Fei Guo, Risheng Pei, Luyo Jing, Dingfei Zhng, Snr Korte-Kerzel,Tll Al-Smmn

aCollege of Materials Science and Engineering, Chongqing University of Technology, 400054 Chongqing, China

b Chongqing Key Laboratory of Mold Technology, Chongqing University of Technology, 400054 Chongqing, China

c Institut für Metallkunde und Metallphysik, RWTH Aachen University, 52056 Aachen, Germany

d College of Materials Science and Engineering, Chongqing University, 400044 Chongqing, China

Abstract The contribution of recrystallization and grain growth to the texture evolution in AZ31 alloy and a modified version AZ31+0.5wt.%Ca was investigated utilizing a multi-step annealing process. The results showed that the addition of Ca triggered a considerable texture modification by increasing the texture spread and decreasing the overall texture intensity. This effect was found to be temperature dependent.When the annealing temperature remained lower than 450 °C, a weak double peak texture with large basal pole tilt towards the RD was formed. This is correlated to microstructure observations of a large number of Ca-containing nano-sized particles that seemed to suppress grain growth below 450°C, which stabilized the weak recrystallization texture. This favorable texture was lost upon annealing at higher temperatures. In AZ31, recrystallization nuclei were found to preserve the orientation of their deformed parents, which offered limited potential to optimize the texture via annealing treatments. Grain growth of recrystallized grains resulted in a distinct sheet texture transition from a double-peak to a single-peak basal texture. Aspects of grain boundary energy and grain topology are discussed to explain the growth advantage of the sharp basal component over other orientations.

Keywords: Magnesium alloys; Microstructure; Texture; Recrystallization; Grain growth.

1. Introduction and background

Magnesium (Mg) alloys are the lightest structural metals,making them one of the most effective choices to enhance fuel efficiency in automotive and aerospace applications, where weight reduction is crucial [1]. Wrought Mg alloys show a larger application potential compared to as-cast ones because of their much better mechanical properties. Common forming operations of Mg alloys, such as rolling, extrusion and forging, usually give rise to well-defined sharp deformation textures [2,3]. In order to restore the ductility of the deformed material that typically possesses high stored energy, subsequent annealing treatments are performed, not only to recrystallize the microstructure but also to release residual stresses,optimize the grain size and weaken the deformation texture.

It is well known that texture modification is one of the most important ways to enhanced formability of Mg alloys sheets at room temperature. There are two basic ways to modify or weaken the basal texture in Mg alloys. One relies on optimizing the processing route to control activity of mechanical twinning and promote activation of non-basal slip modes [4–6]. The other method is based on microstructure recrystallization through annealing treatments to nucleate new grains with large orientation spread [7–10]. As Mg and its alloys are considered to have a low stacking fault energy(SFE) compared to Al alloys, they can undergo recrystallization rather than recovery, which provides a significant grain refinement opportunity [11]. Depending on the recrystallization mechanism, the new fine grains can at the same time exhibit different orientation relative to that of the deformed matrix, which presents an attractive possibility to modify the type of deformation texture by recrystallization.

Texture modification by recrystallization was found to be particularly enhanced when rare-earth elements (REE) are added to the material. In this respect, three main aspects are important in triggering the so-called rare-earth effect[12–19]. Recently, some non-RE elements attracted large R&D attention because of their observed potential to induce modified textures in Mg alloys, similar to those obtained from REE alloying.

In earlier studies, Ca was regarded as an important alloying element to form a thermally stable precipitate structure that improves the high temperature mechanical properties of Mg alloys [20–28]. In further studies, Xu et al. [29] observed that twinned structures in AZX911 alloys were fully recrystallized and that coarsening of the fine recrystallized grains was suppressed by the appearance of Mg17Al12β-phase and Al–Ca particles. Jan et al. [30] observed a TD-split texture in Mg–Zn–(Zr)–Ca alloys subjected to hot rolling and annealing. They ascribed the texture modification to twin-induced recrystallization. On the other hand, Zeng et al. [31] believed the texture weakness, seen in cold-rolled Mg–Zn–Ca alloys to arise from a uniform grain growth of randomly oriented grains rather than twin or shear band-induced nucleation.Also, more recently, Trang et al. [32] developed a Mncontaining AZX310 alloy with an excellent combination of strength and formability that was ascribed to precipitation hardening and enhanced solute segregation effect.

In analogy to Mg–RE alloys, literature reports of texture modification mechanisms by Ca addition are also related to drag effects on the grain boundaries, exerted either by solute atoms or second phase particles or to special recrystallization nucleation mechanisms. These are usually associated with a retarded recrystallization behavior, where the onset of recrystallization is shifted to higher temperatures. Aside from the nucleation aspect of RE orientations and the complex interplay with solute and/or Zener drag, respective investigations should be extended to include aspects of favorable growth during recrystallization and grain coarsening. Favorable growth of certain texture components, and thus texture enhancement during grain growth annealing was reported recently in AZ31 [33,34], where basal oriented grains were found to obtain a grain growth advantage. However, it is still not entirely clear, where the orientation preference during growth comes from and how it affects texture modification during annealing. Hence, a better understanding of these physical processes could provide a great avenue to design alloys and thermomechanical processes in order to obtain textures and microstructures tailored toward a particular application.

Table 1 Chemical composition of the materials used in this study.

In this study, one-step and multi-step annealing experiments were carefully designed to systematically investigate the relationship between recrystallization and grain growth,and the resulting texture and microstructure evolution. Conventional AZ31 alloy and a Ca-modified version AZ31–0.5Ca(wt.%) were used as study materials to explore the impact of Ca addition on the growth characteristics of recrystallized grains and any resulting texture weakening effect. Computer simulations of grain growth using the level-set method were additionally utilized to quantitatively model the relationship between grain growth and texture. By a careful consideration of the findings from the two investigated alloys, potential theories for texture selection mechanisms are discussed along with strategies for microstructure optimization by recrystallization and grain growth treatments, where the alloy chemistry plays a key role.

