Twinning-Induced Abnormal Strain Rate Sensitivity and Indentation Creep Behavior in Nanocrystalline Mg Alloy

Nanocrystalline materials exhibit many unique physical and chemical properties with respect to their coarse-grained counterparts due to the high volume fraction of grain boundaries. Research interests on nanocrystalline materials around the world have been lasting over the past decades. In this study, we explored the room temperature strain rate sensitivity and creep behavior of the nanocrystalline Mg–Gd–Y–Zr alloy by using a nanoindentation technique. Results showed that the hardness and creep displacements of the nanocrystalline Mg–Gd–Y–Zr alloy decreased with increasing loading strain rate. That is, the nanocrystalline Mg–Gd–Y–Zr alloy showed negative strain rate sensitivity and its creep behavior also exhibited negative rate dependence. It was revealed that the enhanced twinning activities at higher loading strain rates resulted in reduced hardness and creep displacements. The dominant creep mechanism of the nanocrystalline Mg–Gd–Y–Zr alloy is discussed based on a work-of-indentation theory in this paper.


Introduction
Mg alloys are promising metallic structural materials and regarded as ideal candidates for lightweight applications in automotive and aerospace industries owing to their low density, high specific strength and rich mineral resources on earth [1,2]. However, the low absolute strength compared with Al alloys limits the wide application of Mg alloys. Alloying with rare earth (RE) elements is proven effective in fabricating high-performance Mg alloys. Among various Mg-RE alloys, the Mg-Gd-Y series alloys are attracting increasing attention due to their excellent combination of tensile strength, ductility, and creep resistance [3][4][5][6][7][8]. Homma et al. [9] reported an extraordinary high-strength Mg-Gd-Y-Zr alloy with an ultimate tensile strength of 542 MPa, yield strength of 473 MPa, and elongation of 8%. Grain refinement via severe plastic deformation is an effective way to strengthen metallic materials [10,11], which has been successfully applied to many face-centered cubic (fcc) [12,13], body-centered cubic (bcc) [14,15], and hexagonal close-packed (hcp) metals and alloys [3,6,16,17]. Using room temperature rotary swaging, Wan et al. [8] successfully fabricated a bulk nanocrystalline (NC) Mg-Gd-Y-Zr alloy which possesses an average grain size of 80 nm and exhibits an ultrahigh ultimate tensile strength and yield strength of 710 MPa and 650 MPa, respectively. This work sheds light on the potential in strengthening Mg alloys via grain refinement. Sun et al. [6] achieved a hardness as high as 145 HV in a nanostructured Mg-8.2Gd-3.8Y-1.0Zn-0.4Zr alloy that was prepared using high-pressure torsion (HPT).
Previous studies have demonstrated that when grain sizes are refined to nanoscale, most metals and alloys can obtain double or even much higher strength with respect to their coarse-grained (CG) counterparts [18][19][20]. With grain sizes entering nanoscale, the volume

Materials Preparation
Initial alloy ingot used in the present work was produced using semicontinuous casting, with a measured chemical composition of Mg-6.0Gd-3.5Y-0.5Zr (wt%). After solid solution treatment at 510 • C for 16 h, the billets with dimensions of Φ115 mm × 200 mm were extruded to Φ18.2 mm rods at 400 • C. Subsequently, the extruded rods were rotary swaged to Φ14.7 mm by four passes at room temperature, with a total area reduction of 34.8% [7,8].

