Microstructural evolution, textural evolution and thermal stabilities of W and W – 1 wt% La2O3 subjected to high-pressure torsion

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Microstructural evolution, textural evolution and thermal stabilities of W and W – 1 wt% La2 O3 subjected to high-pressure torsion Yiming Wang∗, Jarir Aktaa Karlsruhe Institute of Technology (KIT), Institute for Applied Materials, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

a r t i c l e

i n f o

Keywords: Nanocrystalline materials High-pressure torsion Electron backscatter diffraction Thermal stability Tungsten

a b s t r a c t Ultra-fine grained W and nanocrystalline W – 1 wt% La2 O3 (WL10) were successfully fabricated by unconstrained high-pressure torsion at 400 °C. Torsion torque, microstructural evolution, and textural evolution of W and WL10 along torsion revolution were systematically evaluated for the first time. Their deformation mechanisms during high-pressure torsion were proposed. Results show that both materials exhibited work-hardening and geometric dynamic recrystallization during high-pressure torsion. The existence of La2 O3 particles caused discontinuous dynamic recrystallization in WL10 and formed 𝛾-fiber texture. The evolution of 𝛾-fiber texture in WL10 along with torsion strain was analyzed as well. The existence of La2 O3 particles leaded to dispersion-hardening in WL10 at large strain levels when those particles were sufficiently refined. Deformation inhomogeneity occurred in W at ultrahigh strain levels accompanied by coarsening microstructure. In addition, the as-deformed ultra-fine grained W and nanocrystalline WL10 exhibited marked thermal stability at 1000 °C up to 6 h.

1. Introduction High-pressure torsion (HPT) is one of the severe plastic deformation (SPD) methods that can produce remarkable large strain on work pieces [1]. It is an efficient way to achieve grain refinement for coarse-grained materials, improving mechanical properties by the virtue of refined microstructure [2]. Learning the material behavior at ultrahigh strain is also essential to explore the nature of plastic deformation mechanism of nanocrystalline materials. However, research on HPT-deformed material is often focused on FCC metals, such as Cu [3], Ni [4], Al [5,6], Pd [7], and their alloys [8–10]. Systematical investigation of BCC metals subjected to HPT is still rare [11]. Previous research often concerns torsion without compression [12,13], and recent studies mostly focus on mechanical properties improvement [14,15]. In the study presented here, we investigate W and WL10 subjected to HPT with a broad range of strain. These materials were chosen also because that coarse-grained W and WL10 exhibit outstanding high temperature performance. They are often sought-after for armor/structure material in future fusion reactor [16,17]. However, room-temperature brittleness restricts their application [18]. One feasible way to address this shortcoming is to reduce the grain size by HPT [14,15]. In this study, we emphasized microstructural and textural evolution of W and WL10 with torsion revolution. We explored deformation mechanisms and the role of La2 O3 therein. However, the driving force for grain growth is usually high in ultra-fine grained and nanocrystalline metals. With regard to the high operational

∗

temperature window (550–800 °C) in future fusion reactor [19], thermal stability of as-deformed ultrafine grained W and nanocrystalline WL10 was examined. In addition, the equivalent strain in samples processed by constraint HPT is well documented [10,20–22], where sample height maintains almost the same during deformation. However, sample height decreased during unconstrained HPT [23]. Equivalent true strain was calculated in this study by considering compression component. 2. Materials and methods Initial coarse-grained W and WL10 were supplied by Plansee (Austria) with guaranteed purity of 99.97%. Non-metallic impurities (C, H, N, O, and Si) were the same in the two materials. Weight percentage of La2 O3 in WL10 is between 0.9% and1.1%. The La2 O3 is initially of coarse size and doped in W. Unconstrained HPT was performed on disk samples (Φ8 mm × 1 mm) under 5 GPa of pressure with rotation speed of 5 rpm on a Schenck testing machine. The angular range of rotation was limited to 90°. The samples were subjected to an unloading–loading process to sustain the rotation direction during deformation. In situ torque was plotted by recording peak values at each cycle. Heat was generated by a furnace which encircles the anvil and the experiments were carried out in nitrogen gas environment. Orientation imaging microscopy (OIM) and orientation density function (ODF) were obtained by electron backscatter diffraction (EBSD) processed by CHANNEL 5. The electron accelerating voltage, beam current, aperture, and step size were 20 kV, 2.6 nA, 50 μm, and 0.03 μm, respectively. Observation was parallel to

