Materials Science & Engineering A 655 (2016) 269–276
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Effect of tungsten content on the microstructure and tensile properties of Ni–xW–6Cr alloys Shulin Liu a,b, Xiang-Xi Ye a,n, Li Jiang a,b, Chuanyong Cui c, Zhijun Li a,n, Hefei Huang a, Bin Leng a, Xingtai Zhou a,n a
Center for Thorium Molten Salt Reactor System, Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, PR China University of Chinese Academy of Sciences, Beijing 100049, PR China c Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, PR China b
art ic l e i nf o
a b s t r a c t
Article history: Received 22 September 2015 Received in revised form 3 January 2016 Accepted 4 January 2016 Available online 5 January 2016
Ni–xW–6Cr alloys have been considered as one of the potential structural materials for molten salt techniques, whereas their microstructure and mechanical performance have not been sufficiently studied. In this study, the microstructure and tensile deformation behavior of Ni–(10–35 wt%)W–6Cr alloys have been systematically investigated. The phase diagram calculations indicated that the solubility limit of W is 34 wt% in Ni–xW–6Cr alloy. α-W phase is formed in the matrix while the W content exceeds such limit. The fracture of the Ni–(10–35 wt%)W–6Cr alloys at room temperature is in the transgranular ductile fracture mode. The tensile properties of alloys, except for the elongation of Ni–35 wt%W–6Cr alloy, are improved with the increase of W content, which can be explained by the larger lattice distortion, the lower stack fault energy and the higher length fraction of twin boundaries (Σ3 and Σ9 type) in the Ni–(10–35 wt%)W–6Cr alloys caused by the addition of more W. The reduced elongation of the Ni– 35 wt%W–6Cr alloy is ascribed to the particles in α-W phase which act as the main nucleation sites for cracking. & 2016 Elsevier B.V. All rights reserved.
Keywords: Ni–W–Cr alloy α-W phase EBSD Tensile deformation Twin boundaries
1. Introduction Molten salts, owing to their advantageous thermo-physical properties, have been used as media for many decades in applications of industrial process heat transfer, thermal storage, and materials processing [1,2]. On the other hand, they introduce a set of technological and engineering challenges, in which screening materials with excellent mechanical strengths and good compatibilities to molten salts is still being addressed [3,4]. To date, Hastelloy N alloy (70Ni–16Mo–7Cr solid solution strengthening nickelbased alloy), developed by Oak Ridge National Laboratory for the molten salt reactor (MSR) in 1950s to 1960s, is still the only successful metallic structural material for the facilities with fluoride molten salts [4]. To further improve the mechanical performance of Hastelloy N alloy, a new Ni–26W–6Cr based superalloy, in which the main effective solid solute hardener Mo was replaced by W, has been developed [5,6]. In nickel-base alloys, W is more effective in hardening the matrix than Mo. The bond order of Ni–W d–d bond, a measurement of bond strength, was evaluated as 1.730, larger than n
Corresponding authors. E-mail addresses:
[email protected] (X.-X. Ye),
[email protected] (Z. Li),
[email protected] (X. Zhou). http://dx.doi.org/10.1016/j.msea.2016.01.010 0921-5093/& 2016 Elsevier B.V. All rights reserved.
that of Ni–Mo d–d bond (1.611) [7], essentially revealing the nature of better strengthening effect of W than Mo. The preliminary studies on Ni–26W–6Cr alloy show that it maintains good tensile strength and ductility at room temperature [6,8]. Unlike other wellknown Ni–W–Cr alloys such as Haynes 230 [9] and Ni–20W–18Cr based alloy [10–12], which usually contain at least 15 wt% Cr, the content of Cr in this alloy is 6 wt%. It is because Cr can be easily attacked by fluoride molten salts and 6–8 wt% Cr has been proven to be the ideal content in the alloys used for fluoride molten salts technologies for balancing the high temperature oxidation and the molten salt corrosion [13]. It is well known that the tensile properties of a superalloy are seriously affected by its composition and microstructure. Up till now, tremendous efforts have been made to understand the composition–microstructure–properties relationship in the family of Ni–W–Cr alloys [10,11,14–16]. For instance, Ohta et al. [14] found that the creep strength of Ni–Cr–W alloys containing 15–20 wt% Cr increases with their W content. Bai et al. [11] suggested that in a Ni–20W–18Cr alloy, the lamellar M23C6 carbides, which are rich in W and have the width of 1–3 μm, weaken the grain boundary of the alloy and lead to a premature failure at 600 °C. Since Ni–xW–Cr alloys with low Cr content are expected to be used in a harsh environment of fluoride molten salts, the knowledge about the W content–microstructure–mechanical properties correlation of the alloys is an essential.