Materials Characterization
Microstructural observations were performed on a FEI Helios NanoLab 600i dual beam scanning electron microscope (SEM) (Hillsboro, OR, USA) equipped with an Oxford electron backscatter diffraction (EBSD) system (Oxford, UK) and FEI Titan G 2 60-300 transmission electron microscope (TEM) (Hillsboro, OR, USA) operated at 300 kV. EBSD samples were prepared by electropolishing in ethanol solution containing 5 vol% perchloric acid at −40°C. EBSD data were analyzed using HKL Channel 5 software (Oxford, UK). TEM samples were mechanically ground to~40 µm and then ion milled to perforation using a Gatan 691 precision ion polishing system (Pleasanton, CA, USA). X-ray diffraction (XRD) was conducted on a Bruker D8 Advance diffractometer (Karlsruhe, Germany) using CuKα radiation (λ = 0.154 nm) with a scanning step size of 0.02 • , a counting time of 3 s, and a 2θ range of 10-80 • .
Hardness and indentation creep behavior were characterized using an Anton Paar NHT 3 Nanoindenter (Graz, Austria) with a load and displacement resolution of 0.01 µN and 0.01 nm, respectively. Nanoindentation tests were conducted at loading strain rates (LSRs) ranging from 5 × 10 −3 s −1 to 1 s −1 , loaded to a predetermined depth of 2000 nm and held at corresponding maximum loads for 1500 s. Figure 1 shows the interaction between the indenter and the surface of the NC Mg alloy, in which h cr represents the creep displacement during the holding stage ( Figure 1c). For each set of experimental parameters, the tests were repeated five times to ensure data reliability. Samples for nanoindentation tests were mechanically ground and polished to mirror finish. Except for cases specified, all above-mentioned tests were performed on the cross sections of the rods. solution treatment at 510 °C for 16 h, the billets with dimensions of Φ115 mm × 200 mm were extruded to Φ18.2 mm rods at 400 °C. Subsequently, the extruded rods were rotary swaged to Φ14.7 mm by four passes at room temperature, with a total area reduction of 34.8% [7,8].

Materials Characterization
Microstructural observations were performed on a FEI Helios NanoLab 600i dual beam scanning electron microscope (SEM) (Hillsboro, OR, USA) equipped with an Oxford electron backscatter diffraction (EBSD) system (Oxford, UK) and FEI Titan G 2 60-300 transmission electron microscope (TEM) (Hillsboro, OR, USA) operated at 300 kV. EBSD samples were prepared by electropolishing in ethanol solution containing 5 vol% perchloric acid at −40 ℃. EBSD data were analyzed using HKL Channel 5 software (Oxford, UK). TEM samples were mechanically ground to ~40 μm and then ion milled to perforation using a Gatan 691 precision ion polishing system (Pleasanton, CA, USA). X-ray diffraction (XRD) was conducted on a Bruker D8 Advance diffractometer (Karlsruhe, Germany) using CuKα radiation (λ = 0.154 nm) with a scanning step size of 0.02°, a counting time of 3 s, and a 2θ range of 10-80°.
Hardness and indentation creep behavior were characterized using an Anton Paar NHT 3 Nanoindenter (Graz, Austria) with a load and displacement resolution of 0.01 μN and 0.01 nm, respectively. Nanoindentation tests were conducted at loading strain rates (LSRs) ranging from 5 × 10 −3 s −1 to 1 s −1 , loaded to a predetermined depth of 2000 nm and held at corresponding maximum loads for 1500 s. Figure 1 shows the interaction between the indenter and the surface of the NC Mg alloy, in which hcr represents the creep displacement during the holding stage ( Figure 1c). For each set of experimental parameters, the tests were repeated five times to ensure data reliability. Samples for nanoindentation tests were mechanically ground and polished to mirror finish. Except for cases specified, all above-mentioned tests were performed on the cross sections of the rods.

Conventional Theory of Creep Stress Exponent Calculation
According to the classical power-law creep theory, creep stress exponent n, can be defined as [43]: where is a steady state creep strain rate corresponding to stress σ. For indentation creep, the displacement time (h-t) curves during the holding stage can be fitted using an empirical equation [44]:

Conventional Theory of Creep Stress Exponent Calculation
According to the classical power-law creep theory, creep stress exponent n, can be defined as [43]: ε is a steady state creep strain rate corresponding to stress σ. For indentation creep, the displacement time (h-t) curves during the holding stage can be fitted using an empirical equation [44]: where h 0 , a, t 0 , b and k are fitting parameters. Based on Equation (2), creep strain rate . ε can be defined as [45]: where h is an instantaneous indentation depth, and t is creep time. Creep stress σ during the holding stage can be obtained via Tabor relation, σ = H/3 [46], and the hardness H can be calculated by: where F is real time load during the holding stage, h c is contact depth, and c = 24.56 for the Berkovich indenter [45]. Combining Equations (1)-(4), creep stress exponent n can be obtained by plotting .
ε versus H in a double logarithmic coordinate system. The fitting slop of the linear segment of the log . ε-logH curve equals the creep stress exponent n. where h0, a, t0, b and k are fitting parameters. Based on Equation (2), creep strain rate can be defined as [45]:

