*Article* **Microstructures and Mechanical Properties of Precipitation-Hardenable Magnesium–Silver– Calcium Alloy Sheets**

#### **Mingzhe Bian \*, Xinsheng Huang and Yasumasa Chino**

Multi-Material Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Nagoya, Aichi 463-8560, Japan; huang-xs@aist.go.jp (X.H.); y-chino@aist.go.jp (Y.C.)

**\*** Correspondence: mingzhe.bian@aist.go.jp

Received: 17 November 2020; Accepted: 2 December 2020; Published: 4 December 2020

**Abstract:** Precipitation hardening provides one of the most common strengthening mechanisms for magnesium (Mg) alloys. Here, we report a new precipitation-hardenable Mg sheet alloy based on the magnesium–silver–calcium system. In a solution treated condition (T4), the strength of Mg–xAg–0.1Ca alloys is enhanced with increasing the Ag content from 1.5 wt.% to 12 wt.%. The Mg–12Ag–0.1Ca (wt.%) alloy sheet shows moderate tensile yield strengths of 193 MPa, 130 MPa, 117 MPa along the rolling direction (RD), 45◦ and transverse direction (TD) in the T4-treated condition. Subsequent artificial aging at 170 ◦C for 336 h (T6) increases the tensile yield strengths to 236 MPa, 163 MPa and 143 MPa along the RD, 45◦ and TD, respectively. This improvement in the tensile yield strength by the T6 treatment can be ascribed to the formation of AgMg4 precipitates lying on the {1120}<sup>ş</sup> and pyramidal planes. Our finding is expected to stimulate the development of precipitation-hardenable Mg–Ag-based wrought alloys with high strength.

**Keywords:** magnesium alloys; rolling; strength; segregation; precipitate

#### **1. Introduction**

The lightest structural metal magnesium (Mg) and its alloys have attracted significant interest in the past two decades due to their potential applications in the automotive sector [1–3]. However, current applications of wrought Mg alloys as a structural component are very limited, which can be ascribed to their inferior mechanical properties at room temperature (RT) and poor corrosion resistance [4]. Precipitation-hardening, also known as age-hardening, is one of the most effective ways to strengthen Mg alloys [5,6]. For example, an extraordinary high tensile yield strength of 473 MPa was obtained in a heavy rare-earth (RE) containing Mg–10Gd–5.7Y–1.6Zn–0.7Zr (wt.%) alloy processed by a conventional extrusion process followed by 200 ◦C aging for 64 h [7]. A RE-free Mg–6.2Zn–0.4Ag–0.2Ca–0.4Zr (wt.%) alloy subjected to twin-roll cast (TRC), hot-rolling and artificial aging at 160 ◦C for 24 h also yielded a high tensile yield strength of 316 MPa with a large fracture elongation of 17% [8]. Recent studies reported that Mg–Al–Ca–Mn(–Zn) dilute alloys could reach their peak hardness condition at 200 ◦C within 1 h that is significantly shorter than the time to reach the peak-hardness conditions of concentrated Mg–Gd, Mg–Zn and Mg–Sn based alloys [9–11]. Microstructure characterization by transmission electron microscopy (TEM), in conjunction with atom probe tomography, revealed that mono-atomic layer Guinier–Preston (G.P.) zones lying on the (0002) basal plane are formed in the peak-aged samples, and their dense distribution is responsible for the strength improvement in Mg–Al–Ca–Mn(–Zn) alloy sheets [12]. A more recent study demonstrated that bake-hardenability is even obtainable after 170 ◦C aging for only 20 min in a TRC Mg–1.3Al–0.8Zn–0.7Mn–0.5Ca (wt.%) alloy sheet, which opened up a possibility to develop bake-hardenable Mg alloys [13]. Those studies suggest that the development of precipitation-hardenable alloys is a promising approach to strengthen wrought Mg alloys.

In a recent study, we found that the co-addition of Ag (1.5 wt.%) and Ca (0.1 wt.%) to pure Mg could significantly enhance the stretch formability compared to the single addition of Ag or Ca [14]. A subsequent study achieved a high tensile yield strength of 182 MPa along the rolling direction (RD) by increasing the Ag content to 6 wt.%, while keeping a high index Erichsen value of 8.7 mm [15]. In a more recent study, we found that a compositionally optimized Mg–1.5Ag–2Ca (wt.%) alloy is non-flammable up to 1000 ◦C due to the formation of compact and dense CaO film on the surface. [16]. If precipitation-hardenability can be obtained by artificial aging, the Mg–Ag–Ca system is expected to attract more attention. Based on the binary Mg–Ag phase diagram, the maximum solid solubility of Ag is about 15 wt% in Mg at 472 ◦C, and it decreases to about 0 wt.% at 200 ◦C [17]. As shown in Figure 1, the equilibrium mole fraction of AgMg4 phase is about 0.19 at 200 ◦C for the binary Mg–15Ag (wt.%) alloy, indicating there is a high possibility to obtain precipitation-hardenability from the Mg–Ag system. In fact, the Ag addition was reported to enhance the age-hardening response and thus increase mechanical properties of Mg–Nd alloys more than 50 years ago, which has facilitated the development of a commercial casting alloy QE22 (Mg–2.5Ag–2Nd–0.7Zr in wt.%) [18]. Subsequent studies showed that the Ag addition is also very effective in improving the age-hardening response of Mg–6Gd–0.6Zr and Mg–6Y–1Zn–0.6Zr (all in wt.%) casting alloys [19,20]. TEM observations revealed that the remarkable improvement in age-hardening could be ascribed to a dense and uniform distribution of nano-scale basal precipitates. On the other hand, adding a trace amount of Ag (0.4 wt.%) to a binary Mg–6.2Zn alloy was reported to enhance the age hardening response significantly due to a substantial refinement of MgZn2 precipitates [21]. However, a closer look at those precipitation-hardenable Ag-containing alloys developed until now, we could find that Ag was mainly added to refine the size of precipitates formed in Mg–RE or Mg–Zn based alloys. To the authors' knowledge, there is no prior research on the development of precipitation-hardenable Mg–Ag based wrought alloys, which motivated us to explore the feasibility of developing precipitation-hardenable alloy based on the Mg–Ag–Ca system.

**Figure 1.** Calculated equilibrium mole fraction of phases as a function of temperature for a binary Mg–15Ag (wt.%) alloy using the PANDAT software.

In this study, Mg–xAg–0.1Ca alloys with a composition range from 1.5 wt.% to 12 wt.% were prepared and their age-hardening response at 170 ◦C was evaluated. Tensile properties of Mg–1.5Ag–0.1Ca, Mg–6Ag–0.1Ca and Mg–12Ag–0.1Ca alloy sheets were evaluated at RT, and a systematic microstructure characterization was conducted to clarify the strengthening mechanism in precipitation-hardenable Mg–Ag–Ca alloys.

#### **2. Materials and Methods**

Mg–xwt.%Ag–0.1wt.%Ca (x = 1.5, 6 and 12) ingots were produced using pure Mg (>99.9%), pure Ag (>99.9%) and Mg–4.92 wt%Ca master alloy by an induction furnace (IR) under an Argon (Ar) atmosphere. The chemical composition of alloys used in the present study was analyzed by inductively coupled plasma-optical emission spectroscopy (ICP-OES), and the analyzed results were given in Table 1. The as-cast alloys were initially extruded as sheets of 5 mm in thickness at 380 ◦C. The extrusion ratio and the ram speed were 6 and 5 mm/min, respectively. The extruded sheets were homogenized at 400 ◦C for 18 h to avoid hot-cracking during rolling, particularly the concentrated Mg–12Ag–0.1Ca alloy. The homogenized sheets were rolled from 5 mm to 1 mm in thickness with ~ 21% thickness reduction per pass by 7 passes. After each pass, the rolled sheets were immediately quenched into cold water. The water quenched sheets were then re-heated to 350 ◦C prior to subsequent rolling, and rollers were heated to 90 ◦C during rolling. The rolled sheets were solution-treated at 450 ◦C for 1 h (T4) and then quenched into cold water. Some of them were subsequently aged in a silicone oil bath at 170 ◦C.


**Table 1.** Chemical composition of Mg–xAg–0.1Ca (x = 1.5, 6 and 12) alloys analyzed by ICP-OES.

Dog-bone shaped tensile samples having a parallel length of 12 mm, a width of 4 mm and a thickness of 1 mm were machined from the T4-treated sheets along the RD (0◦), 45◦ and TD (90◦). Figure 2 shows a schematic drawing of tensile test samples used in the present study. A screw driven Instron 5565 tensile testing machine was used to evaluate RT tensile properties with a constant testing speed of 2 mm/min. The age hardening response was evaluated by a HM-200 micro Vickers hardness tester (Mitutoyo Corporation, Kawasaki, Japan) under a load of 200 g with a holing time of 10 s. Ten points were measured in each condition. The maximum and minimum hardness values were removed, and the remaining 8-point values were averaged. X-ray diffraction (XRD) patterns were obtained from the mid-layers of sheets using Rigaku RINT Ultima III operating at 40 kV and 40 mA (Rigaku Corporation, Akishima, Japan). Samples for secondary scanning electron microscope (SEM) and electron backscatter diffraction (EBSD) observations were prepared using silicon carbide (SiC) papers, 60 nm alumina suspension, and Ar ion beam using an ELIONIX EIS-200ER ion beam shower system (ELIONIX Inc., Hachioji, Japan). SEM observation was performed at 15 kV using a JEOL JSM-IT500 equipped with a JEOL EX-74600U4L2Q EDS detector (JEOL Ltd., Akishima, Japan). EBSD measurements were performed at 20 kV using the same SEM equipped with TSL OIM 7.0 data collection software (EDAX Inc., Mahwah, NJ, USA). Samples for TEM observation were mechanically ground to about 150 μm in thickness using SiC papers (500, 1000, 2400, and 4000 grit) and subsequently punched to disks of 3 mm in diameter. The disks were twin-jet electropolished at about −50 ◦C with a solution of 15.9 g lithium chloride, 33.6 g magnesium perchlorate, 1500 mL methanol and 300 mL 2-butoxy-ethanol, and finally ion-milled using a Gatan Precision Ion Polishing System (PIPS) (Gatan Inc., Pleasanton, CA, USA). TEM observations were carried out on JEM-2010 and Cs-corrected JEM-ARM200F TEMs operating at 200 kV (JEOL Ltd., Akishima, Japan). The thermodynamic simulation was carried out with the PANDAT software 2020 (CompuTherm LLC, Middleton, WI, USA) [22].

**Figure 2.** Schematic diagram showing the dimensions of tensile test sample used in this study.

#### **3. Results**

Figure 3 shows the age-hardening response of T4-treated Mg–xAg–0.1Ca alloy sheets (x = 1.5, 6 and 12) during isothermal aging at 170 ◦C. The 1.5Ag containing alloy sheet shows a low Vickers hardness value of 41.4 HV in the initial condition (T4), and it exhibits a negligible age-hardening. Increasing the Ag content not only leads to a higher hardness value in the T4-treated condition but also enhances the age-hardening response during aging. The 6Ag containing alloy sheet and the 12Ag containing alloy sheet show hardness values of 51.1 HV and 67.0 HV, respectively. After aging for 336 h, the hardness value of the former is increased to 57.4 HV, and that of the latter is increased to 80.0 HV. Table 2 summarizes initial hardness, peak-hardness, time to reach peak hardness and hardness increment of Mg–xAg–0.1Ca alloy sheets.

**Figure 3.** Age-hardening response of 1.5Ag, 6Ag and 12Ag containing alloy sheets at 170 ◦C.

**Table 2.** Initial hardness (T4 condition), peak-hardness, time to reach peak hardness and hardness increment of 1.5Ag, 6Ag and 12Ag containing alloy sheets.


Figure 4 shows tensile properties of the T4- and T6-treated 6Ag and 12Ag containing alloy sheets at RT. For the purpose of comparison, tensile curves obtained from the T4-treated 1.5Ag containing alloy sheet are given as Figure 4a. The tensile yield strength (TYS) of the T4-treated 1.5Ag containing alloy sheet is measured to be only 85 MPa, 57 MPa and 47 MPa along the RD, 45◦ and TD, respectively. Increasing the Ag content to 6 wt.% increases the TYS to 112 MPa, 70 MPa and 61 MPa along the RD, 45◦ and TD, Figure 4b. When the Ag content is further increased to 12 wt.%, the TYS is significantly increased to 193 MPa, 130 MPa and 117 MPa, Figure 4c. Subsequent artificial aging (T6) at 170 ◦C for 336 h further increases the TYS of 12Ag containing alloy sheet to 236 MPa, 163 MPa and 143 MPa along the RD, 45◦ and TD, respectively. The uniform elongation (UE) and fracture elongation (FE) of T4-treated 6Ag and 12Ag containing alloy sheets are all higher than 20%. However, both UE and FE are substantially reduced to about 10% after the T6 treatment. The tensile properties of 1.5Ag, 6Ag and 12Ag containing alloy sheets such as TYS, ultimate tensile strength (UTS), UE and FE are summarized in Table 3.

**Figure 4.** Tensile curves obtained from (**a**) T4-treated Mg–1.5Ag–0.1Ca alloy sheet, and T4- and T6-treated (**b**) Mg–6Ag–0.1Ca and (**c**) Mg–12Ag–0.1Ca alloy sheets along RD, 45◦ and TD at RT.

Figure 5 show EBSD inverse pole figure (IPF) maps and corresponding (0002) and (1010) PFs obtained from the T4-treated 1.5Ag, 6Ag and 12Ag containing alloy sheets. The 1.5Ag containing alloy sheet shows a coarse-grained microstructure of ~277 μm, and abnormal grain growth occurs. Increasing the Ag content to 6 wt.% refines the microstructure and the average grain size is decreased by about one half (~124 μm). In addition, the microstructure homogeneity is enhanced. An increased addition of the Ag content to 12 wt.% causes further refinement in the microstructure. It is to be noted that a homogeneous microstructure consisting of equiaxed grains with an average grain size of ~74 μm is developed in the 12Ag containing alloy. All alloy sheets show a TD-split texture, in which the (0002) basal poles are tilted toward the TD.


**Table 3.** RT tensile properties of 1.5Ag, 6Ag and 12Ag containing alloy sheets stretched along the RD, 45◦ and TD.

**Figure 5.** EBSD inverse pole figure (IPF) maps and corresponding (0002) and (1010) PFs showing microstructures and textures of T4-treated (**a**) Mg–1.5Ag–0.1Ca, (**b**) Mg–6Ag–0.1Ca, and (**c**) Mg–12Ag–0.1Ca alloy sheets.

To understand the reasons why the grain size is decreased with increasing the Ag content, the microstructures of T4-treated samples were observed by SEM. As can be seen from Figure 6a,b, the microstructures of the 1.5Ag and 6Ag containing alloy sheets consist of only α-Mg, indicating that solute atoms are fully dissolved into the Mg matrix after annealing at 450 ◦C for 1 h. In contrast, the 12Ag containing alloy sheet contains coarse second phase particles that are located both within the grains and along the grain boundaries, Figure 6c. The backscattered electron (BSE) image and corresponding Ag and Ca EDS maps indicate that these particles are mainly enriched with Ag, Figure 6d–f. Point analysis on a particle (marked with a triangle in Figure 6d shows that an atomic ratio between Mg and Ag is close to 4, Figure 6g. Based on our previous study, these particles are believed to be AgMg4 phase [15]. The microstructure of the T4-treated Mg–12Ag–0.1Ca alloy sheet was further observed by TEM. Figure 7a shows the high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image, in which the contrast is proportional to the square of the atomic number [23,24]. The grain boundary is therefore believed to be enriched with Ag (Z = 47) and or Ca (Z = 20) (Mg, Z = 12) because the grain boundary looks much brighter than adjacent grains. The corresponding Ag and Ca EDS maps reveal that Ag and Ca are co-segregated along the grain boundary, Figure 7b,c.

**Figure 6.** Backscattered electron (BSE) images showing microstructures of T4-treated (**a**) Mg–1.5Ag– 0.1Ca, (**b**) Mg–6Ag–0.1Ca, and (**c**) Mg–12Ag–0.1Ca alloy sheets. (**d**) BSE image, and corresponding (**e**) Ag and (**f**) Ca elemental maps obtained from the Mg–12Ag–0.1Ca alloy sheet. (**g**) EDS spectrum obtained from a second phase particle (marked with a triangle) in (**d**).

**Figure 7.** (**a**) High-angle annular dark-field-STEM image and (**b**) Ag and (**c**) Ca elemental maps showing the co-segregation of Ag and Ca atoms along a grain boundary of T4-treated Mg–12Ag–0.1Ca alloy sheet.

To clarify the reasons for the enhanced TYS after aging, the microstructure of the T6-treated 12Ag containing alloy sheet was observed by TEM. Figure 8a,b show the bright field (BF) TEM images taken with the incident beam along the [0001]<sup>ş</sup> and [1010]<sup>ş</sup> zone axes, respectively. The dispersion of precipitates is homogeneous, and the morphologies of the precipitates seem to consist of rod and polygonal shapes. The rod-type precipitates with a length of 0.5–2.5 μm are on the {1120}<sup>ş</sup> plane and their growing direction is parallel to the <1010><sup>ş</sup> or [0001]<sup>ş</sup> directions. It is to be noted that some rod type precipitates lay on the pyramidal plane, as indicated by triangles in Figure 8b.

**Figure 8.** Bright field-TEM images showing the microstructure of T6-treated Mg–12Ag–0.1Ca alloy sheet along (**a**) [0001]<sup>ş</sup> zone axis and (**b**) [1010]<sup>ş</sup> zone axis.

Figure 9a shows the XRD pattern obtained from the T6-treated Mg–12Ag–0.1Ca alloy sheet. For the purpose of comparison, the XRD pattern obtained from the T4-treated sheet is given in Figure 9b. As can be seen that the T4-treated sample mainly consists of <sup>ş</sup>-Mg phase. After the T6-treatment, new peaks are clearly observable, and they are confirmed to be generated mainly by MgAg4 phase. Therefore, the improvement in the tensile yield strength is associated with the formation of AgMg4 precipitates by the T6 treatment.

**Figure 9.** (**a**) X-ray diffraction (XRD) pattern obtained from T6-treated 12Ag containing alloy sheet. For the purpose of comparison, XRD pattern obtained from T4-treated 12Ag containing alloy sheet is given in (**b**).

To know whether there is an orientation relationship (OR) between AgMg4 phase and <sup>ş</sup>-Mg matrix, further microstructure analysis was carried out on the T6-treated 12Ag containing alloy sheet. Figure 10a shows the HAADF-STEM image with the zone axis of [0001]ş, and Figure 10b shows the high resolution (HR) HAADF-STEM image that is enlarged from the rectangular region in Figure 10a. Figure 10c,d are the fast Fourier transform (FFT) patterns generated from the left-hand region and right-hand region of Figure 10b, respectively. Analysis of these patterns reveals that left-hand region is

the α-Mg matrix with the zone axis of [0001]<sup>ş</sup> and the right-hand region is the AgMg4 phase with the zone axis of [0001] AgMg4. By further analyzing the FFT patterns, the OR between the α-Mg matrix and AgMg4 is confirmed to be (0001)<sup>ş</sup> || (0001)AgMg4, [2110]<sup>ş</sup> || [1010]AgMg4.

**Figure 10.** (**a**) HAADF-STEM image recorded along the [0001]<sup>ş</sup> direction. (**b**) Enlargement of the marked region in (a). FFT patterns generated from (**c**) α-Mg matrix and (**d**) AgMg4 phase showing their orientation relationship.

#### **4. Discussion**

In the present study, we have successfully developed a new type of precipitation-hardenable Mg–Ag–Ca sheet alloys. In the T4-treated condition, the 1.5Ag containing alloy sheet shows a large average grain size of ~277 μm. In addition, abnormal grain growth occurs, as shown in Figure 5a. From our previous study, this alloy sheet subjected to 350 ◦C annealing for 1.5 h exhibits a homogeneous microstructure that consists of equiaxed grains with an average grain size of 20 μm [14], indicating abnormal grain growth is likely to occur at higher temperatures. In the case of the pure Mg and Mg alloy AZ31 (Mg–3Al–1Zn–0.3Mn in wt.%) [25,26], it seems that abnormal grain growth occurs at intermediate temperatures rather than higher temperatures, which is different from the trend observed in the present study. For example, abnormal grain growth occurs at an annealing temperature of 220 ◦C, while normal grain grow occurs at a higher temperature of 350 ◦C [25]. It was reported that recrystallized grains with the <1120> || RD orientation grow preferentially at the expense of deformed matrix grains close to the <1010> || RD orientation and neighboring recrystallized small grains, thereby evolving to abnormally large sizes in pure Mg and AZ31 alloy [27,28]. Figure 11 shows EBSD IPF maps and corresponding IPFs from abnormally coarse grains (>100 μm) and normal-size grains (≤100 μm) in the T4-treated 1.5Ag containing alloy sheet. As can be seen, the normal-size grains have mainly the <1120> || RD orientation while the abnormally coarse grains do not have such orientation. These results suggest that the mechanism responsible for abnormal grain growth in Mg–Ag–Ca alloys is likely to be different from that in pure Mg and AZ31 alloy. It is to be noted that a homogeneous microstructure is developed in the 12Ag containing alloy sheet, Figure 5c. Ag and Ca atoms are demonstrated to be enriched in grain boundaries of the T4-treated condition, as shown in Figure 7. It is believed that solute segregation to grain boundaries occurs in the 1.5Ag containing alloy as well. However, the degree of solute segregation should be much lower than that in the 12Ag containing alloy. It is thus hypothesized that the segregated solute atoms effectively reduce grain boundary mobility via solute drag effects, thereby leading to a homogeneous microstructure. This hypothesis is supported by the homogeneous microstructure developed in the 1.5Ag containing alloy sheet after 350 ◦C annealing for 1.5h. Based on

the PANDAT calculation, the solid solubility of Ag in Mg is substantially decreased from 10 wt.% to 1.42 wt.% with decreasing the temperature from 450 ◦C to 350 ◦C, as shown in Figure 12. Considering less Ag atoms will be dissolved into <sup>ş</sup>-Mg matrix and more Ag atoms segregate to grain boundaries at 350 ◦C, the degree of solute segregation is expected to be much stronger than that at 450 ◦C. As such grain boundaries are difficult to break away from the solute drag atmosphere and remain pinned in the 1.5Ag containing alloy after 350 ◦C annealing.

**Figure 11.** EBSD IPF maps and corresponding inverse pole figures showing textures of (**a**) abnormally coarse grains and (**b**) normal-size grains in the T4-treated Mg–1.5Ag–0.1Ca alloy sheet.

