J.Cent.South Univ.(2025) 32: 991-1007
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Graphic abstract:
1 Introduction
Magnesium (Mg) alloys have been the center of interest in the automotive, transportation and aerospace industries due to their low density, high strength-to-weight ratios and good machinability [1-3]. The performance of Mg alloys is highly correlated with their microstructure [4-7]. The low slip systems at room temperature lead to low plasticity, thus limiting their wide application [8]. Furthermore, Mg sheets are usually produced by hot rolling or hot extrusion processes, and basal texture is inevitable and further results in the poor plasticity and formability [9].
Therefore, weakening basal texture of Mg sheets is an effective method to obtain Mg sheets with excellent plasticity and formability [10, 11]. TU et al [12] adopted equal channel angular rolling and continuous bending to weaken the basal texture at 240 ℃. With increasing rolling speed, the basal pole completely splits toward rolling direction (RD), and Erichsen value grows to 7.4 mm at room temperature. HUANG et al [13] prepared AZ80 Mg alloy through differential speed rolling (DSR) at 300 ℃, and 15° tilt to the RD of the DSR-processed sheets was observed and the Erichsen value increased by 22% at room temperature.
Pre-twinning is another method which has been widely concerned to improve the plasticity and formability of Mg sheets [14, 15], and its positive effects can be summarized as follows: 1) Twins provide additional deformation modes and enhance deformability of Mg alloys at low temperatures [16]; 2) The interaction between twins is conducive to accelerating nucleation of recrystallization [17]; 3) Twins can rotate c-axes of grains to obtain favorable orientation, thus enhancing the sustained deformability [18]. Among the common twin types, the critical resolved shear stress (CRSS) of tensile twin (TT) is the lowest, and TT is easily activated under tensile loads parallel to the c-axis of Mg grains [19, 20].
In addition to the significant effect of twinning on the microstructural regulation, the special texture of Mg alloys also plays a crucial role in determining microstructural properties [21-24]. WANG et al [22] demonstrated that the Mg-Gd-Y-Zn-Mn alloy, which exhibits a special <0001>Mg// extrusion direction texture following hot extrusion, provides the best mechanical isotropy in both as-extruded and as-aged conditions. LIU et al [7] successfully fabricated Mg alloy sheets featuring a circular texture through multidirectional rolling, which resulted in enhanced ductility along both RD and transverse direction (TD) and weaker in-plane yield anisotropy when compared to samples with a TD-tilted texture. Furthermore, HAN et al [24] introduced an abnormal bimodal texture in AZ31 Mg alloy sheets utilizing equal channel angular rolling and continuous bending process with subsequent annealing. The total rolling reduction achieved in the sheet exhibiting the abnormal bimodal texture reached 39.2%, which is more than double the reduction of 18.3% observed in sheets characterized by a strong basal texture.
Generally, the relationship between deformation conditions and flow stress can be described by establishing the constitutive relationship of metal materials [25]. Through hot processing maps of the material based on the dynamic material model (DMM), the machinability of deformed metal materials can be evaluated, and the microstructure evolution and deformation mechanism can be predicted, thus optimizing the process parameters [26]. Nowadays, DMM has been widely applied to Mg alloys, but the temperature range of hot-working diagrams of Mg alloys is between 200 and 500 ℃. So far, there have been few studies on the hot working areas at low temperatures [27-29].
In this study, tensile tests along normal direction (ND) were performed on AZ31 Mg sheets in a wider strain rate (0.5-100 mm/min) and temperature (100-400 ℃) range. The microstructure evolution of Mg sheets at 100 and 400 ℃ was analyzed to explain an abnormal phenomenon that flow stress at 100 mm/min decreases compared with that at 10 mm/min at 100 ℃. Conclusions in this paper will provide some valuable suggestions for the forming of Mg alloys at low temperatures.