Microstructure
where h is an instantaneous indentation depth, and t is creep time. Creep stress σ during the holding stage can be obtained via Tabor relation, σ = H/3 [46], and the hardness H can be calculated by: where F is real time load during the holding stage, hc is contact depth, and c = 24.56 for the Berkovich indenter [45]. Combining Equations (1)-(4), creep stress exponent n can be obtained by plotting versus H in a double logarithmic coordinate system. The fitting slop of the linear segment of the log -logH curve equals the creep stress exponent n.     Table 1 lists all the samples that were examined in this work. Figure exemplary nanoindentation load-displacement curves of the RS NC Mg allo pendicular to the cross section. Unexpectedly, with increasing LSR, the max load, Fmax, decreased monotonously. That is, it exhibited negative strain rat Figure 5 summarizes the Fmax corresponding to all the tested LSRs. Fmax d 136.7 mN at 5 × 10 −3 s −1 to 83.2 mN at 1 s −1 . Plotted in Figure 6 is the rate d hardness of RS and aged (200 °C/18 h, designated as RS+A hereafter) NC M double logarithmic coordinate system, in which the linear fitting slope is SR comparison, SRS of the extruded CG alloy is also shown in Figure 6. Whi alloy exhibits positive but virtually negligible m, the NC Mg alloys show un ative m values, which is different from those of most CG and NC materials 31]. A saltation at LSR = 3 × 10 −1 s −1 in the SRS of NC-RS sample existed. I creased abruptly from −0.030 to −0.254. However, the saltation disappeared sample. Moreover, the m value increased to −0.016 after ageing treatment.   Table 1 lists all the samples that were examined in this work. Figure 4 shows four exemplary nanoindentation load-displacement curves of the RS NC Mg alloy loaded perpendicular to the cross section. Unexpectedly, with increasing LSR, the maximum holding load, F max , decreased monotonously. That is, it exhibited negative strain rate dependence. Figure 5 summarizes the F max corresponding to all the tested LSRs. F max decreased from 136.7 mN at 5 × 10 −3 s −1 to 83.2 mN at 1 s −1 . Plotted in Figure 6 is the rate dependence of hardness of RS and aged (200 • C/18 h, designated as RS+A hereafter) NC Mg alloys in the double logarithmic coordinate system, in which the linear fitting slope is SRS index m. For comparison, SRS of the extruded CG alloy is also shown in Figure 6. While the CG Mg alloy exhibits positive but virtually negligible m, the NC Mg alloys show unexpected negative m values, which is different from those of most CG and NC materials [14,[24][25][26][29][30][31]. A saltation at LSR = 3 × 10 −1 s −1 in the SRS of NC-RS sample existed. Its m value decreased abruptly from −0.030 to −0.254. However, the saltation disappeared in NC-RS+A sample. Moreover, the m value increased to −0.016 after ageing treatment.    For materials with specific texture, the change of loading direction may influenc their dominant deformation modes, which would therefore result in the variation of SR Figure         For materials with specific texture, the change of loading direction may influence their dominant deformation modes, which would therefore result in the variation of SRS. Figure 7 exhibits the SRS of the NC-RS sample loaded on different sections. As expected, the SRS of the longitudinal section showed different features with respect to the cross section. When the LSR < 3 × 10 −2 s −1 the m value of the longitudinal section is positive and when 3 × 10 −2 s −1 < LSR < 3 × 10 −1 s −1 , both sections possess similar m values; when LSR > 3 × 10 −1 s −1 , m of longitudinal section maintains −0.029, while that of cross section decreases suddenly to −0.254. Abnormal SRS undoubtedly stems from specific deformation mechanisms. The variation of m with LSR should be correlated to the transition of dominant deformation modes, which will be discussed in detail in Section 4.  where hcr is the indentation creep displacement, and is the LSR. Figure 8b sho the ω of both RS and the RS+A NC alloys are negative. That is, not only the hardn the creep displacements of the NC Mg alloys exhibit negative strain rate depend well.   Figure 8a summarizes the creep displacements under ten LSRs. Attention should be paid to two characteristics. First, within the tested LSR range, creep displacements of the NC Mg alloy decreased monotonously with increasing LSR. Second, the ageing treatment surprisingly weakened the creep resistance of the alloy, as demonstrated by the larger creep displacements of the NC-RS+A sample. Referring to the definition of the SRS index m, here we define the strain rate dependence of indentation creep displacement as ω using Equation (5):