2. Experimental procedure

Production of AZ31 and AZ31–0.5Ca (hereafter AZX310)Mg alloys took place in a vacuum induction-melting furnace under a protective argon atmosphere. All the cast ingots were homogenized at 420°C for 12h. Table 1 gives the actual chemical composition of the two alloys detected by X-ray fluorescence. Rolling plates with dimensions of 60 mm × 40 mm × 5mm were machined from homogenized materials. The rolling procedure was carried out at 420°C(nominal furnace temperature) by 3 passes for a total thickness reduction of 76%. The rolled samples were annealed at various temperatures ranging from 180°C to 525°C for different times between 10s and 1 h. All annealing treatments were carried out in an Al2O3salt-bath furnace to ensure a high heating rate. The heat-treated samples were quenched into water immediately. For optical metallography,the samples were mechanically ground (RD-TD mid-plane)using 4000 grit SiC paper and then polished by 3 and 1 μm ethanol-based diamond paste. To obtain a better surface quality and remove the deformation layer induced by mechanical grinding and polishing, the specimens were electro-polished at a voltage of 20V and a temperature of ?20°C for 90s using AC-2 reagent (Struers). Finally, chemical etching of the electro-polished specimens was carried out using acetic picral solution (4.2g of picric acid, 70ml of ethanol, 10ml of acetic acid and 10ml water) for 15–20s. Phase analysis was conducted on the AZX310 annealed samples by means of X-ray diffraction using a Rigaku D/max 2500PC diffractometer. The observation of second phases was carried out in both a TESCAN Vega 3 scanning electron microscope (SEM) and JEM 2010 transmission electron microscope (TEM) equipped with an energy dispersive X-ray spectrometer (EDS).

Samples without chemical etching were used for electronbackscattered diffraction (EBSD) measurements. EBSD was performed within a LEO-1530 scanning electron microscope equipped with an HKL-Nordlys II EBSD detector. The choice of step size was based on the average grain size of each processing condition and ranged from 0.1 to 0.3 μm.The acquired raw EBSD data were subsequently analyzed using both the commercial Channel 5 software and the free MTEX toolbox [35]. The macrotexture was measured in the as-rolled and annealed conditions in the mid-plane of the sheets using a Bruker D8 Advance diffractometer equipped with an area detector. The orientation distribution functions(ODF) were calculated from six incomplete pole figures and then recalculate the complete pole figures.

3. Computational procedure

Level-set computer simulations of grain growth were utilized to illustrate the role topological aspects on texture evolution. This method has excellent computational stability and has shown a reliable performance in grain growth simulations[36–38].The input microstructure was acquired from the EBSD data of AZ31 annealed at 350°C for 10s, which represented an almost fully recrystallized microstructure without notable grain growth. Each grain in the input microstructure was thus assigned a unique set of Euler angles according to the measured orientation.Grain boundary energies(γGB)were determined by means of the Read-Shockley expression:

For a fully recrystallized microstructure, almost all grain boundaries are high angle boundaries. Hence, the dominant factor for grain growth in the present case came from their curvature-driven motion to reduce the grain boundary surface,and thereby minimize the free energy of the system. This process induces a continuous topological rearrangement,which could have important implications for the grain growth texture development. The time steps in the simulations were correlated with the growth rate of the average grain size, and used to track the temporal changes of grain topology. At any time step, the simulation output can be exported back into the file format of the EBSD data, in order to analyze the corresponding texture and microstructure through the MTEX software.

To verify the second phase formation observed experimentally, the phase diagram of the Mg-3Al-xCa ternary system with Ca concentrations ranging from x = 0 to 1.5wt.%was calculated utilizing the Pandat software. The calculation results reflected the thermodynamics of Ca-containing phases and the solid solubility change of Ca as a function of temperature.

4. Results

4.1. Initial state and single step annealed condition at 250°C

Fig. 1a and b display the optical microstructures and Fig. 1c and d the bulk textures of 76% hot-rolled AZ31 and AZX310 Mg alloys. Both alloys contained large numbers of deformation twins inside grains. For the AZ31 alloy,the microstructure was composed of large grains, elongated along the RD, and shear bands of high density of twins. The deformation microstructure in the AZX310 depicted a much finer grain structure with less strain localization features.Both alloys exhibited double peak basal-type textures with basal poles tilted towards the RD. However, Ca addition seemed to reduce the texture intensity by producing a higher texture spread, which was also reported in [39] for a Mg–Al–Ca alloy. The tilt angle between the ND and basal pole maxima was around 16°, which is larger than that of AZ31(～12°). The AZ31 basal texture exhibited an asymmetrical distribution of pole density maxima with respect to the ND.