**Figure 12.** Calculated Mg-Ag phase diagram using the PANDAT software, in which the Ca content is fixed as 0.1 wt.%.

In the T4-treated condition, the TYS strength is substantially enhanced by increasing the Ag content from 1.5 wt.% to 12 wt.%. The 12Ag containing alloy sheet shows a homogeneous microstructure with an average grain size of ~74 μm. Thus, the increased TYS can be mainly ascribed to the refinement in the microstructure and solid solution strengthening effect. Nonetheless, the average grain size of the Mg–12Ag–0.1Ca alloy is still much coarser than the those developed in precipitation-hardenable Mg-Zn–Ca–Zr and Mg–Al–Ca–Mn(–Zn) alloys (<10 μm) [8,11,12,29]. This is because fine second phase particles that can effectively retard the growth of recrystallized grains are not present in the 12Ag containing alloy. Addition of small amounts of Al and Mn or Zn and Zr to in the Mg–12Ag–0.1Ca alloy might be promising to reduce the average grain size in the T4-condition by forming a densely distributed nano-scale Al8Mn5 or Zn2Zr3 particles [30,31]. On the other hand, all alloys exhibit a higher

TYS along the RD than along the TD due to the formation of the TD-split texture. Such a texture is beneficial for (0001)<1120> basal slip and {1012} tensile twin to accommodate the plastic deformation along the TD than the RD as their Schmid factor values are higher along the TD than the RD [32–36].

The TYS of the 12Ag containing alloy sheet is 193 MPa, 130 MPa and 117 MPa along the RD, 45◦ and TD, respectively. The T6 treatment further increases the TYS to 236 MPa, 163 MPa and 143 MPa. The strength enhancement by the T6-treatment is rather low compared to other alloys such as Mg–Gd [37], Mg–Zn [38] and Mg–Sn [39] based wrought alloys. Microstructure characterization reveals that non-basal AgMg4 precipitates are formed in the T6-treated sample and their coarse microstructure is the main reason for the inferior age hardenability. There are several ways to refine the size of precipitates by increasing the number density of nucleation sites in early stage of aging: (i) deformation prior to aging treatment [40,41]; (ii) double aging consist of low temperature aging followed by high temperature aging [42–44]; and (iii) addition of trace amounts of elements [21,45,46]. Further optimization of the alloy composition incorporated with the modification of thermomechanical process is therefore expected to improve the age-hardening response and accelerate aging kinetics of Mg-Ag-Ca alloys.

#### **5. Conclusions**

Precipitation-hardenable wrought Mg alloy has been successfully developed based on the Mg–Ag–Ca system. In a T4-treated condition, the TYS of Mg–1.5Ag–0.1Ca alloy sheet is only 85 MPa, 57 MPa and 47 MPa along the RD, 45◦ and TD, respectively. With increase in the Ag content to 12 wt.%, the TYS is increased to 193 MPa, 130 MPa and 117 MPa along the RD, 45◦ and TD, which can be mainly ascribed to a refined microstructure and solid solution strengthening effect. Artificial aging at 170 ◦C for 336 h (T6) further increases the TYS of Mg–12Ag–0.1Ca alloy sheet to 236 MPa, 163 MPa and 143 MPa along the RD, 45◦ and TD. AgMg4 precipitates lying on the {1120}<sup>ş</sup> and pyramidal planes are responsible for the strength improvement.

**Author Contributions:** Conceptualization, M.B.; methodology, M.B.; validation, X.H. and Y.C.; investigation, M.B. and X.H.; writing—original draft preparation, M.B.; writing—review and editing, X.H. and Y.C.; project administration, Y.C.; funding acquisition, M.B. and X.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by JSPS KAKENHI, grant numbers JP20K15067 and JP18K04787.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


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## *Article* **Interaction of Migrating Twin Boundaries with Obstacles in Magnesium**

**Andriy Ostapovets 1,\*, Konstantin Kushnir 1, Kristián Máthis <sup>2</sup> and Filip Šiška <sup>1</sup>**


**Abstract:** Interaction of migrating - 1012 twin boundary with obstacles was analyzed by atomistic and finite elements computer simulations of magnesium. Two types of obstacles were considered: one is a non-shearable obstacle and another one is the void inside bulk material. It is shown that both types of obstacles inhibit twin growth and increased stress is necessary to engulf the obstacle in both cases. However, the increase of critical resolved shear stress is higher for the passage of the twin boundary through raw of voids than for interaction with non-shearable obstacles.

**Keywords:** magnesium; twinning; modeling; void; rigid inclusion

#### **1. Introduction**

Magnesium and its alloys are prospective light-weight materials [1]. However, they have poor formability in comparison with aluminium alloys, which leads to limitation in the application of magnesium alloys in automotive and aerospace industries. The pure formability of magnesium is attributed to its hexagonal close packed structure, which does not provide a sufficient number of slip systems. Plastic deformation of magnesium is therefore characterized by significant anisotropy. Basal slip systems allow easy dislocation glide. However, non-basal slip systems are hard, and deformation twinning is often activated instead of non-basal slip [2,3]. Abundant twinning can lead to the formation of structure inhomogeneity during plastic deformation of these materials. Such inhomogeneity can be a serious restriction for engineering applications.

Magnesium formability can be improved by decreasing its plastic anisotropy, which can be overcome by either decreasing the critical resolved shear stresses (CRSS) for non-basal slip systems or by increasing the basal slip CRSS. The former can be reached by alloying of magnesium, for instance, with rare-earth elements such as Y or Gd [4–6]. These elements decrease stacking fault energies on non-basal crystallographic planes. The latter approach based on hardening of the basal slip can be achieved by introducing precipitates inside the alloy microstructure. These precipitates cause the effect called precipitation hardening of material [7,8] due to their interactions with dislocations. The study of dislocation interaction with obstacles has a long history. The nature of dislocation–precipitate interactions is well described by the Orowan mechanism [9]. In contrast, twin-precipitate interactions are more complex and less understood. This has attracted significant attention of material research at the present time [10–16]. For instance, the effect of precipitation on yield elongation in an extruded Mg–4.5 wt% Zn alloy was investigated in [10]. It was shown that precipitation led to the disappearance of the yield plateau on the stress-strain curve. Aging led to an increase in yield stress of about 60 MPa. Twins in the as-extruded sample were thicker and fewer in number than those in the aged sample. Applicability of the Orowan precipitate hardening equation to twin propagation was studied in [11] by two-dimensional dislocation dynamics simulations of a twin tip impinging upon a line of obstacles. It was

**Citation:** Ostapovets, A.; Kushnir, K.; Máthis, K.; Šiška, F. Interaction of Migrating Twin Boundaries with Obstacles in Magnesium. *Metals* **2021**, *11*, 154. https://doi.org/10.3390/ met11010154

Received: 25 November 2020 Accepted: 13 January 2021 Published: 15 January 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

shown that reasonable prediction of propagation stress can occur. However, this approach has limits, e.g., the twin boundary itself is not present in dislocation dynamics simulations. More precise consideration of the twin boundary-precipitate interaction is possible by atomistic simulations. It was demonstrated in [12] by molecular dynamics simulation that spherical precipitates have the strongest hardening effect on the twinning, while the rod-like precipitates have the weakest. Nonetheless, atomistic simulations are applicable, as a rule, to small volumes and high deformation rates only. Other approaches are also useful for analysis of twin-precipitate interactions, especially in the interplay with the dislocation slip. Recently, finite element method analysis allowed the conclusion that precipitates affect twin thickening by changing the slip CRSS values and acting as obstacles for twin propagation [13]. The value of pyramidal CRSS is the most critical one because the activity of the pyramidal slip significantly increases in the vicinity of the twin with an aspect ratio > 0.1. Visco-plastic self-consistent modeling was used to show that the twin systems are hardened more by the precipitation than by the basal planes [14].

Another possible type of obstacle for twin boundary migration is voids [15–17]. Nanoscale twinning is an energy dissipating mechanism for ductile fracture in fine-grained Mg alloys [15]. On the other hand, the void can be formed by particle cracking during deformation of fine-grained magnesium alloys [16]. Recently, interaction of an incoherent basal-prismatic twinning interface with the void was studied by atomistic simulations [17]. It was shown that the location of the void affects the start position of basal-prismatic boundary migration. The void serves as an obstacle during migration, and parts of the boundary are pinned by the void surface.

Suppressing of the twinning by twin interactions with obstacles can also be considered as a way to decrease plastic anisotropy and to improve the mechanical properties of the material.

The present study is focused on the numerical analysis of the interaction between the growing tensile twin and obstacles in magnesium. The study is based on a multiscale approach as the twin growth is simulated using an atomistic model while the overall stress state is evaluated using a finite element method.

#### **2. Model**

#### *2.1. Atomistic Simulations*

The atomistic simulations were performed by using LAMMPS (Sandia National Laboratories, Livermore, CA, USA, lammps.sandia.gov) [18] for simulations and OVITO (Darmstadt University of Technology, Darmstadt, Germany, www.ovito.org) [19] for visualization. The magnesium potential, published in Liu et al. [20], was used in the calculations. The scheme of the used simulation block is shown in Figure 1. The rectangular simulation blocks have their *x*-axis close to the [1011] crystal direction, *y*-axis along the [1210] direction, and *z*-axis close to normal to the (1012) plane. The *x* and *z* axes are inclined from corresponding directions by angle α. The blocks were prepared by the following procedure. The twin boundary was created inside the simulation block by the merging of crystals rotated by the misorientation angle ~86◦. Then, the lattice was rotated by the angle α. The value of α was selected to satisfy the continuity of each (1012) plane through periodic boundary conditions in the *x* direction. Each (1012) plane is continued into the (1012) plane separated by two interplanar distances from it. Due to periodicity, steps on the twin boundary were produced at the block edges. These steps are relaxed into twinning disconnections [21,22] during energy minimization of the block. Thereby, the studied configuration contains the twin boundary with disconnections periodically placed within it.

**Figure 1.** Scheme of the simulation block. The dashed line corresponds to the twin boundary. Shaded areas are periodic images of the central block. Twinning disconnections produce steps on the twin boundary due to periodic boundary conditions.

Two different distances between disconnections (23 nm or 45 nm) were used in our simulations, and different block sizes were used in order to study the influence of the disconnection density on the twin boundary behavior. All blocks have a size of 1.9 nm in the *y*-direction and 50 nm in the *z*-direction. However, the size in the *x*-direction was variable. The block sizes were selected as multiples of the above-mentioned distances between disconnections (23 nm or 45 nm). The larger blocks were produced by merging of several small blocks. Consequently, the larger block contained several disconnections inside and disconnection density was preserved.

The obstacle for twin boundary migration was also inserted into the simulation block. Two types of obstacles were considered. The first one is a void with a squared shape of its xz-section and with infinite size in the y-direction. The size of void was 2 × 2 nm in the xz plane. Another type of obstacle was obtained by freezing atoms inside the selected volume. The size of the obstacle was the same as the size of the void. Such obstacle can be considered a model of non-shearable inclusion. The distance between obstacles was equal to periodicity in the x-direction. The size of obstacle was selected to be small enough in comparison to the simulation block in order to leave space for twin boundary migration between obstacles.

Shear strain (εxz) was applied to the block in order to model the interaction of the migrating twin boundary with rigid inclusion. The strain was applied in small steps, Δεxz = 0.0005. Energy minimization by the conjugate gradient method was performed after each step. The stress value of the block was monitored after energy minimization.

#### *2.2. FE Model*

FEM analysis was used to analyze the stress distribution in the vicinity of the precipitate or cavity. These stresses can describe possible preferable locations of twin nucleation and also probable twin growth.

The FE model was made within the code Z-set (Mines ParisTech, Paris, France, www.zset-software.com) and its layout is provided in Figure 2. It is a 2D planar system that has a rectangular inclusion with an aspect ratio (width/length—*t*/*l*) 1/10 in the middle. The model represents an idealized case of an obstacle perpendicular to the (1012) extension twin plane which is inclined to the global *X*-axis. The loading and boundary conditions are applied as follows. The external tensile stress is applied in the X-direction on the vertical sides which represents tension in the crystallographic c-direction. The horizontal sides are kept straight and parallel. The length of each side is ten times the length (*l*) of the obstacle to avoid the influence of boundary conditions on the stresses in the obstacle vicinity. The analyzed stress is taken within the matrix along the normal axis of the inclusion (red line). The stress component that is analyzed is the shear stress along the 1012 plane.

**Figure 2.** The FE model geometry, with loading conditions and location for stress analysis (red line). The size of the obstacle is not to scale.

A matrix is simulated as anisotropic elastic material with elastic constants of magnesium [23] which are summarized in Table 1. The purely elastic behavior is used to model the situation where twinning is the first inelastic deformation mode occurring prior to slip. The precipitate is isotropic elastic with Young's modulus *E* = 80 GPa and Poisson's ratio 0.35, which are the typical values used for magnesium alloys [24]. The void is simulated by a material with a very low Young's modulus, *E* = 0.008 GPa. Such an approximation was chosen to keep the FE mesh identical in both cases. The "void" elastic constants are four orders of magnitude smaller than the matrix ones which makes it a valid approximation of empty space.


**Table 1.** Elastic constants of Magnesium.

#### **3. Results**

#### *3.1. Atomistic Simulations*

Figure 3 shows strain-stress curves for the migration of the twin boundary in the block without obstacles and for the interaction of the twin boundary with the void. The stress provided in Figure 3 is total shear stress (σxz) in the simulation block. It can be seen that the presence of the obstacle potentially inhibits twin growth. The blue curve shows continuous growth of the stress up to a value of 190 MPa. The movement of disconnections begins at this stress level. Then, the twin boundary begins to migrate continuously under practically constant stress. It is worth noting that calculations are done at 0K and no temperature effect is considered. This is the reason why the observed stress is high.

**Figure 3.** Strain-stress curves for the case of twin boundary migration in the block without the obstacle (blue line) and in the block containing the void (red line).

The stress increases to much higher values than 190 MPa if the void is present (red curve in Figure 3). The disconnections also begin to move at values close to 200 MPa (point B) in this case (Figure 4B). However, the presence of the obstacle leads to a further increase in the stress with the decreasing distance between the twin boundary and the cavity. After reaching the void, the twin boundary stays blocked on it (Figure 4C). The existing twinning disconnections are absorbed by the cavity surface at this moment. New disconnections begin to nucleate at the stress level 550 MPa (point C). They are also absorbed in the cavity surfaces. The twin boundary moves along the cavity during this process. It reaches the upper surface of the cavity at point D, which corresponds to the stress level 830 MPa (Figure 4D). Then, the boundary continues its migration but its stays anchored at the void. The boundary is connected to the void by segments of basal-prismatic interfaces (Figure 4E). These facets grow by 'pile-up' of disconnections gliding on parallel planes, similar to the case described in [25]. The point E in the stress-strain curve corresponds to the moment when basal-prismatic interfaces begin to move by nucleation of disconnection dipoles on them. This process is analogous to the process described in [22]. It happens at a considerably high stress level of 1030 MPa. A sharp decrease in the stress takes place in this moment. However, the stress does not relax completely and subsequent boundary migration takes place at the stress level of about 790 MPa. It is due to stress accumulated inside the twin, which cannot be immediately relaxed by migration of the existing twin boundary. The basal-prismatic interfaces coalesce and the twin boundary is straightened again (Figure 4F).

**Figure 4.** Interaction of the migrating twin boundary with the void: (**A**) initial configuration; (**B**) migration of the preexisting disconnection along the boundary. The disconnection is marked by a black circle; (**C**) the boundary is blocked in the void; (**D**) nucleation of disconnection dipoles in the boundary and subsequent absorption of disconnections by the void surface; The dipoles are marked by ellipses. The red ellipse marks the already developed dipole and the black ellipse marks the location of dipole nucleation in progress. (**E**) formation and migration of basal-prismatic interfaces. Disconnection on the basal-prismatic interface is marked by a circle; (**F**) detachment of the boundary from the void with the formation of two basal stacking faults. The projection of the figure is in the [1210] direction. The atoms in the boundary are colored in white and atoms in stacking faults are colored in green.

Figure 4E,F show configurations with migrating basal-prismatic facets and after their coalescence. The green atoms indicate neighboring, which corresponds to the fcc structure. Consequently, two basal stacking faults are nucleated during detachment of the boundary from the obstacle. These stacking faults are trailed by the migrating boundary and grow together with the twin.

Dependences of the critical shear stress, which is necessary to push the boundary through the row of obstacles on the density of the obstacle (i.e., block size in the *x* direction), are shown in Figure 5. This stress corresponds to the moment when basal-prismatic interfaces begin to move (such as at point E in Figure 3). It can be seen that this stress is dependent on the type of obstacle as well as on the initial density of disconnections. It is interesting that voids serve as a stronger barrier for twin boundary migration than non-shearable obstacles.

**Figure 5.** Dependence of critical stresses on the distance (period) between obstacles for different densities disconnections and kinds of obstacle (cavity or non-sheared obstacles).

#### *3.2. FE Model*

The relative shear stress distribution in the twin direction in the vicinity of the obstacle (along the red line in Figure 2) is shown in Figure 6. The stress is normalized by the applied external stress (*τapp*), and the distance (*L*) from the precipitate/void is normalized by its thickness (*t*). It is clear that the precipitate causes a slight increase in the applied stress in its close vicinity and the stress linearly decreases to the distant applied stress level. The presence of the void shows a different picture. The shear stress is zero at the boundary due to the void's free surface. The stress increases with the distance from the void's surface. It reaches the value for the precipitate at the distance of 2.5 of the void's thickness and further increases to values of 1.3 of the applied stress.

**Figure 6.** Stress distribution inside the matrix in the direction of the precipitate/void normal axis. Shear stress is normalized by externally applied stress *τapp* and distance *L* is normalized by precipitate/void thickness *t*.

#### **4. Discussion**

The stress level obtained from atomistic simulations in this study is quite high in comparison to the experimental CRSS of the twin. It is caused by the fact that existing interatomic potentials were not fitted primarily for these values. However, it is possible to expect that qualitative trends as well as atomistic mechanisms predicted by the model are correct. On the other hand, it worth noting that the experimental increase in the yield stress for the aged AZ91 alloy is at the level of about 100 MPa [26], i.e., they are comparable with our values in order of magnitude. This increase is partially caused by twin interactions with precipitates.

Our simulation revealed that the void is a stronger barrier for twin boundary migration than non-shearable obstacles. Recently, the interaction of the basal-prismatic twin boundary with the void was studied by computer simulations by Xu et al. [17]. It was demonstrated in [17] that boundary migration is hindered by the void. In contrast to our simulation, the boundary was not completely pushed through the void. However, the presence of the void led to a decrease in yield stress in comparison to boundary migration with the absence of the void. This trend is opposite to our observations shown in Figure 3, where the presence of the void led to a slight increase in yield stress. This situation is probably caused by the difference in the initial boundary configuration. In the present paper, we studied the migration of the coherent (1012) twin boundary, which already contained disconnections and was already ready to migrate. The elastic field of the void slowed down the motion of the pre-existing disconnections. However, yielding takes place by nucleation of new boundary defects and subsequent detachment of basal-prismatic segments from raw immobile misfit dislocation [17]. The stress field around the void helps in the nucleation of such defects in the basal-prismatic boundary as claimed by the authors of [17].

The FE model results correspond with the atomistic simulations. The shear stress decrease in the vicinity of the void's surface implies that higher applied stress is needed to move the twinning boundary. Atomistic simulations show about a fivefold increase in the applied stress for initiation of boundary motion near the void (see Figure 3). Similarly, the estimated local shear stress is about fivefold lower in the close vicinity of the void's surface in the FE model (approximately 0.25*t*), which suggests the necessity of an increase in the applied stress for twin initiation. In general, the void can be seen as a limiting case of a very soft precipitate, so the presented simulation shows the effect of precipitate stiffness on the local stress distribution. Soft precipitates inhibit twin boundary motion in their vicinity and increase the probability of twin initiation between precipitates due to the stress increase at this location.

#### **5. Conclusions**

Basal-prismatic facets can be formed by the glide of disconnections on parallel - 1012 planes. The mechanism of their formation agrees with the existing models of twinning such as the theory of admissible interfacial defects. The basal-prismatic facet on the straight twin boundary is equivalent to a wall of twinning disconnections.

The interaction of twin boundaries with obstacles is governed by the mobility of disconnections and basal-prismatic interfaces.

The increase in critical resolved shear stress is higher for the interaction of the twin boundary with cavities than for the interaction with non-shearable obstacles.

Stacking faults can be formed by twin–twin interactions. These stacking faults can be recognized as partial stacking faults reported previously in the literature.

The continuum theory also predicts inhibition of twin boundary movement due to the significant decrease in the shear stress void's surface.

**Author Contributions:** Conceptualization, A.O. and K.M.; investigation, A.O., K.K., F.Š.; writing original draft preparation, A.O. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by CZECH SCIENCE FOUNDATION, grant number 18-07140S, and by the MINISTRY OF EDUCATION, YOUTH AND SPORTS OF THE CZECH REPUBLIC, grant number CEITEC 2020 (LQ1601).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available on request due to restrictions. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to authors' employer restrictions.

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

#### **References**


## *Article* **Texture Selection Mechanisms during Recrystallization and Grain Growth of a Magnesium-Erbium-Zinc Alloy**

**Fatim-Zahra Mouhib \*, Fengyang Sheng, Ramandeep Mandia, Risheng Pei, Sandra Korte-Kerzel and Talal Al-Samman**

> Institute for Physical Metallurgy and Materials Physics, RWTH Aachen, 52056 Aachen, Germany; fengyang.sheng@rwth-aachen.de (F.S.); rmandia@asu.edu (R.M.); pei@imm.rwth-aachen.de (R.P.); korte-kerzel@imm.rwth-aachen.de (S.K.-K.); alsamman@imm.rwth-aachen.de (T.A.-S.) **\*** Correspondence: mouhib@imm.rwth-aachen.de

**Abstract:** Binary and ternary Mg-1%Er/Mg-1%Er-1%Zn alloys were rolled and subsequently subjected to various heat treatments to study texture selection during recrystallization and following grain growth. The results revealed favorable texture alterations in both alloys and the formation of a unique ±40◦ transvers direction (TD) recrystallization texture in the ternary alloy. While the binary alloy underwent a continuous alteration of its texture and grain size throughout recrystallization and grain growth, the ternary alloy showed a rapid rolling (RD) to transvers direction (TD) texture transition occurring during early stages of recrystallization. Targeted electron back scatter diffraction (EBSD) analysis of the recrystallized fraction unraveled a selective growth behavior of recrystallization nuclei with TD tilted orientations that is likely attributed to solute drag effect on the mobility of specific grain boundaries. Mg-1%Er-1%Zn additionally exhibited a stunning microstructural stability during grain growth annealing. This was attributed to a fine dispersion of dense nanosized particles in the matrix that impeded grain growth by Zener drag. The mechanical properties of both alloys were determined by uniaxial tensile tests combined with EBSD assisted slip trace analysis at 5% tensile strain to investigate non-basal slip behavior. Owing to synergic alloying effects on solid solution strengthening and slip activation, as well as precipitation hardening, the ternary Mg-1%Er-1%Zn alloy demonstrated a remarkable enhancement in the yield strength, strain hardening capability, and failure ductility, compared with the Mg-1%Er alloy.