Strain Rate Sensitivity
where h cr is the indentation creep displacement, and . ε L is the LSR. Figure 8b shows that the ω of both RS and the RS+A NC alloys are negative. That is, not only the hardness, but the creep displacements of the NC Mg alloys exhibit negative strain rate dependence as well.
where hcr is the indentation creep displacement, and is the LSR. Figure 8b shows that the ω of both RS and the RS+A NC alloys are negative. That is, not only the hardness, but the creep displacements of the NC Mg alloys exhibit negative strain rate dependence as well. The aforementioned results were obtained based on the mode that the indenter was loaded to a fixed depth, 2000 nm, at a constant strain rate followed by holding at the corresponding maximum load (designated as CSR-depth mode hereafter). Under such a loading mode, the holding load, F max , decreases with increasing LSR in the present work, as shown in Figure 5. It is therefore reasonable to question whether the reduced creep displacements at higher LSRs are caused by reduced holding loads. To answer this, we designed a set of control experiments. The indenter was loaded to a fixed load, 120 mN, at a constant strain rate, followed by holding at 120 mN for the same duration as in the CSR-depth mode (designated as CSR-load mode hereafter). Figure 9 gives the results of the CSR-load experiments. It is apparent that the creep displacements still decreased with increasing LSR, which follows the same variation tendency as in the CSR-depth mode (see Figure 9b). This result rules out the possibility that the lower holding loads at higher LSRs lead to lower creep displacements. Instead, it verifies the fact that the negative strain rate dependence of indentation creep displacements is an intrinsic property of the NC Mg-Gd-Y-Zr alloy in the present work. The aforementioned results were obtained based on the mode that the indenter was loaded to a fixed depth, 2000 nm, at a constant strain rate followed by holding at the corresponding maximum load (designated as CSR-depth mode hereafter). Under such a loading mode, the holding load, Fmax, decreases with increasing LSR in the present work, as shown in Figure 5. It is therefore reasonable to question whether the reduced creep displacements at higher LSRs are caused by reduced holding loads. To answer this, we designed a set of control experiments. The indenter was loaded to a fixed load, 120 mN, at a constant strain rate, followed by holding at 120 mN for the same duration as in the CSR-depth mode (designated as CSR-load mode hereafter). Figure 9 gives the results of the CSR-load experiments. It is apparent that the creep displacements still decreased with increasing LSR, which follows the same variation tendency as in the CSR-depth mode (see Figure 9b). This result rules out the possibility that the lower holding loads at higher LSRs lead to lower creep displacements. Instead, it verifies the fact that the negative strain rate dependence of indentation creep displacements is an intrinsic property of the NC Mg-Gd-Y-Zr alloy in the present work.

