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Deformation mechanism transition with strain rate in Mg–3Al–1Zn alloy at room temperature
Materials Science & Engineering A 647 (2015) 212–215
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation mechanism transition with strain rate in Mg–3Al–1Zn alloy at room temperature T. Matsunaga n, H. Somekawa, H. Hongo, M. Tabuchi National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 13 March 2015 Received in revised form 4 September 2015 Accepted 6 September 2015 Available online 9 September 2015
At room temperature, the strain-rate sensitivity (SRS) was almost negligible at high strain rates in asextruded Mg–3Al–1Zn alloy because of the exponent (m) of 0.008. However, SRS became remarkable with decreasing strain rate down to 10 8 s 1, where the m value increases up to 0.06. & 2015 Elsevier B.V. All rights reserved.
Keywords: Magnesium alloy Strain-rate sensitivity Creep Grain boundary Low thermal assisted process
1. Introduction Although magnesium (Mg) and its alloys are regarded as prospective materials for lightweight structural components in transportation industries because of their low density of ca. 1.7 g cm 3, Mg shows anisotropic mechanical behavior resulting from the axial ratio and low crystalline symmetry of the hexagonal close-packed (HCP) structure. According to the crystal structure, the independent slip systems are few and the von Mises law is not satisfied. Because it leads to low formability, the improvement and understanding of the strain-rate sensitivity (SRS) are important for engineering and material science. Koral et al. concluded that twinning does not affect SRS because it is an athermal process at 373 K, where exponent (m) is nearly zero [1]. Karimi et al. reported that significant SRS was achieved by the activation of dislocation motion in compression at 473–823 K, where the m value increases up to about 0.3 with increasing temperature [2]. A similar trend was reported for a tensile condition [3]. The m value of 0.14–0.2 was observed in Mg–Al–Zn alloys including Mg–3Al–1Zn (AZ31 Mg) alloy. The apparent activation volume (V) was 4 100b3 (where b is the Burgers vector), which reflects dislocation interaction or non-conservative movement of dislocation [4,5]. These results indicate that SRS is generated by diffusion-controlled (thermal activated) dislocation motion in Mg and its alloys. n
Corresponding author. Fax: þ81 29 859 2201. E-mail address: [email protected] (T. Matsunaga).
http://dx.doi.org/10.1016/j.msea.2015.09.029 0921-5093/& 2015 Elsevier B.V. All rights reserved.
A mechanism with low thermal activation like the Peierls mechanism can describe SRS by kink-pair nucleation in body-centered cubic materials [6,7]. Conrad et al. [6] and Arsenault [7] demonstrated that the V value of the mechanism was about 10b3 in iron. Kink-pair nucleation has been described as a single dislocation motion without interaction among dislocations [8]. Actually, HCP metals and titanium alloy show straightly aligned dislocations [9,10], which have a similar dislocation structure to that in the model [8]. According to the results, although HCP materials can show SRS with low thermal activation, a V value of o100b3 has not been reported at strain rates (ε˙) of 410 4 s 1 [1,2]. Therefore, the present study specifically addressed the deformation at ε˙ o10 5 s 1 to elucidate SRS in Mg alloy.
2. Experimental procedure A commercially as-extruded AZ31 Mg alloy was used for this study. Optical micrograph of the sample is shown in Fig. 1(a) and then the grain size evaluated by the intercept length was about 10 μm. Moreover, (0002) pole figure, obtained by the Schultz reflection method at α-angles of 20–90°, is shown in Fig. 1(b). Maximum intensity (Imax) was counted at the center of ED-TD plane, where ED was the extrusion direction and TD was the transverse direction. It means that the basal plane lies parallel to extrusion direction. Tensile and creep tests were conducted at 297 K using round bar type samples with respective gauge length and diameter of
T. Matsunaga et al. / Materials Science & Engineering A 647 (2015) 212–215
213
Fig. 2. (a) Stress vs strain and (b) creep curves of AZ31 Mg alloy at room temperature.
Fig. 1. (a) Optical micrograph and (b) (0002) pole figure of the sample.