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Hence, in this work, the effect of W content on tensile properties of the wrought ternary Ni–xW–Cr alloys with low Cr content (6 wt%) is systematically investigated. Efforts are also made to analyze the correlation between the microstructures and the tensile properties of the alloys.
2. Experimental procedures Six alloys with different W contents were fabricated and the corresponding compositions are shown in Table 1. The raw materials (99.99 wt% pure Ni, Cr and W) were grinded with silicon carbide papers to remove oxide layer, followed by ultrasonic cleaning using acetone and deionized water sequentially. The grinded raw materials were then melted in a vacuum arc furnace. And then ingots were homogenized at 1250 °C for 10 h, followed by a water quenching. Finally, after the ingots were hot rolled to 4 mm thick sheets (70% deformation) at 1200 °C, the sheets were solution-heated at 1260 °C for 0.5 h, followed by a water quenching. Tensile specimens with dimensions of 1 mm thickness, 3.5 mm gage width and 18 mm gauge length were cut from the sheets. Samples used for microstructure and deformation behavior analyses were cut from the solution-heated sheets and the gauge parts of the tested specimens. Standard metallographic techniques were used to prepare scanning electron microscopy (SEM) samples. The polished specimens were etched with aqua regia (HCl:
HNO3 ¼3:1) for 2 min to reveal the microstructure. The specimen surface for the electron backscattered diffraction (EBSD) measurements was further polished in a vibratory polisher for 10 h by colloidal alumina slurry, to produce a strain free surface. Microstructures were examined on a Bruker D8 Advance X-Ray Diffractometer (XRD), a Zeiss AX10 optical microscope (OM) and a Zeiss LEO 1530VP SEM equipped with an energy dispersive spectrometer (EDS) and an Oxford EBSD system. An acceleration voltage of 20 kV was employed for EBSD mapping. EBSD patterns were collected at 2 μm scan step resolution and EBSD data postprocessing was done with Aztec software packages. Standard transmission electron microscopy (TEM) disc specimens (Φ ¼ 3 mm) were punched out from the origin and tested specimens and further thinned to a thickness of 80 μm using silicon carbide paper. The samples were then double-jet polished in 8% perchloric acid carbinol solution at 30 °C. The phase and microstructures were characterized using a Tecnai G2 F20 TEM with an accelerating voltage of 200 kV. Tensile tests of the alloy specimens were carried out at room temperature using a Zwick-Roell Z100 tensile testing machine. According to ASTM E8/E8M-13a [17], a strain rate was maintained 8 10 5 s 1 up to being yielded and 8 10 4 s 1 after being yielded to obtain the yield strength (YS), ultimate tensile strength (UTS) and elongation to fracture (EL). YS and UTS were determined, respectively, at a 0.2% offset and the maximum stress, while elongation percentage was defined as the maximum elongated gauge length divided by the original gauge length.
Table 1 Chemical composition (wt%) of the Ni–xW–6Cr alloys. Name
Ni
W
Cr
Ni–10W–6Cr Ni–15W–6Cr Ni–20W–6Cr Ni–25W–6Cr Ni–30W–6Cr Ni–35W–6Cr
82.32 78.22 71.92 67.59 62.67 58.59
11.82 15.50 22.08 26.12 31.06 35.53
5.86 6.28 5.99 6.29 6.27 5.88
Fig. 1. Optical microstructures of alloys (a) Ni–10W–6Cr, (b) Ni–15W–6Cr, (c) Ni–20W–6Cr, (d) Ni–25W–6Cr, (e) Ni–30W–6Cr, and (f) Ni–35W–6Cr.