Creep Mechanism
Creep stress exponent n is an important parameter in describing the creep process, and its value reflects the creep mechanisms of materials. Generally, n = 1 corresponds to diffusion creep, n = 2 corresponds to GB sliding, and n = 3-7 corresponds to dislocation creep [43]. Figure 10 elaborates the detailed calculation process of n based on conventional theory. Taking LSR = 5 × 10 −3 s −1 as an example, fitting using Equation (2) gives an excellent agreement with the experimental result, as shown in Figure 10a. Based on Equation (3), the -t curve corresponding to Figure 10a can be obtained, as shown in Figure 10b. As holding time exceeded ~1000 s, decreased very slowly, indicating the arrival of a steady state creep. Based on Equation (4), one can obtain the H-t curve corresponding to Figure  10a, as shown in Figure 10c. Combining Equations (1)-(4), the creep stress exponent n can be obtained by plotting versus H in a double logarithmic coordinate system. Figure 10d shows the log -logH curves for RS and the RS+A NC Mg alloys, in which the n values of

Creep Mechanism
Creep stress exponent n is an important parameter in describing the creep process, and its value reflects the creep mechanisms of materials. Generally, n = 1 corresponds to diffusion creep, n = 2 corresponds to GB sliding, and n = 3-7 corresponds to dislocation creep [43]. Figure 10 elaborates the detailed calculation process of n based on conventional theory. Taking LSR = 5 × 10 −3 s −1 as an example, fitting using Equation (2) gives an excellent agreement with the experimental result, as shown in Figure 10a To overcome this difficulty, a redefined creep strain rate and indentation creep hard ness were put forward based on the concept of work of indentation [47][48][49]. According t the work-of-indentation theory by Stilwell and Tabor [50], hardness obtained vi nanoindentation tests can be defined as: where HWI is hardness based on work-of-indentation theory, Wp is plastic work conducte by the indenter, and Vp is plastically deformed volume. Referring to the definition of HW indentation creep hardness, Hcr, can be defined as: where Wcr is the plastic work conducted by the indenter during the creep stage, and ∆V is the variation of the plastically deformed volume during creep stage. Wcr and ∆V cr ca be calculated using Equations (8) and (9): where Fm is holding load, h0 and hm are displacements at the start and end of holding stage To overcome this difficulty, a redefined creep strain rate and indentation creep hardness were put forward based on the concept of work of indentation [47][48][49]. According to the work-of-indentation theory by Stilwell and Tabor [50], hardness obtained via nanoindentation tests can be defined as: where H WI is hardness based on work-of-indentation theory, W p is plastic work conducted by the indenter, and V p is plastically deformed volume. Referring to the definition of H WI , indentation creep hardness, H cr , can be defined as: where W cr is the plastic work conducted by the indenter during the creep stage, and ∆V cr is the variation of the plastically deformed volume during creep stage. W cr and ∆V cr can be calculated using Equations (8) and (9): where F m is holding load, h 0 and h m are displacements at the start and end of holding stage, respectively, and c = 24.56 for the Berkovich indenter [45]. Since creep-induced ∆V cr is very small with respect to V p , it is reasonable to treat V p as constant during the holding stage. Therefore, the creep strain rate based on work-of-indentation theory, can be formulated as: .
where ∆t is the holding duration. According to the hemisphere hypothesis, the plastically deformed volume V p can be obtained as follows [51]: where the radius of hemispherical plastically deformed volume r can be expressed as [49]: where σ s is yield strength and can be obtained via Tabor relation, σ s = H p /3. Based on the work-of-indentation theory, Tuck et al. [48] related H p to holding load F m and plastic work W p using Equation (13): where κ is an indenter shape-dependent constant. For the Berkovich indenter, κ = 0.0408 [48].
Referring to the definition of n in Equation (1), the creep stress exponent based on the work-of-indentation theory n cr can be expressed as: Combining Equations (7)- (13), H cr and .
ε cr corresponding to each LSR can be obtained. According to Equation (14), one can deduce n cr by plotting . ε cr versus H cr obtained above in a double logarithmic coordinate system, as shown in Figure 11. Creep stress exponents of the NC Mg alloys obtained via different data processing approaches are summarized in Table 2. It is clear that the results based on the work-of-indentation theory are much smaller and agree with the classical power-law creep. Values of n cr suggest that room temperature indentation creep mechanisms of RS and RS+A NC Mg alloys are a dislocation creep. For the former, owing to the existence of supersaturated solute atoms inside grains, the dislocation glide is dragged by the solute atmosphere, resulting in a dislocation viscous glide creep mechanism (n cr = 2.9) [43]. For the latter, the supersaturated solid solution decomposed during the ageing treatment, forming solute clusters or grain boundary solute segregations [7], which reduced the solute concentration in the α-Mg matrix and therefore weakened the solute drag effect. Hence, the dislocation climb becomes the rate-controlling step during the room temperature creep of RS+A NC Mg alloy (n cr = 7.7) [43]. inside grains, the dislocation glide is dragged by the solute atmosphere, resulting in a dislocation viscous glide creep mechanism (ncr = 2.9) [43]. For the latter, the supersaturated solid solution decomposed during the ageing treatment, forming solute clusters or grain boundary solute segregations [7], which reduced the solute concentration in the α-Mg matrix and therefore weakened the solute drag effect. Hence, the dislocation climb becomes the rate-controlling step during the room temperature creep of RS+A NC Mg alloy (ncr = 7.7) [43].  H cr (MPa) Figure 11. Calculation of the creep stress exponent based on the work-of-indentation theory.