**Keywords:** magnesium-rare earth alloy; recrystallization; selective grain growth; texture

#### **1. Introduction**

As of late, there is an increasing trend for using magnesium alloys in the automotive and aerospace industries owing to their excellent specific strength properties and lightweighting potential. However, a broad technical application of wrought magnesium alloy products still struggles with the difficulty to form at temperatures below 150 ◦C caused by the formation of a sharp basal texture and limited activation of deformation modes outside of the basal plane [1,2]. Great research efforts have been explored to not only alter the sharp sheet texture but also to control its strength and evolution [2–4]. Magnesium rare earth (RE) alloys have proven very useful in enhancing the cold formability and the work hardening capability of conventional magnesium alloys. This has been attributed to the development of a unique sheet annealing texture characterized by an off-basal pole spread away from the normal direction of the sheet plane [4–7]. Numerous recrystallization and growth mechanisms were explored in an attempt to unravel the underlying mechanisms for the favorable texture development in magnesium rare earth alloys. These included particle stimulated nucleation, deformation twin nucleation, and shear band nucleation mechanisms, which are known to promote random orientations or off-basal orientations of recrystallization nuclei [8]. However, since these mechanisms can also occur in magnesium

**Citation:** Mouhib, F.-Z.; Sheng, F.; Mandia, R.; Pei, R.; Korte-Kerzel, S.; Al-Samman, T. Texture Selection Mechanisms during Recrystallization and Grain Growth of a Magnesium-Erbium-Zinc Alloy. *Metals* **2021**, *11*, 171. https:// doi.org/10.3390/met11010171

Received: 29 December 2020 Accepted: 15 January 2021 Published: 19 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

alloys containing no RE elements [9–11], the research on the origin of the specific texture selection in Mg-RE alloys is still ongoing.

Recent studies in that context looked into a connection between RE solutes and oriented nucleation/growth during recrystallization, given that specific RE-textures have been observed in dilute alloys in which the RE elements were mostly in solid solution. It was also shown that the addition of zinc to Mg-RE alloys has proven to further weaken the texture and augment its off-basal nature [12]. Hence, more studies are needed to investigate the interaction of multiple solute species, particularly ones with largely different atomic radii [12,13]. Additionally, it is essential to examine how different RE and non-RE soluteboundary interactions impact the growth selection during texture evolution in Mg-RE and Mg-RE-Zn alloys.

This study aims at understanding the formation of unique sheet textures and the ensuing selection mechanisms in Er-containing magnesium alloys with and without the presence of Zn. Reports on this alloy system with respect to deformation and recrystallization textures are scarce in the literature. It is therefore important to illustrate the great texture modification potential the present alloys have to offer. In particular, the formation of a double-peak split texture in the transverse direction, similar to what is common for hexagonal metals with c/a < 1.633, is a unique feature that is hardly seen in Mg alloys subjected to rolling and annealing treatments. The discussion addresses the texture development in both binary and ternary versions of the alloy during recrystallization and grain growth under the influence of solutes and second phase precipitates.

#### **2. Materials and Methods**

Binary and ternary Mg-1%Er-(1%Zn) (wt %) alloys were melted in an induction furnace under an Ar/CO2 gas atmosphere and subsequently casted and homogenized at 420 ◦C for 960 min. The resulting microstructure is shown in Figure 1. Table 1 shows the chemical composition measured by ICP/OES (IME RWTH University, Aachen, Germany). Sheets of the dimension 60 × 40 × 4 mm<sup>3</sup> were hot rolled at 400 ◦C with multiple rolling passes (eleven) and a final thickness reduction of 80%.

**Figure 1.** Micrographs of Mg-1%Er (**a**) and Mg-1%Er-1%Zn (**b**) after casting.

**Table 1.** Chemical composition in atomic and weight percentage of Mg-1%Er and Mg-1%Er-1%Zn.


Annealing treatments at 350 ◦C and 400 ◦C were conducted in a Heraeus RL200E air furnace (Heraeus Group, Hanau, Germany) for annealing times ranging from 5 to 1440 min and in a sand bath furnace for annealing times smaller than 5 min.

All samples were mechanically ground to the specimen mid-plane and polished with a diamond suspension up to 0.25 μm. For optical light microscopy (Leica microsystems, Wetzlar, Germany), the samples were electro-polished for 40 min in a 5:3 ethanol H3PO3 solution at 2 V and etched in an acetic picral solution. Grain size measurements from light microscopy images were performed by means of the linear intercept method. Texture measurements were conducted using a Bruker D8 advance diffractometer (Bruker, Billerica, MA, USA) operating at 30 V and 25 mA. Six incomplete pole figures [- 1010 , {0002}, - 1011 , - 1012 , - 1110 , - 1013 ] were measured, from which full pole figures and orientation distribution functions (ODFs) were calculated with the texture analysis toolbox MTEX (MTEX 5.3, Chemnitz, Germany) [14]. For selected samples intended for electron backscatter diffraction (EBSD) analysis under the electron beam an alternative electro-polishing procedure was employed using Lectro-Pol 5 in a Struers AC-2 solution at a voltage of 25 V and −20 ◦C for 120 s. Microstructure analysis via EBSD was performed using a LEO-1530 scanning electron microscope (Carl Zeiss Microscopy GmbH, Jena, Germany) operating at 20 kV, equipped with a HKL-Nordlys II EBSD detector. The detection step size varied according to the grain size in a range from 0.5 to 1.5 μm. EBSD and X-Ray diffraction (XRD) raw data were analyzed using the MTEX toolbox [14].

For the characterization of precipitates panorama back scatter electron (BSE)imaging (50 images per specimen) was conducted under a magnification of 10,000× with a focused ion beam Helios 600i (Thermo Fisher Scientific, Waltham, MA, USA) equipped with a field emission electron gun operating at 5 kV.

Recrystallization (RX) kinetics for both alloys were obtained by Vickers micro-hardness measurements (HMV, Shimadzu, Nakagyo-ku, Kyoto, Japan) (load of 1 N) of specimens ¯ subjected to interrupted annealing at 350 ◦C for durations up to 1000 s. For each annealing condition, 15 indentations were used to determine the average hardness *HVt* at time step *t*. The recrystallized fraction was calculated by the common Equation (1), where *HVinitial* and *HVfinal* denote the initial and final hardness values, respectively [15].

$$X = \frac{HV\_{initial} - HV\_t}{HV\_{initial} - HV\_{final}}\tag{1}$$

The mechanical properties were determined by uniaxial tensile tests at room temperature conducted along the rolling direction on fully recrystallized samples of both alloys. The tensile samples were carefully chosen to have a similar grain size in order to exclude grain size effects on the yield strength response of the material. Dog-bone-shaped samples with gauge dimensions of 5 × 1.5 × 0.8 mm3 were cut out of the rolling sheets and subsequently annealed at 400 ◦C for 15 and 60 min for the binary and ternary alloys, respectively. Tensile tests were conducted using a ZWICK tension-compression testing machine. Specimens were strained under a constant strain rate of 2 × 10−<sup>4</sup> to failure. Each tensile test was performed three times to ensure reproducibility and the average flow curve was considered for the analysis. In order to determine the operating slip systems during uniaxial tension, interrupted tensile tests were performed up to 5% strain on samples annealed at 400 ◦C for 60 min of both alloys. Subsequently, the slip systems were determined by comparison of slip lines from secondary electron (SE) images obtained at 20 kV and the grain orientations determined by EBSD of at least 120 grains each.

#### **3. Results**

#### *3.1. Microstructure Evolution*

Figure 2 shows the optical microstructures of rolled and annealed samples of the binary and ternary Mg-1%Er-(1%Zn) alloys. The annealing temperature was 400 ◦C and the annealing times were 15 and 360 min, respectively. The corresponding XRD textures, presented in terms of (0002) pole figures, as well as the evolution of the average grain size as a function of the annealing time are given in Figure 3. As it can be seen, both alloys exhibited a common deformation microstructure characterized by deformed grains and numerous deformation twins. The rolling texture of the binary alloy showed a typical basal

component with a pole spread towards the rolling direction (RD) and moderate intensity. On the other hand, the ternary alloy exhibited a weaker and much softer rolling texture characterized by two off-basal components at ±20◦ RD that bare a significant pole spread in the transverse direction TD.

**Figure 2.** Micrographs of Mg-1%Er and Mg-1%Er-1%Zn in the as-rolled state and upon annealing at 400 ◦C for 15 and 360 min. The images are taken from the rolling plane (mid-thickness).

**Figure 3.** Texture evolution of binary and ternary (**a**,**b**) Mg-1%Er-(1%Zn) in the as rolled state and after annealing at 400 ◦C for 15 and 360 min, as well as the corresponding evolution of the mean grain diameter over time (**c**).

During a subsequent heat treatment at 400 ◦C, the ternary alloy seemed to develop a fine-grained annealing microstructure with a stable grain size (14 μm) that was not liable to additional grain growth at increased annealing durations (Figure 2). The corresponding annealing texture witnessed a unique transition demonstrated by new off-basal components appearing at ±40◦ TD. This type of annealing texture after rolling is only common for hcp metals like titanium [16], that have a lower c/a ratio than the ideal ratio of 1.633 for close-packed structures, and can thus easily activate prismatic and pyramidal slip. As to the binary alloy, it exhibited an initially stable grain size (16 μm) up to an annealing time of 60 min but underwent significant grain growth (60 μm) after 360 min of annealing

(Figure 3c). The texture of the binary Mg-1%Er alloy during early annealing conserved the dominant pole split in RD seen in the deformation texture but was also significantly weakened as a result of recrystallization (5.6 MRD → 2.3 MRD). With prolonged annealing up to 360 min, the texture spread around the normal direction ND seemed to increase during grain growth and the basal component in the center of the pole figure has vanished.

Given the interesting nature of the texture transition seen upon annealing of the Mg-1%Zn-1%Er alloy, additional annealing experiments were carried out at a lower temperature of 350 ◦C. The annealing durations were kept short—i.e., up to 15 min—in order to capture the effect of early recrystallization stages on the texture transition. The results are shown in Figure 4, which demonstrates how the ±20◦ RD deformation texture transforms into a ±40◦ TD annealing texture accompanied by full recrystallization of the specimen. Figure 5 shows the distribution of the basal poles (or c-axes) with respect to the rolling and transvers directions for the ternary (bottom) and binary alloy (top) along with their inverse pole figure (IPF) maps at 400 ◦C/360 min. Based on the annealing durations, the data clearly reveals that the texture established during recrystallization in the ternary alloy is preserved during subsequent grain growth, as the orientation distribution relative to the TD and RD remains virtually unchanged (Figure 5c). In case of the binary alloy, the total area fraction of grains with a large TD pole spread increases significantly with the annealing duration, whereas the area distribution of the RD spread remains almost constant (Figure 5b).

**Figure 4.** Texture evolution during recrystallization of Mg-1%Er-1%Zn annealed at 350 ◦C for 0, 5, 7, and 15 min.

With respect to second phase precipitates in the microstructure, the ternary alloy was found to exhibit a fine distribution of nano-scale precipitates and also larger ones that were sometimes clustered together, as shown in Figure 6. Energy dispersive X-ray spectroscopy (EDS) point analysis and elemental mapping were employed to investigate the chemical composition of these large precipitates. The results revealed a particle composition with a magnesium to zinc to erbium ratio of approximately 5:5:1. A similar zinc to erbium ratio was previously reported for several hexagonal and icosahedral quasi-crystalline (Mg, Zn)*xEr* compounds [17,18].

**Figure 5.** (**a**) EBSD ND-IPF maps of binary (top) and ternary Mg-1%Er-(1%Zn) (bottom) alloys annealed at 400 ◦C for 360 min; (**b**,**c**) angle distribution profiles between the c-axis and the transverse and rolling directions for different annealing durations.

**Figure 6.** EDS analysis of the Er-containing precipitates observed in the Mg-1%Er-1%Zn alloy.

#### *3.2. Mechanical Properties*

Figure 7a shows the true stress-strain curves of the uniaxial tensile tests in RD, 45◦ and TD for the investigated alloys annealed at 400 ◦C for 15 and 60 min, respectively. The samples of both alloys exhibited a similar annealing grain size (hence the different times) but a drastically different texture (Figure 7b). As evident from the flow curves, the addition of zinc leads to higher ductility, as well as an increase of the ultimate tensile strength, which are indicative of an enhanced work hardening capability.

**Figure 7.** Uniaxial stress–strain response (**a**), optical micrographs and (0002) pole figures of Mg-1%Er annealed for 15 min and Mg-1%Er-1%Zn annealed for 60 min at 400 ◦C (**b**). The grain size prior to the tensile test was in the range of 14 to 16 μm for both samples.

#### **4. Discussion**

The present study revealed distinct differences in the microstructure evolution and mechanical properties between a dilute Mg-1%Er alloy with and without the addition of Zn. During annealing, both alloys developed a significant basal pole spread away from the ND. For the ternary alloy, a titanium rolling texture with off-basal components at ±40◦ TD developed during recrystallization, and was retained during subsequent grain growth. By contrast, the recrystallization texture of the binary alloy with off-basal peaks at ±20◦ RD was further modified with longer annealing resulting in a much larger grain size and increased texture scatter. The stable grain size in the Mg-1%Er-1%Zn alloy in contrary to the excessive growth in Mg-1%Er can be explained by the presence of a fine particle dispersion and the resulting drag force (Zener drag). This is known to have a significant impeding effect on the grain boundary motion and can therefore lead to a stable grain size [19,20]. Figure 8 shows a BSE image of the observed precipitates in Mg-1%Er-1%Zn after 60 min of annealing at 400 ◦C and the corresponding particle size distribution. The precipitate characteristics including particle size, volume fraction, and number density are listed in Table 1.

**Figure 8.** Particle size distribution after 60 min of annealing at 400◦C visualized using a histogram with linear *x*-axis (**a**) and the corresponding grain size distribution obtained by optical microscopy (**b**).

The critical grain size according to classical Zener theory is given by Equation (2), assuming that the radius of curvature equals the critical grain diameter [20].

$$D\_c = \frac{4r}{3f} \tag{2}$$

The calculated critical grain size of 12 μm, obtained by using the values in Table 2, is similar to the measured grain size (13.28 μm) under the same annealing conditions (cf. Figure 8b). This supports the assumption made earlier that the fine precipitates stabilize the recrystallization microstructure during annealing. Similarly, the absence of precipitates in the binary alloy (Mg-1%Er) could explain the excessive growth rate observed after an initial slow growth stage during the first 15 min of annealing (cf. Figure 3). The drag force during this short stage is believed to be caused by solutes inhibiting the motion of grain boundaries [21–23], which were obviously able to break free after 15 min annealing time. Theoretical studies revealed that accelerated grain growth in a system under the influence of solute pinning will occur when the average grain size becomes close to the critical grain size for which the solute drag force and the capillary driving force are equal. Such state allows the pinned boundaries with a slightly higher curvature than the average to break free from their solute atmosphere, while the other boundaries remain pinned [24]. This seems to be in accordance with the observed growth behavior of the Mg-1%Er alloy and the resulting growth of non-basal texture components (cf. Figure 5b) after a critical grain size has been reached.

**Table 2.** Characteristics of the Er and Zn-containing precipitates in Mg-1%Er-1%Zn obtained by means of statistical analysis of BSE images


In the ternary alloy, the process of recrystallization was responsible for the RD → TD transition of the basal pole spread seen in Figure 4, which can be contributed to either oriented nucleation or selective nucleus growth. Selective growth of texture components can be caused by anisotropic segregation behavior and/or an equalization of different grain boundary mobilities annihilating a prior growth advantage of certain orientations, e.g.,

of basal oriented grains as suggested by Barrett et al. [25]. Figure 9 presents EBSD maps (ND-IPF) of the microstructure of the ternary alloy at 5 and 10 min annealing at 350 ◦C. The orientation of recrystallized grains was evaluated separately from the orientation of the overall microstructure in order to discern the effect of recrystallization on the development of the ±40◦ TD texture. For this, the common criterion of grain orientation spread (GOS) was used, where recrystallized grains typically depicted GOS < 1◦. The overall texture revealed that the RD-tilted components were a feature of the deformation microstructure. They did not exist in the recrystallization texture that was solely composed of the TD-tilted components, readily after 5 min of annealing (Figure 9a). After completion of recrystallization at 10 min of annealing, the RD-tilted components were no longer a feature of the overall texture that was only dictated by the TD- recrystallization texture (cf. Figure 9b).

**Figure 9.** EBSD IPF maps (with respect to ND) and their (0002) pole figures of Mg-1%Er-1%Zn annealed at 350 ◦C for 5 min (**a**) and 10 min (**b**). The left column features the overall map data, and the right column only the recrystallized fraction with GOS < 1◦.

Additional grain size vs. texture analysis of the recrystallized structure in Figure 9b (400 ◦C/10 min) revealed that the ±40◦ TD texture in the ternary alloy intensifies during recrystallization growth of the nuclei. A similar effect was not observed in the binary system (Figure 10b), as no significant size dependence of texture during recrystallization was found. While there was a progressive texture change in the binary alloy during annealing, which involved both recrystallization and grain growth, the texture change in the counterpart ternary alloy was much more rapid, and in that regard, limited to recrystallization. As the drag force exerted by particles of a given size and volume fraction is too small to match the capillary driving force of grains significantly smaller than the critical grain size *Dc*, particle pinning should only play a minor role during recrystallization and early grain growth. Accordingly, selective growth at the recrystallization stage is likely to be governed by solutes. In comparison to the binary alloy, specific boundaries in the ternary alloy seem to break free from their solute atmosphere much sooner enabling texture selection readily during recrystallization. This may be a result of a lower solute content due to the large amount of fine Er/Zn-rich precipitates, whereas in the binary alloy the Er content is fully dissolved in the matrix.

**Figure 10.** Grain size distributions from EBSD measurements of Mg-1%Er annealed at 400 ◦C for 4 min (**a**) and Mg-1%Er-1%Zn annealed at 350 ◦C for 10 min (**b**) along with the orientation distribution of the c-axis with respect to TD for small and large recrystallized grains. The threshold used in each case was the average grain size obtained from EBSD.

The observed recrystallization kinetics of the two alloys further indicates a difference in the drag force during recrystallization. Figure 11 shows the recrystallized volume fraction as a function of annealing time and the corresponding JMAK (Johnson-Mehl-Avrami-Kolmogorow) fit for both Mg-1%Er and Mg-1%Er-1%Zn alloys. A Comparison of the recrystallization curves reveals a quicker recrystallization in the ternary alloy (~210 s) compared to the counterpart binary alloy (~500 s). Additionally, the initial stage (linear portion of the curve) until the onset of stable nuclei growth is extended in Mg-1%Er compared to the other alloy, indicating a longer incubation time in the first. As the incubation time is related to reduced boundary mobility, a stronger solute drag effect in Mg-1%Er may cause a longer incubation period.

Mg-1%Er-1%Zn exhibited an elevated yield strength, strain hardening capability, and failure ductility. The elevated yield stress is partially caused by precipitation hardening, which contributed by approximately 5 MPa to the 20 MPa offset (approximation by Orowan). Furthermore, the addition of zinc might have magnified the impact of solid solution strengthening by means of synergetic solute effects. To investigate the role of texture and microstructure in the activation of deformation modes during tension, EBSD-assisted slip trace analysis of at least 120 grains per strained sample was employed in the current study. A slip trace appears as a straight line as a result of the intersection of an active slip plane with the free surface. Figure 12 shows the frequency of slip traces corresponding to the active slip systems during 5% tension in RD, for the binary and ternary alloys. Additionally, the frequency of twinning was evaluated by a visual investigation of each grain. Basal, pyramidal I and <c + a> pyramidal II, as well as - 1012 tensile twining were detected with almost equal shares of approximately 22% in the ternary system. In the binary alloy, basal slip prevailed with about 64%, while all other slip systems accounted for less than 20% of the overall observed slip traces. A large contribution of basal slip to deformation could justify the lower yield point in the flow curve of the Mg-1%Er alloy. This is because basal slip, even in rare-earth containing Mg alloys, requires a much lower critical resolved shear stress (CRSS) than non-basal slip [26]. The observed enhanced slip activity on non-basal slip planes in the strained Mg-1%Er-1%Zn sample can be attributed to both a favorable texture and a change of the CRSS ratio between basal and non-basal slip, evoked by the present Zn and Er solutes. The relatively low contribution of prismatic slip to deformation might be attributed to the investigated low strain of 5% being insufficient to activate cross-slip of basal screw dislocations onto the prismatic plane [27,28].

**Figure 11.** (**a**) Recrystallization kinetics of binary and ternary Mg-1%Er-(1%Zn) annealed at 350 ◦C and the corresponding Avrami exponents (**b**).

**Figure 12.** (**a**) Distribution of slip traces corresponding to the active slip systems in Mg-1%Er and Mg-1%Er-1%Zn during tension to 5% strain. The initial condition of the sample corresponded to annealing at 400 ◦C for 60 min. (**b**) Exemplary SE images of one grain exhibiting the morphology of slip traces with overlaid possible slip systems obtained from EBSD for the determination of the active slip system. (**c**) Schmid factor distribution calculated from the initial texture of the grains, in which the slip traces were detected in both alloys.

Figure 12 also shows the distribution of Schmid factors (SF) of both alloys with respect to the applied external stress corresponding to different slip traces detected. Generally, non-basal slip (particularly pyramidal) seems to be the main plasticity carrier in both alloys. It also seems to comply principally well with the Schmid law, i.e., corresponding slip traces are preferentially detected in grains with the highest SF, and their frequency drops consecutively with decreasing SF. In the binary alloy, it is evident that the activation of basal slip in grains with a very low SF deviates from the Schmid behavior. This is likely due to the naturally low CRSS of basal slip but also to local stress concentrations at grain boundaries that could cause non-Schmid activation of different slip modes. Another important finding from the SF distribution in Figure 12 is the large difference in the contribution of basal vs. non-basal slip to deformation between the two alloys. In the Mg-Er sample at SF = 0.5, nonbasal slip (including prismatic and both <a> and <c + a> pyramidal slip) was ~2–3 times more active than basal slip. In contrast, the level of contribution of these slip modes to deformation at SF = 0.5 in the Mg-1%Er-1%Zn sample was more comparable. Both types of pyramidal slip were still preferential with a frequency ratio of ~1.2–1.5 to basal slip. Prismatic slip was no longer favorable compared to basal slip (frequency ratio of ~0.7).