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3. Results
3.2. Lattice distortion
3.1. Initial microstructure
Fig. 3a demonstrates the XRD patterns of pure Ni and Ni–xW– 6Cr with W content from 10 wt% to 35 wt%. It is obvious that the diffraction peaks of (111), (200) and (220) shift to lower angle with increasing W content, indicating W atoms effectively expand the lattice of the alloys. According to Vegard's law [18], the lattice parameter of nickel solid soluted by W and Cr can be calculated as,
Table 1 shows the chemical composition of the Ni–xW–6Cr alloys. Fig. 1 illustrates the typical microstructures of the specimens in the solution treatment condition. Ni–xW–6Cr alloys with W contents ranging from 10 wt% to 30 wt% show a typical equiaxed grain structure with an average grain size of about 200 μm (Fig. 1a–e). In the case of Ni–35W–6Cr alloy, there are lots of stick-like and ball-like particles with sizes of 500 nm to 10 μm randomly dispersed inside the grains as well as along the grain boundaries (Figs. 1f and 2a). TEM analysis shows that the particle possesses a body-centered cubic (bcc) lattice and the estimated lattice parameter is 0.316 nm (Fig. 2b). EDS spectrum (Fig. 2c) reveals that the particle shown in Fig. 2b is rich in tungsten with the composition of 94.6 wt% W, 5.3 wt% Ni and 0.1 wt% Cr. Thus, the particles are determined as α-W phase. The average grain size of Ni–35W–6Cr alloy is about 20 μm, much smaller than those of the other Ni–xW–6Cr alloys. This may be ascribed to the very small particles in α-W phase, inhibiting the grain growth during the final solid–solution process of Ni–35W–6Cr alloy.
a = 3.524 + 0.110X cr + 0.444Xw ,
(1)
where Xcr and Xw are the molar percent of Cr and W, respectively. The lattice distortion of the Ni–xW–6Cr alloys evaluated by XRD spectra is in good accordance with that calculated by Vegard's law (Fig. 3b). For the Ni–xW–6Cr systems, the addition of 5 wt% W causes about 0.25% lattice distortion (Fig. 3b). In addition, XRD spectrum also indicates that α-W phase exists in Ni–35W–6Cr alloy. 3.3. Grain boundary character distribution As shown in Fig. 1, there are many annealing twins in all of the Ni–xW–6Cr alloys. Since twins may greatly affect the deformation process of the alloys [19], the grain boundary character distribution of the Ni–xW–6Cr alloys was analyzed according to the EBSD
Fig. 2. (a) SEM image of the α-W particles, (b) TEM image of an individual α-W particle in the Ni–35W–6Cr alloy, and (c) EDS spectrum of the α-W particle shown in (b).
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Fig. 3. (a) XRD spectra of the Ni–xW–6Cr alloys with W content from 10% to 35%, and (b) the dependence of lattice distortion on W content, evaluated by XRD data fitting and Vegard’s law.
maps by Aztec software. As shown in Fig. 4a–f, the Ni–xW-6Cr alloys mainly consist of Σ3 type and random grain boundaries, though a very small fraction of other coincident site lattice boundaries exist. The length fraction of Σ3 type grain boundaries increases in the alloys with W content when it is less than 30 wt%; while the Σ3 type grain boundaries becomes saturated when the W content is beyond 30 wt% (Fig. 4g).
alloy at room temperature obtained from the tensile tests. The uniform elongation, similar to the total elongation to failure, increases with the W content, except for the alloy sample with W content of 35 wt%. Fig. 5c shows the plots of the work hardening rate against the true plastic strain. The work hardening rate Θ can be defined as [20]:
Θ= 3.4. Tensile properties Fig. 5a shows the dependence of the room-temperature tensile properties of the Ni–xW–6Cr alloys on their W content. The YS and UTS increase monotonously with increasing W content, and it is worth noting that both YS and UTS increase sharply when the W content increases from 30 wt% to 35 wt%. The EL of all the alloys samples exceeds 36%. Similarly, with increasing W content, EL also slightly increases when W content is less than 30 wt.%, but decreases when the W is more than 30 wt%, which indicates that the tensile properties of the alloys are highly sensitive to the W content. Fig. 5b shows the true stress–strain curves of all the Ni–xW–6Cr
⎛ ∂σ ⎞ ⎜ ⎟ ⎝ ∂ε ⎠ε
(2)
where σ and ε are the true stress and the true strain, respectively. The work hardening rate slightly increases with increasing W content. 3.5. Fractography Fracture morphologies of the corresponding test alloys after tensile test at room temperature are shown in Fig. 6. From the lateral fracture morphology of the Ni–30W–6Cr (Fig. 6a) and Ni– 35W–6Cr (Fig. 6b) alloys, it can be found that a large number of cracks go through into some grains. It is evident that the fracture morphology of the alloys changes with W content. Fig. 6c shows
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Fig. 4. Grain boundary character distribution in Ni–xW–6Cr alloys (a) Ni–10W–6Cr, (b) Ni–15W–6Cr, (c) Ni–20W–6Cr, (d) Ni–25W–6Cr, (e) Ni–30W–6Cr, (f) Ni–35W–6Cr, and (g) dependence of the area fraction of Σ3 and Σ9 type grain boundaries measured by EBSD on W content.