DSA works via solute-dislocation interactions [62]. At relatively lower strain rates, solute atoms can segregate onto mobile dislocations, increasing their motion resistance. With increasing strain rate, the amount of solute atoms that can follow mobile dislocations decreases, reducing motion resistance and leading to NSRS. Thus, at a fixed temperature, DSA can only work below a critical strain rate, beyond which solute atoms can no longer follow dislocations and dislocation-accumulation-induced PSRS takes over [54,55]. It is therefore appropriate to claim that the NSRS of the NC Mg alloy in the present work is not caused by the DSA effect for the following reasons. First, the m value for the cross section remains negative under all tested strain rates, and not only does it not increase gradually with increasing strain rate, but it decreases abruptly when LSR > 3 × 10 −1 s −1 (see Figure 7). Meanwhile, the result on the longitudinal section indicates that it shows NSRS at higher strain rates, but exhibits PSRS at lower strain rates (see Figure 7), which is opposite of the features of DSA. Second, the stress-strain curves of the Mg-Gd-Y-Zr alloy used in the present work (not shown here) do not show serrated flow behavior, a typical characteristic induced by the DSA effect [52,53,63]. This is owing to the fact that Gd and/or Y atoms diffuse slowly in the Mg matrix and cannot follow mobile dislocations [64], while the ability to follow dislocations is a prerequisite for the occurrence of DSA.
SIPT commonly lead to NSRS in materials that may experience phase transformation under applied stress, such as β-Ta [56], 304 austenitic steel [65], and Ti-10V-2Fe-3Al alloy [57]. Obviously, the prerequisite for the occurrence of SIPT-induced NSRS is the polymorphism of the investigated materials. However, except for the Mg-Li alloy [66], there is no report claiming the discovery of a new crystal structure in Mg alloys in addition to hcp structure by far. Thus, the possibility of SIPT is also ruled out.
Recently, studies on metallic multilayers suggests that the propensity of crack formation increases at higher strain rates, and this can result in NSRS [58]. This such mechanism does not apply to the present situation considering the nature of bulk single-phase material other than multilayers. Moreover, SEM inspection of residual indentations verifies that all the indentations are intact, with no microcrack (see Figure 12). report claiming the discovery of a new crystal structure in Mg alloys in addition to hcp structure by far. Thus, the possibility of SIPT is also ruled out.
Recently, studies on metallic multilayers suggests that the propensity of crack formation increases at higher strain rates, and this can result in NSRS [58]. This such mechanism does not apply to the present situation considering the nature of bulk single-phase material other than multilayers. Moreover, SEM inspection of residual indentations verifies that all the indentations are intact, with no microcrack (see Figure 12). It is well-known that twinning propensity is enhanced at higher strain rates [67]. Therefore, under circumstances where the dislocation slip is suppressed or saturated, enhanced twinning activities might result in NSRS. Chun et al. [60] found that when the true strain is lower than 0.08, tension in the ND and compression in the RD for a strong-textured AZ31 rolled plate can result in NSRS; with increasing strain level, the SRS index m increases gradually and turns out to be positive when the true strain exceeds 0.08. Microstructural examination indicates that twinning dominates plastic deformation when the strain is lower than 0.08, while the dislocation slip takes over when the strain is higher than 0.08, where twinning is saturated. Accordingly, it can be concluded that materials exhibit NSRS when plastic strain is dominantly mediated by deformation twinning. Karimpoor et al. [59] also found the twinning-induced NSRS phenomenon in NC Co with a strong basal texture. The NC Mg alloy in the present work has two things in common with the above two materials: strong texture and the same crystal structure (HCP). It is reasonable to infer that enhanced twinning activities at higher strain rates lead to NSRS phenomenon in the NC Mg alloy. This mechanism can well explain those special features aforementioned. First, ageing treatment can result in a grain boundary solute segregation and formation of solute clusters [7], which can suppress twin nucleation [68,69]. Thus, contribution of twinning to plastic strain decreases, while that of the dislocation slip increases, leading to the increase in m from −0.030 to −0.016 (see Figure 6). Second, when the loading direction is perpendicular to the longitudinal section, a part of the grains are oriented ins such a way that the basal slip is readily activated and therefore dominates deformation in the low strain rate range, resulting in PSRS (see Figure 7). When LSR exceeds 3 × 10 −2 s −1 , twinning is activated and takes over plastic deformation, causing NSRS (see Figure 7). Third, the abrupt decrease in m of the cross section at 3 × 10 −1 s −1 might result from the activation of less favored twin variants in addition to the most favored ones, which further enhances twinning activities at higher strain rates (see Figure 7).