The present findings certainly highlight the effect of solutes on the deformation behavior, particularly the non-basal slip behavior. There are also indications of solute-induced basal slip strengthening in the current alloys in accordance with previous experimental and computational reports [29–31]. The addition of Zn that alters the substitutional solute chemistry of the Mg-1%Er alloy would obviously lead to complex interaction of solute species within the matrix. From energetic perspectives, Zn and Er can cluster in the lattice to relieve the misfit strains arising from the solute size mismatch. They would also cosegregate to defects in the microstructure, and can be hence expected to have a stronger interaction with grain boundaries and dislocations leading to strikingly different slip system activation during deformation and boundary migration characteristics during annealing. This is indeed demonstrated in the current work by the unique texture development upon rolling and upon annealing of the Mg-1%Er-1%Zn alloy.

#### **5. Conclusions**


**Author Contributions:** Conceptualization, F.-Z.M. and T.A.-S.; Methodology, F.-Z.M. and R.P.; Software, R.P.; Validation, F.-Z.M. and F.S.; Formal analysis, F.-Z.M. and F.S.; Investigation, F.S., R.M., and F.-Z.M.; Resources, S.K.-K. and T.A.-S.; Data curation, F.-Z.M. and T.A.-S.; Writing—original draft preparation, F.-Z.M.; Writing—review and editing, T.A.-S.; Visualization, F.-Z.M.; Supervision, S.K.-K. and T.A.-S.; Project administration, T.A.-S. and S.K.-K.; Funding acquisition, T.A.-S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Deutsche Forschungsgemeinschaft (DFG), grant number grant no. AL 1343/7-1.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The financial support of the Deutsche Forschungsgemeinschaft (DFG) under grant no. AL 1343/7-1 is gratefully acknowledged. We also thank Burak Erol for his assistance during the experimental work.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


## *Article* **Adjustment of the Mechanical Properties of Mg2Nd and Mg2Yb by Optimizing Their Microstructures**

**Jonas Schmidt 1,\*, Irene J. Beyerlein 2, Marko Knezevic <sup>3</sup> and Walter Reimers <sup>1</sup>**


**Abstract:** The deformation behavior of the extruded magnesium alloys Mg2Nd and Mg2Yb was investigated at room temperature. By using in situ energy-dispersive synchrotron X-ray diffraction compression and tensile tests, accompanied by Elasto-Plastic Self-Consistent (EPSC) modeling, the differences in the active deformation systems were analyzed. Both alloying elements change and weaken the extrusion texture and form precipitates during extrusion and subsequent heat treatments relative to common Mg alloys. By varying the extrusion parameters and subsequent heat treatment, the strengths and ductility can be adjusted over a wide range while still maintaining a strength differential effect (SDE) of close to zero. Remarkably, the compressive and tensile yield strengths are similar and there is no mechanical anisotropy when comparing tensile and compressive deformation, which is desirable for industrial applications. Uncommon for Mg alloys, Mg2Nd shows a low tensile twinning activity during compression tests. We show that heat treatments promote the nucleation and growth of precipitates and increase the yield strengths isotopically up to 200 MPa. The anisotropy of the yield strength is reduced to a minimum and elongations to failure of about 0.2 are still achieved. At lower strengths, elongations to failure of up to 0.41 are reached. In the Mg2Yb alloy, adjusting the extrusion parameters enhances the rare-earth texture and reduces the grain size. Excessive deformation twinning is, however, observed, but despite this the SDE is still minimized.

**Keywords:** Mg-RE alloys; extrusion; mechanical properties; microstructure; in situ diffraction; crystal plasticity; deformation twinning; texture

#### **1. Introduction**

Magnesium is one of the lowest density (*ρ* = 1.7 g/cm3) metallic structural materials. Due to its high specific strengths, it is suitable for lightweight construction applications in the electronic industry, the biomedical industry, and the sports equipment sector [1–4]. However, the poor formability at room temperature limits the processing possibilities of magnesium alloys [5,6].

The low ductility and formability is caused by the hexagonal crystal system of magnesium, which only offers primary deformation systems in the basal plane. The <a> basal slip contributes to plastic deformation at low applied stresses due to its small critical resolved shear stresses (CRSS). Together with the <a> prismatic slip system, which requires higher activation energies, deformation can only can be realized in the <a> direction. Deformation in the <c> direction is only possible with <c + a> pyramidal slip systems, which are hard to activate [7–10]. Recently published studies show that <c + a> pyramidal slip is important for high elongations of magnesium alloys [11].

Plastic deformation can also be realized by twinning. In twinning, the crystal structure is reoriented by a defined angle along a plane of symmetry [12,13]. This induces a

**Citation:** Schmidt, J.; Beyerlein, I.J.; Knezevic, M.; Reimers, W. Adjustment of the Mechanical Properties of Mg2Nd and Mg2Yb by Optimizing Their Microstructures. *Metals* **2021**, *11*, 377. https:// doi.org/10.3390/met11030377

Academic Editor: Dmytro Orlov

Received: 15 January 2021 Accepted: 19 February 2021 Published: 25 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

microscopic change in length and contributes to macroscopic deformation [14,15]. The twin systems are divided into {10.1} tension twinning (TTW-ing) and {10.2} compression twinning (CTW-ing), depending on the stress applied along the c-axis of the unit cell. TTWs are formed when applying either tension along the c-axis or compression perpendicular to it and feature an 86◦ rotation about a <11.0> axis [12,13,16]. TTWs usually have a low CRSS and are, therefore, more easily activated. In contrast, CTWs with a higher CRSS feature a 56◦ rotation about a <11.0> axis when compression stress is applied parallel to the c-axis.

Twin formation is a unidirectional deformation mechanism that depends on the orientation of the crystals and the applied stress. In both monocrystalline and polycrystalline magnesium products, the properties depend on the orientation of the crystals and are affected by the production parameters. Typically extruded AZ31-alloys show fiber textures after extrusion [17] in which the basal planes are oriented parallel to the direction of extrusion. When compressive stress is applied along the extrusion direction, the perpendicular aligned c-axes of the grains are subjected to tensile stress, preferably forming tensile twins [18]. Due to the low CRSS of tensile twins, the compressive yield strength (CYS) is much lower than the tensile yield strength (TYS) in the extrusion direction. This asymmetric mechanical behavior is described by the Strength Differential Effect (SDE) [19,20]. For practical applications of structural materials, it is desirable to have a symmetrical material behavior, equivalent to an SDE close to 0.

The texture can be modified by changing the production/extrusion parameters and alloying elements. Studies have shown that rare earth [RE] elements can have a strong influence on the recrystallization texture [17,21,22]. They alter the grain orientations and weaken the texture during hot deformation/extrusion. Depending on the resulting orientations, various deformation mechanisms are active during subsequent cold deformation. The CRSS and the contribution to the total deformation of the individual systems have an influence on the resulting macroscopic mechanical properties.

RE solutes are used in the Mg alloys of the WE-series, containing 7 to 9% RE, mainly yttrium (Y) and neodymium (Nd) [23,24]. Although the alloys are characterized by high strength, high costs make it desirable to reduce the RE content while maintaining the advantageous properties. Neodymium in particular is suitable, as it achieves good properties and strongly influences the texture [25]. Seitz et al. [26] extruded an Mg2wt.%Nd alloy and found a small asymmetry in the tension and compression.

For this study, two magnesium alloys with 2 wt.% rare earth content, Mg2Nd and Mg2Yb, were investigated with regard to their microstructure, deformation behavior, and mechanical properties. By varying the process parameters, the microstructure can be changed so that the strength and ductility can be adjusted over a wide range. In particular, a significant reduction in the SDE can be achieved.

In a first step, two casted billets of each alloy were extruded, varying the cooling conditions. The extruded bars were investigated by electron microscopy (SEM, TEM), laboratory X-ray texture measurements, and mechanical testing (compression, tension) to determine the mechanical properties, the microstructure, and their changes during deformation. To gain further insight into the different deformation behavior, a combination of in situ energy-dispersive X-ray synchrotron diffraction and simulations with the elastoplastic self-consistent (EPSC) model was used [27]. The particular version of the model used in the present work is from [28]. These methods allow an analysis of the active deformation mechanisms as a function of load. Furthermore, the parameters of a dislocation densitybased strain hardening model of the different deformation mechanisms are obtained. By adding Nd, an advantageous texture can be achieved. The texture activates similar deformation systems at the beginning of plastic preforming and, in particular, effectively suppresses the formation of tensile twins under compressive stress. The addition of Yb has a lower impact on the texture and a more pronounced dynamic recrystallization can be observed. This results in low strengths and high SDEs.

In the next step, heat treatments and variations in extrusion parameters were used to modify the microstructure and thus the mechanical properties. The grain size was reduced while maintaining or even improving the advantageous texture. Due to the low solubility of Nd and ytterbium (Yb) in Mg, subsequent heat treatments were used to further increase the strength. In the Mg2Nd alloy, subsequent heat treatments lead to the formation of fine precipitates, generating a significant hardening effect. In the case of the Mg2Yb alloy, heat treatments for precipitation hardening are less effective. However, by adjusting the process parameters the grain size can be reduced and the texture improved as well, so that, despite differences in plastic deformation, the yield strengths in compression are almost equal to the yield strengths in tension. This resulted in high strengths and low SDEs.

#### **2. Materials and Methods**

#### *2.1. Material, Microstructure*

The extrusion billets had a nominal composition of Mg2wt.%Nd (Mg2Nd) and Mg2wt.%Yb (Mg2Yb) with a diameter of 123 mm and a length of 115 mm. They were casted at the Helmholtz-Zentrum Geesthacht (HZG). The billets were homogenized and solution annealed in the single-phase region of the phase diagram [29]. Depending on the composition and phase diagram, the temperature was 500 ◦C (6 h) for the Mg2Nd alloy and 450 ◦C (10 h) for Mg2Yb with an 8 h heating period. After the heat treatment, the billets were quenched in water. Prior to extrusion, the billets were inductively heated rapidly to extrusion temperature and then immediately extruded. The indirect extrusion process was carried out at the Technische Universität Berlin, Extrusion Research and Development Center, varying some of the extrusion parameters including billet temperature (TB), cooling method, extrusion ratio (R), and product speed (vP), as shown in Table 1.

**Table 1.** Extrusion parameters.


To improve the mechanical properties with regard to technological application, the extruded bars were subsequently heat-treated at different temperatures (150, 204, and 300 ◦C). To determine the heat treatment duration, hardness tests were performed on samples of different ageing times. Samples with the highest hardness were further selected for mechanical testing with tensile and compression tests.

For optical microscopy and grain size analyses, the as-extruded specimens were prepared by grinding and polishing and subsequent chemical polishing with a solution of 12 mL hydrochloric acid (37%), 8 mL nitric acid (65%), and 100 mL ethanol. Etching with a picric etching solution (4.2 g picric acid, 10 mL acetic acid, 10 mL H2O, and 70 mL ethanol) revealed the grain structure. To examine precipitates in the SEM, polished samples in the as-extruded and heat-treated states were used.

Thin TEM foils were cut, mechanically polished, and electrolytically thinned by a twin-jet TenuPol 3 with a solution of 5.3 g lithiumchloride, 11.16 g magnesiumperchlorate, 500 mL methanol, and 100 mL 2-butoxy-ethanol.

HR-TEM images were recorded on a FEI Tecnai G2 20 S-TWIN TEM and a FEI Titan 80–300 Berlin Holography Special TEM (Technische Universität Berlin, Zentraleinrichtung Elektronenmikroskopie).

For energy-dispersive synchrotron in situ tests, compression specimens with a diameter of 7 mm and a length of 15 mm and tensile specimens with a diameter of 6 mm and a length of 36 mm were used.

The texture of the polished specimens in the as-extruded conditions and deformed state were measured with the laboratory X-ray diffraction method using CoK*α* radiation and a 3 mm collimator. The experimental pole figures for the (10.0), (0002), (10.1), (10.2) and (11.0)-reflections were measured and the inverse pole figures were calculated from the experimental data using the MTEX software package [30].

Compression samples (D = 10 mm, l0 = 20 mm) and tensile samples (D = 6 mm, l0 = 36 mm) were machined from the extruded bar. Compression samples were compressed up to engineering strains of −0.01, −0.04, −0.08, −0.15, and to fracture, while tensile samples were deformed to fracture. The quasi-static tension and compression tests were carried out with a universal testing machine (MTS810) with strain rates of 2.5 × 10−<sup>4</sup> s<sup>−</sup>1.

For extruded magnesium alloys, the yield strength in tension (TYS) has been reported to be higher than the yield strength in compression (CYS). This difference in strength is called the strength differential effect (SDE) and can be expressed as:

$$\text{SDE} = \frac{|\text{CYS}| - |\text{TYS}|}{|\text{CYS}| + |\text{TYS}|}. \tag{1}$$

#### *2.2. In Situ Energy Dispersive Synchrotron X-Ray Diffraction*

In situ energy-dispersive synchrotron X-ray diffraction experiments were carried out at the 7T-MPW-EDDI-beamline at the BESSY-II synchrotron [31]. The beamline is equipped with a superconducting 7T multipole wiggler, which provides a white beam with a usable range of about 8 to 150 keV. For the experiments, an energy range of 20 to 60 keV and the Bragg angle 2*θ* of 10.34◦ were used. The beam was limited by slit systems to 1 × 2 mm2 on the incoming and 0.1 × 7 mm<sup>2</sup> on the detector side. The in situ compression and tensile tests were carried out with a tensile-compressive loading device designed by Fa. Walter+Bai AG, which is mounted on a 4-axes positioner to allow x-y-z translation and Ψ rotation around the axis of the beam.

In the unloaded sample state, the lattice spacings d0 hkil were measured in 11 Ψ angles between 0 and 89.9◦ with an exposure time of 60 s. These data were used for the determination of d0 hkil. During mechanical testing, the dhkil were measured at several uniaxial tensile and compression steps at 0◦ and 89.9◦ to determine the elastic lattice strains εhkil in the axial and transversal direction by Equation (2) [32]:

$$
\varepsilon^{\text{hkill}} = \frac{\text{d}^{\text{hkil}}}{\text{d}^{\text{hiki}}} - 1 \, = \frac{\text{E}\_0^{\text{hiki}}}{\text{E}^{\text{hiki}}} - 1. \tag{2}
$$

Here, dhkil, d0 hkil, and Ehkil, E0 hkil are the lattice spacings and their corresponding diffraction lines at a load step and prior loading. The in situ measurements were stress controlled in the linear elastic region. After reaching the yield strength, displacement control was used.

#### *2.3. EPSC Modeling*

The elasto-plastic self-consistent (EPSC) model [27] is a polycrystal plasticity model which simulates the constitutive response of a material based on single crystal data, a hardening model, given texture, and initial grain shape and size. A recent description of the formulation used here can be found in [28,33,34].

To describe hardening, separate models are employed for slip and twinning. For slip, a dislocation density-based hardening model for the CRSS values in different crystallographic slip systems is employed [35,36]. For twinning, a model for the domain reorientation and twin expansion as well as the twin boundary effect on slip is used, as described by the composite grain model [37]. To activate twinning, we employ the finite initial fraction (FIF) assumption [7], which states that twin nucleation is accompanied by twin growth to a finite initial fraction. For the simulations here, an FIF of 0.01 is used.

The material parameters used in the model pertain to elasticity, the initial stress to activate slip, the rates of dislocation storage, and the critical stress for twin growth. These are listed in Table 3. For the first of these, we used single-crystal elastic constants for Mg, which are C11 = 59.5 GPa, C12 = 26.1 GPa, C13 = 21.8 GPa, C33 = 65.6 GPa, and C44 = 16.3 GPa for both alloys. The remaining parameters were identified iteratively and specifically for each alloy until the simulation results matched all the experimental results. The simulation results enable da direct comparison with the synchrotron X-ray diffraction measurements from the compression and tensile tests. The average stress–strain response, the texture evolution, and the elastic lattice strains allow to check the EPSC predictions by the experimental diffraction data. The EPSC simulation further gives information on the active deformation modes and their CRSS as a function of the strain. For the final simulation, a grain set of 10,000 grains, which represent the as-extruded texture, was used.

#### **3. Results**

#### *3.1. Microstructure*

The microstructure of the as-extruded material is presented in Figure 1 via optical micrographs to show the grain structure and inverse pole figures to show the texture. The microstructures of all three series are dominated by globular recrystallized grains. The average grain size of the Mg2Nd alloy decreases from 13 ± 1 μm for the air-cooled A-series to 7 ± 1 μm for the water-quenched B-series. This is due to hindered grain growth after the dynamic recrystallization caused by the rapid drop in temperature. An additional decrease to an average grain size of 3 ± 1 μm for the C-series was achieved by reducing the extrusion speed. The Mg2Yb alloy shows an average grain size of 49 ± 4 μm for the air-cooled A-series and 26 ± 2 μm for the water-quenched B-series. Extrusion at a reduced temperature decreases the grain size of the C-series to 8 ± 2 μm. In the slower extruded C-series of the Mg2Nd alloy and both water-quenched series of the Mg2Yb alloy, elongated grains that are not fully recrystallized are occasionally found in the longitudinal sections (Figure 1h,n,q).

The X-ray diffraction texture measurements reveal pronounced RE-fiber-textures with overall low maximum intensities (Figure 1). The texture of the A-series of the Mg2Nd alloys has a maximum at the <11.2>pole and the B-series shows additional intensity between the <10.2> and <10.1>pole. The C-series has its maximum at the <10.0> pole with additional intensities at the <10.1> and<11.2> pole. The A- and C-series of the Mg2Yb alloys show a very weak extrusion texture with of maximum of just 1.3 multiples of random distribution (mrd) and 1.5 mrd, respectively, and intensities at the <10.2> and <11.2> pole. The B-series, in contrast, shows the highest observed intensity of 2.3 mrd at the <10.0> pole. The texture of the C-series is similar to the A-series, with an additional intensity at the <10.0> pole.

**Figure 1.** Cross section, longitudinal section, and inverse polfigures in the extrusion direction (ED) of the Mg2Nd alloy (**a**–**c**) A-series, (**d**–**f**) B-series, (**g**–**i**) C-series, and of the Mg2Yb alloy (**j**–**l**) A-series, (**m**–**o**) B-series, (**p**–**r**) C-series.

#### 3.1.1. Mg2Nd

All series of the Mg2Nd alloy show coarse precipitates in different shapes and diameters up to 4 μm. These precipitates are randomly distributed in the grains. In the slowercooled A-series, additional precipitates can be seen on the grain boundaries (Figure 2a). The area fraction of the precipitates was determined to approx. 3.2% for the A- and Bseries and 3.5% for the C-series. Due to the high number of precipitates, analyses of the solution content of Nd in the Mg-matrix were carried out using a high-resolution electron probe micro-analyzer (EPMA). These showed that a Nd concentration of 1.6 wt.% was present in the matrix. Further measurements show that these are stable Nd-rich *β*<sup>e</sup> (Mg41Nd5) precipitates [38]. Heat treatments at 150 ◦C and 204 ◦C promote the formation of coherent Guinier–Preston zones and *β* precipitates with diameters of 10 to 20 nm (Figure 2b) [29,38,39]. Heat treatments at higher temperatures produce stable *β*eprecipitates that either do not lead to precipitation hardening or, even worse, reduce the strength. These samples were, therefore, not investigated further.

**Figure 2.** (**a**) SEM Mg2Nd A-series, (**b**) TEM images of precipitates in the heat-treated (150 ◦C, 7 h) Mg2Nd B-series, <0002> zone axis, (**c**) SEM Mg2Yb A-series.

#### 3.1.2. Mg2Yb

In the water-quenched B and C series, only the larger precipitates with diameters of 1 to 2 μm are found in the as-extruded state. They are located within the grains and are homogeneously distributed. In samples of the A series, the same precipitates are found within the grains. In addition, predominantly smaller precipitates (Ø~0.5 to 1 μm) are observed at the grain boundaries (Figure 2c). These precipitates are the *β* -phase (Mg2Yb) precipitates [40], and formed after extrusion during slow cooling. Heat treatments at 150 ◦C have little effect on the microstructure and mechanical properties of the Mg2Yb alloy. In contrast, an increase in the phase fraction of the *β* precipitates can be observed after a heat treatment for 15 min at 300 ◦C. No changes in grain size and texture were observed during all heat treatments of the Mg2Nd and Mg2Yb alloys.

#### *3.2. Mechanical Properties*

The yield strengths (CYS, TYS) and elongations to failure (εfc, εft), as determined from the stress–strain curves, are summarized in Table 2. For the Mg2Nd alloy, the flow curves of the A-series look similar in compression (Figure 3a) and tension (Figure 3b), and achieve elongations to failure above 0.32. We find that the B-series shows similar behavior (Supplementary Materials Figure S3). In contrast, the shape of the flow curves of the C-series differ between the compression and tensile tests (Figure S3). The air-cooled Aseries yields at −105 and 107 MPa in the uniaxial compression and tensile tests, respectively, resulting in nearly zero SDE (Table 2). Reducing the grain size to 7 μm by adjusting the cooling method (B-series) after extrusion increased the CYS and TYS to −125 and 122 MPa, respectively. In the case of the C-series alloy, the associated additional grain size reduction to 3 μm, by the slower extrusion rate, increased the CYS and TYS further to −176 and 175 MPa, resulting in an SDE of 0. However, in this case the flow curve of the compression test exhibits a sigmoidal shape (Figure S3), which is a well-known signature of tension twinning [18]. Still, the increased activity of TTW-ing significantly reduces the elongation to failure (ductility) in the compression test. The tensile test had similarly good values, just as with the A- and B-series.



**Figure 3.** Comparison of the flow curves from the in situ experiment, ex situ experiment and the simulation of the Mg2Nd A-series (**a**) compression and (**b**) tensile tests and the Mg2Yb B-series (**c**) compression and (**d**) tensile tests.

The Mg2Yb alloy is significantly more anisotropic in its plastic deformation and mechanical properties than the Mg2Nd alloy, especially in the B-series. The flow curves of the compression tests (Figure 3c and Figure S3) show a strong sigmoidal shape and the CYS are significantly lower than the TYS. This leads to SDEs of high magnitude (Table 2). Nevertheless, a strong influence of the grain size can be observed in both the CYS and TYS. As grain size decreases, the yield strengths increase and this effect is more pronounced in compression than in tension. Therefore, the C-series ultimately achieves a low SDE of −0.04.

