The variation of stress as a function of effective strain rate in nanoindentation creep test.
misorientation angle of 23° is the highest among the three kinds of misorientation angles. The experimental results using bicrystals have shown that the grain boundary sliding in the low-angle grain boundaries and the coincidence site lattice (CSL) boundaries is smaller than that in the high-angle grain boundaries [3]. In addition, when the dominant deformation mechanism is the grain boundary sliding, the superplastic behavior in the high-angle grain boundaries is superior to that in the low-angle grain boundaries and CSL boundaries [17–19]. The difference in grain boundary sliding resulted from the disordered structures and/ or the fraction of free volume at the grain boundaries. MD simulations have indicated that the kite structures affect the grain boundary sliding, and the existence of pore structures is important for the occurrence of grain boundary sliding [20–22]. The present 78°-tilted boundary model is constructed from a similar type of kite structure, shown in the inset in Fig. 1(d). The other tilted models in this study include the same structures, AAAEAAAE in the 23°-tilted boundary model and AAEAAE in the 44°-tilted boundary model, although each model contains a different fraction of this kite structure. The grain boundary sliding is also known to have a close relation to the grain boundary energy [23–25], i.e., the grain boundaries with high energy tend to enhance the grain boundary sliding. The calculated grain boundary energies using the MD simulation are listed in Table 1. This table includes the previously reported results, which were obtained using the tight biding potential [26]. The present grain boundary energies are higher than the previous ones due to the difference in using a potential; however, they show the same tendency, where the grain boundary energy; 23° > 44° > 78°-tilted boundaries. This table shows that the grain boundary with high energy is found to have a higher m-value. One of the inherent factors for the occurrence of grain boundary sliding in magnesium is the grain boundary energy, which is the same as that in the other metallic materials. The influence of the alloying element on the deformation behavior at the interface is discussed hereafter. Typical results of the nanoindentation creep tests in the Mg–Al alloy are plotted in Figs. 2 and 3, and the average m-value for the Mg–Al alloy is included in Table 1. These figures show that the m-value of the misorientation angle of Table 1 The results of nanoindentation creep tests and MD simulations.
4. Summary The deformation behavior around three kinds of grain boundary structures in magnesium was investigated using nanoindentation creep tests. The following results were obtained. (1) The dominant deformation mechanism near the grain boundary was the grain boundary sliding even at room temperature. The grain boundary structure affected the strain rate sensitivity, i.e., m-value. (2) The grain boundary energy was one of the factors to influence the m-value. The grain boundary with a high energy, which was obtained using the MD simulation, showed a high m-value. (3) The m-value and grain boundary energy in the Mg–Al alloy were lower than those in pure magnesium. The addition of aluminum atoms into magnesium had the role of decreasing the grain boundary energy and suppressing the grain boundary sliding. Acknowledgments One of the authors (HS) is grateful to Ms. M. Isaki (National Institute for Materials Science) for her technical help. This work was supported by the JSPS Grant-in-Aid for Young Scientists (B) No. 21760564 and 23760675. References [1] [2] [3] [4] [5]
angle, degree
m-value
γgb, J/m2
γgb, J/m2 [26]
23 44 78 78
0.50 ± 0.15 0.43 ± 0.13 0.39 ± 0.14 0.30 ± 0.15
1.25 0.56 0.40 0.32
0.91 0.43 0.33 –
(magnesium) (magnesium) (magnesium) (Mg–Al)
78° for the Mg–Al alloy is found to be lower than that for pure magnesium. Using Eq. (1), the grain boundary energy is obtained to be 0.32 J/m 2 in the 78°-tilted boundary of the Mg–Al alloy, which is also lower than that in pure magnesium (0.40 J/m 2), shown in Table 1. The detailed electric distribution analysis using the first principle calculation is necessary to understand the mechanism for the decrease in the grain boundary energy in the future; however, a recent MD simulation shows that the aluminum atoms provide stability to the magnesium atoms due to the strong bonding between the aluminum and magnesium atoms [27]. Thus, one of the reasons for the lower m-value in the Mg–Al alloy is the reduction in grain boundary energy by the addition of aluminum atoms. Recent experimental studies have shown that the elongation-tofailure in the fine-grained pure magnesium exceeds ~ 50% at room temperature [28], while the typical magnesium alloys, i.e., Mg–3Al– 1Zn (AZ31) alloys, show an elongation of up to 20–30% despite their similar grain size [29]. Watanabe et al. also examined the effect of alloying elements on the superplastic behavior in fine-grained magnesium with a grain size of 2 μm through the damping capacity [30]. They reported that the addition of aluminum atoms was effective for suppressing the grain boundary sliding, which corresponds to the present result. Therefore, the addition of aluminum atoms into magnesium enhances the strength due to well known solid solution strengthening; however, the ductility tends to decrease due to the prevention of grain boundary sliding.
Where γgb is the grain boundary energy and the m-value is obtained from the nanoindentation creep test.
[6] [7] [8] [9] [10] [11] [12]
Su JQ, Demura M, Hirano T. Philos Mag 2002;A82:1541. Hauser JJ, Chalmers B. Acta Metall 1961;9:802. Kokawa H, Watanabe T, Karashima S. Philos Mag 1981;A44:1239. Matsunaga K, Nishimura H, Muto H, Yamamoto T, Ikuhara Y. Appl Phys Lett 2003;82:1179. Yoshida H, Yokoyama K, Shibata N, Ikuhara Y, Sakuma T. Acta Mater 2004;52: 2349. Tsurekawa S, Tanaka T, Yoshinaga H. Mater Sci Eng 1994;A176:341. Koike J, Kobayashi T, Mukai T, Watanabe H, Suzuki M, Maruyama K, et al. Acta Mater 2003;51:2055. Koike J, Ohyama R, Kobayashi T, Suzuki M, Maruyama K. Mater Trans 2003;44: 445. Frost HJ, Ashby MF. Deformation-mechanism map. Oxford: Pergamon Press; 1982. Wang CL, Mukai T, Nieh TG. J Mater Res 2009;24:1615. Chua BW, Lu L, Lai MO. Mater Res Bull 2006;41:2102. Somekawa H, Mukai T. Philos Mag Lett 2010;90:883.
H. Somekawa, T. Mukai / Materials Letters 76 (2012) 32–35 [13] [14] [15] [16] [17] [18] [19] [20] [21]
Tabor DS. The hardness of metals. Oxford: Clarendon Press; 1951. Mayo MJ, Nix WD. Acta Metall 1988;36:2183. Wang CL, Lai YH, Huang JC, Nieh TG. Scr Mater 2010;62:175. Alkorta J, Martinez-Esnaola JM, Sevillano JG. Acta Mater 2008;56:884. Kaibyshev R, Goloborodko A, Musin F, Nikulin I, Sakai T. Mater Trans 2002;43: 2408. Hirata T, Osa T, Hosokawa H, Higashi K. Mater Trans 2002;43:2385. Valiev RZ, Langdon TG. Prog Mater Sci 2006;51:881. Sansoz F, Molinari JF. Acta Mater 2005;53:1931. Yuasa M, Nakazawa T, Mabuchi M. Mater Sci Eng 2010;A527:2629.
[22] [23] [24] [25] [26] [27] [28] [29] [30]
35
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