Negative Strain Rate Dependence of Creep Displacement
During the plastic deformation of NC metallic materials, dislocations are emitted from GBs, traverse through the grains, and are eventually accumulated at or absorbed by the opposite GBs. The dislocation absorption model established by Carlton et al. [70] suggests that the probability of a dislocation to be absorbed by GB is related to strain rate. The higher the strain rate, the lower the absorption probability. Due to the lower absorption probability, higher LSRs will induce a higher density of dislocations stored in grains. During the holding stage, these stored dislocations can continue to move forward under applied loads, leading to creep. Accordingly, the higher the LSR, the more the stored dislocations, and consequently, the larger the creep displacements during the holding stage. This model well explains the normal strain rate dependence of indentation creep displacements in previous studies on CG and NC materials [17,42,71]. In the present work, with increasing LSR, twinning activities are enhanced, generating more twin boundaries. During the holding stage, these twin boundaries will impede the motion of stored dislocations and shorten their mean glide distances, which therefore reduces creep displacements. The higher the LSR, the more the twin boundaries, and consequently, the smaller the creep displacements. This results in the negative strain rate dependence of indentation creep displacements (see Figure 8). As discussed in Section 4.1, ageing treatment can suppress twinning activities. Consequently, the amount of twin boundaries in the RS+A NC alloy is less than those in RS sample, and the corresponding impeding effect on dislocation motion is weakened, leading to larger creep displacements in the RS+A NC Mg alloy, which is distinctly different from the common sense that ageing can strengthen alloys and therefore improve their creep resistance [72,73].

Conclusions
The strain rate sensitivity and indentation creep behavior of a bulk nanocrystalline Mg-Gd-Y-Zr alloy were investigated. The main findings were as follows:

1.
Nanocrystalline Mg-Gd-Y-Zr alloy exhibits negative strain rate sensitivity. Enhanced twinning activities at higher loading strain rates lead to the decrease in hardness, that is, the negative strain rate sensitivity.

2.
Initial unaged nanocrystalline Mg-Gd-Y-Zr alloy creeps via a dislocation viscous glide mechanism due to the solute drag effect, while the creep mechanism of aged alloy turns to a dislocation climb owing to the depletion of solute atoms by segregation and clustering.

3.
Indentation creep displacements of nanocrystalline Mg-Gd-Y-Zr alloy exhibit a negative strain rate dependence. Enhanced twinning activities at higher loading strain rates generate more twin boundaries in the alloy, which impede dislocation motion, shorten their mean glide distances, and therefore reduce the creep displacements. Suppressed twinning activities in aged alloy result in larger creep displacements than those in unaged alloy. Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.