To examine the evolution of the texture in both alloys during annealing, the rolled samples from Fig. 1 were subjected to 250°C anneals for different times. Fig. 2a and b show the texture evolution in the (0001) pole figure for two alloys upon annealing at 250°C for 10s, 60s, 600s and 3600s. The texture intensity in both alloys seemed to decrease during the annealing process. Although the AZX310 alloy did not show a new texture character with entirely new texture components,the presence of Ca has a positive influence by decreasing the overall intensity and promoting the off-basal RD-split character of the texture. In comparison, the TD spread in the AZ31 annealing texture was considerably less than that of AZX310. In addition, the basal poles in the AZ31 texture appeared to move gradually towards the center of the pole figure with increasing annealing time. This behavior gave rise to an undesired texture transition from a double-peak type to a single peak basal texture, seen in Fig. 2a at 600s and 3600s annealing times. The different characteristics in the texture evolution of two alloys indicate possible different nucleation and/or growth behavior during recrystallization. For a quantitative description of the texture evolution shown in Fig. 2a and b, we used a method shown in Fig. 2c and d. The double peak initial deformation texture for both alloys is decomposed into three texture components: (i) the primary peak component with maximum intensity (MP), (ii) the secondary peak component (SP) with less intensity than the primary one, and(iii) the central texture component (CE) (Fig. 2e), which in a(0002) pole figure usually corresponds to an ideal basal orientation. Additionally, a fourth parameter was also taken into account, namely the misorientation angle of the two texture peaks (ω). The average tilt angle of basal poles (θ), plotted in Fig. 2c and d is defined as half of ω as shown in Fig. 2e.

Fig. 1. Microstructure and XRD bulk texture of hot rolled (a,c) AZ31 and (b,d) AZX310.

Fig. 2. (0002) pole figures showing the texture evolution of (a) AZ31 and (b) AZX310 annealed at 250°C for different times. Analysis of the texture characteristics as a function of annealing time for (c) AZ31 and (d) AZX310. (e) Schematic (0002) pole figure to help with the interpretation of the texture analysis in (c) and (d).

Fig. 3. EBSD maps featuring grain misorientation spread (GOS) for the samples annealed at 250°C for 10s and 600s of (a-b) AZ31 and 600s for (c) AZX310.Correlation of GOS, ND tilt angle of basal poles and grain size in AZ31 samples annealed for (e) 10s, (f) 600s and in AZX310 annealed for (g) 600s.

As evident, the intensity of MP and SP in AZ31 was remarkably decreased after short time anneals up to 60s. The maximum intensity of the texture remained at ～5.6 MRD(multiples of a random distribution) during further heating up to 600s. At the same time, the CE component began to show an increase already after 10s of annealing at 250°C, and became stronger than the SP component after annealing for 600s. This behavior points to the above-mentioned texture transition. The average tilt angle of basal poles showed a slight increase at the very beginning of annealing and then dropped to ～6°, indicating a basal pole concentration in the ND. During longer anneals up to 1h, the intensity of the SP component revealed an increase, concurrent to the increase of the central peak. By contrast, the intensity of all three texture components in the AZX310 alloy exhibited a continuous decrease throughout the whole annealing process. A decrease in the intensity of the ND component signals a move in the right process direction to depart from a basal texture. The average tilt angle of the basal poles varied between 17° and 22° for each annealing time but it was in all cases higher than in the as-rolled condition.

Fig. 3a–c displays the microstructures of AZ31 and AZX310 samples annealed at 250°C for 10 or 600s. The grain misorientation spread (GOS) was extracted from the EBSD data and used to reflect the intragranular stored energy.The critical GOS value to distinguish between deformed and recrystallized structure is 1°. As can be seen, most of the grains in AZ31 were already recrystallized after 10s of annealing. Few larger grains had GOS values up to 6°. After annealing for 600s, the maximum GOS value dropped below 3°. Unlike the fast recrystallization kinetics in AZ31, recrystallization in AZX310 was largely retarded by Ca addition.Fig. 3c shows a GOS map of the annealed microstructure of the AZX310 sample at 250°C/600s. With increasing annealing time up to 600s, recrystallization did take place but the annealed microstructure still contained a considerable proportion of grains with high GOS values up to 10°(Fig. 3f).

In order to quantitatively investigate the relation between the annealing time and the evolution of texture and microstructure, several grain parameters were extracted from the EBSD data and plotted in Fig. 3e–g. These parameters were the grain diameter, representing the grain size, the tilt angle of basal poles from ND, as an indication of texture modification, and the GOS value. Each bubble in the diagrams represents a grain and the diameter of the bubble is proportional to the grain size. In case of AZ31 annealed for 10s, the vast majority of fine grains (small bubbles) correspond to the recrystallized fraction of the microstructure with GOS < 1°. Among these grains, the ones with a larger grain size had their c-axis tilted from ND by 8° to 40°. On the other hand, much larger unrecrystallized grains exhibited less basal pole tilt on average. For the 600s annealing condition,the distribution of GOS values was more concentrated in the range of 0.2–0.4° with very few grains (bubbles) populating the right side of the diagram at GOS > 1°. The grown recrystallized grains still exhibited a broad orientation spectrum,which was now extended to very low tilt angles close to 0°.In case of the AZX310 alloy annealed for 600s, the sampled data constituted two equally prominent groups of grains with GOS values higher and lower than 1°. In both groups larger grain sizes were associated with tilt angles spanning between 15° and 45° that give rise to the off-basal texture components seen in the corresponding pole figure in Fig. 2.

Fig. 4. (0002) pole figures showing the texture evolution of the samples annealed isochronally for 10s at various temperatures of (a) AZ31 and (b) AZX310,corresponding texture information for (c) AZ31 and (d) AZX310.

4.2. Annealed condition between 350°C and 525°C

Fig. 4 displays the evolution of the deformation texture for the two alloys after 10s of annealing at different temperatures. For AZ31, the texture transition from a double peak to a single peak basal texture occurs faster (600s→10s)when the annealing temperature is raised from 250°C to 450°C. This indicates that double-peak texture in AZ31 is not stable regardless of the annealing temperature. The measured texture intensity after the short anneals at the different temperatures remained more or less unchanged (6–7 MRD).For the AZX310 sample, annealing at 350°C exhibited the best texture in terms of the lowest intensity and largest off-basal tilt (～22°). The annealing temperature increased to 450°C and 525°C seemed to have a negative influence on the texture demonstrated by an undesired, rapid texture transition to single peak basal texture, similar to AZ31. This indicates that any solute or particle-related effect of Ca on altering the texture is temperature dependent. In terms of texture weakness, the AZX310 alloy still depicted weaker textures as compared to its counterpart AZ31 (6 vs. 4 MRD).

