Tension-compression asymmetry of extruded Mg-Gd-Y-Zr alloy with a bimodal microstructure studied by in-situ synchrotron diffraction

Materials and Design 170 (2019) 107705

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Tension-compression asymmetry of extruded Mg-Gd-Y-Zr alloy with a bimodal microstructure studied by in-situ synchrotron diffraction Y.Q. Chi a, X.H. Zhou b, X.G. Qiao a, H.G. Brokmeier b,c, M.Y. Zheng a,⁎ a b c

School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China Institute of Materials Science and Engineering, Clausthal University of Technology, Agricolastrasse 6, D-38678 Clausthal-Zellerfeld, Germany Helmholtz Zentrum Geesthacht, Max Planck Straße 1, D-21502 Geesthacht, Germany

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Tension-compression asymmetry of an extruded Mg-Gd-Y-Zr alloy was studied by in-situ diffraction measurement. • The alloy exhibits symmetric macroscopic yielding and asymmetric strain hardening after yielding. • The underlying mechanisms governing the deformation asymmetry was revealed.

a r t i c l e

i n f o

Article history: Received 16 December 2018 Received in revised form 15 February 2019 Accepted 12 March 2019 Available online 13 March 2019 Keywords: Magnesium alloy Bimodal microstructure Tension-compression asymmetry Synchrotron diffraction

a b s t r a c t In this work, the tension-compression asymmetry of an extruded Mg-8.4wt.%Gd-2.3wt.%Y-0.2wt.%Zr alloy with a bimodal microstructure, consisting of fine DRXed grains and coarse unDRXed grains, was investigated by in-situ synchrotron diffraction testing and microstructure analysis. It is found that the as-extruded alloy exhibits good tension-compression yielding symmetry, which is attributed to the same deformation mechanisms (prismatic and basal slip) governing the tensile and compressive yielding. However, the strain hardening response after the macroscopic yielding is different under tension and compression, since tensile twinning, which mainly occurs in the unDRXed grains, makes an important contribution to the deformation under compression, but not under tension. The alloy shows a somewhat linear strain hardening after yielding under compression, which is mainly due to the inhibition of tensile twinning and enhancement of prismatic slip. The suppression of tensile twinning mainly results from the high concentration of rare earth solute elements, weak texture and grain refinement of the DRXed regions. This work suggests that the tension-compression asymmetry of Mg alloys can be effectively reduced by the addition of rare earth elements and grain refinement. © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

⁎ Corresponding author. E-mail address: [email protected] (M.Y. Zheng).