15 mm and 3 mm. The loading direction corresponded to ED. To evaluate strain-rate sensitivity exponent (m), the following equation was used:
m = log (σ 2 − σ1)/log (ε2̇ − ε1̇ )
(1)
where s1 and s2 are the flow stresses or the applied stresses at respective strain rates of ε˙1 and ε˙2. In addition, the V value was evaluated to reveal the thermal activation process using the following equation [11]:
V=
⎛ ∂ ln ε ̇ ⎞ 3 kT 3 kT ⎜ ⎟= ⎝ ∂σ ⎠ mσ
(2)
where k is the Boltzman constant, T is temperature, and s is stress. The Burger's vector of 3.21 10 10 m for Mg [12] was used to normalize the V value in this study. After mechanical testing, fractography was performed for comparison with the fracture mode between tensile and crept samples using scanning electron microscope (SEM). Then, samples were sectioned along the loading direction using an electro-discharged machine. They were also ground and etched with 10 ml nitric acid and 100 ml distilled water before optical microscopy.
3. Experimental results Fig. 2 shows (a) nominal stress vs strain curves and (b) creep curves of the sample at room temperature. Tensile tests showed almost equal flow stress for ε˙ ¼ 10 4–10 3 s 1, but it decreased slightly at ε˙ ¼10 5 s 1. However, creep tests showed clear stress dependency in curves. These data are shown as a double
Fig. 3. (Left vertical axis) Double logarithmic plot of strain rate and applied stress or flow one at ε ¼0.1. (Right vertical axis) Single logarithmic plot of strain rate and rupture strain. The m values are 0.008 at high strain rates and 0.06 at low strain rates.
logarithmic plot of ε˙ and the applied stress or the flow stress at strain of 0.1 in Fig. 3. Although small SRS with m ¼0.008 appeared at high strain rates, which corresponds to an early report [13], the m value increased by one order, i.e., m ¼0.06, with decreasing strain rate down to about 10 9 s 1. Moreover, Fig. 3 depicts rupture strain (εr) functioned by strain rate, where it increased from 0.14 to 0.27 with decreasing strain rate. Furthermore, the V value was evaluated as about 100 b3 at high strain rates but as
214
T. Matsunaga et al. / Materials Science & Engineering A 647 (2015) 212–215
Fig. 5. Optical micrographs near the fracture surface of (a) the tensile-tested sample at ε˙ ¼ 10 3 s 1 and (b) the crept sample at ε˙ ¼1.9 10 8 s 1. Arrows in the figure indicates deformation twins. Loading direction (LD) was parallel to the vertical direction.
Fig. 4. Typical fracture surfaces: (a) dimple and quasi-cleavage fracture with shallow dimples and (b) shearing plane after the tensile test at ε˙ ¼10 3 s 1; (c) dimples after the creep test at ε˙ ¼1.9 10 8 s 1.
approximately 15 b3 at low strain rates. The former value corresponds to that of thermal processes [1,2,4,5]. However, the latter value indicates that SRS resulted from a process with low thermal activation and that it might reflect the transition of deformation mode form diffusional to non-diffusional with decreasing strain rate in the alloy. Fig. 4 shows typical fracture surfaces after (a, b) the tensile test at ε˙ ¼ 10 3 s 1 and (c) the creep test at ε˙ ¼1.9 10 8 s 1. Tensiletested specimen showed dimples, quasi-cleavage fracture with shallow dimples and a shearing plane, whereas the crept sample mainly showed dimples. Fractography revealed that ductile fracture was occurred in wide-ranged strain-rate region at room temperature, but the feature of brittle fracture was observed at the high strain rate. The difference between both regions was coincident with εr, i.e., 0.14 at high strain rate and 0.27 at low strain rate, as shown in Fig. 3. Fig. 5 depicts optical micrographs near the fracture surface of the same samples in Fig. 4. The tensile-tested specimen showed
many deformation twins near the fracture surface. The twin is well known to act as the crack path. Quasi-cleavage as shown in Fig. 4 (a) was generated by the behavior, engendering poor ductility at high strain rates. However, deformation twins were rarely observed even near the fracture surface in the creep condition. Therefore, the deformation proceeds predominantly by dislocation motion. In Mg, nucleation of twin occurs at the grain boundary (GB) and propagates into the grain interior [14,15]. Because the process requires stress concentration at GB, the stress might be accommodated at low strain rates to suppress twin nucleation by a mechanism.