Fig. 5 displays the relationship of grain size and texture evolution in AZ31 as a function of annealing time (Fig. 5a)and annealing temperature (Fig. 5b). At the beginning of annealing at 250°C, the maximum texture intensity dropped due to the initiation of recrystallization. With increasing annealing time, the intensity of the basal component kept increasing at the cost of other texture components. Accordingly, the maximum texture intensity remained almost constant. After 3600s (1h) of annealing, the intensity of the basal component was equal to the maximum intensity. The corresponding grain size variation showed a noticeable increase up to 600s. From 600s to 3600s, the increase in grain size was negligible. Annealing at elevated temperatures gave rise to a relatively larger grain size, even at the early stage of annealing. The average grain size of the samples annealed at 350°C and 450°C was about 1.8 and 2.7 times larger than the one of the 250°C annealed sample. By comparison with the texture intensity data, it can be presumed that the strengthening of the basal texture component at elevated annealing temperatures was facilitated by grain growth.

4.3. Texture and microstructure after multi-step annealing

In most cases, it is complicated to track the relationship between texture and microstructure during annealing because recrystallization and grain growth, which are hard to separate,may affect the process of texture formation differently. In this work, we have added a series of multi-step annealing experiments consisting of a first annealing of the as-rolled sample at 180°C up to 5h, followed by a second annealing at 250°C up to 1h. The choice of these parameters was based on previous experience and is believed to allow a more suitable investigation of recrystallization and grain growth in two separate steps.

Fig. 5. Relationship between texture evolution and average grain size in the AZ31 samples annealed at 250°C for various periods (a) and for 10s at different temperatures (b).

Fig. 6. Multi-step annealing microstructures and XRD bulk textures of the samples annealing at 180°C for 10s (a), 60s (b), 5h (c) and then annealed at 250°C for 10s (d), 60s (e), 600s (f), 1000 s (g) and 1h (h).

Fig. 7. Quantitative texture information of the multi-step annealing scheme: (a) annealing at 180°C for 5h and then (b) additional annealing at 250°C for 1h.

Fig. 6 shows the microstructures and corresponding XRD textures of rolled AZ31 samples that were first annealed at 180°C for 10s, 60s and 18000s (5h), respectively, and then annealed again at 250°C for 10s, 60s, 600s, 1000s and 3600s, respectively. The microstructures of the samples annealed at 180°C for 10s and 60s (Fig. 6a and b) were similar to the as-rolled microstructure. The observed severe shear banding upon rolling deformation was still evident, but there were also bands of very fine (<1 μm), recrystallized grains that can be associated to the presence of shear bands and deformation twins, in which the stored deformation energy is typically high. Static recrystallization (SRX) was completed after annealing for 600s (not shown here), which gave rise to a fully recrystallized microstructure. Deformation twins were no longer present, either because they were consumed by SRX or due to the movement of twin boundaries. After 5h of annealing (Fig. 6c), the average grain size of the recrystallized microstructure was approx.3.4 μm,indicating negligible grain growth at the chosen 180°C for the first annealing step.In the next annealing step at 250°C, the grain size showed a noticeable increase up to ～6 μm after 1h annealing. With respect to the texture, the first annealing step showed almost no change in the texture characteristic and intensity. During the second annealing step, the texture intensity decreased slightly from 6.3 to 5.6 MRD. This was accompanied by a clear shift in the basal pole concentration from an off-basal position along the RD towards the ND (double peak→single peak).

In addition to the (0002) pole figures shown in Fig. 6,Fig. 7 provides a quantitative analysis of the texture evolution during both annealing steps, analogous to Fig. 2. It is noted that in the first annealing step, where there was a transition from a deformed to a fully recrystallized microstructure, the average tilt angle of basal poles in the obtained textures remained more or less constant (～11°) (Fig. 7a). The slight decrease of texture intensity is typical for recrystallization in this class of alloys. A variation in the tilt angle of basal pole,namely a decrease from 11° to 6° was only seen during the second part of annealing (Fig. 7b), at which the recrystallization process was already complete and grain growth was active. This observation strongly suggests that the transition from a double peak to a single peak basal texture, frequently observed in rolled and annealed magnesium sheet alloys is more attributed to grain growth rather than recrystallization.This insight is very important to understand how the strengthening of the basal texture occurs during sheet processing.

A more detailed analysis of the variation of texture intensity as a function of basal pole tilt from ND to RD is given in Fig. 8a for several one-step and multi-step annealing conditions. Before annealing at 250°C, most of the grains in the 180°C/5h sample had their c-axis tilted at ～12° from the ND towards the RD. The difference of the maximum and central intensity at 0° was 2.1 MRD. With increasing annealing time at 250°C, the increase in texture intensity at 0° in Fig. 8a is obvious for all the respective samples. For comparison purposes, the data of 350°C/10s and 450°C/10s anneals is included in the graph and shows even higher intensities due to the advanced role of grain growth at these temperatures. By examining the intensities at 12°, it is apparent that the tendency for basal pole splitting diminishes during annealing at step 2. Fig. 8b reveals that there is a linear relationship between the average grain size and the intensity of the (0002) central texture component. Regardless of the annealing route the texture intensity seems to increase with increasing grain size. The fact that all data points fall on the same line indicate that all grains grow at roughly the same rate, i.e. grain growth is of continuous (normal)nature.