https://doi.org/10.1016/j.matdes.2019.107705 0264-1275/© 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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1. Introduction Tension-compression asymmetry in macroscopic yielding and subsequent flow behavior is a common phenomenon in many metallic materials with different crystal structures, including the body-centered cubic (bcc) structure (e.g. tungsten [1], tantalum [2]), face-centered cubic (fcc) structure (e.g. copper [3,4], nickel base superalloy [5,6], aluminum alloys [7]) and hexagonal closed-packed (hcp) structure (e.g. magnesium alloys [8,9], titanium alloys [10,11]). Overall speaking, the asymmetry is essentially attributed to different deformation behaviors under tension and compression. However, the specific mechanisms are quite complex and varied with different materials. Several theories have been proposed to account for the asymmetry of bcc materials, including the unusual activities of screw dislocations [12] and the sensitivity of the motion of screw dislocation to non-Schmid's stresses, i.e. stresses on planes other than slip planes [13]. As emphasized by Hirsch et al. [14], a screw dislocation in the bcc metals lies along a three-fold symmetry axis of the structure, so the atomic arrangement of its core is nonplanar and three-dimensional. This core structure is suggested to be responsible for certain mechanical asymmetry [12]. On the other hand, atomistic simulations conducted by Wang and Beyerlein [13] suggest that the motion of screw dislocations in bcc metals is sensitive to non-Schmid's stresses. Therefore, the slip characteristics highly depend on the direction and sense of the applied loading, thus leading to the tension-compression asymmetry. Concerning the fcc materials, Tschopp et al. [3] identified a strong tension-compression asymmetry in copper via molecular dynamic simulations. The authors revealed that the asymmetry is mainly due to the distinct dislocation nucleation under tension and compression, which is sensitive to the grain boundary structure [3] and crystallographic orientation [4]. Additionally, Jiao et al. [5] observed tension-compression asymmetry of the (001) single crystal nickel base superalloy SC16 under fatigue test, which is also attributed to the different dislocation nucleation and propagation under tensile and compressive loading. In view of the above introduction, it is concluded that the asymmetry in bcc and fcc materials is mainly associated with distinct behavior of dislocation glide under tension and compression. However, the pronounced asymmetry of hcp Mg and its alloys is primarily owing to the sharp texture formed under thermomechanical processing and the polar nature of tensile twinning which results in a strong dependence of the occurrence of twinning on the direction of applied loading. Under compression along the extrusion direction (ED) of an extruded Mg alloy or along the in-plane directions (rolling direction (RD) or transverse direction (TD)) of a rolled Mg alloy, the macroscopic yielding is dominated by tensile twinning [15,16]. Under tension, however, tensile twinning is suppressed, and the yielding is mainly governed by prismatic and basal slip [15,17]. Since tensile twinning always has a lower critical resolved shear stress (CRSS) than prismatic slip [18], the compressive yielding strength is commonly lower than the tensile yielding strength [8,9]. Furthermore, the tensile flow curve has a convex shape due to the dominant role of dislocation slip during the whole loading process [15,17], while the compressive flow curve always exhibits an ‘S’ (sigmoidal) shape [9]. A low strain hardening stage, including a possible Lüders plateau, commonly appears after compressive yielding, especially in the fine-grained alloys [19,20]. Subsequently, the strain hardening rate is rapidly increased until a peak, after which the hardening rate is gradually decreased. As revealed by Muránsky et al. [19], the low hardening stage is dominated by collaborative twin nucleation which occurs without notable hardening. Several mechanisms have been proposed for the rapid hardening stage, including the crystallographic lattice reorientation of twins [21], the Basinski effect [22] and the Hall-Petch-like effect resulting from twin boundaries [23,24]. Recently, Wu et al. [25] clarified that the rapid hardening is most significantly due to a composite response associated with elasticity of the twin-reoriented crystals with plastically hard orientations, that is triggered by the exhaustion of tensile twinning. Once the plasticity in the

twinned regions is activated, via pyramidal slip or contraction twinning, the strain hardening rate will decrease. The strong tension-compression asymmetry is one of the most significant problems that limit the wide applications of wrought Mg alloys [26]. Therefore, weakening or elimination of asymmetry is crucial for the development of Mg alloys. Mg alloys containing rare-earth elements (REs), including Gd, Y, Dy, Nd, Er et al., have received intensive attention due to the combination of high strength, good ductility [27–34] and largely reduced deformation asymmetry [35–38]. The effect of REs on weakening the asymmetry of Mg alloys was firstly observed by Ball and Prangnell [35] in the extruded Mg-Y-Nd-Zr WE54 alloy, and the uncommonly small tension-compression yielding asymmetry was suggested to be due to a random texture. However, Robson et al. [36] suggested that the elimination of yielding asymmetry cannot be totally attributed to the texture weakening, but also to a change in the CRSS ratio of different deformation mechanisms. Particularly, to realize the symmetric flow behavior after macroscopic yielding, the ease activation of pyramidal slip is strongly required [38]. It is noted that previous studies concerning the tension-compression asymmetry in the Mg-RE alloys, e.g. the literature mentioned above, mainly refer to a fully recrystallized microstructure, whereas the deformation asymmetry in the bimodal microstructure, consisting of fine recrystallized grains and coarse unrecrystallized grains, has rarely been studied. The bimodal microstructure is commonly formed under thermomechanical processing, especially in Mg-RE alloys [27,39], due to the strong impeding effect of REs on the dynamic recrystallization (DRX). This kind of microstructure can provide a good balance between mechanical strength and ductility, since the fine DRXed grains with weak texture are beneficial to the ductility, while the strongly textured unDRXed grains contribute to the strength [39,40]. In this work, a Mg-Gd-Y-Zr alloy was subjected to indirect extrusion to generate a bimodal microstructure. In-situ synchrotron diffraction testing and microstructure analysis were conducted on the asextruded samples to investigate the tension-compression asymmetric behavior. It is worth mentioning that in-situ diffraction is a useful tool to study plasticity in Mg alloys. It can separate the individual contribution of each collection of grains with similar orientation, so this technique is particularly useful for the bimodal microstructure, of which each microstructure component possesses different texture.