2 Material and methods
Hot rolled AZ31 Mg alloy sheet with a thickness of 70 mm was selected in this study. The raw sheet was cut into pieces with dimensions of 3 mm (RD) ×50 mm (TD) × 70 mm (ND). The hot tensile test employs dog-bone shaped specimens with a nominal gage size of 15 mm × 4 mm, as demonstrated in Figure 1(a). Prior to the tension tests, the residual stresses of the samples were relieved via heating at 200 ℃ for 6 h. Hot tensile tests were performed on Gleeble-3800 simulator along the ND in vacuum (degree of vacuum is 0.1 torr), as shown in Figure 1(b). The deformation temperatures (T) are 100, 200, 300 and 400 ℃, respectively, and the strain rates (
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The specimens for electron backscattered diffraction (EBSD) observation were mechanically ground on 2000# and 3000# SiC papers, and then electron-polished in a 5% perchloric acid and 95% ethanol at 0.1 A and 45 V for 75 s. EBSD was conducted on a field emission scanning electron microscope (SEM, Tescan S8000), equipped with an Oxford EBSD system and energy dispersive spectrometer (EDS). The obtained EBSD data were imported into Channel 5 software for analysis. Pole figure (PF), inverse pole figure (IPF) maps, misorientation angles, kernel average misorientation (KAM) maps, Schmid factor (SF) distribution and a series of EBSD subsets were obtained. Figure 1(b) shows the scanned area and coordinate system of the EBSD sample. Microstructure of the as-received (AR) sample is presented in Figure 1(c), which exhibits a typical {0001} strong basal texture with a maximum intensity of 13.19. Most of the grains are equiaxed, with an average value of about 30.14 μm.
3 Results
3.1 True stress-strain curves
Figure 2 shows the true stress-strain curves of AZ31 alloys. For the same deformation temperature, the ultimate tensile strength increases with increasing strain rate in the range of 0.5 mm/min to 100 mm/min, except at 100 ℃. The flow stress curves at 100 ℃ under different strain rates are basically the same. However, at high temperatures (200-400 ℃), the flow stress curves present a significant change at different strain rates.
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It can be seen from Figures 2(a)-(c) that the decrease of flow stress is caused by dynamic softening at lower strain rates (0.5-10 mm/min), especially for 300-400 ℃. The flow stress is small and the change of flow stress is also small from 0.5 to 10 mm/min at 300-400 ℃, which is a typical feature of complete dynamic recrystallization (DRX) [30]. In contrast, the rapidly increasing flow stress at 100 mm/min is due to the fraction of TTs being enhanced at high strain rates, and twinning dominates the deformation in tension tests at high temperatures and high strain rates [31].
Therefore, it is reasonable to speculate that the difference in mechanical behavior among various temperatures may be related to twinning and DRX. The following content first gives the hot processing map and then uses EBSD to reveal microstructural evolution in different conditions.
3.2 Activation energy of hot deformation and constitutive equation
Generally, the steady flow stress and strain rate description is preferred for the exponential relationship under relatively lower stresses, as shown in Eq. (1). In high stress, the relationship between them is suitable for the power exponent, as shown in Eq. (2). In this paper, the modified hyperbolic sinusoidal Arrhenius equation [32, 33] was used to establish a constitutive model of AZ31 Mg alloy, as shown in Eq. (3):
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where
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Figure 3(d) shows T-1-ln[sinh(ασ)] linear relationships and the slope of T-1-ln[sinh(ασ)] is b. The combination of R, n and b can calculate the value of Q, which is 134.6 kJ/mol. The widely used Zener-Holomon parameter to describe the effect of temperature and strain rate on the hot deformation behavior of metallic materials, Z, is introduced, as shown in Eq. (5) [34]. Through numerical variations of Eqs. (3) and (5), and organize them to get Eq. (6):
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Figure 3(e) shows the ln [sinh(ασ)]-lnZ linear relationship, and regression analysis of Eq. (6) gives A=5.523×1012. Then all constants in the constitutive equation are obtained. Finally, construct the Z parameter constitutive equation and constitutive equation of AZ31 alloy during hot tension as shown in Eqs. (7) and (8).
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3.3 Processing map prediction
Processing maps can be divided into three types based on mathematical models, including atomic model [35], polar reciprocity model [36] and DMM [37]. Considering the flow stress curves under different conditions in Figure 2, the most significant difference in flow stress between the conditions occurs when the strain reaches 0.2. Therefore, the hot processing map of AZ31 alloy under strain of 0.2 is established by DMM.
According to the DMM, the external input energy (P) consists of dissipation (G) and dissipation covariates (J):
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where σ is the flow stress;
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When temperature and strain are certain, the relationship between stress and strain rate conforms to the dynamic continuity equation:
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Generally, m is between 0 and 1, and it is defined as a non-ideal linear state J. However, the dissipation covariance is in the maximum state (Jmax) when m=1, which is linear dissipation in the ideal state, and J and Jmax can be represented by Eq. (12) and ():
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In general, hot processing performance is characterized by introducing the power dissipation factor (η), which is obtained by comparing the instantaneous J occurring in the work piece with Jmax.