Next, we heat-treated the series of the Mg2Nd alloys at 150 ◦C. We find that heat treating increases the TYS of the A-series slightly more than the CYS, leading to a larger SDE than without heat treatment. The yield strengths become similar to those of the Bseries in the as-extruded state. In the case of the B-series, heat treating causes the CYS and TYS to increase asymmetrically, resulting in a strongly increased SDE. The strength of the

C-series can be increased in a similar way as that seen in the A-series. A 3 h heat treatment at 204 ◦C leads to a CYS and a TYS of -191 and 195 MPa (SDE = −0.03) anda7h heat treatment at 150 ◦C to −197 and 203 MPa (SDE = −0.03), respectively. While the ductility of the A series decreases significantly, the ductility of the heat-treated C-samples remains unchanged in the tensile tests. However, it decreases slightly in the compression tests.

Asymmetric precipitation hardening is even more pronounced in the Mg2Yb alloy. For both the A- and B-series, the TYS increases more than the CYS. Therefore, an increase in the SDE can be observed in both cases. While the ductility during compression deformation remains nearly the same after heat treatment, it decreases significantly during tensile deformation.

#### *3.3. Deformed Microstructure*

In order to investigate the development of the microstructure during deformation, compression tests were stopped at certain deformation steps. Figure 4 shows the grain structure and texture for the Mg2Nd A-series and Mg2Yb B-series for some of these intermediate strain levels (the microstructure and textures for the other series and at other strain levels can be found in Figures S4 and S5).

**Figure 4.** Cross sections and comparison of the measured and simulated texture at (**a**,**b**)−0.01, (**c**,**d**)−0.04, (**e**,**f**)−0.15 strain and elongation to failure in (**g**,**h**) compression and (**i**,**j**) tension for the Mg2Nd A-series and the Mg2Yb B-series, respectively.

#### 3.3.1. Mg2Nd

No twins are observed in the optical micrographs of the A- and B-series of the Mg2Nd alloy. While the flow curves of the Mg2Nd alloy show a similar shape, there is a clear difference in the texture evolution between the compression and tensile tests (Figure 4g,i). The inverse pole figures show a continuous shift in texture during deformation. During compression, the maximum intensity is close to the <11.2>-pole in as-extruded state, gradually shifting towards the <0002>-basal pole with increasing deformation (Figure 4a,c,e,g). During tensile testing, however, the initial <11.2>-texture with low maximum intensities changes to a sharp <10.0>-texture (Figure 4i) with increased maxima of 3.9 and 4.4 mrd for the A- and B-series, respectively (B-series shown in Figure S4).

#### 3.3.2. Mg2Yb

On the contrary, the excessive twinning of the Mg2Yb alloy is observed in the compressive deformation of the A- and B-series. For as little as −0.01 strain, thin twin lamellae can be observed in the optical micrographs (Figure 4b). However, these fine twins have no effect on the texture. With increasing the strain to −0.04, the area fraction of the twinned grains increases and the existing twin lamellae widen. Together the resulting rise in twin activity leads to a noticeable change in texture towards a <0002>-basal texture (Figure 4d). Specifically, due the formation and growth of twins, the maximum intensity at the <0002> pole increases, while the initial texture slowly depletes. The intensity at the <10.0>-pole decreases both in the A- and B-series and disappears at −0.04 strain. While the <10.1> and <11.2>-texture components from the A-series can still be recognized, they too disappear at −0.08 and a strong <0002>-basal texture remains (Figure S5 and Figure 4f). With increasing deformation, the maximum intensity at the <0002>-pole further increases, an increase that is more pronounced in the B-series than in the A-series.

#### *3.4. EPSC Simulation*

To understand the deformation behavior of the investigated alloy, in situ experiments were performed. Table 3 shows the parameters used for the hardening models in the EPSC simulation. With these parameters, a good agreement was obtained between the simulated and the experimental data in terms of flow curves (Figure 3 and Figure S3) and texture evolution (Figure 4 and Figure S2). As validation, we find that the model is capable of calculating the elastic lattice strains of different crystallographic planes. The calculated elastic lattice strains are compared with those determined experimentally in the in situ tests in Figure 5, Figure S4, and Figure S5 and also show good agreement. As a result of the simulation, further insights into the deformation behavior and the activities of the deformation systems (Figure 6, Figure S6, and Figure S8), as well as their CRSS (Figure 7, Figure S7, and Figure S9), during the deformation process are gained.


**Table 3.** Hardening parameters for slip and twin systems.

**Figure 5.** Comparison of the experimentally measured and simulated axial elastic lattice strains of the Mg2Nd A-series during (**a**) compression and (**b**) tensile tests and the Mg2Yb B-series during (**c**) compression and (**d**) tensile tests.

**Figure 6.** Deformation mode activity as a function of strain of the Mg2Nd A-series during (**a**) compression and (**b**) tensile tests and the Mg2Yb B-series during (**c**) compression and (**d**) tensile tests.

**Figure 7.** Critical resolved shear stresses (CRSS) of the different deformation systems as a function of strain of the Mg2Nd A-series during (**a**) compression and (**b**) tensile tests and the Mg2Yb B-series during (**c**) compression and (**d**) tensile tests.

#### 3.4.1. Flow Curves

In the mechanical testing, the strains were applied step by step, and at each step EDS-XRD measurements were carried out. During the data acquisition steps, the material rapidly relaxed, leading to a reduced stress. The stress measurement is recorded in the relaxed state for most of the time. The simulated flow curves were matched to the experimental flow curves from the in situ tests at these reduced stresses. It should be noted that an elongated yield point (Lüders strain) was observed in the in situ tensile tests of the Mg2Nd alloy (Figure 3). However, this region was not used in the simulation model, since it does not take into account localized plastic deformation.

#### 3.4.2. Elastic Lattice Strains

The elastic strains were calculated from the data of the in situ compression and tensile tests. These provide further information on the deformation behavior. Figure 6; Figure 7 show the evolution of the elastic lattice strains for the A- and B-series of the Mg2Nd and Mg2Yb alloys in axial direction of the (10.0), (0002), (10.1), (10.2), (11.0), (10.3), (11.2), and (20.1) reflections during the compression and tensile tests.

During deformation, grains with (10.1), (10.2), (10.3), and (11.2) orientations possess high Schmid Factors (SF) for <a> basal slip, making it the most likely active slip system in these grains. Grains with (10.0), (11.0), and (20.1) orientations have a high SF for <a> prismatic slip. Grains oriented in (0002) require <c> axis deformation to accommodate the applied load. They cannot deform by either <a> basal or <a> prismatic slip since the slip direction is perpendicular to the loading direction, and this results in an SF of zero for these <a> slip modes. Consequently, <c + a> pyramidal slip is the only possible slip system. Another mechanism accommodating <c>-axis deformation is mechanical TTW-ing. Since TTW-ing is a unidirectional deformation system accommodating only <c>-axis extension and not compression, the behavior of the alloy in tension and compression tests differs. During compression (10.0) and (11.0) -oriented grains possess a high SF for TTW-ing, whereas in tensile tests (0002) grains have a high SF for TTW-ing.

#### Mg2Nd

For both compression and tensile tests, the grains associated with <a> basal slip ((10.1), (10.2), (10.3), and (11.2)) show the lowest initial elastic lattice strains in the axial direction. With increasing deformation, only a small increase in elastic lattice strains can be observed. Grains associated with <a> prismatic slip ((10.0), (11.0), and (20.1)) exhibit higher initial elastic lattice strains, which increase with further deformation. During compression, the intensity of these reflections decreases and gradually disappears, leading to greater inaccuracies of the calculated elastic lattice strains. Eventually the (10.0), (11.0), and (20.1) reflections disappear, so the elastic lattice strains can no longer be determined. Equivalent observations were made for the (0002) grains during tensile deformation. During compression, the grains oriented in (0002) initially show the highest elastic lattice strains, which increase the most during plastic deformation. They reach their maximum at a strain of −0.15 and remain almost constant thereafter.

#### Mg2Yb

For the A- and B-series of the Mg2Yb alloy, a similar evolution of the elastic lattice strains is observed. However, during compression grains associated with <a> prismatic slip ((10.0), (11.0), and (20.1)) can be analyzed at all times. Yet, similar to the Mg2Nd alloy, increasing inaccuracies can be observed with increasing deformation. Small initial elastic lattice strains in these orientations associated with <a> basal slip ((10.1), (10.2), (10.3), and (11.2)) indicate a low CRSS to activate plastic deformation, or, vice versa, higher elastic lattice strains indicate a higher CRSS. In addition, the increase in the elastic lattice strains can be associated with the work hardening of the active slip system. The EPSC model can quantify these qualitative predictions and calculate the evolution of the CRSS of the different deformation systems and their contribution to the total deformation.

3.4.3. Activities and CRSS of Deformation Systems Mg2Nd

#### *Compression*

The deformation during uniaxial compression is mainly carried by <a> basal slip with a constant contribution of approximately 0.6 (Figure 6a) and little work hardening. This can be seen in the low increase in the CRSS (Figure 7a). The maximum SF of <a> basal slip is not affected by the continuous texture change and remains at a high value of 0.49. Initially, the <a> prismatic slip system is the second most active, but its activity decreases continuously. It shows more hardening (increase in the CRSS) than the <a> basal slip system. TTW-ing only has a minor role at the beginning. As previously seen in Figure 4, there are only few twinned grains at a strain of −0.08. After a total strain of −0.1 to −0.15, the activity of TTW-ing is negligible. As the activity of <a> prismatic slip and TTW-ing decreases, the <c + a> pyramidal slip system becomes more important at higher strains. The elastic lattice strain of the (0002) plane increases continuously up to a deformation of approximately −0.15 true strain. Afterwards, they remain at a constant level. This means that up to this strain, the deformation of the grains in (0002) or c-direction is mainly carried out elastically. Subsequently, an increase in the deformation activity of the <c+a> pyramidal slip can be observed, accompanied by a significant increase in the CRSS. *Tension*

As with compression deformation, the <a> basal slip system is the most important deformation system in the early stages of straining. However, the contribution decreases continuously from 0.55 to 0.4, while the share of the <a> prismatic slip system increases and exceeds the share of the <a> basal slip system at a total strain of about 0.15 (Figure 6b). The CRSS of the <a> prismatic slip system behaves in the same way as the <c + a> pyramidal slip system under compressive stress. The increased activity of the <a> prismatic slip system is accompanied by a much stronger increase in CRSS (Figure 7b). Compared to the compression test too, an increased activity of TTW-ing is observed in the tensile test, thus leading to a higher final total volume of twinned grains.

#### Mg2Yb

#### *Compression*

As suggested in the texture evolution, TTW-ing contributes to deformation at small strains. The B-series alloys achieve a higher volume fraction of TTW than the A-series alloys. The B-series also has a higher proportion of TTW volume fraction than the A-series. This can be attributed to the more pronounced <10.0> texture component. For the slip systems, the <a> basal slip is the most active. Its volume fraction increases up to 0.6 with decreasing TTW-ing (Figure 6c). The portion of <a> prismatic slip decreases slightly with increasing deformation. In the range of ×0.1 to −0.15 deformation an increase in <c + a> pyramidal slip can be observed. The twinned grains, which are oriented in (0002), can now only deform further by <c + a> pyramidal slip. The CRSS of the <c + a> pyramidal slip increases highly for the twinned grains (Figure 7c). In contrast, the CRSS of the <a> basal and <a> prismatic slip shows a weaker increase. The CRSS of the TTW-ing increases more than the CRSS of the slip systems.

#### *Tension*

In the tensile tests, <a> prismatic slip is the dominant deformation system (Figure 6d). The share of the total deformation increases with increasing strain, whereas the contribution of the <a> basal slip continuously decreases. Since there are only a few grains oriented in (0002) in the original texture, a low activity of TTW-ing can only be observed at the beginning. After completion, there are no more grains with this orientation. Therefore, the proportion of <c + a> pyramidal slip is also low. Just as in compression tests, the CRSS of TTW-ing increases strongly as soon as all favorably oriented grains are twinned (Figure 7d).

#### **4. Discussion**

#### *4.1. Strength*

Plastic deformation can be carried out by different deformation systems such as crystallographic slip and mechanical twinning. A deformation system is activated if the shear stress τ exceeds the CRSS of the respective deformation system. The magnitude of the shear stress depends on the orientation of the planes with respect to the direction of loading. Thus, the texture has a significant influence on which deformation systems can be activated to which extent. The activity of the respective deformation systems and their CRSS, in turn, have a significant influence on the mechanical properties. Additionally, the CRSS of polycrystalline materials depends on the grain size.

From the yield strengths displayed in Table 2, the following dependencies (Table 4), regarding grain size can be calculated using the Hall–Petch relationship:

$$\text{YS} = \sigma\_0 \frac{\text{K}}{\sqrt{\text{d}}}.\tag{3}$$

**Table 4.** Calculated Hall–Petch parameters.


As seen in Table 4, the Hall–Petch parameters for the Mg2Nd alloy show similar values for compression and tension, with both having large values for the K-factor. This indicates the direct dependence on the grain size. The initial texture of the A- and B-series activates similar slip systems at the beginning of the compression and tensile deformation. As a result, the CYS and TYS are also similar, resulting in a low SDE. In contrast, the texture of the C-series is altered and grains elongated in ED are observed (Figure 1h). This favors TTW-ing, as seen in the flow curves (Figure S3) [16,41]. However, this does not lead to a reduced CYS (−176 MPa) compared to the TYS (175 MPa). This is due to the strong dependence of the CRSSttw on grain size (Table 5), maintaining an SDE of 0.

**Table 5.** Initial critical resolved shear stresses (CRSS) for the different slip and twinning modes.


On the other hand, the Hall–Petch parameters of the Mg2Yb alloy for CYS and TYS are different. For the CYS, a stronger dependence on grain size can be observed than for the TYS. This can be explained by the fact that during compression tests of the Mg2Yb alloy, a high activity of TTW-ing and <a> basal slip carry the plastic deformation initially (Figure 7b). The CRSS values for TTW-ing and <a> basal slip have a strong dependence on grain size (Table 5). In contrast, the <a> prismatic slip system is more active during tensile deformation. With a decreasing grain size from 49 μm to 26 μm for the A- and B-series, the CRSS of TTW-ing and <a> basal slip increases by 30% and 18%, respectively. On the other hand, the CRSS of <a> prismatic and <c + a> pyramidal slip only increases by 8% and 1%, respectively. The sigmoidal shape of the flow curve in the compression test (Figure S3) indicates that TTW-ing is still an important deformation system in the C-series. Due to further reductions in grain size, however, the CRSSttw has most likely continued to increase. As a result, the CYS increases relatively more than the TYS, which was also observed in the mechanical data (Table 2). According to this, the SDE was reduced from −0.42 for the A-series to −0.04 for the C-series. Subsequent heat treatments at 300 ◦C further increased the yield strengths of the A- and B-series. Since the CYS increases less than the TYS, it can be assumed that the precipitates have a stronger hardening effect on the initially dominant <a> basal and <a> prismatic slip systems in tensile deformation than on the TTW-ing, which occurs during compression.

#### *4.2. Plastic Deformation*

Under compressive load, the slip plane normal of an active slip system rotates in the direction of the load. During tensile deformation, the crystal also rotates continuously in such a way that the slip direction approaches the loading direction.

#### 4.2.1. Mg2Nd

Since the texture shifts continuously toward the <0002> basal pole, it can be associated with <a> basal slip. Figure 8 shows that the initial texture (Figure 1) also exhibits high Schmid Factors for the <a> basal slip system, making it even more favorable for activation. The slow rotation of the grains toward the <0002> orientation results in a smaller SF for <a> prismatic slip and a larger SF for <c + a> pyramidal slip. In simulation, a continuous decrease in the activity of the <a> prismatic slip is observed with increasing deformation and texture shift, while the activity of the <c + a> pyramidal slip increases (Figure 6a). During tensile deformation, the texture shifts toward the <10.0> pole; therefore, <a> slip systems must be responsible for this as well (Figure 4i). Initially, the <a> basal slip system has a higher SF than the <a> prismatic slip system. Yet, at higher strains, this changes and <a> prismatic slip becomes the favored deformation system, resulting in an increase in the deformation mode activity. The increased activity of <c + a> pyramidal slip in compression tests and <a> prismatic slip in tensile test leads to higher dislocation densities and work hardening. This can be observed in the different increases in their CRSS (Figure 7b). The CRSS of the <c + a> pyramidal slip system shows the highest increase during compression, while <a> prismatic slip hardens the most under tension.

**Figure 8.** Theoretical calculated Schmid Factors as a function of grain orientation for uniaxial tension, displayed as inverse polfigures.

#### 4.2.2. Mg2Yb

Compared to the continuous texture shift in the compression and tensile tests of the Mg2Nd series, the compression tests of the Mg2Yb series show an abrupt texture change (Figure 4d). This is related to the formation of TTWs. After approx. −0.1 deformation, the TTW-ing is mostly completed. The twinned grains initially also deform with <a> slip systems, but as the deformation increases <c + a> pyramidal slip becomes the dominant deformation system. This leads to grain rotation in the direction of the <11.3> slip direction, so that the <0002> texture becomes less pronounced and the intensity is spread further around the basal pole. In tensile tests, a similar behavior to the series of the Mg2Nd alloy is observed. Yet, since the initial texture is different and <a> prismatic slip is favored, a higher activity can be observed at the beginning of the deformation. As a result, it becomes the dominant deformation system even at lower strains compared to the Mg2Nd alloy series.

#### *4.3. Ductility*

Mg and most Mg alloys have a low ductility at room temperature. This is mainly due to the hexagonal crystal structure, which bears only a small number of easily activated slip systems. At room temperature, the <a> basal slip system usually has significantly lower CRSS values than the non-basal slip systems, which is why deformation at low temperatures is mainly realized by <a> basal slip. The <a> basal slip system, however, has only two independent slip systems and thus does not meet the von Mises criterion of deformation compatibility, which states that at least five independent slip systems are required for uniform plastic deformation.

By modifying the texture, the deformation behavior and thus the mechanical properties can be improved. Additions of rare earth elements showed texture changes that may have had a positive effect on the deformation behavior and especially on the ductility at low temperatures. Investigations by Stanford et al. [21] showed that the extrusion product of a binary Mg-Gd alloy (1.5wt.%Gd) with modified Mg extrusion texture achieves twice the elongation to failure of an extrusion product of pure magnesium with a comparable grain size and typical Mg extrusion texture (<10.0>/<11.0> double fiber texture). Due to the comparable grain size, the increase in ductility could be directly attributed to the texture modification.

These findings and the presented microstructure and texture suggest good ductility and good mechanical properties of the extruded products. In these modified textures, a significantly higher number of grains shows a favorable orientation for the activation of the <a> basal slip system. At the same time, fewer grains are favorably oriented for the activation of the TTW system, which further can reduce the asymmetry of the tensile and compressive yield strength (SDE). The higher activity of the basal slip system results in a higher ductility at room temperature.

The A- and B-series of the Mg2Nd alloy show <11.2> textures (Figure 1). This means that the c-axis of the majority of grains is tilted by 45–50◦ to the extrusion direction. The grains are in a favorable orientation for the activation of the <a> basal slip system. The higher activity of the <a> basal slip system results in a higher ductility at room temperature. Meanwhile the C-series has an additional <10.0> texture component and therefore increased TTW activity in compression tests, as seen in the flow curves (Figure S3). This leads to reduced elongation to failure in compression tests, compared to the A- and B-series, while the elongation to failure in tensile tests reaches similar values (Table 2). In all cases, heat treatments for precipitation hardening result in reduced elongation at failure for the Mg2Nd alloy. Considering this, the grain size reduction by adapting the cooling conditions, as seen in the B-series, is preferable to a subsequent heat treatment of the A-series. Similar yield strengths can be achieved by both methods. However, the ductility of the B-series is better than that of the A-series, suggesting that the additional process step of heat treatment is not necessary.

In contrast, the A- and B-series of Mg2Yb alloy have different textures. The A-series has an extraordinarily weak texture with a maximum intensity of just 1.3 mrd, nearly completely random, with intensities at <11.2> and <10.1> poles, while the B-series has a distinct <10.0> texture. This results in a difference in the ductility. Despite the unfavorable texture, the A-series deformed at lot due to TTW-ing in the compression test due to the large grain size (as explained in 4.1). The TTW are reoriented by 89◦, so that they are not exactly oriented in <0002> but slightly tilted, depending on the initial orientation. This results in a wider spread compared to the B-series, which has a strong <0002> texture with a higher intensity (Figure S5). The TTW in the A-series can deform by <a> basal and <a> prismatic slip due to the tilt. While the majority of the twinned grains in the B-series are unfavorably oriented for the <a> basal slip system, the activity of the <a> basal slip system is, therefore, correspondingly low. As a result, the twinned grains deform primarily due to <c+a> pyramidal slip (Figure 6c). This leads to limited ductility and crack initiation due to stress concentrations.

#### **5. Conclusions**

Three approaches were used to modify the microstructure to adjust the mechanical properties and reduce the asymmetric yield behavior and anisotropy of the investigated magnesium alloys: texture weakening, grain size reduction, and precipitation strengthening.

As a result, the Mg2Nd series, which had high yield strengths and was symmetrical in compression and tension, resulting in an SDE close to 0, could be extruded. Thus, products with a wide variety of yield strengths (CYS −105 to −197 MPa, TYS 107 to 203 MPa) and good ductility, with elongation to failures of −0.18 to −0.32 in compression and 0.17 to 0.41 in tension tests, were obtained. The YSs of the Mg2Yb alloy are below those of the Mg2Nd alloy and range from −58 to −111 MPa for the CYS and 89 to 115 MPa for the TYS, with similarly high elongations to failure between −0.22 and −0.3 in compression and 0.21 and 0.32 in tensile tests.

By adjusting the extrusion parameters, the grain size of the Mg2Nd alloy can be gradually reduced, thereby significantly increasing the strength. The texture of the Aand B-series effectively suppresses TTW-ing. At the beginning of compressive and tensile deformation, similar deformation mechanisms are active. This leads to a symmetrical yielding behavior and SDEs close to zero. A slower extrusion speed decreases the grain size and weakens the texture. The appearance of a <10.0> texture component in the Cseries promotes TTW-ing during compression. However, because of the small grain size, CYS and TYS are similar and the SDE remains at 0. The precipitation state can be changed by subsequent heat treatment, which, in turn, further increases the yield strengths while maintaining good ductility.