2. Experiments The alloy with an actual composition of Mg-8.4wt.%Gd-2.3wt.%Y0.2wt.%Zr was fabricated by direct-chill (DC) casting. The actual composition of the alloy was analyzed using X-ray fluorescence (XRF). A billet with a diameter of 60 mm and a height of 45 mm was cut from the cast ingot. After homogenization at 500 °C for 12 h, followed by water quenching, the sample was cut to the dimensions of Ф42 × 35 mm and then subjected to indirect extrusion at 450 °C, with a ram speed of 0.1 mm/s and an extrusion ratio of 12. Before extrusion, the sample was preheated in the die at 450 °C for 10 min to homogenize the sample temperature. When the extrusion was completed, the extruded bar was immediately subjected to water quenching. Finally, an extruded bar with dimensions of Ф 12.5 × 270 mm was obtained. The microstructure of the as-extruded alloy was characterized by Talos F200X Transmission electron microscope (TEM) operating at 200 kV and ZEISS Supra 55 SAPPHIRE scanning electron microscope (SEM) equipped with an electron backscattered diffraction (EBSD) detector using a step size of 0.8 μm. The macro texture of the as-extruded alloy was determined by synchrotron diffraction. The experimental pole figures were measured for f 1010g, {0002}, f1011g, f1012g, f1120g and f1013g planes with a step size of 5°. Then the pole figures were recalculated using the MTEX software package [41]. The synchrotron diffraction measurement was performed under insitu uniaxial tension and compression at the P07B-HEMS beamline of

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Perkin-Elmer XRD 1622 flat-panel detector with an exposure time of 0.5 s. The diffraction patterns as a function of 2θ were obtained by azimuthal integrating the Debye-Scherrer rings between ±5° about the loading axis, using the software of Fit2D. Afterwards, the diffraction patterns were analyzed by a single-peak fitting approach to determine the corresponding peak intensities and peak positions, following which the lattice spacing can be obtained by applying the Bragg diffraction relationship. Subsequently, the lattice strains within grains that satisfy the Bragg condition for a given (hkl) reflection were computed following the equation: hkl

ɛ hkl ¼ Fig. 1. Schematics of the tensile and compressive samples (unit is mm): (a) tensile sample; (b) compressive sample.

PETRA III, at the Deutsches Elektronen-Synchrotron (DESY). Tension samples with a diameter of 4 mm and a gauge length of 24 mm and compression samples with a diameter of 6 mm and a height of 9 mm were cut from the extruded bar such that the loading axis is along ED. The schematics of tensile and compressive samples are shown in Fig. 1. The tensile and compressive loading were both applied continuously under displacement control at room temperature with a displacement rate of 0.001 mm/s, meanwhile, the synchrotron beam with wavelength of 0.014235 nm and size of 0.5 × 0.5 mm2 was positioned on the sample. The Debye-Scherrer rings were recorded using a

hkl

d −d0 hkl d0

ð1Þ

where dhkl is the measured lattice spacing, and d0hkl is the lattice spacing prior to mechanical loading. Ex-situ loading was performed under uniaxial tension and compression on samples with the dimensions shown in Fig. 1. The samples were loaded with a displacement rate of 0.001 mm/s to measure the mechanical responses. The ex-situ flow curves are used to compare with the insitu ones. Additionally, three more samples were subjected to compressive loading interrupted at different true strains: 2%, 4% and 8%. Then the interruptedly compressed samples were characterized by EBSD with a step size of 0.2 μm. The samples for EBSD observation were firstly ground with 1000, 2000 and 4000 grit SiC paper, and then electropolished in a solution of ethanol and phosphoric acid. The EBSD data were analyzed

Fig. 2. EBSD results of the as-extruded alloy: (a) Inverse pole figure (IPF) map; (b) DRXed grain size distribution; (c) Pole figures of the whole microstructure, DRXed regions and unDRXed regions. The extrusion direction (ED) in (a) is in the vertical direction, while ED in (c) is vertical to the map.