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Furthermore, the Prasad criterion suggests that deformation instability occurs at a given deformation temperature if J and the strain rate are in accordance with Eqs. (15) and (16):
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Combining Eqs. (10), (12) and (16), the equation for the flow instability criterion is:
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Figure 4 shows the three-dimensional hot processing map of AZ31 alloy under strain of 0.2. The contour lines are power dissipation rate values, the gray filled area is the region of instability, and the rainbow area is the region of preferred process parameters for the hot working process. The instability zone is composed of two parts: A and B, and the corresponding deformation parameters are 0.001-0.11 s-1 (0.9-100 mm/min) at 200-214 ℃ and 0.001-0.01 s-1 (0.9-9 mm/min) at 380-400 ℃. A higher η value means that the machining region has a high plastic mobility and good machinability [38]. The AZ31 alloy has high η values at high temperatures and low strain rates, with the highest η value of 0.89 at 400 ℃ and 0.00056 s-1 (0.5 mm/min). The main reason may be that the microstructure transformation is sufficient under high temperature and low strain rate.
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Figure 4 shows that the effect of strain rate on η at 300-400 ℃ is greater than that at 200 ℃, especially at 400 ℃. The η generally increases sharply (from 0.18 to 0.89) with a decrease in the strain rate at 400 ℃. Considering the most tremendous changes of η at 400 ℃, so take two conditions of 400 ℃-0.5 mm/min and 400 ℃- 100 mm/min as examples to investigate the microstructures, and the samples were named 400-0.5 and 400-100, respectively.
Another interesting phenomenon is that there is a slight decrease in the flow stress when the strain rate rises from 10 mm/min to 100 mm/min at 100 ℃ (marked by red arrows in Figures 2(c) and (d)), resulting in a negative m value, which does not conform to the conventional range of m values in Eq. (11). Additionally, there are few literature reports on traditional magnesium alloy hot working diagrams that provide theoretical support for this anomalous phenomenon at 100 ℃ [27-29]. Hence, two samples of 10 mm/min and 100 mm/min at 100 ℃ named 100-10 and 100-100 respectively are also selected to supplement the understanding of the relationship between mechanical properties and microstructures of Mg sheets at low temperature.
4 Discussion
4.1 Microstructure evolution of 400-0.5 and 400-100
Figure 5 shows the EBSD results of 400-0.5 and 400-100. TT boundaries,
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Figures 5(e) and (f) show that the basal texture intensity of 400-0.5 (11.79) and 400-100 (5.53) decreases after hot tension. The weakening of basal texture in 400-0.5 can be attributed to the increased chance of initiating non-basal slips at high temperature of 400 ℃ [41]. For 400-100, TTs play a significant role in weakening of basal texture via c-axes rotation of ~86° [42, 43].
In the machinability field, the variation of η corresponds to the degree of DRX [44], because DRX promotes the stable flow and good workability of materials during deformation. The distribution of recrystallized grains (blue area), substructured grains (yellow area) and deformed grains (red area) is given in Figures 6(a) and (b). The volume fraction of DRXed grains is 72.85% in 400-0.5. As the strain rate enhances to 100 mm/min, the volume fraction of DRXed grains decreases to 12.31%. In 400-0.5, the η reaches the peak (0.89) and DRX is the dominant mechanism of microstructure evolution. Contrarily, the η (0.46) decreases and the twinning is the dominant mechanism in 400-100.
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Both the twinning and DRX behavior are related to the accumulated strain energy. KAM maps are used to determine the stored strain energy [45], as shown in Figures 6(c) and (d). The average KAM value increases from 0.512 at 400-0.5 to 1.147 at 400-100 with increasing strain rate. It should be noted that DRX and dislocation density during hot tension are closely related to the strain rate. The dislocation density and the fraction of tensile twin boundaries (TBs) are higher for samples at high strain rates compared to those at low strain rates.
To better explain the differences between the two samples mentioned above, a schematic map of the microstructural evolution is shown in Figure 7.
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1) During deformation, the generated energy is retained in the form of dislocations [46]. During the initial stage of deformation, dislocations with a high density are formed in the grains, and the density of dislocations also increases with increasing strain rate [47], as shown in Figures 7(a), (b) and (e).