Corresponding author. E-mail address: [email protected] (Y. Wang).

https://doi.org/10.1016/j.mtla.2018.05.009 Received 13 March 2018; Received in revised form 24 May 2018; Accepted 24 May 2018 Available online xxx 2589-1529/© 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: Y. Wang, J. Aktaa, Materialia (2018), https://doi.org/10.1016/j.mtla.2018.05.009

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Fig. 1. (a) Sample height reduction during unconstrained HPT and (b) the equivalent true and engineering strain at 3 mm from sample center.

the shear plane of sample. To analyze grain size, “line cut” was employed for at least 500 grains separated by high angle grain boundaries (HAGB, misorientation angle >15°). The expected value (E) of grain size distribution fitted by lognormal function was acquired. Grain size was calculated by 2(ESD · ETD /𝜋)1/2 , where ESD and ETD are E along shear direction (SD) and E along transverse direction (TD) of sample, respectively. To investigate the thermal stability of deformed samples, heat treatment at 1000 °C was conducted in a vacuum furnace (10−6 mbar) for durations of 1, 3, and 6 h. 3. Results 3.1. Equivalent true strain during unconstrained HPT Materials overflowed during unconstrained HPT. Accordingly, sample height (h) was decreased following an exponential decay, and only 20% of the initial height √ was left after 2 turns (Fig. 1(a)). Thereby, the formula 𝜀𝑒 = 2𝜋𝑁𝑟∕ 3ℎ with constant h was no longer suitable for the true equivalent strain (ɛt ) calculation. Instead, it was labeled as engineering strain (ɛe ). In this formula, N stands for torsion revolution and r is the distance from torsion axis. Equivalent true strain (ɛt ) was derived according to von Mises criteria by adding a compression component (see Appendix). The ɛe and ɛt at r = 3 mm were compared in Fig. 1(b). The difference between them is remarkable at ultrahigh strains. We also noticed that ɛt imposed by unconstrained HPT can be as high as 174 after 4 turns and 400 after 8 turns.

Fig. 2. Torque curves of W and WL10 during HPT.

direction (Fig. 3(b), (h), and (i)). They changed the geometry from elongated to equiaxed shape after 1 turn for W (Fig. 3(c)) and after 2 turns for WL10 (Fig. 3(j)). This means that lamellar microstructure sustained longer in WL10 than in W. It may due to the particle movement which can divide grains, as shown in Fig. 5(c). The microstructure difference between W and WL10 becomes more obvious after 2 turns. Grain refinement saturated in W with grain size of 160–170 nm (Fig. 3(d)–(e), and (l)). A slight microstructural coarsening was observed in W after 8 turns, in which coarse grains were over 200 nm and mostly showed green color in OIM (Fig. 3(f)). Nanocrystalline array was also found near the coarsening region, which exhibited blue color in OIM (Fig. 3(f)). It suggests that different crystal orientation dominated the coarsening and nanocrystalline region. In contrast to W, grain refinement continued in WL10 after 2 turns, nanocrystalline microstructure with grain size of 76 nm was obtained after 4 turns (Fig. 3(k) and (l)). This means that different deformation mechanism operated between W and WL10 after 2 turns. Furthermore, high fraction of HAGB is a typical feature of HPT deformed materials. Grain boundary misorientation increased with deformation for both materials, the fraction of HAGB is 81–85% after 2 turns (Fig. 3(l)).

3.2. Torque during HPT Three stages were identified from torque curves during HPT, as indicated in Fig. 2. Torque reflected flow stress in the material during deformation, and this is further related to dislocation density [7,22,24]. The rapid increase of torque at stage I refers to dislocation multiplication. It is followed by a single peak, suggesting an extensive softening at stage II. Moreover, torque was almost constant after 2 turns for W, while it raised again for WL10. This indicates a balance between workhardening and softening for W at stage III, and different deformation mechanism was operated for WL10. Furthermore, a slight decrease of torque was observed in W after about 4.5 turns (𝜀t ≈ 200, Fig. 2), which suggests a softening phenomenon at ultrahigh strain levels.