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Fig. 3. Characterization of the precipitates in the as-extruded alloy: (a) Backscattered electron image observed along the extrusion direction (ED); (b) TEM micrograph. The insert in (b) shows the selected area electron diffraction pattern of the globular precipitates in (b).

using Channel 5 EBSD software. High angle boundaries with misorientation angle larger than 15° and low angle boundaries with misorientation angle between 2° and 15° are represented by black and white lines, respectively. The twin types were identified according to the misorientation between the matrix and twins. The misorientation angle/axis for the f1012g tensile twinning, f1011g contraction twinning and f1011g -f1012g double twinning are 86° h1210i, 56° h1210i and 38° h1210i, respectively. The Schmid factor in the present work refers to the “macroscopic Schmid factor” which is calculated by assuming the local stress in individual grains equal to the macroscopic applied stress. 3. Results Fig. 2 shows the EBSD results of the as-extruded alloy. The alloy possesses a bimodal microstructure, consisting of fine DRXed grains with an area fraction of 72.5% and elongated unDRXed grains. The grain size distribution of DRXed grains is displayed in Fig. 2b, with a mean diameter of 5.9 μm. There are a large number of low angle boundaries within the unDRXed grains, resulting from the plastic deformation during the extrusion process. No twins are observed in the microstructure. Fig. 3 presents the characterization of precipitates in the as-extruded alloy. There are several coarse precipitates in the microstructure, as indicated by the triangles in Fig. 3a. These are Gd/Y-rich phases, which are commonly observed in Mg\\Gd alloys [42,43]. Additionally, some fine precipitates can also be observed in Fig. 3a, which are characterized by TEM, as shown in Fig. 3b. These precipitates are identified to be β-Mg5(Gd,Y) phase according to the selected area electron diffraction pattern. They have a globular shape with a size of about 300 nm and mainly distribute at DRXed grain boundaries. The β phases are formed along with the occurrence of DRX, so they only exist in the DRXed regions. Due to the low number density of the Gd/Y-rich phases and β phases, they do not impose much influence on the mechanical properties of the alloy. As shown in Fig. 2c, the unDRXed regions exhibit a sharp fiber texture with h1010i axis parallel to ED (referred to as “h1010i fiber texture” hereinafter), while the DRXed regions present very weak texture. Furthermore, a weak prismatic texture component with basal poles parallel to ED can be observed in the basal pole figure of the DRXed regions. The macro texture of the as-extruded alloy measured by synchrotron diffraction is displayed in Fig. 4. It also shows a h1010i fiber texture and a weak prismatic texture, which is in good agreement with the micro texture. The prismatic texture component was also reported in some previous studies [36,44,45], while the underlying mechanisms governing the texture formation has not been clarified yet. Fig. 5 shows the flow curves and strain hardening responses of the as-extruded alloy under tension and compression along ED. The exsitu flow curves and hardening responses are also included for comparison. It is observed that the results of in-situ and ex-situ testing are in

good agreement. The alloy possesses an identical macroscopic yielding strength which is defined as the stress at the 0.2% true strain and an asymmetric strain hardening response after initial yielding under tension and compression. During tensile loading, the strain hardening rate is monotonically decreased after the plasticity is activated. In contrast, the strain hardening rate under compression is firstly decreased, then nearly kept constant until a certain strain, after which the hardening rate is gradually decreased again. Fig. 6 shows the lattice strains and diffraction intensities under insitu tension and compression, plotted against the applied stress. It is noteworthy that the lattice strains and diffraction intensities shown here provide information about oriented grains that present their {hkil} poles parallel to the loading direction (referred to as “{hkil} grains” hereinafter), which can illustrate the operation of some specific deformation modes in the corresponding grain sets. Due to the nearly elastic isotropy of Mg alloys, all grain sets accumulate their strains linearly with a similar rate at the elastic stage. However, once the plastic deformation occurs in a given grain set, the grains of this set will not load

Fig. 4. Pole figures the as-extruded alloy measured by synchrotron diffraction and recalculated by MTEX code. The extrusion direction (ED) is vertical to the map.