5. Discussion

The following discussion focuses on two major elements of the study. One is the distinct sheet texture transition from a double-peak to a single peak basal texture upon grain growth of recrystallized grains in the AZ31 alloy.In this regard, aspects of grain boundary energy and grain topology are considered and discussed in order to shed light on the material behavior. The other is the remarkable texture weakening in AZX310 alloy that was triggered by recrystallization. Effects of Ca addition on recrystallization and grain growth are separately discussed. This includes the effect of second phase precipitates on the migration of grain boundaries during growth and the related texture evolution.

Fig. 8. (a) Intensity changes of the basal texture component during grain growth annealing treatments, (b) the relationship between average grain size and central texture intensity for several grain growth annealed samples.

5.1. Texture selection mechanisms during annealing

In the present study, the dominant texture evolution character during grain growth of annealed hot-rolled AZ31 Mg alloy was the strong concentration of basal poles close to ND.This type of basal texture was different from the preceding deformation and recrystallization textures, which were both double-peak basal textures with basal pole tilt toward the RD.This kind of texture transition seems to apply to other Mg–Zn based alloys that are subjected to annealing treatments after rolling deformation.In a recent study on hot rolled Mg–5.7Zn[40], the authors observed a TD-tilted double peak basal texture after 40% single-pass rolling at 400°C. They reported that this texture was replaced by a sharp, single-peak basal texture after elevated temperature annealing up to several hours,i.e.under favorable grain growth conditions [40].Their argument was based on a higher nucleation rate for the recrystallized grains with a basal orientation, which gave them the advantage to eclipse other competing orientations and dominate the annealing texture. In face centered cubic (fcc)metals, such as aluminum, a strong texture transformation is also observed during annealing, seen by the development of a strong cube orientation in recrystallized grains by consuming S-oriented deformed regions [41]. Experimental investigations of cube recrystallization textures often gave rise to oriented nucleation and also for oriented growth.

In our case, the growth advantage of (0002)<10-10>basal grains did not seem to arise from recrystallization but rather from grain growth (not to be confused with nucleus growth). Alloying effects, such as those of particles and solute elements that have the ability to drag grain boundary motion by pinning or segregation are not very typical for AZ31,and thus were not considered in this work to contribute to the observed texture transformation. Possible reasons for the dominance of the single peak basal component over others during grain growth are discussed in the following with respect to anisotropic boundary migration properties and topological, as well as geometrical aspects.

5.1.1. Role of special grain boundaries

Theoretical grain growth models, such as the one of Burke and Turnbull [42] assume the grain boundary energy and mobility to be isotropic.However,when strong textures arise due to experimentally observed preferential growth, one can reasonably argue that a special boundary with relatively higher mobility should exist. For this reason, advanced modeling techniques of grain growth are modified to consider the role of anisotropic grain boundary mobilities in texture modification [43]. The mobility (v) of a grain boundary is controlled by its mobility (M) and the driving pressure (P), given as

Under an applied force a curved boundary will always tend to move towards its center of curvature to become straighter,and thus reduce its surface energy. The driving pressure for the motion of a grain boundary is thus given by:

where γbis the grain boundary energy, and ˉR the radius of curvature. The growth advantage of (0002)<10-10> basal grains would be attributed to a higher growth rate, which results from either a higher relative mobility and/or a larger driving pressure. Simulations carried out by Dillon and Rohrer [44] in order to explain the anisotropic nature of grain boundary character distributions during normal grain growth revealed that higher energy boundaries were easily eliminated from the microstructure, which contributes to the reduction in the energy of the system. Considering that low angle grain boundaries have naturally a lower energy (as per Eq. (1)), the increase of their fraction during annealing by elimination of high angle boundaries can be well correlated with the strengthening of the texture.

Fig. 9. Grain boundary misorientation axes distribution for the misorientation angles presented in Table 2 for possible low energy boundaries in the AZ31 specimens annealed at (a) 180°C for 5h (Sample A), (b) further annealed for 250°C for 1000s (Sample B), (c) 350°C 10s (Sample C) and (d) 350°C 60s(Sample D). EBSD maps with highlighted special GBs and basal grains of (e) Sample C and (f) Sample D.

Table 2 Summary of special grain boundaries in hexagonal metals [40,41] and their absolute frequency in the current study (ratio of segments of special GBs and that of total GBs).

Aside from low angle boundaries,low energy grain boundaries in hexagonal metals (also known as special boundaries)can also exist in the high angle (>15°) regime [45]. These special boundaries are listed in Table 2 along with their measured frequency at various annealing conditions. Additionally,Fig. 9a–d displays plots of misorientation axes distribution for the misorientation angles for special boundaries (listed in Table 2) which may occur as a function of annealing condition. The samples annealed at 180°C for 5h revealed obvious clustering in the stereographic standard triangle at～75°<30–31> (Fig. 9a), which is not close to any of the misorientations in Table 2. Under moderate grain growth conditions (+250°C/1000 s and 350°C/10s) the distributions in Fig. 9b and c exhibited a high frequency of <11-20> grain boundaries with misorientation angles of ～58° and ～75°.According to Table 2, the 62°<11-20> boundary is considered a special, low energy boundary, which might explain its persistence during incipient annealing at 350°C (Fig. 9c).Longer annealing durations at this temperature gave rise to the 30°[0001] boundary (Fig. 9d), which is very close to the 28°[0001] (∑13) perfect coincidence boundary. It is noted that these boundaries were present during the other annealing conditions but their fraction was significantly lower. Among all special boundaries in Table 2, the ～30°[0001] boundaries are the only ones capable of strengthening the basal single peak component, and thus the increase of their frequency during progressive annealing could be assumed to be postulated by the grain growth texture. If the frequency of the 30°[0001] boundaries would have remained low as in Fig. 9c,we should have instead witnessed a strengthening of an offbasal component resulting from grain boundaries with <11-20> or <10-10> misorientation axes. Fig. 9e and f shows EBSD maps of the annealed samples at 350°C for 10 and 60s, respectively, with the basal grains highlighted in red and the special boundaries from Table 2 outlined in different colors. Note that the detection of the 30°[0001] boundary in the EBSD maps is occasionally associated with indexing errors that have a higher incidence when the measuredmicrostructure has a strong basal orientation [33]. The frequency of the other low energy grain boundaries was very low and their distribution in the microstructure appeared random.