3.4. Textural evolution during HPT

3.3. Microstructural evolution during HPT

ODFs and the selected orientation densities f(g) of HPT-deformed W and WL10 are provided in Fig. 4. The initial texture component C (001)<100> and D (110)<11̄ 1>, which was inherited from the drawing process, decreased rapidly after HPT (Fig. 4(a), (b), (g), and (h)). Meanwhile, the main texture developed by HPT in W referred to component A (112)<111̄ >, G(110)<001>, and J (110)<1̄ 12> (Fig. 4(b)–(f)). These components grew progressively during deformation to their max.

Unconstrained HPT exhibited high efficiency in grain refinement, as shown in OIM and the corresponding grain size evolution (Fig. 3). The grain size in deformed samples was already below 400 nm after 0.5 turn, which was much smaller than that in the initial microstructure (≈10 μm) (Fig. 3(l)). After initial deformation, grains were elongated align shear 2

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Fig. 3. OIM at 3 mm from sample center of as received (a) W and (g) WL10; deformed samples after (b) (h) 0.5 turn, (c) (i) 1 turn, (d) (j) 2 turns, (e) (k) 4 turns; (f) deformed W after 8 turns; (l) corresponding grain size and average boundary misorientation vs. torsion revolution.

Fig. 4. ODFs in the section of 𝜑2 = 450 of (a)–(f) W and (g)–(k) WL10 with (l) typical components position. Orientation density of these components in (m) W and (n) WL10.

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Fig. 5. (a) Morphology and (b) OIM of WL10 after initial deformation (ɛt < 0.1). Position of La2 O3 particle was indicated. (c) Morphology and OIM of selected rectangle region of WL10 deformed after 0.5 turn at 3 mm from sample center, HAGB is in black and LAGB is in gray.

Fig. 6. Microstructure mapped by components of HPT deformed W after 8 turns.

intensity after 1–2 turns. However, they later diffused after 4 turns and became stronger again after 8 turns (Fig. 4(m)). The texture in HPTdeformed WL10 was more complicated than in HPT-deformed W, involving occurrence of 𝛾-fiber texture, i.e., {111} (E and F), as well as components A, G, and J (Fig. 4(h)–(k)). The 𝛾-fiber texture can be generated at the beginning of HPT, as indicated by the blue dots at slightly deformed part of WL10 in Fig. 5(b) (left). Most of them were found near oxide particles (Fig. 5(a)). Since the observation surface is clean and smooth (Fig. 5(a)). It suggests that 𝛾-fiber texture was stimulated by La2 O3 particles. Moreover, 𝛾-fiber texture overwhelmed A, J, and G components from 1 turn to 2 turns in WL10, but decreased after 4 turns (Fig. 4(n)). To study the deformation inhomogeneity caused by HPT at ultrahigh strain levels, the microstructure of W deformed after 8 turns is mapped by selected components (Fig. 6). Component A, J, D, and G dominated coarse grains, three of them (G, D, and J) refer to grains with {110} // shear plane. Whereas 𝛾-fiber texture (E and F) occupied nanocrystalline array, which concerns grains with {111} // shear plane. This indicates that coarsening region and nanocrystalline array preferred different dislocation systems.

deformed W intensified with the increase of 131% and 65%, respectively (Fig. 8(a)). This means that some crystals reorientated to preferred orientations during heat treatment. In addition, the texture intensities in as-deformed WL10 are more stable during heat treatment than in asdeformed W (Fig. 8). 4. Discussion 4.1. Deformation mechanism during HPT Three deformation stages can be identified during HPT for W and WL10, as schematically illustrated in Fig. 9. W exhibited workhardening, geometric dynamic recrystallization (GDRX), and saturation accompanied by local deformation inhomogeneity. WL10 revealed similar working-hardening and GDRX at the first two stages. However, the addition of La2 O3 particles caused additional discontinuous dynamic recrystallization (discontinuous DRX) in WL10. La2 O3 particles also induced a dispersion-hardening in WL10 at stage III. 4.1.1. Stage I Work-hardening occurred at stage I (W: 𝜀t < 9, WL10: 𝜀t < 24), typical feature refers to rapid grain refinement (Fig. 3(l)), dislocation multiplication (Fig. 2), and lamellar microstructure (Fig. 3(b), (h), and (i)). Both compression and torsion played crucial role in grain refinement at stage I. HAGBs were compressed closer along the axis as sample height decreased during unconstrained HPT (Fig. 1(a)) [25]. Grains were stretched and curved by torsion (Fig. 9), leading to an increase in boundary misorientation and grain fragmentation. Importantly, HPT changed the initial texture by developing deformation components A, J, and G (Fig. 4). These components refer to the main ideal orientations in torsion for BCC metals [12,13]. Their formation is related to deformation constraints [26], tightly connected to crystal type and deformation mode [11]. Interestingly, there is similarity between BCC-torsion texture [11–13] and FCC-rolling texture [27], which is {110} and {hkl}<111>; so as FCC-torsion texture [3,6,9,28] and BCC-rolling