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Fig. 5. (a) Flow curves of the as-extruded alloy under tensile and compressive loading along the extrusion direction; (b) Strain hardening responses calculated from (a).

as much stress as they do at the elastic stage. In the meantime, the other grain sets with harder orientations need to share more load. As a consequence, the lattice strain curves of the related grain sets will deviate from the elastic linearity, with softer and harder oriented grains accumulating their lattice strains slower and faster, respectively. Note that the lattice strain data of {0002} grains have a relatively large uncertainty at the elastic stage, which may be due to the experimental error resulting from the small number of grains on this set. Under tensile loading, the lattice strain curve of f1011g grains firstly deviates from the elastic linearity when the applied stress reaches

213 MPa, with a slight decrease of lattice strain, which suggests the occurrence of plasticity in this grain set. Since f1011g grains have a high Schmid factor for basal slip (0.36), which is the softest deformation mode in Mg alloys [46], the plastic deformation in these grains is mainly realized by basal slip [47]. In the meantime, the f1010g, f1120g and {0002} grains accumulate their strains with a faster rate than at the elastic stage, after the initiation of plasticity in the f1011g grains, indicating these grain sets with harder orientations are sharing more load. With further loading to about 235 MPa, there appears an inflection point in the lattice strain curves of f1010g and f1120g grains, after which the

Fig. 6. Lattice strains and diffraction intensities plotted against applied stress under loading along the extrusion direction: (a) and (b) under tension; (c) and (d) under compression. The insert in (c) is an enlarged graph of the region marked by rectangle.

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strains are accumulated slower than at the previous stage. It indicates

compressive loading, the f1010g grains are favorable for tensile twin-

the occurrence of plasticity in these grains. In the f1010g and f1120g

ning [19], which reorients the crystal in the twinned regions about h112 0i axis by 86°, resulting in the {0002} poles rotating toward the loading axis [19]. As revealed previously [51], the newly twinned regions have a relaxed stress state with respect to their surrounding grains. Therefore, the {0002} grains exhibit stress relaxation, i.e. decreasing lattice strain, when the tensile twinning initially occurs. Since the plastic deformation in the {0002} grains can only be accommodated by pyramidal slip or contraction twinning under compression [47], both of which have high activation stress at room temperature [46], these grains are considerably plastically harder than the other grain sets. Consequently, the {0002} grains rapidly accumulate strain after they are formed by tensile twinning mechanism, until the activation of plasticity in these grains around 330 MPa, after which the accumulation of lattice strain in the {0002} grains becomes slower. Accordingly, the intensity of {0002} grains starts to decrease at 330 MPa, since the operation of pyramidal slip or contraction twinning will rotate the basal poles away from the loading axis. In the f1010g grains, tensile twinning and prismatic slip are competitive deformation mechanisms under compression, since these grains have high Schmid factors for both mechanisms. Specifically, the maximum Schmid factors for tensile twinning and prismatic slip in

grains, basal slip and f1012g tensile twinning are suppressed under tension, instead, prismatic slip is preferentially activated in these grains due to a high Schmid factor (0.43) [48,49]. Additionally, the lattice strain curve of {0002} grains exhibits an inflection point around 249 MPa, which is associated with the activation of tensile twinning, since these grains are ideally oriented for tensile twinning under tensile loading [50]. As shown in Fig. 6b, the f1010g grains have the highest diffraction intensity, followed by the f1011g grains, whereas both f1120g and {0002} grains possess very low intensity. Note that the f1010g grains mainly originate from the unDRXed regions, while the other grain sets are primarily attributed to the DRXed regions, as illustrated in Fig. 2c. During the whole tension process, the diffraction intensities of f1011g and f1120g grains are nearly unchanged, suggesting the rare orientation change of these grains. The intensities of f1010g grains present a slight decrease when loaded to relatively large strain, which is due to the substantial activation of prismatic slip. In addition, the intensity decrease of {0002} grains is due to the tensile twinning, which reorients the crystal in twinned regions about h1120i axis by ~86°. Under compression, the lattice strain curve of f1011g grains also firstly deviates from the elastic linearity at a similar applied stress with that under tension, indicating the occurrence of plasticity in these grains via the operation of basal slip. When loaded to 240 MPa, the {0002} grains present a lattice strain decrease. At the corresponding stress, the f1010g grains exhibit an abrupt decrease of diffraction intensity, accompanied by a rapid intensity increase of {0002} grains, which is characteristic of the tensile twinning occurrence [19]. Upon