2) The large amount of dislocation entanglement after deformation makes the intracrystalline deformation enter into the second stage. At low strain rates, the large amount of dislocation entanglement will release energy through dislocation rearrangement: the formation of low-angle grain boundaries (LAGBs) and the bulging of grain boundaries (GBs) [48-50], as shown in Figures 7(b) and (c). With the increase of strain rate, plastic deformation occurs in a very short time, which leads to the increase of CRSS for non-basal slip [51], so the dislocation entanglement is difficult to be released in a short time. Meanwhile, the number of LAGBs decreases, and the tendency of twinning increases (twin embryos can be generated in the dislocations entangled) [52, 53], as shown in Figures 7(e) and (f).
3) As the deformation continues, the LAGBs absorb dislocations and increase their disorientation to form high-angle grain boundaries (HAGBs), forming boundaries of new DRX grains [54], as shown in Figures 7(c) and (d). At high strain rates, the twin embryos transform into intact TTs by absorbing dislocations, and the formation of twins results in an increase in TB, and then results in the impeding of dislocation slip [55], causing dislocations to stack around the TB and leading to higher dislocation densities [56, 57], as shown in Figures 7(f) and (g).
Therefore, the difference of η at different strain rates at 400 ℃ is closely related to the absorption and dissipation of dislocations. The dislocations are absorbed at low strain rate via DRX, while they are restricted at high strain rate due to TTs generation, which is harmful to the sustainable flow behavior.
4.2 Flow stress decrease and texture evolution at 100 ℃
Figure 8 displays the microstructures of 100-10 and 100-100. CT and ST are hardly observed, while TTs account for the largest proportion, as shown in Figures 8(c) and (d). Besides, Figure 8(h) shows the number of TBs has a slight increase (from 21.9% in 100-10 to 26.8% in 100-100). Figure 8(g) represents that the average grain sizes of 100-10 and 100-100 are 10.17 μm and 9.12 μm, respectively, which can be attributed to the subdivision effect of TTs.
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Figures 8(e) and (f) show that basal texture component is almost eliminated in 100-10 and 100-100. The maximum intensity of 100-10 and 100-100 is 4.06 and 3.84, respectively, both of which are smaller than that of AR. AR exhibits basal texture, and SFs of six variants of TTs are approximate when tensile loading is along the ND, resulting in similar occurrence probability of TT variants [58]. That is mainly responsible for the even distribution of ~86° tilt of c-axes [59], which is particularly obvious in 100-100.
There is a subtle flow stress decline of 25.94 MPa in 100-100, compared to that of 100-10. The final flow stress of materials is the competition between hardening and softening during tensile deformation, and the corresponding mechanisms are as follows: 1) Hardening due to the reduced average grain size caused by TBs, which is also called dynamic Hall-Petch effect [60]; 2) TBs acting as obstacles for dislocation movement, resulting in dislocation entanglement and pinning and then resulting in hardening [61, 62]; 3) TTs as preferential nucleation sites of DRX and DRX can consuming and reorienting parent grains, then causing softening effect [63].
First, according to the Hall-Petch equation (
Then, the influence of dislocation density can be quantitatively measured by KAM values, which decreases from 1.304 in 100-10 to 1.219 in 100-100, as shown in Figure 9(c) and (d). As the increase of strain rates, the volume fraction of TTs grows, resulting in dislocation density remaining stable or increasing [64], which is also against the KAM results. Hence, DRX may play a role in the reduction of dislocation density [49-65]. Both increasing strain rate and inducing TTs can promote DRX [66]. With the deformation rate increasing, the dislocation slips are difficult to complete in a short time [53] and large deformation energy can be generated, which is conducive to the acceleration of DRX to some extent [67]. Figures 9(a) and (b) show that the number of DRXed grains increases with the increase of strain rate, so DRX is partly responsible for the decrease of dislocation density, which provides a softening effect to some extent.
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Except for the influence factors discussed above, texture altering is also closely associated with the change of flow stress [18]. A significant difference can be observed from the PF of 100-10 and 100-100 in Figures 8(e) and (f), where the maximum intensity is formed at a deviation of approximately 34° from ND at the PF of 100-100. Figure 10 shows the SF distribution of different slip systems. Compared with the SF of basal <a> slip of AR (0.214), the values of 100-10 (0.292) and 100-100 (0.291) significantly increase, while the SFs of other slip systems decrease obviously, especially the prismatic <a> slip, which is because TTs help to enhance basal slip by rotating c-axes [68].