3.5. Heat treatment of as-deformed W and WL10 Microstructural changes of two samples during heat treatment are illustrated in Fig. 7, involving W and WL10 deformed by HPT after 4 turns. Grain growth was obvious at the first 3 h but almost ceased thereafter (Fig. 7(i)). The total growth in average grain size is limited to 70 nm after 6 h, which is from 160 nm to 230 nm for W and from 76 nm to 135 nm for WL10. Microstructures during heat treatment are self-similar without abnormal grain growth for both materials (Fig. 7(a)–(h)). These phenomena suggest impressive thermal stability of HPT-deformed W and WL10. The intensity changes of the selected texture components during heat treatment are provided in Fig. 8. In general, the texture obtained from HPT retained up to 6 h for both materials. Component G and A in 4

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Fig. 7. OIM changes of HPT deformed W and WL10 after heat treatment at 1000 0 C after (a) (e) 0 h, (b) (f) 1 h, (c) (g) 3 h and (d) (h) 6 h. And (i) the corresponding grain size.

Fig. 8. Orientation density measured from the section of 𝜑2 = 450 of ODF along typical components for (a) W and (b) WL10 during heat treatment at 1000 0 C.

Fig. 9. Schematic representation of microstructural and textural evolution in W and WL10 during HPT; La2 O3 particles and traces were in red; crystals with 𝛾 fiber orientation were in magenta; HAGB is in black, whereas LAGB is in gray.

texture [29,30], which is {111} and {hkl}<110>. The above regularities can shed light on the deep understanding of metal deformation mechanism. In contrast to W, particle stimulated nucleation (PSN) occurred near La2 O3 particles in WL10 after initial deformation (Fig. 5(a) and (b)). Therefore, 𝛾-fiber texture was also developed at stage I in WL10 beside A, J and G (Fig. 4(h), (i), and (n)). Recrystallized grains originated adjacent to large second-phase particles in the deformation zones, because of the local constraints induced by these particles [31]. The orientation of the recrystallized grains can be determined by the matrix orientation and deformation conditions [31]. In our case, 𝛾-fiber texture is preferred, which is consistent with our previous research [11]. In addition, stage I was preserved longer in WL10 (0–1 turn) than that in W (0–0.5 turn) (Fig. 3). This is because the movement of La2 O3 particles divided grains, and left parallel lines align shear direction (Figs. 5(c) and 9), which facilitated the lamellar structure.

4.1.2. Stage II Extensive softening with sufficient dislocation annihilation operated at stage II (W: 9 < 𝜀t < 68, WL10: 24 < 𝜀t < 68). It is indicated by a characteristic single peak in torque curves, which is at 0.5–2 turns for W and 1–2 turns for WL10 (Fig. 2). The mechanism behind torque curve is discussed elsewhere [32]. In that discussion, a single peak curve is associated with dynamic recrystallization (DRX) for coarse-grained starting materials with Do > 2Ds , where Do and Ds are the initial and stable grain size after ultrahigh strain. This is consistent with our study, where the starting materials are coarse-grain (Do ≈ 60Ds , Fig. 3). The space between grain boundaries is enough for compression or DRX grain growth during impingement, leading to both extensive softening and microstructural refinement [32] at stage II. Another evidence of DRX refers to grain geometric transition at stage II, which is from elongated to equiaxed shape (Figs. 3(c), (j), and 9). Therefore, DRX is considered to be the main softening mechanism operated at stage II for both materials.