the f1010g grains are 0.50 and 0.43, respectively. Therefore, the relative contribution of these two mechanisms mainly depends on their CRSS and hardening behavior. As shown in the insert of Fig. 6c, the lattice strain curve of f1010g grains shows an inflection point around 216 MPa which corresponds to the initiation of plasticity, lower than the activation stress of tensile twinning (240 MPa). So it is assured that the plastic deformation in the f1010g grains is initially accommodated by prismatic slip. Afterwards, both prismatic slip and tensile twinning contribute to the

Fig. 7. Inverse pole figure (IPF) maps, corresponding boundary misorientation maps and basal pole figures of twins and their parent grains in the compressed samples with three different compressive true strains: (a)–(c) 2%; (d)–(f) 4%; (g)–(h) 8%. The basal pole figure of the sample with 8% compressive strain is not included since the twins and parent grains are hard to identify. The compression direction (CD) in (a), (b), (d), (e), (g) and (h) is in the vertical direction, while CD in (c) and (f) is vertical to the map.

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deformation. These results indicate that the tensile twinning has a higher CRSS than prismatic slip in the present alloy. Similarly, the f1120g grains are also well oriented for both tensile twinning and prismatic slip, and the activation of both mechanisms can accommodate the plastic deformation and reduce the strain accumulation rate. Fig. 7 shows the inverse pole figure (IPF) maps, boundary misorientation maps and basal pole figures of twins and their parent grains in the compressed samples with three different compressive true strains: 2%, 4% and 8%. The colors in the IPF maps represent the orientation of the compression axis with respect to the crystal reference frame according to the standard IPF triangle shown in the figure. The boundaries of different twin types (tensile, contraction and double twins) in the boundary misorientation maps are represented by lines with different colors. After compression to 2% strain, only several fine tensile twins are observed in the unDRXed grains. With further compression to 4% strain, more tensile twins are formed in the unDRXed grains and within some DRXed grains. However, the twins are still rather thin and the area fraction of the tensile twins is only about 6%. The basal pole figures shown in Fig. 7c and f indicate that the tensile twinning mainly occurs in the grains with basal planes parallel to the compression axis due to their favorable orientations for the twinning and the twinned regions reorient the basal poles toward the compression axis, which is in agreement with the diffraction intensity evolution in Fig. 6d. After compression to 8% strain, the unDRXed grains are almost fully overtaken by tensile twinning, as indicated by the elongated grains with red color in Fig. 7g, while some lenticular-shaped twins can still be found in the fine DRXed grains. As a result of the tensile twinning development with increasing compressive strain, the basal texture is weakened, accompanied by the strengthening of the prismatic texture, as shown in

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Fig. 8. In addition, no contraction or double twins are obviously detected in all the compressed samples, indicating these two twin types are significantly hindered. The tensile twinned grains in the sample with a compressive strain of 4% are extracted and shown in Fig. 9a. The distribution of Schmid factor for tensile twinning in these grains is presented in Fig. 9b, which suggests a mean value of 0.46. The results indicate the occurrence of tensile twinning is highly governed by the Schmid law, namely, the twinning only takes place in the grains with large Schmid factor for tensile twinning. Fig. 9c and d show the grains with a Schmid factor for tensile twinning larger than 0.35 in the samples with 4% compressive strain and 8% compressive strain, respectively. The tensile twins are also included in Fig. 9c. It is found that in the sample with 4% compressive strain, most of the twins are formed in the coarse unDRXed grains, while plenty of fine DRXed grains are free of twins although they are also well oriented for tensile twinning. Furthermore, after compression to 8%, a large fraction of fine DRXed grains with high Schmid factor for tensile twinning are still not engulfed by twinning or even free of twinning, while the coarse unDRXed grains are fully occupied by twins (Fig. 7g). These results suggest that grain refinement strongly suppresses both the nucleation and thickening of tensile twins. Fig. 10 shows the intragranular misorientation axis (IGMA) distributions of the grains with Schmid factor for tensile twinning larger than 0.35 in the as-extruded and compressed samples. The IGMA analysis only concerns the misorientation angle from 0.5° to 2°, as suggested by Chun and Davies [52]. The IGMA distributions can provide important indications for the dominant slip systems, since slip-induced lattice rotation has a specific rotation axis for each slip system [52]. Weak 〈0002〉 IGMA distributions corresponding to prismatic slip [52] can be observed