plenty of river patterns and some dimples distributed at the nearfracture surface region of the Ni–10W–6Cr alloy, featuring a quasicleavage fracture behavior. With increasing W content, the proportion of cleavage decreases and the number of dimple increases. The dimples shift from an elongated shape to an entirely equiaxed one (Fig. 6d and e). Therefore, it is suggested that the presence of W can improve the ductility of the Ni–xW–6Cr alloys. The fracture morphologies indicate that the alloys exhibit a transgranular ductile fracture behavior at room temperature. In addition, for the Ni–35W–6Cr alloy, it is found that numerous α-W phase particles are located at the bottom of the dimples (inset in Fig. 6e) and the TEM analysis (Fig. 6f) shows that a large number of dislocations surround the α-W phase particles.
4. Discussion Figs. 1 and 2 reveal that there is a solubility limit of W content in the Ni–xW–6Cr system. Through the calculation of Ni–xW–6Cr ternary phase diagram by Thermo-Calc software, α-W phase emerges when the content of W exceeds 34 wt% at 850 °C (Fig. 7).
Ohta et al. [14] investigated the Ni–Cr–W alloys with Cr content from 15 wt% to 20 wt% and found that the solubility limit of Cr and W is shown as Crþ WE39 wt%. When the total content of W and Cr exceeds this limit, particles of α-W phase begin to be precipitated. Ni–xW–6Cr system exhibits the same behavior and its solubility limit is suggested as Crþ W¼40 wt%. The mass fraction of α-W phase is evaluated as 2.86% in the Ni–35W–6Cr alloy by the phase diagram calculation (Fig. 7). It is well known that a material may be strong or ductile but rarely both at the same time [21]. Surprisingly, below the solid solution limit of W content, the strength (YS and UTS) and EL of the Ni–xW–6Cr alloys increase with increasing W content simultaneously. This may be due to the points as follows: (1) the atomic radius of W (0.137 nm) is about 10% larger than that of Ni (0.125 nm) [22]. The dissolved W atoms produce a compressive stress and make an elastic distortion of the lattice as shown in Fig. 3, interacting with edge dislocations in the vicinity and further impeding their movements. (2) W can lower the stacking fault energy (SFE) in the crystal lattice [23,24]. The SFE of the Ni–xW–6Cr alloys show a linear
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Fig. 5. (a) Dependence of tensile properties of Ni–xW–6Cr alloys on their W content. (b) Tensile true stress–strain curves of the alloys. The open squares mark the uniform elongations. (c) Plots of work hardening rate of the alloys, Θ, against the true strain. The true stress–strain curves and the Θ–strain curves are calculated from the engineering stress–strain curves by assuming a uniform deformation.
decrease with the increase of W content (Fig. 8), evaluated by JMatPro software. A set of previous researches demonstrated the possibility of lowering the SFE to simultaneously enhance the strength and ductility of some metallic materials [25–27]. A lower SFE makes it more difficult for some full dislocations to cross slip or climb when the dislocations encounter a barrier. Therefore, the alloys with lower SFE usually present more persistent work hardening and have higher Θ [27]. In addition, SFE is known as an important parameter which can induce the formation of twins [28]. As shown in Fig. 4, the main grain boundary of the Ni–xW–6Cr alloy is Σ3 type one and the length fraction of Σ3 plus Σ9 ones of the Ni–xW–6Cr alloys monotonously increases from 57.3% (Ni–10W–6Cr) to 65.4% (Ni–30W–6Cr) with increasing W content (below 30 wt%). Twin boundaries (Σ3 and Σ9) were reported to be significant to the tensile strength and ductility improvement because they are believed to be tough and crack-resistant boundaries [29–31]. It should be noted that the YS and UTS of Ni–35W–6Cr alloy is larger, while its EL lower remarkably, compared to the alloys with lower W content, indicating a different mechanical behavior from the other Ni–xW–6Cr alloys. Relative to the alloys with lower W content, the larger YS and UTS of the Ni–35W–6Cr alloy is mainly