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However, the specific DRX phenomenon in WL10 and W can be different. New DRX grains were barely detected in as-deformed W (Fig. 4(m)). As one of the continuous DRX phenomena, GDRX can operate without nucleation [25], and it mainly occurred in W at stage II. At that time, grain boundaries impinged and were accompanied by serrations that formed equiaxed grains. This usually results in microstructure consisting of almost entirely HAGBs [25], which is consistent with our result (Fig. 3(l)). Although the intensity of A, J, and G components were raised twofold, the texture type maintained in W at stage II (Fig. 4(m)), which is another feature of GDRX owing to lack of HAGB migration [25]. In contrast to W, discontinuous DRX operated in WL10 at stage II beside GDRX. A crucial feature of discontinuous DRX refers to texture transition [25], which is from A, J, and G components to 𝛾-fiber texture domination (Fig. 4(n)). Meanwhile, a decrease of average misorientation angle was found after 2 turns in WL10 (Fig. 3(l)). This can because that the newly formed DRX grains coalesced during boundary impingement. Substitution of 𝛾-fiber texture for A, J, and G components was also found in Cu and Cu–Zn alloy subjected to cold rolling [27]. This suggests again the resemblance of BCC-torsion and FCC-rolling texture.

reason for continuous SRX to occur. Because that grain boundary movement was hindered by them during annealing. Nucleation and growth of recrystallized grains were thus not obvious in such case. It is consistent with other results [34] that suggest microstructure can be stabilized by HAGB when the fraction of it is over 65−75%. Therefore, continuous SRX is usually considered to be a consequence of continuous DRX in deformed W [25,32]. La2 O3 particle dispersion was also a main factor in the stabilization of the as-deformed WL10 microstructure. Because that La2 O3 particles can pin boundaries and affect recrystallization kinetics [35]. Therefore, the texture in deformed WL10 is even more stable than that in W during annealing (Fig. 8). 5. Conclusions W and WL10 were subjected to unconstrained HPT at process temperature of 400 °C. Ultra-fine grained and nanocrystalline samples were obtained. i. In general, three stages can be identified in W during HPT, including work-hardening (𝜀t < 9), continuous DRX (9 < 𝜀t < 68), and saturation (68 < 𝜀t < 400). The existence of La2 O3 particles in WL10 altered the material behavior by extending work-hardening stage to 𝜀t ≈ 24, giving rise to discontinuous DRX and causing dispersion-hardening (68 < 𝜀t < 174). ii. Typical torsion texture was obtained in HPT-deformed W, including {110} and {hkl}<111>. 𝛾-fiber texture was also formed in WL10 due to particle stimulated nucleation, and developed further by discontinuous DRX. iii. Plastic deformation inhomogeneity occurred at ultrahigh strain levels (𝜀t > 200) in W during HPT. It gave rise to the formation of nanocrystalline array and microstructural coarsening (grain size ≈ 200 nm) in the adjacent area. iv. We found that ultra-fine grained W (grain size ≈ 160 nm) and nanocrystalline WL10 (grain size ≈ 76 nm) obtained by HPT exhibited impressive thermal stability under 1000 °C up to 6 h. Continuous SRX operated on annealing due to the high fraction of HAGB in asdeformed W and WL10, and particle pinning stabilized WL10 under given condition. v. The research on deformation behavior of W and WL10 subjected to HPT is important for understanding the deformation mechanism of nanocrystalline BCC metals. The findings of marked thermal stability of ultra-fine grained W and nanocrystalline WL10 is crucial for learning the nature of microstructure after severe plastic deformation. It also sheds light on developing stable nanocrystalline materials for high-temperature applications.