Fig. 8. Pole figures of the compressed samples with three different compressive true strains: (a) 2%; (b) 4%; (c) 8%. The compression direction (CD) is vertical to the map.

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Fig. 9. (a) Inverse pole figure (IPF) map of the tensile twins and their parent grains in the sample with 4% compressive strain; (b) Distribution of Schmid factor for tensile twinning in the parent grains shown in (a); (c) IPF map of the grains with Schmid factor for tensile twinning larger than 0.35 in the sample with 4% compressive strain, along with tensile twins formed within these grains; (d) IPF map of the grains with Schmid factor for tensile twinning larger than 0.35 in the sample with 8% compressive strain. The tensile twins in (a) and (c) have a lenticular shape and are mainly displayed in red color. The compression direction (CD) is in the vertical direction.

in the as-extruded and compressed samples. Although a weak IGMA generally indicates the activation of a number of slip systems [53], the IGMA distributions in Fig. 10 suggest that a large fraction of plasticity is accommodated by prismatic slip. For the as-extruded sample, prismatic slip is mainly activated in the unDRXed grains under extrusion

process and results in the alignment of h1010i axis to ED [54]. With increasing compressive strains, the distribution intensities around 〈0002〉 axis are overall enhanced, indicating that the plasticity under compression is largely accommodated by prismatic slip. 4. Discussions

Fig. 10. The intragranular misorientation axis (IGMA) distributions of the grains with Schmid factor for tensile twinning larger than 0.35 in the as-extruded sample and compressed samples with different compressive strains. The compressive true strains are shown at the top of each distribution figure. The IGMA analysis concerns the misorientation angle from 0.5° to 2°.

The lattice strain evolutions shown in Fig. 6a suggest that the macroscopic yielding under tension is mainly associated with prismatic and basal slip, among which the DRXed grains with weak texture mainly undergo basal slip and the unDRXed grains with strong h1010i fiber texture mainly undergo prismatic slip. These results are consistent with the previous study [55] which employed post-deformation transmission electron microscopy observation. Although tensile twinning is also activated under tension, its contribution to the deformation is very limited, due to the rather small fraction of the tensile twinning favored grains, i.e. the {0002} grains (Fig. 6b). Considering the texture of the as-extruded alloy, the plastic deformation throughout the tension process is dominated by dislocation slip [15,17,38]. Therefore, the strain hardening rate exhibits a continuous decrease with increasing tensile strain [56]. Under compression, the lattice strains and diffraction intensities in Fig. 6c and d indicate that tensile twinning mainly starts when loaded to 240 MPa, corresponding to the true strain of 1.4%. In fact, the EBSD results in Fig. 7a and b confirm that few twins are formed when compressed to 2% strain. Instead, prismatic slip is activated in the f1010g grains (mainly refers to the unDRXed grains) before the occurrence of