4. Discussion According to the mechanical tests and microscopy, the SRS mechanism changed with decreasing strain rate at room temperature, where the m value increased by one order and the V value at low strain rate became one-fifth of that at high strain rates. These parameters indicate that (1) deformation is influenced by dislocation motion, (2) interaction among dislocations becomes weak, and (3) valuable SRS appeared with decreasing strain rate. Results show that conventional SRS influenced by the thermal
T. Matsunaga et al. / Materials Science & Engineering A 647 (2015) 212–215
process is inhibited in the condition. Therefore, a new process might generate SRS in AZ31 Mg alloy in a low strain-rate region at room temperature. The Peierls mechanism might be useful for increasing SRS with low V value, where deformation is influenced by kink-pair nucleation. However, the mechanism was not able to satisfy an accommodation in the steady state creep region, as shown in Fig. 2 (b), because it describes not a recovery but a deformation process. Moreover, although cross slip is a recovery process with low thermal effect, the stacking fault energies of Mg–Al alloys are calculated as less than 30 mJ m 2 [3]. The process suppressed constriction strongly. It affects SRS only slightly in this condition. Another prospective mechanism related to SRS in the Mg alloy is slip-induced GB sliding (GBS), which is generated by dislocation absorption by GB at 298–573 K [9,16]. This deformation process is brought about by sliding of GB dislocation absorbed into GB from a grain interior. In this case, SRS can be described by the time-dependent change of dislocation density at GB [17,18], which can accommodate the stress concentration there. In addition, because the phenomenon is activated with the activation energy of 20 kJ mol 1[16], slip-induced GBS might engender SRS with low thermal assist.
5. Conclusions This study examined SRS in AZ31 Mg alloy at room temperature. According to the observed variables, the deformation mode changed from diffusional type with m ¼0.008 and V¼ 100b3 to non-diffusional type with m ¼0.06 and V ¼ 15b3 with a decreasing strain rate. Other conclusions were the following. (1) Although quasi-cleavage fracture was observed at a high strain
215
rate, ductility increased with decreasing strain rate, where dimples were observed in the creep condition. (2) Twinning was rarely observed even near the fracture surface in a crept sample. SRS was generated dominantly by dislocation motion. (3) Slip-induced GBS was a prospective deformation mode with a low V value. It might generate SRS at low strain rates.
References [1] R. Korla, A.H. Chokshi, Scr. Mater. 63 (2010) 913–916. [2] E. Karimi, A. Zarei-Hanazaki, M.H. Pishbin, H.R. Abedi, P. Changizian, Mater. Des. 49 (2013) 173–180. [3] H. Somekawa, K. Hirai, H. Watanabe, Y. Takigawa, K. Higashi, Mater. Sci. Eng. A 407 (2005) 53–61. [4] H. Conrad, L. Hays, G. Schoeck, H. Wiedersich, Acta Metall. 9 (1961) 367–378. [5] A.G. Evans, R.D. Rawlings, Phys. Status Solidi 34 (1969) 9–31. [6] H. Conrad, S. Frederick, Acta Metall. 10 (1962) 1013–1020. [7] R.J. Arsenault, Acta Metall. 15 (1967) 501–511. [8] A. Segger, Philos. Mag. 1 (1956) 651–662. [9] T. Neeraj, D.-H. Hou, G.S. Daehn, M.J. Mills, Acta Mater. 48 (2000) 1225–1238. [10] T. Matsunaga, T. Kameyama, K. Takahashi, E. Sato, Mater. Trans. 50 (2009) 2865–2872. [11] H. Somekawa, T. Mukai, Metall. Mater. Trans. A 46 (2015) 894–902. [12] H.J. Frost, M.F. Ashby, Deformation mechanism map, Pergamon Press, Oxford, 1982. [13] Y.B. Chun, C.H.J. Davies, Mater. Sci. Eng. A 528 (2011) 5713–5722. [14] M.A. Kumar, A.K. Kanjarla, S.R. Niezgoda, R.A. Lebensohn, C.N. Tome, Acta Mater. 84 (2015) 349–358. [15] P.D. Wu, X.Q. Guo, H. Qiao, D.J. Lloyd, Mater. Sci. Eng. A 625 (2015) 140–145. [16] J. Koike, R. Ohyama, T. Kobayashi, M. Suzuki, K. Maruyama, Mater. Trans. 44 (2003) 445–451. [17] T.G. Langdon, Acta Metall. Mater. 42 (1994) 2437–2443. [18] T. Matsunaga, E. Sato, Scanning probe microscopy-physical property characterization at nanoscale, in: V. Nalladega (Ed.), Scanning Probe MicroscopyPhysical Property Characterization at Nanoscale, InTech, Croatia, 2012, pp. 203–214.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation mechanism transition with strain rate in Mg–3Al–1Zn alloy at room temperature T. Matsunaga n, H. Somekawa, H. Hongo, M. Tabuchi National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 13 March 2015 Received in revised form 4 September 2015 Accepted 6 September 2015 Available online 9 September 2015
At room temperature, the strain-rate sensitivity (SRS) was almost negligible at high strain rates in asextruded Mg–3Al–1Zn alloy because of the exponent (m) of 0.008. However, SRS became remarkable with decreasing strain rate down to 10 8 s 1, where the m value increases up to 0.06. & 2015 Elsevier B.V. All rights reserved.