due to the finer grains and very small particles in α-W phase, besides the larger lattice distortion and lower SFE. For instance, the grain size of the Ni–35W–Cr alloy is only about 1/10 of the other alloys. It is well known that YS can be improved through the refinement of the grain size, and YS is proportional to the inverse square root of the average grain size [32]. The α-W phase precipitates in the matrix can also increase the strength by impeding the movement of dislocation and then harden the Ni–35W–6Cr alloy. However, at the same time, the voids and dislocations are piled up around the α-W particles (Fig. 6f), which are relatively brittle and could act as nucleation sites of crack. The presence of the α-W particle at the bottom of dimple (Fig. 6e) supports this point. Therefore, the α-W particles lead to the premature failure of the N–35W–6Cr alloy. In this work, it is found that W can improve the strength and ductility of the Ni–xW–6Cr alloys simultaneously below the solubility limit. Hence, it sounds plausible that the Ni–xW–6Cr alloy with W content close to 34 wt% may exhibit much better mechanical performance than the Ni–26W–6Cr alloy. The method [15,33] developed by Watanabe et al. for the designing of Haynes 230 alloy, was applied to screen the best content scope of W for the Ni–xW–6Cr alloy systems. The results indicate that if used in 850 °C, Ni–xW–6Cr alloys with the W content from 27.7 wt% to 37 wt% have the most stable structure, meaning that they have the
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Fig. 6. Fracture morphologies of the Ni–xW–6Cr alloy with W content from 10% to 35% stretched at room temperature. Lateral view of (a) Ni–30W–6Cr and (b) Ni–35W–6Cr. The insets of (a) and (b) show the enlarged images of the deformation regions (5 mm from the fracture) of the above samples, respectively. The fracture morphologies of (c) Ni–10W–6Cr, (d) Ni–30W–6Cr and (e) Ni–35W–6Cr, characterized by SEM; and (f) TEM analysis of the fracture structure of Ni–35W–6Cr.
best mechanical performance. Taking into account that the α-W phase reduce the ductility, the ideal content of W in the Ni–xW– 6Cr alloys is supposed to be 27.7–34 wt%.
5. Conclusion The microstructures and tensile properties of the Ni–(10– 35 wt%)W–6Cr alloys have been investigated. The results are summarized as follows:
(1) Solubility limit of W and Cr in the Ni–xW–6Cr system is shown as W þCr¼40 wt%. The formation of α-W phase occurs while the W content exceeds such limit. (2) When W content is below the solubility limit, the increase of W content brings a significant improvement of mechanical properties for the Ni–xW–6Cr alloys, which is presumably attributed to the lower SFE and higher length fraction of twin boundaries (Σ3) in the alloys caused by the addition of more W content. (3) The presence of α-W phase in Ni–35W–6Cr alloy reduces the ductility of this alloy. This may be due to the preferential nucleation of crack around the particles of α-W phase.
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Research Program of the Chinese Academy of Sciences (Grant no. XDA02004210).
References
Fig. 7. Dependence of α-W phase content in Ni–xW–6Cr alloys at 850 °C on W their content, calculated by Thermo-Calc software (TTNi8 database).
Fig. 8. Dependence of stacking fault energy of the Ni–xW–6Cr alloys at 25 °C on their W content calculated by JMatPro software (TTNi8 database).