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The CRSS of non-basal slips of Mg is much larger than that of basal slip at room temperature [69], and the average SFs of non-basal slips in 100-10 and 100-100 are approximate, which can be clearly seen from Figures 10(f)-(h), (j)-(l). So, in this part the effect of basal slip on flow stress is mainly discussed. Figures 10(e) and (i) show that grains with their c-axes parallel to TD/RD or rotating from ND to TD present small SFs of basal slip. By contrast, the grains with their c-axes parallel to ~45° (marked by black ellipse in Figure 10(i)) have a higher SF of basal slip.
Purple circle and the black rectangle in Figures 10(e) and (i) illustrate the regions with the maximum texture intensity (Figures 8(e) and (f)) in 100-10 and 100-100, respectively. The average SFs of basal <a> slip of these two regions are calculated, which are ~0.38 in 100-100 and ~0.21 in 100-10, indicating that the special 34° texture components are favorable to activation of basal slip and lead to the decrease of flow stress.
Regions marked by white rectangle plotted in Figure 8(b) are enlarged in Figure 11 to investigate the special 34° texture component, and the corresponding {0001} PF map is given. Figures 11(a) and (b) show that two kinds of twin variants are observed in regions A and B. It can be seen in Figure 11(c) that the rotation angles between the matrix grains (M1 and M2) and the corresponding twin variants are larger than 86°, which can be attributed to excessive number of twins causing the deflection of matrix grain orientation [70, 71].
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Figures 11(d) and (e) show the SF of basal <a> slip of regions A and B. The SF of T1 is 0.22 and SF of T2 is 0.44 in region A. The SF of T3 is only ~0.12, while the SF of T4 is four times that of T3 in region B. Difference in SFs between twin laminas results in different activated values of basal slips in TTs in the same grain. Figures 11(f) and (g) show that abundant dislocations accumulate in the TTs with low SFs, and there is nearly no dislocation accumulation in the TTs with high SFs. This inhomogeneity of intra-grain deformation generates stress and causes c-axes of matrix grains to deflect [72].
Figure 11(h) shows the point-to-point and point-to-origin directional deviations along lines 1-3 in M1 and M2. Through the point-to-point curves, it can be noticed that the misorientation of line 1 gradually increases to ~4.8°, thus indicating that the internal distortion of M1 is small. However, the misorientation of line 2 and line 3 increases to ~17.5° and ~14.5°, respectively, which indicates that the internal distortion of M2 is larger. It can be inferred that when more difficult-to-slip twin variants lead to dislocation accumulation, the matrix grains containing these TTs are prone to tilt to a direction favorable to slip.
In summary, the decrease of flow stress at strain of 0.2 in 100-100 is partly because of the softening effect brought by DRX via absorbing dislocations, but the main reason is that the special ~34° texture component promotes the activity of basal slip. The strengthening effect brought by grain refinement is negligible.
5 Conclusions
The deformation behavior of Mg sheets subjected to uniaxial tension at temperatures ranging from 100 to 400 ℃ and strain rates ranging from 0.5 to 100 mm/min was investigated, and the following conclusions can be drawn:
1) The best processing parameters are 400 ℃ and 0.00056 s-1 (0.5 mm/min). Mg alloy sheets experience flow instabilities in the strain rate
and temperature ranges of 0.001-0.112 s-1 (0.9- 100 mm/min) and 200-214 ℃ and 0.001-0.01 s-1 (0.9-9 mm/min) and 380-400 ℃.
2) The strain rate shows η is the most sensitive to strain rate at 400 ℃ via absorption and dissipation of dislocations. 400-0.5 possesses a higher η of 0.89 because of its lower dislocation density of 0.512, which can be attributed to absorption of DRX. However, 400-100 possesses a lower η of 0.46 with higher dislocation density of 1.147, and the reason is that dislocations tangle with each other and are pinned at TBs.
3) The flow stress presents a slight decrease of 25.94 MPa in 100-100 compared to that of 100-10, and it is closely associated with the special ~34° texture component in 100-100, which is favorable to activation of basal slip. Besides, DRX also provides softening effect to some extent by absorbing dislocations.
4) Difference in SFs between twin laminas results in the inhomogeneity of intra-grain deformation, which generates stress that helps matrix grains tilt in a direction favorable to basal slip, and finally, a novel texture component of 34° appears.
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ZHANG Hong-yang, NIE Hui-hui, XU Xiong, LIANG Wei. Abnormal texture and sensitivity to strain rate during hot-tension of Mg alloy sheets [J]. Journal of Central South University, 2025, 32(3): 991-1007. DOI: https://doi.org/10.1007/s11771-025-5926-2.
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