Keywords: Magnesium alloy Strain-rate sensitivity Creep Grain boundary Low thermal assisted process
1. Introduction Although magnesium (Mg) and its alloys are regarded as prospective materials for lightweight structural components in transportation industries because of their low density of ca. 1.7 g cm 3, Mg shows anisotropic mechanical behavior resulting from the axial ratio and low crystalline symmetry of the hexagonal close-packed (HCP) structure. According to the crystal structure, the independent slip systems are few and the von Mises law is not satisfied. Because it leads to low formability, the improvement and understanding of the strain-rate sensitivity (SRS) are important for engineering and material science. Koral et al. concluded that twinning does not affect SRS because it is an athermal process at 373 K, where exponent (m) is nearly zero [1]. Karimi et al. reported that significant SRS was achieved by the activation of dislocation motion in compression at 473–823 K, where the m value increases up to about 0.3 with increasing temperature [2]. A similar trend was reported for a tensile condition [3]. The m value of 0.14–0.2 was observed in Mg–Al–Zn alloys including Mg–3Al–1Zn (AZ31 Mg) alloy. The apparent activation volume (V) was 4 100b3 (where b is the Burgers vector), which reflects dislocation interaction or non-conservative movement of dislocation [4,5]. These results indicate that SRS is generated by diffusion-controlled (thermal activated) dislocation motion in Mg and its alloys. n
Corresponding author. Fax: þ81 29 859 2201. E-mail address: [email protected] (T. Matsunaga).
http://dx.doi.org/10.1016/j.msea.2015.09.029 0921-5093/& 2015 Elsevier B.V. All rights reserved.
A mechanism with low thermal activation like the Peierls mechanism can describe SRS by kink-pair nucleation in body-centered cubic materials [6,7]. Conrad et al. [6] and Arsenault [7] demonstrated that the V value of the mechanism was about 10b3 in iron. Kink-pair nucleation has been described as a single dislocation motion without interaction among dislocations [8]. Actually, HCP metals and titanium alloy show straightly aligned dislocations [9,10], which have a similar dislocation structure to that in the model [8]. According to the results, although HCP materials can show SRS with low thermal activation, a V value of o100b3 has not been reported at strain rates (ε˙) of 410 4 s 1 [1,2]. Therefore, the present study specifically addressed the deformation at ε˙ o10 5 s 1 to elucidate SRS in Mg alloy.
2. Experimental procedure A commercially as-extruded AZ31 Mg alloy was used for this study. Optical micrograph of the sample is shown in Fig. 1(a) and then the grain size evaluated by the intercept length was about 10 μm. Moreover, (0002) pole figure, obtained by the Schultz reflection method at α-angles of 20–90°, is shown in Fig. 1(b). Maximum intensity (Imax) was counted at the center of ED-TD plane, where ED was the extrusion direction and TD was the transverse direction. It means that the basal plane lies parallel to extrusion direction. Tensile and creep tests were conducted at 297 K using round bar type samples with respective gauge length and diameter of
T. Matsunaga et al. / Materials Science & Engineering A 647 (2015) 212–215
213
Fig. 2. (a) Stress vs strain and (b) creep curves of AZ31 Mg alloy at room temperature.
Fig. 1. (a) Optical micrograph and (b) (0002) pole figure of the sample.