Depending on the extrusion parameters, the Mg2Yb series tend to have larger grain sizes and less pronounced rare earth textures. This leads to intensive TTW-ing under compressive stress, resulting in high SDEs. Subsequent heat treatments can increase the YS. Since the effect on the slip systems is stronger than on the formation of TTWs, this leads to further increased SDEs. However, by reducing the extrusion temperature the grain size of the Mg2Yb alloy is also reduced and an advantageous texture can be achieved. This is accompanied by a significant increase in YS. Since CRSSttw in particular is very sensitive to grain size, the CYS increases more than the TYS. Therefore, it is also possible to obtain an SDE close to 0 for the Mg2Yb alloy.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/2075-470 1/11/3/377/s1: Figure S1: Cross sections of the A- and B-series of the Mg2Nd and Mg2Yb alloy at different strains and elongation to failure. Figure S2: Comparison of the measured and simulated texture development during deformation of the A- and B-series of the Mg2Nd and Mg2Yb alloy at different strains. Figure S3: Comparison of the flow curves from compression and tensile tests of the A-, B- and C-series of the Mg2Nd and Mg2Yb alloy. Figure S4: Comparison of the experimentally measured and simulated axial elastic lattice strains during (a, b) compression and (c, d) tensile tests of the A- and B-series of the Mg2Nd alloy. Figure S5: Comparison of the experimentally measured and simulated axial elastic lattice strains during (a, b) compression and (c, d) tensile tests of the Aand B-series of the Mg2Yb alloy. Figure S6: Deformation mode activity as a function of strain of the A- and B-series of the Mg2Nd alloy. Figure S7: CRSS of the different deformation systems as a function of strain of the A- and B-series of the Mg2Nd alloy. Figure S8: Deformation mode activity as a function of strain of the A- and B-series of the Mg2Yb alloy. Figure S9: CRSS of the different deformation systems as a function of strain of the A- and B-series of the Mg2Yb alloy.

**Author Contributions:** Conceptualization, J.S., I.J.B., W.R.; methodology, J.S., I.J.B.; software, J.S., I.J.B., M.K.; validation, J.S., I.J.B., W.R.; formal analysis, J.S., I.J.B.; investigation, J.S.; resources, I.J.B., W.R.; data curation, J.S., I.J.B.; writing—original draft preparation, J.S.; writing—review and editing, I.J.B., M.K., W.R.; visualization, J.S, I.J.B.; supervision, W.R.; project administration, J.S., I.J.B., W.R.; funding acquisition, W.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Deutsche Forschungsgemeinschaft (DFG), grant number AOBJ595087.

**Acknowledgments:** The authors would like to thank Katrin Böttcher, Mateus Dobecki, Felix Hohlstein, Alexander Poeche, Tim Plöger, Jakob Schröder (TU Berlin, Metallische Werkstoffe), and Manuela Klaus (HZB) for the support of the in situ experiments; Sören Selve (TU Berlin, Zelmi) for conducting the HR-TEM analysis; Jörg Nissen (TU Berlin, Zelmi) for conducting the EPMA analysis; and Christoph Fahrenson (TU Berlin, Zelmi) for conducting the EBSD analysis. I.J.B. acknowledges financial support from the National Science Foundation Designing Materials to Revolutionize and Engineer our Future (DMREF) program (NSF CMMI-1729887). M. K. gratefully acknowledges support from the U.S. National Science Foundation (NSF) under grant no. CMMI-1727495.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analysis, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **References**


### *Article* **Hot Rolling of Magnesium Single Crystals**

**José Antonio Estrada-Martínez 1, David Hernández-Silva 1,\* and Talal Al-Samman <sup>2</sup>**


**Abstract:** To analyze the effect of the initial orientation in the activity of twinning and texture development, magnesium single crystals were rolled at 400 ◦C (nominal furnace temperature) in two specific orientations. In both orientations, the rolling direction of the sheet (RD) was parallel to the *c*-axis. For orientation 1, the 1120 direction was parallel to the normal direction (ND), and for orientation 2, it was parallel to the 1010 direction. The samples were rolled at 30%, 50% and 80% of thickness reduction. After rolling, all the samples were quenched in water to retain the microstructure. The microstructure and texture evolution were characterized by X-ray diffraction and Electron Backscatter Diffraction (EBSD). The initial single crystals were turned into polycrystals, where most grains had their *c*-axis almost parallel to the ND, and this reorientation was explained by extension twinning. The active twin variants in orientation 1 aligned the basal plane ~30◦ from the sheet plane and caused a weaker basal texture compared to orientation 2, where the twin variants aligned the basal plane almost parallel to the sheet plane. Strain localization inside contraction twins was observed, and consequently, non-basal grains nucleated inside these twins and weakened the final basal texture only in orientation 1.

**Keywords:** magnesium single crystal; texture; twinning

**Citation:** Estrada-Martínez, J.A.; Hernández-Silva, D.; Al-Samman, T. Hot Rolling of Magnesium Single Crystals. *Metals* **2021**, *11*, 443. https://doi.org/10.3390/met11030443

Academic Editor: Andrey Belyakov

Received: 30 January 2021 Accepted: 3 March 2021 Published: 8 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

Magnesium has a hexagonal closely packed structure, which causes high mechanical anisotropy and low formability at room temperature, owing to the limited number of easily activate slip systems. In addition, it is well known that magnesium develops a basal texture after deformation [1,2]. The above has given rise to many investigations seeking to improve the mechanical properties and formability of this material, which requires a vast understanding of the deformation mechanisms present in the forming processes.

Studies on deformation of single crystals have several advantages compared to deformation of polycrystals. The use of specifically oriented single crystals with respect to the loading axes allow to isolate and identify the deformation mechanisms depending on the initial orientation of the crystal, since the operating deformation mechanisms, at least at early stages of deformation, can be determined using the Schmid's Law [3–6].

First studies on magnesium single crystals were performed by Wonziewicz et al. [5] and Kelly et al. [6]. In these studies, the crystals were subjected to plane strain compression (PSC) tests in different orientations, which showed profuse deformation by twinning and recrystallization. However, these investigations were limited to small strains and focused on the effect of temperature on the activity of the deformation mechanisms.

More recently, Chapuis et al. [7] evaluated the temperature dependency of critical resolved shear stresses (CRSS) of the slip and twinning systems of Mg single crystals by PSC tests and concluded that basal slip and - 1012 twinning are not temperaturedependent mechanisms, prismatic and pyramidal II slip were identified only at about 300 ◦C and contraction twinning systems - 1011 and - 1013 were identified as temperaturedependent systems because their CRSS decreased with the temperature increase.

Molodov et al. [8–14] characterized the deformation behavior and microstructure evolution of Mg single crystals in plane strain compression, using Electron Backscatter Diffraction (EBSD) and X-ray pole figure measurements. They focused on the activation of twinning and dynamic recrystallization mechanisms and its influence on the texture evolution.

Currently, no works on rolling of magnesium single crystals have been reported, and considering the contributions of the previously described works, single crystals could help us to understand the deformation behavior of magnesium during rolling deformation, which allows a certain broadening of the sample, contrary to PSC, where broadening is usually suppressed by the walls of the channel die. Therefore, the aim of this work is to provide a basic understanding of the deformation mechanisms involved in hot rolling of magnesium single crystals at 400 ◦C and its contribution to the final texture.

#### **2. Materials and Methods**

The single crystals of commercially pure magnesium (min. 99.95%) were fabricated by crystal growth using the Bridgman method in a vertical configuration. To manufacture monocrystalline rolling samples with their geometric axes coinciding with specific crystallographic directions, each grown single crystal was oriented by means of the Laue X-ray back diffraction method [15], then, slabs with dimensions of 40 mm × 20 mm × 6 mm were cut by electrical discharge machining (EDM). Figure 1 shows the schemes of the rolling samples and their orientation relationship with the crystal directions. The *c*-axis of the crystals were aligned parallel to the rolling direction in both orientations. In the sample labeled "orientation 1" (O-1), the normal direction (ND) was aligned parallel to 1120 crystal direction and the transversal direction (TD) corresponds to 1010 . In the sample of "orientation 2" (O-2), the normal direction (ND) was aligned parallel to 1010 crystal direction and the transversal direction (TD) corresponds to 1120 . The misalignment between the crystallographic directions and the specimen axes was less than 0.5◦.

**Figure 1.** Single crystal orientations (O) for the rolling experiments.

It is well known that above about 250 ◦C, additional slip systems become operative in the deformation of pure magnesium and fulfill the Von Mises criterion, which states that in a polycrystalline material, five independent sliding systems must be activated to perform any possible deformation without fail. That is why the typical temperature range for magnesium rolling is between 300 and 500 ◦C [16–19]. In the current work, considering that the specimens were single crystals, and it might be a little harder to deform them successfully compared to polycrystalline material, the slabs of both orientations were heated at 400 ◦C for 30 min to ensure the deformation ability of the material and avoid cracking during deformation. Subsequently, each slab was rolled at 200 mm/s to ~30%, ~50% and ~80% of thickness reductions, using 7, 11 and 16 rolling passes, respectively. The complete rolling schedule is presented in Table 1. Between each rolling pass, the samples

were returned to the furnace for reheating at 400 ◦C for 10 min. After the final pass, the sheets were quenched in water to freeze the microstructure and prevent post-mortem static recrystallization. For the microstructural and texture analysis, several samples were cut from the sheets mid-plane using EDM.

**Table 1.** Rolling schedule.


The sample preparation for X-ray and EBSD measurements consisted of soft grinding with 2000 and 4000 grinding paper of silicon carbide during 10 min for each particle size, followed by 3 and 1 μm diamond suspension polishing for 15 and 20 min, respectively. After that, electropolishing in a solution of 125 mL ethanol and 75 mL H3PO4 was performed at 2.0 V, submerging the specimens in the electrolyte for 40 min. In the case of microstructural characterization by optical microscopy, a chemical color-etching with a freshly prepared solution of 10 mL H2O, 10 mL CH3-COOH and 70 mL picral 4% was applied.

To characterize the crystallographic texture, X-ray pole figure measurements were conducted in a Bruker D8 Advance diffractometer (Bruker, Billerica, MA, USA), equipped with a HI-STAR multi-wire area detector (Bruker, Billerica, MA, USA) with a circular beryllium window, operating at 30 kV and 25 mA. A set of six incomplete pole figures of the - 1010 , (0002), - 1011 , - 1012 , - 1120 and - 1013 families were measured and used to determine the orientation density function (ODF) using the MTEX 5.1.1 toolbox [20].

Electron Backscatter Diffraction (EBSD) measurements were conducted on a JEOL JSM-6701F (JEOL Ltd., Tokyo, Japan) scanning electron microscope equipped with a field emission gun (LaB6 filament) and an HKL-Nordlys II EBSD detector (Oxford Instruments PLC, Abingdon, UK). An acceleration voltage of 30 kV was used for all measurements. The HKL Channel5 5.11 (Oxford Instruments PLC, Abingdon, UK) software was used for the post-processing of the raw data.

#### **3. Results**

The sheets of pure Mg single crystals rolled at 400 ◦C are shown in Figure 2, which reveal a smooth surface without visible cracks for both orientations. There were no significant changes in the final dimensions (as a broadening) between the sheets of two orientations, which could indicate small changes in the deformation behavior caused by the difference of the initial crystallographic orientation.

**Figure 2.** Pictures of magnesium hot-rolled sheets of orientation 1 and orientation 2 at 0% (raw material) 30%, 50% and 80% of thickness reduction.

#### *3.1. Microstructure Evolution during Rolling Process*

The microstructure of the rolled samples was examined by optical microscopy and the results are presented in Figure 3. The single crystal has been totally turned into a polycrystal of relatively large grains with a particular characteristic, featured by their straight grain boundaries. Thus, they can be described as polygonal grains. In both orientations, many twins and recrystallized twin bands, consisting of fine dynamic recrystallized grains along the twin bands, were observed. The network of twins distributed homogeneously along the microstructure formed symmetric sets, and an inclination angle of ~60◦ can be observed between them.

At 30% of reduction, many lenticular twins were observed, in O-1 as well as in O-2. In the case of O-2, some recrystallized grains inside the twins can be observed, suggesting the occurrence of dynamic recrystallization (DRX) process. In the O-2, coarser grains compared to O-1 can be observed, but this feature is not so evident in subsequent reductions.

With further deformation (at 50%), the microstructure of O-1 was characterized by the presence of more and finer twins compared to 30%. In O-2, fewer twins were observed, but in this case, they were coarser than those observed in this orientation at 30% and tended to form clusters. In both orientations, fine grains were observed inside the twins and some twin-free grains were identified.

**Figure 3.** Optical micrographs at 200× and 500× magnifications of the rolling direction (RD)-transversal direction (TD) plane after magnesium single crystal rolling at different strains of both studied orientations.

Finally, at ε = 80%, the O-1 exhibited a partially recrystallized and heterogeneous microstructure described by two zones. In the first, to the left of the micrograph, recrystallized grains almost consumed all the matrix (there was a grain growth considering the size of recrystallized grains observed in previous strains). In the second, at the center, some recrystallized and coarse twin bands as well as recrystallization-free twin bands were found, suggesting that the grains initially recrystallize within the twins, grow, and consume the surrounding matrix.

It can be observed that the fraction of recrystallized grains increases as the rolling progresses, especially inside the twins, and consumes them (O-1 at 80%). These observations indicate that the DRX process plays a dominant role in the microstructure evolution during rolling, giving rise to new grains and, in consequence, new orientations that could modify the texture, and it is interesting to analyze them.

#### *3.2. Texture Evolution during Hot Rolling*

Texture measurements were carried out along the sheets and the average texture was reported by means of pole figures (PF) in Figure 4. For O-1 at the early stage of 30%, the (0002) pole figure exhibits a strong basal texture with an intensity value of 17.8. On the other hand, the O-2 presents a stronger basal texture with a maximum of 23. The corresponding - 1010 and - 2110 pole figures of both orientations reveal that the prismatic plane distributes homogeneously along the transversal and rolling direction of the sheet. Other components can be clearly detected at the center of these; in the - 1010 , a weak pick indicates that some prismatic planes are parallel to the ND of the sheet. A texture fiber component can be observed at ~30◦ from the ND in this PF, which is the same component shown by the weak peak at ND of the - 2110 pole figure.

**Figure 4.** Pole Figures of texture measurements of magnesium sheets at different thickness reductions for both orientations.

With increasing strain at 50% of reduction thickness, in the O-1 texture, the basal texture intensity became strengthened and reached a value of 19.4. Meanwhile, (0002) PF of O-2 shows an intensity of 26. The increment in the intensity is slightly higher for O-2 than for O-1 with respect to the PF at 30%. Regarding the - 1010 and - 2110 pole figures, the same components described at 30% can also be observed at 50%.

At the final reduction thickness of 80%, the (0002) PF of O-1 reveals the emergence of a double-pick component slightly deviated from ND with a maximum of 17.3, weakening the basal texture compared with previous stages. In the case of O-2, the maximum of the basal PF increased until 29.0 and no changes in the components that have already been described in previous deformations were found.

According to the microstructure evolution, it is certain that the texture development is strongly associated with the changes on the microstructure during rolling. In general, a strong basal texture with a non-preferential orientation of the a-axis was observed in both orientations since 30% until 80% of thickness reduction, but this basal texture is weaker in O-1 than in O-2. Also, at 80% in O-1, there is a decrease in the intensity of basal texture and the presence of a new double-pick component, the opposite to O-2, where there is always a strengthening of the texture and the components stay the same.

#### *3.3. EBSD Measurements*

The microstructure evolution was characterized by EBSD to reveal the twin types during magnesium single crystal rolling. The orientation maps are presented in terms of inverse pole figure coloring with respect to the ND. A step size of 0.7 μm was used for all measurements. High-angle grain boundaries (HAGBs, >15◦) were highlighted in black and low-angle grain boundaries (LAGBs, 2–15◦) in gray. Black areas show remaining zero solutions (non-indexed EBSD patterns) correlating with high local strain areas. Noise reduction was carefully applied to improve the original indexing using a minimum of five neighbors. In the twin boundary misorientation map, the types of twins were determined based on their particular misorientation angles and rotation axes [21]. The deviation of angle and axis to identify the twin boundaries was within 5◦ of the ideal values. It is important to mention that the Schmid Factor (SF) maps and misorientation profiles will be analyzed in Section 4.

Figure 5 shows the EBSD results of the interrupted rolling at 30% of reduction of O-1. The original indexing for the mapping was 87% and was improved to 97% by noise reduction, and the map size consists of a grid of 818 × 1063 points. The area fraction of extension twins was 0.019 and 0.048 for contraction twins. In the orientation map (Figure 5a), yellow squares point to high-angle grain boundaries (HAGBs), and these belong to grains that recrystallize at the triple junctions (TJ). Blue boxes enclose low-angle grain boundaries that bulged at the triple junctions (LAGBs-TJ). The nucleation of new grains at the triple junction could be related to the discontinuous dynamic recrystallization (DDRX) mechanism occurrence [22], but it is not the purpose of this paper to address this analysis. Meanwhile, green boxes point out zones where it is possible to observe the transition from a LAGB to HAGB (gray-grain boundary to black-grain boundary), but not at the triple junctions. Cyan rectangles enclose LAGBs that completely cross an extension twin, indicating that the dislocations can slip into the parent grain, completely cross the twin, and move onto the parent grain again.

**Figure 5.** Electron Backscatter Diffraction (EBSD) results obtained from an O-1 specimen at 30% of thickness reduction: (**a**) EBSD map in inverse pole figure (IPF) coloring relative to normal direction (ND), corresponding scattered data (0002) PF and misorientation profiles, (**b**) twin boundary misorientation map, (**c**) Schmid Factor map for (0002) 1120 slip system, (**d**) Schmid Factor map for - 10111123 slip system.

The corresponding orientation map of O-2 at 30% is presented in Figure 6: the original indexing was 88% and was improved to 97% by noise reduction, and the map size consists of a grid of 545 × 926 points. The area fraction of extension twins was 0.009 and for contraction twins it was 0.076. In the orientation map (Figure 6a), yellow squares point to high-angle grain boundaries (HAGBs), and these belong to grains that recrystallize at the triple junctions (TJ). Blue boxes enclose low-angle grain boundaries that bulged

at the triple junctions (LAGBs-TJ). Cyan rectangles enclose nets of LAGBs that do not crowd at triple junctions. Green frames show zones where the transition from a LAGB to HAGB can be observed. As in O-1, the new matrix has basal-oriented grains, and consequently, compression twins were formed inside. Compared to O-1, more contraction twins (CTs) were observed (Figure 6b), and this can be explained if we analyze the EBSD map where grains of more solid red coloration were observed, i.e., the basal plane in this orientation was aligned almost parallel to the sheet, rendering the *c*-axis almost parallel to the compression load induced by rolling. This can also be observed in the PFs of Figure 4, where the intensity of the basal component of O-2 is higher and sharper than O-1.

**Figure 6.** Electron Backscatter Diffraction (EBSD) results obtained from an O-2 specimen at 30% of thickness reduction: (**a**) EBSD map in inverse pole figure (IPF) coloring relative to normal direction (ND), corresponding scattered data (0002) PF and misorientation profiles, (**b**) twin boundary misorientation map, (**c**) Schmid Factor map for (0002) 1120 slip system, (**d**) Schmid Factor map for - 10111123 slip system.

Figure 7 shows the EBSD result of O-1 at 50%, where the original indexing of the map was 78% and was improved to 84% by noise reduction, and the map size consists of a grid of 505 × 788 points. The area fraction of extension twins of this map was 0.008 and 0.07 for contraction twins. Twin bands embedded in a 'hard' basal orientation matrix (*c*-axis nearly parallel to ND) were observed. The orientation map of Figure 7a shows thicker twin bands (some of them were recrystallized) and more low-angle grain boundaries (LAGBs) than those observed at 30%. Yellow boxes point out grains that recrystallize inside the contraction twin. There are many areas with zero solution along the bands of contraction twins, which indicate a high deformation inside them. Despite the low index ratio in these zones, fine grains can be observed inside the twin-like morphologies derived from the high concentration of plastic deformation within the twins and its subsequent partial recrystallization. Cyan rectangles enclose nets of LAGBs that do not crowd at triple junctions.

**Figure 7.** Electron Backscatter Diffraction (EBSD) results obtained from an O-1 specimen at 50% of thickness reduction: (**a**) EBSD map in inverse pole figure (IPF) coloring relative to normal direction (ND), corresponding scattered data (0002) PF and misorientation profiles, (**b**) twin boundary misorientation map, (**c**) Schmid Factor map for (0002) 1120 slip system, (**d**) Schmid Factor map for - 10111123 slip system.

In the orientation map of O-2 at 50%, shown in Figure 8, the original indexing for the mapping was 81% and was improved to 88% by noise reduction, and the map size consists of a grid of 511 × 743 points. The area fraction of extension twins of this map was 0.12 and 0.018 for contraction twins. In the orientation map (Figure 8a), yellow squares point out high-angle grain boundaries (HAGBs) that belong to recrystallized grains subdividing the pre-existing grains. Cyan rectangles enclose nets of LAGBs that do not crowd at triple junctions. Green frames show zones where the transition from a LAGB to HAGB can be observed. Also, in this case, most of the grains have the basal plane almost parallel to the sheet plane and therefore many lenticular - 10111012 twins were located inside, but were thinner than those observed in O-1, and recrystallized grains are not clearly observed inside the twinned area.

**Figure 8.** Electron Backscatter Diffraction (EBSD) results obtained from an O-2 specimen at 50% of thickness reduction: (**a**) EBSD map in inverse pole figure (IPF) coloring relative to normal direction (ND), corresponding scattered data (0002) PF and misorientation profiles, (**b**) twin boundary misorientation map, (**c**) Schmid Factor map for (0002) 1120 slip system, (**d**) Schmid Factor map for - 10111123 slip system.

Figure 9 shows an EBSD map for O-1 at 80% of thickness reduction. The original indexing for the mapping was 89% and was improved to 98% by noise reduction, and the map size consists of a grid of 850 × 1145 points. The microstructure is not homogenous, and a typical bimodal microstructure consisting of fine and coarse grains was observed. The coarse grains belong to the basal matrix observed in the previous strains. On the

other hand, most of the fine grains were originated by the DRX process inside the twins. Practically, all grains have a basal orientation or very close to it. However, some grains near to 1011 , 1013 , 2111 , 2112 and 2114 components can also be observed inside the twin-like morphologies, although in a much smaller proportion. The map does not show twinning activity despite the same temperature of deformation and similar texture compared to 30% and 50%, but an evident smaller grain size, indicating the susceptibility of the twinning to the grain size compared to other parameters.