4.1.3. Stage III The difference between W and WL10 became more apparent at stage III (𝜀t > 68) (Fig. 9). A saturation state was achieved in W after 2 turns, including constant torque, saturated grain refinement (160 nm) and steady boundary misorientation angle (Figs. 2 and 3(l)). Numerous studies have discussed the mechanism behind this [20,22,25,32]. In such studies, continuous DRX is proposed for metals subjected to large strain, where nucleation and growth of recrystallized grains was not recognizable [25,32]. Which is consistent with our results and we agree that similar mechanism was involved in W at stage III. In addition to that, sample height stayed almost constant during stage III (Fig. 1(a)). Therefore, it was difficult to fragment grains only by torsion without compression in W, especially for the ultrafine equiaxed grains, due to strong repulsive force. Dislocations emitted from boundaries were mostly absorbed again, thus grain refinement cannot continue. However, grain rotation can still occur and lead to texture weakening in W after 4 turns (Fig. 4(e) and (m)). An alternative softening phenomenon was discovered in W after about 4.5 turns, indicated by a slight decrease of torque (𝜀t ≈ 200, Fig. 2). It corresponds to the deformation inhomogeneity that observed after 8 turns, which shows flow localization (nanocrystalline array) and microstructure coarsening in the adjacent area (Fig. 3(f)). Stress was released near flow localization, and hence softening occurred accompanied by coarse grains (Figs. 3(f) and 6).The flow localization can be caused by impurities, nano-cracks, or plastic instability [33]. It leaded to a change in slip plane of dislocation that from {110} and {112} to {111}. Therefore, 𝛾-fiber texture dominated nanocrystalline array, whereas the typical HPT texture (A, J, D, and G components) composed the coarse grains (Fig. 6). Dispersion-hardening was activated only when the La2 O3 particles are sufficiently refined at stage III. The torque value increased steadily in WL10 and the grain refinement procedure continued at this stage (Figs. 2 and 3(l)). This was due to the evolution of La2 O3 particles, which were initially micrometers in size (Fig. 5(a) and (b)), and then gradually fragmented during HPT.

Acknowledgments This work, supported by the European Communities under the contract of Association between EURATOM and Karlsruhe Institute of Technology (KIT), was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Support from China Scholarship Council (CSC) is gratefully acknowledged. Thanks to Prof. Dingyong He at Beijing University of Technology for data processing facility.

4.2. Thermal stability of HPT-deformed W and WL10

Appendix

Limited grain growth (<70 nm) was observed after heat treatment for the selected as-deformed samples at 1000 °C up to 6 h (Fig. 7), suggesting marked thermal stability of HPT-deformed W and WL10. Microstructures are self-similar without abnormal grain growth (Fig. 7), and the texture is sustained with little changes (Fig. 8). These are features of continuous static recrystallization (SRX) [25]. High fraction of HAGB (81−85%) generated by HPT process (Fig. 3(l)) was the main

The strain status of HPT-deformed material can be described as: ⎧𝜀 ⎪ 𝑟𝑟 ε=⎨0 ⎪0 ⎩

0 𝜀𝜑𝜑 𝜀𝑧𝜑

0 ⎫ ⎪ 𝜀𝜑𝑧 ⎬ 𝜀𝑧𝑧 ⎪ ⎭

𝜀𝑟𝑟 = 𝜀𝜑𝜑 = −(1∕2)𝜀𝑧𝑧 6

(1)

(2)

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Where ɛzz refers to the axial strain component, ɛ𝜑z is related to pure shear strain component. von Mises strain is expressed as following: √ √ √ 𝜀𝑣 = 2∕3 ⋅ 𝜀 ∶ 𝜀 = 2∕3 𝜀rr 2 + 𝜀𝜑𝜑 2 + 𝜀zz 2 + 𝜀𝜑𝑧 2 + 𝜀𝑧𝜑 2 (3) =

√ 𝜀zz 2 + (4∕3)𝜀𝜑𝑧 2

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Lücke, Texture and microstructure of rolled and annealed tantalum, Mater. Sci. Technol. 10 (4) (1994) 299–305. [30] X. Zhang, Q. Yan, S. Lang, Y. Wang, C. Ge, Evolution of hot rolling texture in pure tungsten and lanthanum oxide doped tungsten with various reductions, Mater. Des. 109 (2016) 443–455. [31] F.J. Humphreys, Particle stimulated nucleation of recrystallization at silica particles in nickel, Scr. Mater. 43 (7) (2000) 591–596. [32] T. Sakai, A. Belyakov, R. Kaibyshev, H. Miura, J.J. Jonas, Dynamic and post-dynamic recrystallization under hot, cold and severe plastic deformation conditions, Progr. Mater. Sci. 60 (2014) 130–207. [33] J. Gil Sevillano, P. van Houtte, E. Aernoudt, Large strain work hardening and textures, Progr. Mater. Sci. 25 (2) (1980) 69–134. [34] F.J. Humphreys, P.B. Prangnell, J.R. Bowen, A. Gholinia, C. Harris, Developing stable fine-grain microstructures by large strain deformation, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 357 (1756) (1999) 1663–1681. [35] F.J. Humphreys, M. Hatherly, Recrystallization textures, Recrystallization and Related Annealing Phenomena, second ed., Elsevier, Oxford, 2004, pp. 379–413. Chapter 12.