15 mm and 3 mm. The loading direction corresponded to ED. To evaluate strain-rate sensitivity exponent (m), the following equation was used:
m = log (σ 2 − σ1)/log (ε2̇ − ε1̇ )
(1)
where s1 and s2 are the flow stresses or the applied stresses at respective strain rates of ε˙1 and ε˙2. In addition, the V value was evaluated to reveal the thermal activation process using the following equation [11]:
V=
⎛ ∂ ln ε ̇ ⎞ 3 kT 3 kT ⎜ ⎟= ⎝ ∂σ ⎠ mσ
(2)
where k is the Boltzman constant, T is temperature, and s is stress. The Burger's vector of 3.21 10 10 m for Mg [12] was used to normalize the V value in this study. After mechanical testing, fractography was performed for comparison with the fracture mode between tensile and crept samples using scanning electron microscope (SEM). Then, samples were sectioned along the loading direction using an electro-discharged machine. They were also ground and etched with 10 ml nitric acid and 100 ml distilled water before optical microscopy.
3. Experimental results Fig. 2 shows (a) nominal stress vs strain curves and (b) creep curves of the sample at room temperature. Tensile tests showed almost equal flow stress for ε˙ ¼ 10 4–10 3 s 1, but it decreased slightly at ε˙ ¼10 5 s 1. However, creep tests showed clear stress dependency in curves. These data are shown as a double
Fig. 3. (Left vertical axis) Double logarithmic plot of strain rate and applied stress or flow one at ε ¼0.1. (Right vertical axis) Single logarithmic plot of strain rate and rupture strain. The m values are 0.008 at high strain rates and 0.06 at low strain rates.
logarithmic plot of ε˙ and the applied stress or the flow stress at strain of 0.1 in Fig. 3. Although small SRS with m ¼0.008 appeared at high strain rates, which corresponds to an early report [13], the m value increased by one order, i.e., m ¼0.06, with decreasing strain rate down to about 10 9 s 1. Moreover, Fig. 3 depicts rupture strain (εr) functioned by strain rate, where it increased from 0.14 to 0.27 with decreasing strain rate. Furthermore, the V value was evaluated as about 100 b3 at high strain rates but as
214
T. Matsunaga et al. / Materials Science & Engineering A 647 (2015) 212–215
Fig. 5. Optical micrographs near the fracture surface of (a) the tensile-tested sample at ε˙ ¼ 10 3 s 1 and (b) the crept sample at ε˙ ¼1.9 10 8 s 1. Arrows in the figure indicates deformation twins. Loading direction (LD) was parallel to the vertical direction.
Fig. 4. Typical fracture surfaces: (a) dimple and quasi-cleavage fracture with shallow dimples and (b) shearing plane after the tensile test at ε˙ ¼10 3 s 1; (c) dimples after the creep test at ε˙ ¼1.9 10 8 s 1.
approximately 15 b3 at low strain rates. The former value corresponds to that of thermal processes [1,2,4,5]. However, the latter value indicates that SRS resulted from a process with low thermal activation and that it might reflect the transition of deformation mode form diffusional to non-diffusional with decreasing strain rate in the alloy. Fig. 4 shows typical fracture surfaces after (a, b) the tensile test at ε˙ ¼ 10 3 s 1 and (c) the creep test at ε˙ ¼1.9 10 8 s 1. Tensiletested specimen showed dimples, quasi-cleavage fracture with shallow dimples and a shearing plane, whereas the crept sample mainly showed dimples. Fractography revealed that ductile fracture was occurred in wide-ranged strain-rate region at room temperature, but the feature of brittle fracture was observed at the high strain rate. The difference between both regions was coincident with εr, i.e., 0.14 at high strain rate and 0.27 at low strain rate, as shown in Fig. 3. Fig. 5 depicts optical micrographs near the fracture surface of the same samples in Fig. 4. The tensile-tested specimen showed
many deformation twins near the fracture surface. The twin is well known to act as the crack path. Quasi-cleavage as shown in Fig. 4 (a) was generated by the behavior, engendering poor ductility at high strain rates. However, deformation twins were rarely observed even near the fracture surface in the creep condition. Therefore, the deformation proceeds predominantly by dislocation motion. In Mg, nucleation of twin occurs at the grain boundary (GB) and propagates into the grain interior [14,15]. Because the process requires stress concentration at GB, the stress might be accommodated at low strain rates to suppress twin nucleation by a mechanism.