**Figure 9.** Electron Backscatter Diffraction (EBSD) results obtained from an O-1 specimen at 80% of thickness reduction: (**a**) EBSD map in inverse pole figure (IPF) coloring relative to normal direction (ND) and corresponding scattered data (0002) PF, (**b**) Schmid Factor map for (0002) 1120 slip system, (**c**) Schmid Factor map for - 10111123 slip system.

Finally, Figure 10 shows the EBSD map of O-2 at reduction of 80%, where the original indexing for the mapping was 71% and was improved to 78% by noise reduction, and the map size consists of a grid of 375 × 622 points. This presents partially recrystallized twin bands, leading to grains with orientations slightly deviated from 1010 , 1011 , 1012 , 2110 and 2114 components. These bands could also be grains elongated by deformation and then recrystallized, since some of them were observed parallel to the RD in particular cases, however due to their morphology (some bands are

almost perpendicular to the RD), they were considered as recrystallized twins. There is still a prominent matrix with a basal orientation, which has many LAGBs, but any twin could be found inside.

**Figure 10.** Electron Backscatter Diffraction (EBSD) results obtained from an O-2 specimen at 80% of thickness reduction: (**a**) EBSD map in inverse pole figure (IPF) coloring relative to normal direction (ND) and corresponding scattered data (0002) PF, (**b**) Schmid Factor map for (0002) 1120 slip system, (**c**) Schmid Factor map for - 10111123 slip system.

#### **4. Discussion**

#### *4.1. Extension Twinning and Its Influence on the Basal Texture*

There are different reports in the literature regarding the twinning activity during deformation of magnesium. Some works report that this activity is negligible during deformation at high temperatures [23–25], while others report that twinning is active at high deformation rates regardless of deformation temperature [5,26]. There are also other works that relate twinning activity at high temperatures to large grain sizes [27,28]. In the current work, twinning was an important deformation mechanism, where both high deformation temperature and very large grain size (single crystal) are investigated.

In O-1, the starting orientation was aligned for - 1012 tensile twinning (Schmid factor of 0.37, compression perpendicular to *c*-axis). Blue areas from the original orientation ( - 1120 ) can still be observed but in a very marginal proportion, and it is important to note that most of these blue areas correspond to - 1012 extension twins (ETs) according to the twin boundary misorientation map (Figure 5b), and according to the (002) PF of scattered data, these areas appear close to the RD, as in the case of initial orientation, which could indicate that these zones are leftovers of initial single crystal. In this way, we can explain how the single crystal was almost completely rotated from 1120 //*ND* (blue grains) to 0001//*ND* (red grains) by means of nucleation and growth of extension twinning.

The twinned red grains now constitute a new matrix wherein contraction twinning was favorable. This is owing to the *c*-axis being at 30◦ from ND (Schmid factor of 0.49, compression load almost parallel to *c*-axis). At this strain, according to the orientation map, most of the grains have basal planes deviated ~30◦ from the sheet plane (red-orange grains), so they were subject to compression on the *c*-axis during rolling; consequently, they show compression twins inside.

As the O-1, the O-2 was aligned for extension twinning (SF = 0.49, compression perpendicular to *c*-axis), but the active variants according to Schmid's Law were slightly different in each case. The initial orientation 2 must be colored in green according to the standard IPF, but no grains with this characteristic were detected.

It is possible that - 1012 twinning explains this lattice rotation from the *c*-axis parallel to RD to the *c*-axis almost parallel to ND, and the consequent basal texture in both orientations. The activation of - 1012 twinning depends on the strain path, compression perpendicular to the *c*-axis or tension parallel to the *c*-axis, and their activity is governed by the Schmid law. Usually, the twin variant with the higher Schmid Factor (SF) takes place favorably [29–33], but there are, of course, cases where twinning does not obey a Schmid law [11,34,35]. Therefore, in the following, the - 1012 twinning behavior was analyzed with respect to the loading and crystal orientation. Its corresponding effect on the evolution of grain orientation was also discussed.

Under rolling, the initial single crystals with the *c*-axis parallel to the RD were favorably aligned for - 1012 twinning (compression perpendicular to the *c*-axis). Theoretically, - 1012 twinning is possible on six twin variants, 1012 1011 , 0112 0111 , 1102 1101 , 1012 1011 , 0112 0111 and 1102 1101 [29–31]. Figure 8a,b shows basal pole figures depicting the calculated - 1012 extension twin orientations for the initial specimen orientations. To explain the lattice rotation during single crystals' rolling, the following can be assumed: - 1012 twins gradually consumed its parent grain (single crystal) and reoriented it by ~86.3◦, with basal planes almost parallel to the RD since the early stage of deformation, contributing to the formation of the basal texture but in two very different ways:

For O-1, 01120111 , 11021101 , 11021101 and 01120111 variants have a SF value of 0.37, as shown in Figure 11a, making them equally active considering the Schmid law. These twin variants transformed the matrix into twin orientations with the *c*-axis aligned at an angle of ~30◦ from ND, as shown in Figure 11c. These orientations have a non-zero Schmid factor for basal, prismatic and pyramidal slip, but - 1011 twinning continues to have higher SF. According to Chapuis et al. [7], the CRSS for contraction twins is estimated between 30 and 150 MPa, and it is therefore higher compared to CRSS of basal (1.5–3.6 MPa), prismatic (6–15 MPa) and pyramidal slip (20–25 MPa), and the variations depend on the temperature. Despite the high CRSS (but also a high SF), contraction twins are visible in the twin boundary misorientation map (Figure 5b).

**Figure 11.** (0002) calculated PF showing the initial orientations (**a**) O-1 and (**b**) O-2, as well as their corresponding extension twin variants. Schematic representation of twin variants for (**c**) O-1 and (**d**) O-2.

On the other hand, regarding O-2, only 10121011 and 10121011 variants have a SF = 0.49 (Figure 11b) and lay the basal plane almost parallel to the sheet plane, which strengthens the basal texture (Figure 11d), converting the initial matrix into a 'hard' orientation, in which slip was suppressed. According to Molodov [36], the specimens under plane strain compression (PSC) with the starting orientation D (O-2) were again almost single-crystalline, with only low-angle grain boundaries after the conversion of the initial matrix by twinning, so, the crystal rotation from 1120 //*ND* to 0001//*ND* by extension twinning is not baseless.

As a result of this reorientation, the intensity of the basal component in the O-2 was higher than O-1. The broadening along the RD in the texture component of (0002) PF for O-1 (Figure 4) points out that these variants: 01120111 , 11021101 , 11021101 and 01120111 , accommodated the basal plane ~30◦ rotated from the sheet plane according to the predicted poles of high SF twin variants (Figure 11a). Unlike orientation 2, where the basal component of (0002) PF is sharper (Figure 4) and again agrees with the predicted pole figures (Figure 11b).

#### *4.2. Shear Localization on* - 1011 *Twins and Their Influence on the DRX*

At 30% of thickness reduction, the misorientation profiles along the black arrows in the EBSD maps (Figures 5 and 6) reveal a continuous change of orientation inside the grains. At some points, this misorientation reaches 13◦, revealing that dislocations were also active in addition to the twinning. In O-1 (Figure 5a), the line profiles L1 and

L3 are inside grains with high SF for basal slip according to Figure 5c, meanwhile L2 and L4 cross areas with low SF for basal slip; however, these show a high misorientation, which indicates that not only the basal slip was active. The maps of SF for other slip systems of <a> type dislocations are not shown because the SF was close to zero in these maps. The slip system that shows a high SF inside the basal orientation grains was - 10111123 (Figure 5d) and this is totally in accordance with the study of Kelvin et al. [37], where the first-order (pyramidal-I) slip - 10111123 was presumably the more dominant slip system in *c*-axis compression at room temperature, with a CRSS of 54 MPa. In O-2 (Figure 6a), a similar behavior was observed, but in this case, all the line profiles (L1–L4) are inside grains with low SF for basal slip (Figure 6c), despite this, they reach misorientations of ~14◦.

As mentioned above, the orientation maps of O-1 and O-2 at 50% (Figures 7a and 8a, respectively) show areas with high concentration of deformation and consequently, they were not indexed. From the quality of the EBSD patterns of the matrix, we can deduce that these have not been deformed at the same magnitude as twin bands, implying that deformation is heavily concentrated in the softer twins. If we analyze the SF maps for both orientations (Figure 7c,d and Figure 8c,d), we can observe that basal slip has a high SF inside the contraction twins opposite to first-order pyramidal-I, which has a high SF in the basal-oriented grains. Considering the reported values of CRSS of slip basal ~2 MPa [7] and first-order pyramidal-I slip ~54 MPa [37], it is logical to expect that the basal slip will be the dominant mechanism due to its low CRSS, causing the high concentration of deformation within the twin bands. The line profiles L2 and L4 in Figure 7a are inside grains with high SF for basal slip according to Figure 7c, meanwhile L2 and L4 in Figure 7a and L1–L4 in Figure 8a cross areas with low SF for basal slip, however, these reach a high misorientation of 8◦ and 14◦ respectively, indicating the activation of the - 10111123 slip system.

In O-1 at 80% of thickness reduction (Figure 9a), the morphological features of recrystallized regions revealed band arrangements embedded within un-recrystallized zones. These kind of arrangements seem to be recrystallized twin bands (DRXed-TBs), and it is evident that the grains inside them have a non-basal orientation, unveiling the effect of contraction twins (CTs) to nucleate them. The rest of the microstructure (out of the bands) shows that most of the recrystallized grains retain a basal orientation. In large grains that presumably belong to the initial basal orientation matrix, LAGBs can be observed, and it suggests that these kind of grains were divided into recrystallized small grains that retain their basal orientation. The many LAGB and SF maps (Figure 9b,c) suggest that basal slip is active inside the grains with non-basal orientation (inside twin bands) and first-order pyramidal-I slip inside the basal-oriented grains of the matrix.

In the case of O-2 at 80% of thickness reduction (Figure 10), there was not a grain refinement, the recrystallized twin bands (DRXed TBs) were coarser and show grains with a large spread orientation (away from basal orientation), allowing the basal slip. As in O-1, there are many LAGBs and sub-grains inside the matrix and recrystallized grains. SF maps (Figure 10b,c) suggest that basal slip is active inside the grains with non-basal orientation, i.e., recrystallized grains inside twin bands and the first-order pyramidal-I slip system inside the basal matrix.

It has been widely reported that - 1011 twins act as nucleation sites for DRX due to localized strain accumulation within the twin owing to the slip activity inside twin bands and difficult mobility of the twin boundaries, which is referred to as twin-induced dynamic recrystallization. This accumulation of energy produced dynamic recovery in these zones until the misorientation between the low-angle grain boundaries, by more than 15◦, and became high-angle grain boundaries and acquired a definitive non-basal orientation [8,25–28,38–40]. Nevertheless, the grains that nucleate inside - 1011 twins generally cannot grow outside the twin boundaries, so the efficacy of the twin-induced dynamic recrystallization mechanism on the final texture weakening is limited [26,27].

In this investigation, the contraction twin bands in the O-1 were thicker than O-2 at all thickness reductions. At 80%, the orientation map of O-1 (Figure 9a) clearly shows a net

of twin-like band morphologies, as described above. If we compare this feature with the one observed in the orientation map of O-2 (Figure 10a), we can easily notice that there is a greater amount of twin-like band morphologies in O-1 than in O-2, which suggests a profuse compression twinning in O-1 during the last rolling step. The recrystallized grains that nucleate inside the contraction twin band without a non-basal orientation seem to have grown slightly out of the twin boundary in O-1, contrary to O-2, where no profuse twin-like morphologies and recrystallized grains inside them can be observed. This explains very well the weakening in the basal texture of O-1 at 80% of thickness reduction, where the recrystallized grains with non-basal orientation contributed to weakening the basal texture from 19.4 to 17.3 multiples of a random distribution (m.r.d,) only in O-1, and gave rise to a new double-pick component in the PF (Figure 4).

#### **5. Conclusions**

In the present study, the deformation mechanisms of commercially pure magnesium single crystal during rolling at 400 ◦C of 30%, 50% and 80% thickness reduction were observed. The microstructural and textural development was investigated by means of EBSD. The following conclusions were drawn:


**Author Contributions:** Conceptualization, J.A.E.-M. and T.A.-S.; methodology, J.A.E.-M.; software, J.A.E.-M.; validation, D.H.-S. and T.A.-S.; formal analysis, J.A.E.-M. and D.H.-S.; investigation, J.A.E.-M.; resources, T.A.-S. and D.H.-S.; data curation, J.A.E.-M. and D.H.-S.; writing—original draft preparation, J.A.E.-M.; writing—review and editing, D.H-S. and T.A.-S.; visualization, J.A.E.-M.; supervision, D.H.-S. and T.A.-S.; project administration, D.H-S. and T.A.-S.; funding acquisition, D.H.-S. and T.A.-S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data is not publicly available due to ongoing research based on it.

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

#### **References**


## *Article* **Effect of Al Content on Texture Evolution and Recrystallization Behavior of Non-Flammable Magnesium Sheet Alloys**

**Sumi Jo \*, Dietmar Letzig and Sangbong Yi \***

Magnesium Innovation Centre, Institute of Material and Process Design, Helmholtz-Zentrum Geesthacht, Max-Planck-Str. 1, D-21502 Geesthacht, Germany; dietmar.letzig@hzg.de

**\*** Correspondence: su.jo@hzg.de (S.J.); sangbong.yi@hzg.de (S.Y.); Tel.: +49-4152-87-2002 (S.J.); +49-4152-87-1911 (S.Y.)

**Abstract:** The effect of Al content on the texture evolution and recrystallization behavior of the non-flammable Mg sheet alloys containing Ca and Y was investigated in this study. With a decrease in the Al content from 3 wt.% to 1 wt.%, the amounts of the other alloying elements dissolved in the matrix, especially Ca, are increased. The increase of the alloying elements in a solid solution brought out the retarded recrystallization and weakened texture with the basal poles tilted toward the sheet transverse direction. Extension twinning activity increased when Al content with decreasing, resulting in the texture broadening towards the sheet transverse direction in the as-rolled sheets. The textures of the AZXW1000 and AZXW2000 sheets weaken uniformly in all sample directions during annealing, while the AZXW3000 sheet shows less weakening of the rolling direction split component. The texture weakening of the alloys with lower Al contents is attributed to the retarded recrystallization caused by the larger amount of the dissolved Ca solutes. Based on the non-basal texture and relatively stable grain structure, the Mg alloy sheet containing a relatively small amount of Al is advantageous to improve the formability.

**Keywords:** magnesium; sheets; recrystallization; texture; formability; non-flammability

#### **1. Introduction**

As the lightest structural metallic material, Mg alloys are attractive for application in the transportation sectors to increase energy efficiency. However, a wide application of Mg alloys has been hindered by some drawbacks, such as poor room temperature formability, poor corrosion resistance, and high flammability. While the early studies regarding the formability improvement were conducted using the commercial AZ31 alloy sheet [1–5], it has been well acknowledged that the alloying of rare earth elements (RE), Ca or Sr [6–9] significantly improve the room temperature formability to be comparable to that of 6000 series aluminum alloy sheets [10]. The addition of Ca into Mg alloys has been known to improve high temperature mechanical properties and ignition-proof behavior. Moreover, the simultaneous addition of Ca with Y results in an excellent ignition-proof behavior and improved corrosion resistance [11–13].

A large amount of alloying elements cause difficulties in controlling the microstructure during the sheet processes, including continuous casting. Strong microstructure inhomogeneity caused by high alloying amount, e.g., centerline segregation formed in a strip produced via continuous casting and high quantity of secondary phases due to the high affinity Al with other alloying elements, like RE and Ca, deteriorates the mechanical and corrosion properties. Furthermore, the formation of secondary phases consumes the alloying elements dissolved in the matrix, such that the role of such elements in the texture weakening is diminished by high Al content [10,14–17]. In view of the effects of Al on microstructure and texture evolution, recent studies of highly formable Mg sheet alloys put focus on the development of low-Al containing alloys. It was reported that the Mg

**Citation:** Jo, S.; Letzig, D.; Yi, S. Effect of Al Content on Texture Evolution and Recrystallization Behavior of Non-Flammable Magnesium Sheet Alloys. *Metals* **2021**, *11*, 468. https://doi.org/10.3390/ met11030468

Academic Editor: Håkan Hallberg

Received: 26 February 2021 Accepted: 9 March 2021 Published: 12 March 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

alloy sheets containing Al close to 1 wt.%, Mg-1.2Al-0.5Ca-0.4Mn-1.6Zn [18], Mg-1.3Al-0.5Ca-0.7Mn-0.8Zn [19], and Mg-1Zn-1Al-0.5Ca-0.4Mn-0.2Ca [20], exhibit a weak texture, high formability, and improved mechanical properties. In this study, the texture evolution and recrystallization behavior of the Mg sheet alloys having excellent non-flammability containing Al, Ca, and Y, which are essential elements to achieve the non-flammability, as well as texture weakening, were investigated by varying the Al content from 1 wt.% to 3 wt.%. The focus of the present study is laid to clarify the relationship between the Al content and microstructural evolution of the non-flammable alloys in consideration of the amount of the dissolved alloying elements in the matrix.

#### **2. Materials and Methods**

The ingots of AZXW1000, 2000, and 3000 alloys, with the nominal compositions of Mg-xAl-1Zn-0.5Ca-0.5Y-0.1Mn, x = 1, 2, 3 (in wt.%), were prepared by gravity casting. The molten metal with the target composition was cast in a steel crucible under a protective atmosphere of Ar and SF6 mixture. The furnace temperature was set to 780 ◦C until the melts were poured into steel crucibles preheated at 700 ◦C. After pouring the melt, the crucible was quenched in water. It is to mention that the protection gas was used to ensure a high safety during the casting experiments, while the examined alloys exhibited an excellent ignition-proof behavior, e.g., no ignition during the pouring of the molten metal. The billets with a thickness of 10 mm were machined from the cast materials, and then hot rolled at 450 ◦C to a final thickness of 1.2 mm. The step reduction degree was increasing from 10 to 30% with the rolling passes, and the intermediate annealing of the rolled sheet was conducted at 450 ◦C for 10 min prior to each rolling step. The recrystallization annealing of the rolled sheet was conducted at 400 ◦C for 10 min. The textures of the as-rolled and annealed sheets were measured using a Panalytical X-ray diffractometer (Malvern Panalytical, Malvern, UK) and Cu Kα radiation. The (0002) pole figures were recalculated using a MATLAB-based toolbox MTEX [21] from six measured pole figures. Stretch formability (Index Erichsen, I.E) of the annealed sheets was tested at room temperature. The tests were carried out with a blank holding force of 10 kN, a punch diameter of 20 mm, and a deformation rate (punch displacement) of 0.5 mm/min. Microstructural analyses were performed using a scanning electron microscope (SEM, Vega 3 SB, TESCAN, Brno, Czech Republic), equipped with an energy-dispersive X-ray spectroscope (EDS, eumeX, Heidenrod, Germany). Electron backscatter diffraction (EBSD) analysis was performed by using an FEG-SEM (Ultra 55, Zeiss, Jena, Germany) equipped with an EBSD detector (Hikari camera (EDAX, Mahwah, NJ, USA)) with TSL OIM software (version 7, EDAX, Mahwah, NJ, USA). Specimens for electron microscopy were prepared by electro-polishing in a Struers AC2 solution at −20 ◦C and 30 V. The thermodynamic calculation for the corresponding alloy compositions was carried out using Pandat software (version 2017, Compu Therm LLC, Wisconsin, USA) [22] to calculate the amount of the dissolved Ca solutes in the matrix.

#### **3. Results and Discussion**

The recalculated (0002) pole figures of the as-rolled and annealed sheets are presented in Figure 1. The maximum pole densities of the (0002) pole figures of the asrolled AZXW1000, 2000, and 3000 sheets are 5.5, 4.9, and 6.2, respectively. The as-rolled AZXW1000 and AZXW2000 sheets show the basal poles tilted towards the rolling direction (RD) and, simultaneously, the basal pole spread in the transverse direction (TD), whereas the texture of the as-rolled AZXW3000 sheet is presented by the basal pole spread from the normal direction (ND) towards the RD. The annealed AZXW1000 and AZXW2000 sheets show the weak texture with the basal pole split toward the TD contrary to the texture of the annealed AZXW3000 sheet. These textures obtained in the AZXW1000 and AZXW2000 sheets normally develop in the highly formable Mg alloy sheets containing RE, Ca and Zn [14,16,23–28]. The appearances of the Erichsen samples of the examined sheets are shown in Figure 2. The annealed AZXW2000 sheet (IE = 6.2) indeed has higher formability

than the AZXW3000 sheet (IE = 4.8), while both sheets have higher IE values than the commercial AZ31 sheet (IE = 2~3). The improved formability can be understood as a result of the texture weakening and the accompanying development of the non-basal type texture.

**Figure 1.** Recalculated (0002) pole figures of the (**a**–**c**) as-rolled and (**d**–**f**) annealed AZXW1000, 2000, and 3000 alloy sheets, respectively.

**Figure 2.** Appearances of the Erichsen samples of the AZXW2000 and AZXW3000 sheets, respectively.

The optical micrographs, which are taken at the longitudinal section, of the as-rolled and annealed sheets are shown in Figure 3a–f, respectively. The microstructure of the asrolled sheets commonly consists of the deformed grains, deformation twins and secondary phases. The fully recrystallized microstructures were obtained in all examined alloys after annealing treatment at 400 ◦C for 10 min. The average grain sizes of the recrystallized AZXW1000, 2000, and 3000 sheets are comparable, 5.2, 6.9, and 6.1 μm, respectively.

**Figure 3.** Optical micrographs of the (**a**–**c**) as-rolled and (**d**–**f**) annealed AZXW1000, 2000 and 3000 sheets, respectively.

Figure 4 shows the variation of the phase fractions as a function of Al content, calculated by using the Pandat software. The total fraction of the secondary phases of the alloys

containing 1, 2, and 3 wt.% of Al increases with the Al content, 1.85, 2.42, and 3.97 wt.%, respectively. The amounts of Al4MgY and Al8Mn5 phases increase when Al content is higher than 1 and 2 wt.%. The formation of Mg2Ca and Al2Y phases is found only in the alloy containing 1 wt.% Al, while Al2Ca phase is formed in the alloys with Al amount higher than 2 wt.%. Considering the calculated fractions of the equilibrium phases, it is plausible that the fine particles with the average size of 0.2 μm observed in the as-rolled and annealed AZXW1000 and AZXW2000 sheets, Figure 3a,b,d,e, are inferred to be Mg2Ca and Al2Y phases.