Acknowledgments The authors wish to thank Dr. Li LI for her helpful discussions on the XRD data analysis. This work was supported by the Program of International S&T Cooperation, ANSTO-SINAP (Grant no. 2014DFG60230), the National Natural Science Foundation of China (Grant nos. 51371188 and 51501216), the Strategic Priority
[1] D. Williams, L. Toth, K. Clarno, ORNL/TM-2006/12, United States. Department of Energy, 2006 ⟨http://web.ornl.gov/ webworks/cppr/y2006/rpt/124584. pdf〉. [2] J. Serp, M. Allibert, O. Benes, S. Delpech, O. Feynberg, V. Ghetta, D. Heuer, D. Holcomb, V. Ignatiev, J.L. Kloosterman, L. Luzzi, E. Merle-Lucotte, J. Uhlir, R. Yoshioka, Z. Dai, Prog. Nucl. Energy 77 (2014) 308–319. [3] T. Allen, J. Busby, M. Meyer, D. Petti, Mater. Today 13 (2010) 14–23. [4] W. Ren, G. Muralidharan, D.F. Wilson, D.E. Holcomb, Considerations of alloy N for fluoride salt-cooled high-temperature reactor applications, 2011. [5] S. Delpech, E. Merle-Lucotte, T. Auger, X. Doligez, D. Heuer, G.S. Picard, in: Proceedings of GIF Symposium, Paris, 2009, pp. 201–208. [6] Evaluation and Viability of Liquid Fuel Fast Reactor System (Project no. 249696) Final report, 2013. [7] M. Morinaga, Y. Murata, H. Yukawa, J. Mater. Sci. Technol. 19 (2003) 73–76. [8] A. Surenkov, Fist ACSEPT Internatioal Workshop, Lisbon, Portugal, 2010. [9] D.L. Klarstrom, The Development of Haynes (R) 230 (R) Alloy, Minerals, Metals & Materials Society, Warrendale, 2001. [10] G.H. Bai, J.S. Li, R. Hu, X.Y. Xue, J. Ma, S.T. Hu, H.Z. Fu, Rare Met. Mater. Eng. 40 (2011) 1300–1304. [11] G.H. Bai, J.S. Li, R. Hu, Z.W. Tang, X.Y. Xue, H.Z. Fu, Mater. Sci. Eng. A 528 (2011) 1974–1978. [12] G.H. Bai, J.S. Li, R. Hu, T.B. Zhang, H.C. Kou, H.Z. Fu, Mater. Sci. Eng. A 528 (2011) 2339–2344. [13] H.E. McCoy, Oak Ridge Nat. Lab. Rev. 3 (1969) 35–48. [14] S. Ohta, K. Aota, T. Motoda, Tetsu to Hagane 65 (1979) 1031–1040. [15] R. Watanabe, Y. Chiba, Tetsu to Hagane 63 (1977) 118–124. [16] T. Ohmura, K. Sahira, A. Sakonooka, N. Yonezawa, Tetsu to Hagane 62 (1976) 1363–1372. [17] ASTM E8 / E8M-13a, Standard Test Methods for Tension Testing of Metallic Materials, 2013. [18] R.C. Reed, The Superalloys: Fundamentals and Applications, Cambridge University Press, 2006 ⟨http://www.cambridge.org/us/academic/subjects/en gineering/materials-science/superalloys-fundamentals-and-applications? format ¼ PB&isbn ¼9780521070119〉. [19] L. Tan, T.R. Allen, J.T. Busby, J. Nucl. Mater. 441 (2013) 661–666. [20] F.H. Dalla Torre, E.V. Pereloma, C.H.J. Davies, Acta Mater. 54 (2006) 1135–1146. [21] R. Valiev, Nature 419 (2002) 887–889. [22] B. Geddes, H. Leon, X. Huang, Superalloys: Alloying and Performance, ASM International, 2010 ⟨http://www.asminternational.org/search/-/journal_con tent/56/10192/05300G/PUBLICATION〉. [23] P.C.J. Gallagher, Metall. Trans. 1 (1970) 2429–2461 ⟨http://link.springer.com/ article/10.1007/BF03038370〉. [24] J. Unfried-Silgado, L. Wu, F. Furlan Ferreira, C. Mario Garzón, A.J. Ramírez, Mater. Sci. Eng. A 558 (2012) 70–75. [25] X.X. Wu, X.Y. San, X.G. Liang, Y.L. Gong, X.K. Zhu, Mater. Des. 47 (2013) 372–376. [26] Y.H. Zhao, X.Z. Liao, Z. Horita, T.G. Langdon, Y.T. Zhu, Mater. Sci. Eng. A 493 (2008) 123–129. [27] Y.H. Zhao, Y.T. Zhu, X.Z. Liao, Z. Horita, T.G. Langdon, Appl. Phys. Lett. 89 (2006) 121906. [28] V. Randle, Acta Mater. 47 (1999) 4187–4196. [29] T. Watanabe, S. Tsurekawa, Acta Mater. 47 (1999) 4171–4185. [30] C. Cui, M. Demura, K. Kishida, T. Hirano, J. Mater. Res. 20 (2005) 1054–1062. [31] C.Y. Cui, Y.F. Gu, Y. Yuan, T. Osada, H. Harada, Mater. Sci. Eng. A 528 (2011) 5465–5469. [32] E.O. Hall, Yield Point Phenomena in Metals and Alloys, Plenum Press, 1970. [33] R. Watanabe, Y. Chiba, T. Kuno, Tetsu to Hagane 61 (1975) 2405–2417.