4. Discussion According to the mechanical tests and microscopy, the SRS mechanism changed with decreasing strain rate at room temperature, where the m value increased by one order and the V value at low strain rate became one-fifth of that at high strain rates. These parameters indicate that (1) deformation is influenced by dislocation motion, (2) interaction among dislocations becomes weak, and (3) valuable SRS appeared with decreasing strain rate. Results show that conventional SRS influenced by the thermal
T. Matsunaga et al. / Materials Science & Engineering A 647 (2015) 212–215
process is inhibited in the condition. Therefore, a new process might generate SRS in AZ31 Mg alloy in a low strain-rate region at room temperature. The Peierls mechanism might be useful for increasing SRS with low V value, where deformation is influenced by kink-pair nucleation. However, the mechanism was not able to satisfy an accommodation in the steady state creep region, as shown in Fig. 2 (b), because it describes not a recovery but a deformation process. Moreover, although cross slip is a recovery process with low thermal effect, the stacking fault energies of Mg–Al alloys are calculated as less than 30 mJ m 2 [3]. The process suppressed constriction strongly. It affects SRS only slightly in this condition. Another prospective mechanism related to SRS in the Mg alloy is slip-induced GB sliding (GBS), which is generated by dislocation absorption by GB at 298–573 K [9,16]. This deformation process is brought about by sliding of GB dislocation absorbed into GB from a grain interior. In this case, SRS can be described by the time-dependent change of dislocation density at GB [17,18], which can accommodate the stress concentration there. In addition, because the phenomenon is activated with the activation energy of 20 kJ mol 1[16], slip-induced GBS might engender SRS with low thermal assist.
5. Conclusions This study examined SRS in AZ31 Mg alloy at room temperature. According to the observed variables, the deformation mode changed from diffusional type with m ¼0.008 and V¼ 100b3 to non-diffusional type with m ¼0.06 and V ¼ 15b3 with a decreasing strain rate. Other conclusions were the following. (1) Although quasi-cleavage fracture was observed at a high strain
215
rate, ductility increased with decreasing strain rate, where dimples were observed in the creep condition. (2) Twinning was rarely observed even near the fracture surface in a crept sample. SRS was generated dominantly by dislocation motion. (3) Slip-induced GBS was a prospective deformation mode with a low V value. It might generate SRS at low strain rates.
References [1] R. Korla, A.H. Chokshi, Scr. Mater. 63 (2010) 913–916. [2] E. Karimi, A. Zarei-Hanazaki, M.H. Pishbin, H.R. Abedi, P. Changizian, Mater. Des. 49 (2013) 173–180. [3] H. Somekawa, K. Hirai, H. Watanabe, Y. Takigawa, K. Higashi, Mater. Sci. Eng. A 407 (2005) 53–61. [4] H. Conrad, L. Hays, G. Schoeck, H. Wiedersich, Acta Metall. 9 (1961) 367–378. [5] A.G. Evans, R.D. Rawlings, Phys. Status Solidi 34 (1969) 9–31. [6] H. Conrad, S. Frederick, Acta Metall. 10 (1962) 1013–1020. [7] R.J. Arsenault, Acta Metall. 15 (1967) 501–511. [8] A. Segger, Philos. Mag. 1 (1956) 651–662. [9] T. Neeraj, D.-H. Hou, G.S. Daehn, M.J. Mills, Acta Mater. 48 (2000) 1225–1238. [10] T. Matsunaga, T. Kameyama, K. Takahashi, E. Sato, Mater. Trans. 50 (2009) 2865–2872. [11] H. Somekawa, T. Mukai, Metall. Mater. Trans. A 46 (2015) 894–902. [12] H.J. Frost, M.F. Ashby, Deformation mechanism map, Pergamon Press, Oxford, 1982. [13] Y.B. Chun, C.H.J. Davies, Mater. Sci. Eng. A 528 (2011) 5713–5722. [14] M.A. Kumar, A.K. Kanjarla, S.R. Niezgoda, R.A. Lebensohn, C.N. Tome, Acta Mater. 84 (2015) 349–358. [15] P.D. Wu, X.Q. Guo, H. Qiao, D.J. Lloyd, Mater. Sci. Eng. A 625 (2015) 140–145. [16] J. Koike, R. Ohyama, T. Kobayashi, M. Suzuki, K. Maruyama, Mater. Trans. 44 (2003) 445–451. [17] T.G. Langdon, Acta Metall. Mater. 42 (1994) 2437–2443. [18] T. Matsunaga, E. Sato, Scanning probe microscopy-physical property characterization at nanoscale, in: V. Nalladega (Ed.), Scanning Probe MicroscopyPhysical Property Characterization at Nanoscale, InTech, Croatia, 2012, pp. 203–214.