Table 3 Grain size and topological data at different conditions of annealed samples subjected to multi-step annealing.

5.1.2. Role of grain topology

While the grain boundary properties can influence the textural evolution during growth, there is also an important link between the variation in grain topology and texture selection.Favored growth of grains with a specific texture component during recrystallization can be sometimes explained by the concept of ‘orientation pinning’ of grain boundaries,which considers that some orientation relationships, such as low-angle and twin grain boundaries are disfavored during the growth selection process [46,47]. Growing nuclei of a very similar orientation (e.g. basal) will have immobile grain boundary segments that will pin their further growth.Accordingly, grains with a low chance of creating immobile grain boundaries are preferred and would eventually predominate in the recrystallization texture. This hypothesis is in accordance with the two-peak textures observed during recrystallization [48]. If we consider basal and off-basal orientations to be two competitive texture components, their trend of expansion during heat treatments would have great influence on the recrystallization and grain growth textures.

For the investigated AZ31 alloy, the growth advantage of a particular grain is assumed to be affected by its size,boundary curvature and its direct neighbors (collectively referred to in this section as topological aspects). Table 3 gives grain size and topological data of basal (ND tilt <12°) and off-basal grains (>12°) collected from EBSD measurements of systematic sample conditions upon multi-step annealing treatments. The corresponding EBSD microstructures are shown in Fig. S2. The difference of basal and non-basal grain size was insignificant during recrystallization but seemed to increase by subsequent grain growth. From seminal works on statistical grain growth theories by Lücke and Abbruzzese[49], topological relationships between the number of sides of a grain and its size were introduced (Eqs. (4) and 5), which were suggested to generally apply to equiaxed polygonal grain structures resulting from grain growth:

ri=is the normalized grain size,is the mean size of grains with n sides, ξ is a correlation coefficient equal to 0.85. It follows, grains which have more than 6 sides would grow, and thus reduce the contact angle at triple junctions to approach a stable equilibrium configuration. In a two-dimensional case, the grain structure is only stable when it maintains six-sided grains with 120° angles at the vertices[47]. Obviously, in a real polygonal microstructure, other configuration can be found, which inevitably lead to grain growth driven by the boundary curvature in order to reduce the boundary area. From the analysis, it was found that the average number of sides of basal grains in the partially recrystallized sample was much larger than that of off-basal grains because some large deformed basal grains were still present. In the fully recrystallized condition, the difference of average number of sides of both orientations was reduced to 0.42 (6.1 for basal grains vs. 5.7 for off-basal grains).This is most likely because off-basal grains in this particular case introduce instability into the microstructure, and would thus tend to disappear. Basal grains, on the other hand,keep enjoying the growth advantage during further annealing stages and can engulf residual off-basal grains to eventually reach the stable equilibrium condition.

To understand the relationship between the variation in the grain topology during growth and texture, a novel level-set technique [33] was utilized to investigate whether the single peak texture prevailing during grain growth emerged directly from the grain size distribution created during recrystallization or from certain advantages in grain boundary energy or mobility. The effective driving pressure acting on a grain boundary segment was computed from the relative size difference between adjacent grains. The respective mobility values were then scaled with respect to the estimated driving pressures. For numerical reasons, the mobilities were normalized to the interval (0, 1].

where; mijis the mobility of GB segment between grains i and j, diand djare the mean grain diameters, and dmaxis the mean grain diameter of the largest grain in the microstructure at a particular time step [36,38].

The EBSD data of the AZ31 sample annealed at 350°C for 10s served as the input microstructure for the simulations with a total of 8300 grains. As shown in Fig. 10a, the number of grains undergoing grain growth dropped from 8300 to 4800 when the average grain size increased from～2.6 to ～5.4 μm. Grain growth was homogeneous and no abnormally growing grains were observed. Fig. 10b and c shows the calculated corresponding textures ((0002) pole figures) and related quantitative information regarding the maximum intensity and tilt angle of maximum peaks. The results show a slight strengthening of the texture accompanied by a decrease of the tilt angle of the maximum texture peak, which is consistent with the experimental observations.

Fig. 10. (a) Simulated grain growth microstructures and (b) their corresponding textures using the Level Set method. (c) Quantitative information of the simulated textures.

The difference in the topological aspects discussed above originated most likely from the recrystallization nucleation behavior of basal and off-basal grains. Recrystallization nucleation of basal grains seemed in fact to be delayed(Fig. 3d and Fig. S2), presumably due to their low stored energy during deformation. A heterogeneous deformation behavior of basal/off-basal grains would affect their recrystallization nucleation mechanisms and extend further into the topological aspects during their growth.

5.2. Impact of alloy chemistry on recrystallization

Ca has a low solid solubility in magnesium (0.12 at.%at room temperature, 0.49 at.% at 560°C) [50]. Hence, Ca addition is more likely to form second phases with Mg and other present alloying elements. In the Mg–Ca or Mg–Zn–Ca systems, Mg2Ca and Mg–Zn–Ca phases have been reported[51,52]. In the Mg–Al–Ca systems, the type of second phases incorporating calcium was found to be dependent on the content ratio of Ca/Al. It varies from Mg2Ca to (Mg, Al)2Ca and then to Al2Ca Laves phase by a decrease of the Ca/Al content from more than 1 to 0.4 and then to lower than 0.4,respectively [22,53–56].