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tensile twining, as analyzed previously, and contributes to the initial yielding. On the other hand, the DRXed grains primarily undergo basal slip. In other words, the initial yielding under compression is also dominated by prismatic and basal slip, which is the same as that under tension. Due to the symmetric nature of slip, the prismatic and basal slip should have identical behavior under tension and compression, thus leading to a good tension-compression yielding symmetry. It is noted that the excellent yielding symmetry is essentially attributed to the suppression of tensile twinning under compression, which results from the high activation stress of tensile twinning. It is interesting to point out that although previous study [35] emphasized the importance of weak texture on the small tension-compression yielding asymmetry, our present work demonstrates that the condition of tensile twinning having higher CRSS than prismatic slip plays a more important role than texture to obtain the yielding symmetry. On the other hand, the asymmetric strain hardening response after yielding suggests the important contribution from tensile twinning to the deformation under compression. Note that tensile twinning mainly occurs in the coarse unDRXed grains, as suggested by the previous microstructure observation (Fig. 7 and Fig. 9). It is expected that the absence of unDRXed grains may result in the elimination of asymmetric strain hardening after yielding, as displayed in fully recrystallized WE43 and WE54 alloys [37,38]. However, different from the conventional Mg alloys [9,19,20], which always involve a low strain hardening stage and subsequent rapid hardening stage after yielding, resulting from the dominant role of tensile twinning, the present alloy exhibits a somewhat linear hardening after initial yielding, which is mainly due to the inhibition of tensile twinning. As shown in Fig. 7, the area fraction of tensile twins is only 6% after compression to the true strain of 4%, while in the extruded AZ31 alloy, nearly 40% of the grains are overtaken by tensile twins after 4% strain compression [57]. As an alternative deformation mechanism, prismatic slip is significantly activated for the plastic deformation, as supported by the IGMA results in Fig. 10. Therefore, it is expected that the immediate post-yielding stage is synchronously governed by basal slip, prismatic slip and tensile twinning, rather than dominated by twinning, thus resulting in a linear hardening. The inhibition of tensile twinning in the present alloy is mainly attributed to the following factors. Firstly, the solid solute Gd and Y can potently increase the activation stress of tensile twinning and restrict the thickening of twins. In fact, several studies [47,58,59] have reported the effect of REs on suppressing the tensile twinning. Concerning the underlying mechanisms, Stanford et al. [59] proposed that the large atomic radius of REs may restrict the atomic shuffling process which is required for the twinning shear, thus imposing strong hardening on the tensile twinning. Very recently, Kumar. et al. [60] employed a crystal plasticity Fast Fourier Transform (CP-FFT) based model to investigate the effect of alloying addition on twin thickening and twin transmission. Their results suggested that the anisotropy in CRSS values, namely, difference of CRSS, of different deformation mechanisms have a significant effect on twin thickening and transmission. With the addition of REs, the anisotropy in CRSS values will be reduced, which was found unfavorable for twin thickening and transmission. Secondly, the addition of REs significantly weakens the texture of DRXed grains, which has also been reported in many literatures [61–64]. Due to the high CRSS of tensile twinning in the present alloy, twins are mainly formed in the grains with high Schmid factor, as displayed in Fig. 9b. The weakening of texture will reduce the amount of grains which are well oriented for tensile twinning, thus hindering the occurrence of twinning. Thirdly, the tensile twinning is additionally suppressed in the DRXed grains by grain refining. Similar to slip, the effect of grain size on twinning can also be accounted for by the Hall-Petch relationship [65], and it was found that the grain size effect on twinning is much stronger than that on slip in Mg alloys [56]. Therefore, there are much less twins formed in the fine DRXed grains than those in the coarse unDRXed grains.

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5. Conclusions (1) The as-extruded Mg-Gd-Y-Zr alloy has a bimodal microstructure, consisting of fine DRXed grains and coarse unDRXed grains. The unDRXed regions have a strong h1010i fiber texture, while the DRXed regions exhibit weak texture. (2) The initial yielding under both tension and compression is dominated by prismatic and basal slip, thus leading to an excellent tension-compression yielding symmetry. (3) Under compression, tensile twinning occurs after initial yielding, mainly in the coarse unDRXed grains, and makes an important contribution to the deformation, thus resulting in different strain hardening response from that under tension, which is only governed by prismatic and basal slip. (4) The alloy exhibits a somewhat linear strain hardening after macroscopic yielding under compression, which is mainly due to the inhibition of tensile twinning and enhancement of prismatic slip. The suppression of tensile twinning mainly results from the solid solute REs, weak texture and grain refinement of DRXed regions. (5) Addition of REs and grain refinement are in favor of weakening the tension-compression asymmetry of Mg alloys.

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