(3)

The height reduction of sample under given condition can be described as: ( ) ℎ(𝜃) = ℎ∞ − ℎ∞ − ℎ0 ⋅ exp(−θ𝑏) (4) where h0 refers to sample height after initial compression, h∞ is the sample height after infinite torsion revolution, 𝜃 is torsion angle in radian and b corresponds to material property. The axial strain component can be written as: ℎ ( ) ( ) 𝜀𝑧𝑧 = ∫ (1∕ℎ)𝑑ℎ = ln ℎ(𝜃)∕ℎ0 = ln ℎ∞ − 𝑐1 exp (−θ𝑏) − 𝑐2 ℎ0

(5)

where 𝑐1 = ℎ∞ − ℎ0 and 𝑐2 = ln ℎ0 . Assuming no slippage occurs during HPT: 𝑑 𝛾 = 𝑑 𝑙∕ℎ = 𝑟𝑑 𝜃∕ℎ(𝜃)

(6)

Where 𝛾 is increment of shear strain, and the shear strain component is expressed as: 𝜃 ( ( ) ( ( ) )) 𝜀𝜑𝑧 = ∫ (𝑟∕2ℎ(𝜃))𝑑𝜃 = 𝑐3 𝑟 ⋅ ln exp (𝑏𝜃) − 𝑐4 − ln exp 𝑏𝜃0 − 𝑐4 𝜃0

(7)

where 𝑐3 = 1∕(2𝑏ℎ∞ ) and 𝑐4 = 1 − ℎ0 ∕ℎ∞ . Given θ = 2π𝑁, combining Eqs. (A.3), (A.5) and (A.7), the true von Mises strain is: 𝜀𝑡 =

[m5GeSdc;June 6, 2018;21:8]

√ ( ( ( ( ) )2 ) ( ( ) )) 2 ln ℎ∞ − 𝑐1 exp (−2𝜋𝑁𝑏) − 𝑐2 + (4∕3)(𝑐3 𝑟 ⋅ ln exp (𝑏𝜃) − 𝑐4 − ln exp 𝑏𝜃0 − 𝑐4 )

In this work, the fitting parameters are h∞ =0.20 mm; h0 =0.80 mm and b = 0.28. References [1] P. Bridgman, Effects of high shearing stress combined with high hydrostatic pressure, Phys. Rev. 48 (10) (1935) 825–847. [2] Y. Estrin, A. Vinogradov, Extreme grain refinement by severe plastic deformation: a wealth of challenging science, Acta Mater. 61 (3) (2013) 782–817. [3] H. Jiang, Y.T. Zhu, D.P. Butt, I.V. Alexandrov, T.C. Lowe, Microstructural evolution, microhardness and thermal stability of HPT-processed Cu, Mater. Sci. Eng. A 290 (2000) 128–138. [4] R. Pippan, Influence of impurities and deformation temperature on the saturation microstructure and ductility of HPT-deformed nickel, Acta Mater. 59 (19) (2011) 7228–7240. [5] S.V. Dobatkin, E.N. Bastarache, G. Sakai, T. Fujita, Z. Horita, T.G. Langdon, Grain refinement and superplastic flow in an aluminum alloy processed by high-pressure torsion, Mater. Sci. Eng. A 408 (1–2) (2005) 141–146. [6] S. Naghdy, L. Kestens, S. Hertelé, P. Verleysen, Evolution of microstructure and texture in commercial pure aluminum subjected to high pressure torsion processing, Mater. Character. 120 (2016) 285–294. [7] Y. Ivanisenko, L. Kurmanaeva, J. Weissmueller, K. Yang, J. Markmann, H. Rösner, T. Scherer, H.J. Fecht, Deformation mechanisms in nanocrystalline palladium at large strains, Acta Mater. 57 (11) (2009) 3391–3401. [8] X.H. An, Q.Y. Lin, S.D. Wu, Z.F. Zhang, R.B. Figueiredo, N. Gao, T.G. Langdon, The influence of stacking fault energy on the mechanical properties of nanostructured Cu and Cu–Al alloys processed by high-pressure torsion, Scr. Mater. 64 (10) (2011) 954–957.

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