As known from literature, in the early stages of nucleus growth, the driving pressure for recrystallization PRXis opposed by a retarding pressure PSE, stemming from the increase of the surface energy of the growing nucleus. For the AZX310 alloy, the net driving pressure (P = PRX– PSE) has an additional opposing Zener pressure, PZ, arising from the dispersion of particles in the microstructures of the annealed states. A lower net driving pressure (P = PRX– PSE– PZ)can be expected to affect the nucleation and the growth rates of recrystallizing grains in AZX310 vis-à-vis AZ31.Hence, this could modify the orientation relationships of the growth texture that is naturally dependent on the migration characteristics of high angle boundaries.

In order to analyze the recrystallization behavior in the two alloys, samples of AZ31 (annealed at 250°C for 10s)and AZX310 (annealed at 350°C for 10min) were selected as they had a similar recrystallized fraction and average grain size. Considering the described role of Zener pinning in retarding recrystallization it is rational that AZX310 required a higher temperature and a longer annealing time than AZ31 to display a similar microstructure. The selected samples were analyzed by EBSD using a GOS criterion to separate their sampled microstructures into recrystallized and unrecrystallized regions. This allowed evaluating the respective textures separately, as shown in Fig. 11a–d. In both cases, there is a clear and anticipated texture softening in the recrystallized fraction as opposed to the deformed one.Interestingly, however, the extent of this ‘desirable’ softening was notably larger in the AZX310 material. During further analysis to investigate the relative roles of nucleation and growth in determining the annealing texture, recrystallized grains in each material were divided into two datasets of‘small’ and ‘large’ grains based on the average grain size of the recrystallized fraction in the respective microstructures. This allowed direct correlation with the corresponding textures with respect to texture spread and sharpness.

Fig. 11. EBSD (0002) pole figures showing the microtextures of (a,c) deformed grains and (b,d) recrystallized grains of AZ31 annealed at 250°C for 10s and AZX310 annealed at 350°C for 10min. EBSD maps of recrystallized grains with (e,g) smaller size and (f,h) larger size.

For AZ31, the texture of the small grains (Fig. 11e) very much resembled the deformation texture (Fig. 11a) in terms of its off-basal split character and the peak position in the pole figure. This is explained by the fact that the orientations of the nuclei are simply limited to those orientations present in the deformed microstructure. The counterpart small grains texture of the AZX310 material (Fig. 11g) seemed to show a similar trend of being qualitatively similar to its ‘parent’deformation texture (Fig. 11c). However, careful examination of the scatter component in both textures indicates that the recrystallizing nuclei occupied a broader range of orientations surrounding the main hot spot component. This can be understood in terms of a high deformation heterogeneity in the AZX310 material that rendered a wide spread of orientations available to the recrystallization nuclei. Fig. 11f and h shows the large grains and their orientations. As already mentioned,basal oriented grains in AZ31 did not seem to receive a significant advantage during nucleus growth. By contrast, in AZX310, the ‘off-basal’ oriented nuclei seem to enjoy a size advantage over grains with basal orientations, giving them a lead with respect to the grain size. This was most likely due to the drag effects on the boundary mobility caused by the addition of Ca. Taking into account the relatively large number of particles found in the annealed structures of AZX310, it is reasonable to assume that deformed grains adjacent to particles will have several deformation zones of large misorientations. Potential nuclei would therefore have a wide range of orientations that could contribute to the overall weakening of the recrystallization texture.

5.3. Impact of alloy chemistry on grain growth

As discussed above, basal texture component was strengthened in AZ31 as basal grains took the advantage of grain growth due to topological aspects. Recrystallized nuclei in AZX310 exhibited large spread of orientations, which was benefit to texture modification. While the modified texture transited to basal texture when annealing at temperature above 450°C. It is reasonable to consider the difference of texture evolution at various temperatures was a result of distinguish grain growth kinetics of basal and off-basal grains. The growth advantage of basal grains returned in AZX310 when annealed at 525°C. This change should correlate to failure of Zener pinning or solute drag effect at high annealing temperature. Previous study [32] showed solute segregation was barely observed in the AZX310 alloy. Hence,Zener pinning effect might be a reason for the restriction of grain growth at relatively low annealing temperature.

Fig. 12. Data of grain growth kinetics for AZX310 annealed at three temperatures and a comparison with growth kinetics of AZ31 at 350°C.

Fig. 12 presents a plot of the average grain diameter as a function of the annealing time for AZX310 Mg alloys obtained at three temperatures between 250°C and 450°C.For comparison purposes, respective data for AZ31 annealed at 350°C is also provided. The plot shows that the kinetics of the AZX310 annealed samples did not follow a typical parabolic growth law, as it was the case for AZ31. At 350°C, for example, the first 60s of annealing caused a rapid increase of the grain size up to ～6 μm, which could be attributed to recrystallization considering its much larger driving pressure.It should be emphasized the driving pressure for recrystallized nucleus growth (PRX) was dependent on store energy or dislocation density. This pressure is usually much larger than the driving pressure for grain growth(Pg) at the beginning of recrystallized nucleation. The rapid increase of grain size at the first 60s in AZX310 (Fig. 12)mostly attributed to nucleation growth with high store energy. After that, the average grain size of the AZX310 was almost unchanged due to stagnation of grain growth. This stagnation could be ascribed to either a pinning effect or a solute drag effect. At 450°C, it seemed to allow an increase in the average grain size after 600s indicating that the stagnation effects were weakened or overcome by elevating temperature.

As discussed before, the type of annealing texture in AZX310 was strongly dependent on the annealing temperature, revealing a double peak characteristic up to 350°C vs. single peak at 450°C and 525°C (Fig. 4). Since this behavior is not observed in the other alloy AZ31 it is most likely attributed to the particles discussed in 5.2 with respect to recrystallization. Because the driving pressure for grain growth is essentially very low (～0.01MPa), dispersed particles within a microstructure can produce a strong Zener pinning effect on grain boundaries. This effect would have a strong impact on the kinetics of grain growth and the resultant texture and grain size, but it will also primarily depend on the particle size, shape, spacing and volume fraction. For random distribution of spherical particles with radius r and volume fraction Fv, the drag pressure exerted on unit area of the boundary is given by

From this equation it is clear that for very fine particles and a sufficiently large volume fraction the pinning pressure will be maximized. Fig. 13 presents bright field TEM micrographs of AZX310 sample annealed at 350°C for 10min. High density of nano-sized particles can be observed within the matrix of two adjacent grains, as well as the grain boundary area (Fig. 13a). Examples of particle-boundary interaction are evident in Fig. 13b and c.

Based upon the shape and size of these particles, we can distinguish two types: rod-like and ellipsoidal particles with a size range of 50nm–150nm, spherical particles of a significantly finer size range of 10nm–20nm. TEM coupled EDS analysis of several particles showed that they were generally enriched with Al, Ca and Mn in comparison to the bulk composition. The smaller particles seemed to contain less Ca as opposed to the larger ones. From thermodynamic calculations, the current AZX alloy can be expected to form Al8Mn5and Al2Ca precipitates, which reduces the amount of Al that can react with Ca to form the Al2Ca phase. Consequently, this will increase the amount of Ca solutes in the bulk and could have important implications for Ca segregation to grain boundaries, which would cause an additional boundary drag effect (solute drag). The net driving pressure of grain growth under Zener drag is given by:

c is a microstructural parameter incorporating the grain size and the size and volume fraction of pinning particles. Obviously, if the particles are thermally stable during grain growth, the latter will take place when c is positive.As increase of grain size, the driving pressure of grain growth would decrease. Subsequently, when c becomes zero(Pg=Pz)grain growth was prohibited, and a particle limiting grain size (DZ= 4r/3Fv) is then reached [57].

To estimate the magnitude of Zener drag pressure and limiting grain size exerted by the nano-sized particles in the AZX310 alloy, several TEM images were examined along different zone axes. The collected data of average particle size, area (assuming spherical particles) and area fraction is presented in Table 4 along with calculated values of the degree of dispersion Fv/r, and Dz. For simplicity, the average of the area fraction of particles was assumed to be equal to their volume fraction, and the mean grain radius was taken to equal the mean radius of boundary curvature. α was set to 1.

Fig. 13. TEM bright field image of the AZX310 alloy annealed at 350°C for 10s for (a) phase identification and (b-c) pinning effect on the movement of grain boundaries.

Table 4 Statistical results of nano-sized particles analyzed in four different regions of the 350°C / 600s annealed AZX310 sample, along with calculated results of Zener drag pressure.

If we consider a recrystallized spherical grain size of 0.5 μm,the driving pressure for grain growth will be of the order of 2MPa (for γ = 1J/m2). By comparison with Table 4,the opposing drag pressure of particles lies theoretically within the same order of magnitude. This indicates that in theory, and under the assumed circumstances, the nano-sized particles in the AZX310 material should have prevented grain growth above the limiting grain size of 0.5–0.7 μm.This is not in agreement with the experimental ～6 μm average grain size obtained at 350°C. This can be due to an overestimated volume fraction of particles, and also the fact that the stagnation of grain growth is strongly dependent on the thermal stability of the particle dispersion at the chosen annealing temperature. At elevated temperatures, dissolution of particles can reduce or entirely remove the retarding pressure and promote grain growth with its characteristic grain size distribution and texture formation.

6. Summary and conclusions

The contribution of recrystallization and grain growth to the texture evolution in AZ31 alloy and a Ca-modified version AZ31+0.5wt.% Ca (AZX310) alloy was investigated utilizing a one-step and multi-step annealing process. The following key conclusions were drawn:

1) Ca addition to AZ31 triggered a considerable texture weakening by static recrystallization, which is temperature dependent. The recrystallization texture was characterized by a weak double peak component with large basal pole tilt towards the RD. The obtained favorable weak texture was thermally stable during grain growth annealing below 450°C but was lost upon annealing at higher temperatures.

2) The reference AZ31 alloy depicted texture weakening only during recrystallization.Grain growth of recrystallized grains resulted in a distinct sheet texture transition from a double-peak to a single peak basal texture. The intensity of this component increased with increasing grain size during grain growth annealing.The observed texture transition was ascribed to favorable growth conditions of grains within the basal component due to topological aspects.

3) Recrystallization was retarded by the addition of Ca to the AZ31. This was most likely due to the pinning effects on the boundary mobility. High density of nano-sized particles acted as strong barriers for grain boundary migration in AZX310, which strongly limited grain growth during annealing under 450°C. This prevented the formation of a strong basal texture during annealing. Due to partial dissolution of particles at annealing temperatures exceeding 450°C, the weak, double split texture in AZX310 was eliminated upon annealing at 525°C.

Declaration of Competing Interest

None.

Acknowledgments

F. Guo and R.S. Pei are grateful for financial support from the Chinese Scholarship Council (CSC). F. Guo also thanks for the support of Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201801114) and Scientific Research Foundation of Chongqing University of Technology (2017ZD35). L.Y.Jiang is sponsored by Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2018jcyjAX0107)and China Postdoctoral Science Foundation (2018M643407).

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jma.2019.07.010.