**Figure 4.** Calculated phase fraction of the investigated alloys at 400 ◦C as a function of Al content.

The SEM images of the annealed AZXW1000, 2000, and 3000 sheets are demonstrated in Figure 5. The chemical compositions analyzed by SEM-EDS are listed in Table 1 for the secondary phases marked with yellow arrows. The stoichiometry of the particles B, E, and C corresponds to Al2Ca and (Mg,Al)2Ca phases, respectively, and the particle D to Al2Y phase. The particles observed in the AZXW1000, 2000, and 3000 sheets, from the SEM-EDS, does not follow the thermodynamic calculation, and the formation of the Al2Ca, Mg2Ca, as well as (Mg,Al)2Ca, are not clearly distinguished depending on the Al content. The formation of Ca-containing phases, Al2Ca, Mg2Ca, and (Mg,Al)2Ca mainly depends on the Ca/Al ratio. That is, the increase of Ca/Al ratio induces the formation of Mg2Ca and (Mg,Al)2Ca phases rather than Al2Ca phase [29], as shown in Figure 4. The chemical composition of the points A and F consisted of Al, Mn, and Y, do not match the equilibrium phases, i.e., Al8Mn5, Al2Y, or Al4MgY. Structural similarity among these phases [30,31] and solidification in non-equilibrium result in the formation of non-equilibrium phases. Additionally, the high affinity [32] of Al to Mn and Y is considered to agglomerate Al, Mn, and Y, and form the non-equilibrium phase.

**Figure 5.** Secondary electron micrographs of the annealed (**a**) AZXW1000, (**b**) AZXW2000, and (**c**) AZXW3000 alloy sheets, respectively. The energy-dispersive X-ray spectroscopy results on the second phases marked by arrows A to G are given in Table 1.


**Table 1.** Chemical composition (in at.%) of the second phases in the annealed AZXW1000, 2000, and 3000 sheets indicated by yellow arrows in Figure 5, analyzed by SEM-EDS.

As the Al content increases from 1 wt.% to 3 wt.%, the volume fraction and size of the secondary phases also increase, as shown in Figure 4, as well as the point A and F in Figure 5. It indicates that the high amount of Al is likely to consume the Ca, Y, and Mn solutes by the formation of the secondary phases during the thermo-mechanical treatments. On the contrary, in the alloys with low Al content the other alloying elements can be dissolved in the matrix without forming secondary phases. The amounts of the Ca solutes dissolved in the matrix are plotted as a function of the Al content in Figure 6. The experimental values and the calculated values using by Pandat software confirm that the amount of the dissolved Ca solutes increases with decreasing the Al content. Especially, the dissolved Ca solutes sharply increases by reducing the Al content to 1 wt.%. The differences between the amount of the calculated and the measured Ca solutes arise from the restricted resolution of the SEM-EDS and the formation of the non-equilibrium phases, like Al-Mn-Y, that are not expected from the thermodynamic calculation. It is important to mention that the amount of the Mn and Y solutes dissolved in the matrix also increase as Al content decreases, but the increment is much smaller in comparison to that of the Ca solutes.

**Figure 6.** Amount of the dissolved Ca solutes in matrix according to the Al content at 400 ◦C, comparing the experimentally measured values by SEM-EDS and the calculated amounts by Pandat software.

To investigate the recrystallization behavior and texture evolution during the annealing treatment, EBSD analysis was performed on the sheets annealed to various times. Inverse pole figure maps (IPF) of the examined sheets annealed at 400 ◦C for 0 s (as-rolled), 10 s, and 30 s are presented in Figure 7 with the corresponding (0001) pole figures. The EBSD measuring points with the confidence index (CI) higher than 0.08, without an additional data clean-up, are shown in the IPF maps, and the non-indexed areas with black color correspond to either highly deformed region or secondary phases. The as-rolled

AZXW1000, 2000, and 3000 sheets have a strong texture with the basal poles mostly tilted to the RD. The as-rolled AZXW1000 sheet shows a distinct broadening of the basal poles towards the TD, in comparison to that of the as-rolled AZXW2000 and AZXW3000 sheets. Accordingly, a large number of grains having the tilted basal pole to the TD (green grains) are found in the as-rolled AZXW1000 sheet. Misorientation angle distribution plots of the as-rolled AZXW1000, 2000 and 3000 sheets are shown in Figure 8. All of the examined sheets show three peaks at around 38◦, 56◦, and 86◦, and the peaks correspond to secondary, contraction and extension twins, respectively [33]. Interestingly, the fraction of the extension twin in the as-rolled AZXW1000 sheet is higher than that in the as-rolled AZXW2000 and AZXW3000. It can be mentioned that the AZXW1000 sheet have higher extension twinning activities than that of the AZXW2000 and AZXW3000 sheets, which matches to the distinct broadening of the basal poles towards the TD. Meanwhile, a higher fraction of the secondary twin is found in the AZXW3000, in comparison to that of the AZXW1000 and AZXW2000 sheets.

**Figure 7.** Inverse pole figure maps of the AZXW1000, 2000, and 3000 alloy sheets annealed for 0 s (as-rolled), 10 s, and 30 s.

**Figure 8.** Misorientation angle distribution of the as-rolled AZXW1000, 2000 and 3000 sheets calculated from the IPF maps in Figure 7.

A few papers reported that the secondary twin is an origin of strain localization and shear band formed in the as-rolled sheet [33,34]. The secondary twins were commonly observed in the shear bands with a high density of dislocations. The basal planes reoriented by secondary twins are favorable for the basal slip, and dislocation slip abundantly occurs and piles up around the twin boundaries, resultantly then, bring out stress concentration and distortion of the twin regions [34]. The as-rolled microstructure of the AZXW3000 sheet, Figure 3c, shows the distinct strain localization region developed across more grains in comparison to that of the as-rolled AZXW1000 and AZXW2000 sheets, Figure 3a,b. It arises from the highest fraction of secondary twins due to the stress concentration in the AZXW3000 sheet.

As the recrystallization proceeds during the annealing treatment for 10 s, the basal pole distribution of the investigated sheets broaden to the RD and TD. Even though the maximum pole densities of the sheets annealed for 10 s are barely changed, the basal pole densities weaken uniformly along all sample directions without a preferred weakening at a certain sample direction. After 30 s of annealing, the AZXW1000 and AZXW2000 sheets show further a uniform texture weakening accompanying the basal pole broadening towards the RD and TD. On the contrary, the weakening of the tilted basal pole to the RD is relatively less in the annealed AZXW3000 sheet for 30 s, resulting in a higher texture intensity.

The fraction of the recrystallized grains for the investigated sheets along the annealing time are shown in Figure 9, indicating distinct recrystallization kinetics of each alloy sheet. The recrystallized grains are defined by the grain orientation spread (GOS) less than 1◦. The fraction of the recrystallized grains in the as-rolled AZXW1000, 2000, and 3000 sheets are close to 0, and the recrystallization of the three alloy sheets is almost complete after the annealing treatment for 30 s as shown in Figure 7. Comparing the fractions of the recrystallized grains in the annealed sheets for 10 s, i.e., at the beginning stage of the recrystallization, it is clear that the examined alloy sheets exhibit different recrystallization kinetics. The fraction of the recrystallized grains in the AZXW1000, 2000, and 3000 sheets are 0.17, 0.21, and 0.26, respectively, indicating that the AZXW3000 sheet has faster recrystallization kinetics than the AZXW1000 and AZXW2000 sheets. It is reported that the recrystallization of the Mg alloy sheets containing RE, Ca, and Zn [14,16,23–25] is retarded by solutes segregation at the grain boundaries, stacking faults and twin boundaries, and resultantly, the recrystallization kinetics of the sheets become slow. For example, the ZW01 [16] and Mg-0.8Zn-0.2Ca [14] alloy sheets show slower recrystallization kinetics than the investigated alloy sheets in this study. The amount

of the dissolved solutes in the above alloys are calculated by Pandat software at the same temperature, 400 ◦C, for comparison. The amounts are 0.79 wt.% of Y, 0.05 wt.% of Zn, and 0.2 wt.% of Ca and 0.8 wt.% of Zn, respectively, which are higher than those in the examined sheets of the present study, Figure 6. Again, it is plausible that the recrystallization kinetics is influenced by the amount of the dissolved solutes. Accordingly, the recrystallization kinetics of the AZXW1000 and AZXW2000 alloy sheets are slower than that of the AZXW3000, which corresponds to the larger amount of the dissolved Ca solutes in the alloys with lower Al contents.

**Figure 9.** Fraction of the recrystallized grains of the AZXW1000, 2000, and 3000 alloys according to the annealing time calculated from the IPF maps in Figure 7.

The EBSD IPF maps and (0001) pole figures of the annealed sheets for 600 s, which correspond to Figures 1 and 3, are shown in Figure 10. While the AZXW1000 and AZXW2000 sheets maintain the basal poles tilted toward the TD and RD, the AZXW3000 sheet shows a higher concentration of the basal poles at the ND. The tendency of the basal-type texture development, i.e., alignment of the basal poles in the ND, with increasing the annealing time is commonly observed during the recrystallization of the commercial Mg alloy sheets, resulting in basal-type texture. The development of the basal-type texture is effectively hindered by the higher amount of the dissolved solutes, and brings out a more randomized texture with the basal pole tilted towards TD [14].

**Figure 10.** IPF maps and corresponding (0001) pole figures of the AZXW1000, 2000, and 3000 annealed for 600 s.

In addition to the retarded boundary motion by the dissolved solutes, the pinning effect by precipitates is also to be considered. As reported in [35], the thermally stable Y-containing precipitates in the Mg-0.7Ca-0.7Y alloy sheet hinder the grain boundary movement during the homogenization treatment, and contribute to obtaining the fine microstructure. Likewise, the fine particles that are observed in the microstructure of the asrolled and annealed AZXW1000 and AZXW2000 sheets, Figure 3a,b,d,e, can contribute to retarding the recrystallization. A more detailed analysis regarding the interaction between the precipitates and grain boundary motion will clarify the role of the fine precipitates on the recrystallization kinetics of the examined alloys.

#### **4. Conclusions**

The effect of the Al content on the texture evolution and recrystallization behavior of the Mg alloy sheets containing Ca and Y were investigated in this study. The decrease of the Al content in the alloy leads to the increase in the amount of the dissolved alloying elements in matrix, i.e., increase of the Ca solute. The retarded recrystallization and the texture weakening observed in the AZXW1000 and AZXW2000 sheets, in comparison to that of the AZXW3000 sheet, are attributed to the relatively high amount of the solutes. These results clearly show that the formability of the Mg sheet, which contains the alloying elements contribute to the texture weakening like Ca and Y, can be improved in 2~3 times by reducing Al content from 3 wt.% to 1 wt.%.

**Author Contributions:** Conceptualization, S.J. and S.Y.; Experiments and analyzed the experimental results, S.J.; Writing—original draft preparation, S.J.; Writing—review and editing, S.Y. and S.J.; Project administration, D.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was partly funded by NST-National Research Council of Science & Technology (No. CRC-15-06-KIGAM), Ministry of Science and ICP (MSIP).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

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

**Acknowledgments:** The authors gratefully acknowledge Y.M. Kim at Korea Institute of Material Science (KIMS) for a fruitful discussion on the experimental results and non-flammable alloys. The authors are grateful to Y.K. Shin, at Helmholtz-Zentrum Geesthacht (HZG), for supporting the sample preparation and EBSD analysis.

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

#### **References**


## *Article* **Superplasticity at Intermediate Temperatures of ZK60 Magnesium Alloy Processed by Indirect Extrusion**

**César Palacios-Trujillo 1, José Victoria-Hernández 2,3, David Hernández-Silva 1,\*, Dietmar Letzig 2,3 and Marco A. García-Bernal 4,\***

	- D-21502 Geesthacht, Germany; jose.victoria-hernandez@hzg.de (J.V.-H.); dietmar.letzig@hzg.de (D.L.)

**Abstract:** Magnesium alloys usually exhibit excellent superplasticity at high temperature. However, many Mg alloys have poor formation ability near room temperature. Therefore, preparation of Mg alloys with suitable microstructures to show low or intermediate temperature superplasticity is an important goal. In this work, the superplastic behavior at intermediate temperatures of a commercial ZK60 magnesium alloy processed by indirect extrusion was investigated. After extrusion, the alloy showed a refined and homogeneous microstructure with an average grain size of 4 ± 2 μm. Overall texture measurement indicated that the alloy showed a strong prismatic texture with the highest intensity oriented to pole 1010. A texture component 1211 parallel to the extrusion direction was found; this type of texture is commonly observed in Mg alloys with rare earth additions. Tensile tests were performed at temperatures of 150, 200, and 250 ◦C at three strain rates of 10<sup>−</sup>2, 10<sup>−</sup>3, and 10−<sup>4</sup> s<sup>−</sup>1. A very high ductility was found at 250 ◦C and 10−<sup>4</sup> s<sup>−</sup>1, resulting in an elongation to failure of 464%. Based on calculations of the activation energy and on interpretation of the deformation mechanism map for magnesium alloys, it was concluded that grain boundary sliding (GBS) is the dominant deformation mechanism.

**Keywords:** magnesium alloys; texture; indirect extrusion

#### **1. Introduction**

Magnesium alloys are increasingly used in electronics, automotive, and aerospace industries due to their low density, high specific strength, and excellent machinability [1]. However, the hexagonal crystal structure of magnesium limits its ductility, particularly at low temperatures. Magnesium exhibits only three slip systems at low temperature. Recent studies have shown that the ductility of this alloy can be improved with the reduction of grain size, and this could lead to superplastic behavior [1–5].

Superplasticity refers to the ability of a material to achieve high elongations of at least 200% when a sample is tested in tension [6]. By definition, superplasticity allows some metals and alloys to reach extensive ductility under restricted circumstances such as (1) low strain rates (usually between 10−<sup>5</sup> and 10−<sup>3</sup> s<sup>−</sup>1), (2) a fine and stable microstructure, and (3) a deformation temperature around 0.5 Tm or higher (with Tm being the absolute melting temperature) [7]. The superplastic behavior in magnesium alloys can provide the ability to deform complex parts that are difficult to form [8].

One advantage of Al-free Mg alloys is the exceptional grain-refining ability of Zr. Furthermore, in combination with a severe plastic deformation process such as rolling,

**Citation:** Palacios-Trujillo, C.; Victoria-Hernández, J.; Hernández-Silva, D.; Letzig, D.; García-Bernal, M.A. Superplasticity at Intermediate Temperatures of ZK60 Magnesium Alloy Processed by Indirect Extrusion. *Metals* **2021**, *11*, 606. https://doi.org/10.3390/ met11040606

Academic Editor: Daolun Chen

Received: 1 February 2021 Accepted: 20 February 2021 Published: 9 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

extrusion, drawing, equal channel angular pressing (ECAP), and friction stir processing (FSP), it can lead to stable fine grain structures in wrought alloys [9–13]. Among these, extrusion processes have aroused special interest, through which the microstructure can be strongly deformed, resulting in a refined microstructure and a suitable texture [13–16]. Specifically, the indirect extrusion process has shown a good combination of high strength and ductility at room temperature and superplasticity at elevated temperatures [16,17].

The purpose of this work is to investigate the superplastic behavior in a ZK60 commercial magnesium alloy processed by indirect extrusion by means of tensile tests at intermediate temperatures at three different strain rates and to elucidate the deformation mechanisms involved.

#### **2. Materials and Methods**

The commercial magnesium ZK60 alloy used in this study was processed by indirect extrusion, and it was provided by the consortium responsible for the MAGFORGE Project, a European Community Research on Forging of Magnesium Alloys [18]. The alloy was provided in the form of round bars of 2 in. diameter. The chemical composition of the alloy is given in Table 1.

**Table 1.** Alloy composition in weight percentage.


Samples for microstructural analysis were cut from the bars in order to analyze a plane parallel to the extrusion direction, as shown in Figure 1. Subsequently, they were ground and polished with a solution of OPS (colloidal silica of 0.05 μm), using as lubricant a solution of distilled water, liquid soap, and sodium hydroxide. The chemical attack to reveal the microstructure was carried out with a picric acid solution (150 mL of ethanol, 36 mL of distilled water, 6.5 mL of acetic acid, and 36 g of picric acid). An EBSD measurement was carried out using a field emission gun scanning electron microscope Zeiss Ultra 55 (Carl Zeiss AG, Oberkochen, Germany) equipped with an EDAX-TSL OIM system (EDAX-TSL OIM-7, Ametek-EDAX inc, Draper, UT, USA). The sample used was prepared in the same way as described above. In addition, it was electropolished using a Struers AC2 solution (Struers GmbH, Willich, Germany) at 16 V for 35 s at −25 ◦C to obtain a surface free of defects, such as deformation from mechanical polishing and scratches. The measurement was also carried out on the extrusion direction (ED)–normal direction (ND) plane. The EBSD measurement was conducted with an acceleration voltage of 15 kV and a step size of 0.3 μm.

**characterization** 

**Figure 1.** Location and orientation of samples for microstructural characterization and tensile tests.

The global texture was measured by means of a PANalytical X-ray diffractometer (Malvern Panalytical GmbH, Almelo, The Netherlands), using a texture goniometer and a sample in the form of a disc with a diameter of 1 cm. Before measurement, the sample was ground and polished. The results obtained were processed with the software X'Pert Texture (Data collector 2.0, Malvern Panalytical GmbH, Almelo, The Netherlands) to obtain the pole figures.

Tensile test samples were machined from the bars with the load direction parallel to the extrusion direction according to DIN 50125 M6, as shown in Figures 1 and 2. Tensile tests were carried out at intermediate temperatures of 150, 200, and 250 ◦C and strain rates of 10<sup>−</sup>2, 10<sup>−</sup>3, and 10<sup>−</sup><sup>4</sup> s<sup>−</sup>1.

**Figure 2.** Dimensions of tensile samples according to DIN 50125 M6.

The heating of the tensile test samples was applied by means of an electric furnace, which kept the specimens at a constant temperature within a range of ±1 ◦C. Before the test, the specimens were preheated to the selected temperature for 10 min in order to have a homogeneous and stable temperature. Once the test specimens had fractured, they were immediately quenched in water.

#### **3. Results and Discussion**

#### *3.1. Initial Microstructure and Global Texture*

The microstructure of the as-received commercial ZK60 alloy (see Figure 3a) showed recrystallized grains with an average grain size of 4 ± 2 μm measured by the linear intercept method. The microstructure showed additional bands of unrecrystalized grains. Shahzad et al. [17] studied these bands and found that they were zones of unrecrystallized grains formed by Zr segregations. Additionally, an analysis by EDS in SEM revealed particles rich in Zr and Zn. It is possible to consider that such particles belong to the Zr2Zn phase previously identified [19].

**Figure 3.** Microstructure of alloy ZK60 as received (**a**) and inverse pole figure (0001) (**b**).

In order to determine the texture of this alloy, pole figures of basal, prismatic, and pyramidal planes were constructed by means of X-ray diffraction. The inverse pole figures (IPFs) were obtained with the help of the MTEX software (Version 5.3.1, free and open source software toolbox).

The commercial ZK60 alloy showed a strong prismatic texture (see Figure 3b), and the highest intensity was found at the pole 1010. That means that most of the grains were oriented in such a way that their basal plane was parallel to the extrusion direction.

During extrusion, a texture component 1121 was developed parallel to the extrusion direction (ED), which caused the grains oriented in this direction to be favorable for basal slip, resulting in an improvement in ductility at room temperature [20]. This type of texture component is not often found in conventional alloys, but it has been seen more frequently in magnesium alloys with additions of rare earth (RE) elements such as Ce, Nd, Gd, and Y [20,21]. However, a minor influence on the mechanical behavior of this texture component in tension was expected, since most of the grains were aligned around the 1010 pole. On the other hand, it could have contributed to a decrease in the yield asymmetry in samples tested in compression in comparison to the yield stress in tension. However, the analysis of the yield asymmetry is out of the focus of the present work. For more details on the influence of the 1121 texture component, readers are referred to [22].

#### *3.2. Ductility*

Figure 4 shows the engineering stress–strain curve of ZK60 magnesium alloy at room temperature at a strain rate of 10−<sup>3</sup> s<sup>−</sup>1. As a result, the material presented a yield stress = 223 MPa, UTS = 290 MPa, and a ductility of ~13%. These data agree with the literature [20].

**Figure 4.** Stress–strain curve at strain rate of 10−<sup>3</sup> s−<sup>1</sup> for alloy ZK60.

At a temperature of 150 ◦C with a strain rate of 10−<sup>2</sup> s<sup>−</sup>1, the commercial ZK60 alloy exhibited a good ductility of 49%. As the strain rate decreased, the ductility increased, reaching an elongation to fracture of 89% at the lowest strain rate (see Figure 5). On the other hand, the yield stress and peak stress decreased as the strain rate decreased, while elongation to fracture increased, as shown in Figures 6 and 7. When increasing the test temperature to 200 ◦C, the behavior was very similar to that observed at the temperature of 150 ◦C, and at the lowest strain rate tested, an elongation to fracture of 137% was obtained.

Finally, at the highest test temperature used in this work (250 ◦C) and a strain rate of 10−<sup>4</sup> s<sup>−</sup>1, superplastic behavior was observed in this alloy, since it reached 464% of elongation to fracture. Several authors have already reported large percentages of elongation for this alloy. For example, W.J. Kim [23] reported ~1000% with a temperature of 250 ◦C and strain rate of 10−<sup>3</sup> s−<sup>1</sup> and attributed this percentage to a very fine grain size of 1.4 μm obtained by differential speed rolling. H. Watanabe et al. [24] also obtained a refined microstructure with a grain size of 1.4 μm processed by equal channel angular extrusion (ECAE) that reached elongation percentages above 400% at low strain rates and a temperature of 200 ◦C. The value reached in this study turns out to be quite acceptable, since this alloy was processed by conventional indirect extrusion and deformed at low temperature.

**Figure 5.** True stress–true strain curves at different temperatures and strain rates: (**a**) 150, (**b**) 200, and (**c**) 250 ◦C.

**Figure 6.** Flow and peak stress as a function of strain rate at different temperatures.

The samples deformed in tension at intermediate temperatures and three different strain rates, as well as at room temperature, are shown in Figure 8. In general, the samples present a ductile fracture. This type of fracture occurs when the material is subjected to a severe or excessive plastic deformation. In addition, this type of fracture can be recognized by the characteristic neck formation in the fractured area; however, this neck was less pronounced at lower strain rates. This is especially noticeable in the sample that reached superplastic-like behavior in which a rather diffuse neck can be observed.

**Figure 7.** Elongation to fracture as a function of strain rate at different temperatures.

**Figure 8.** Appearance of tensile specimens after deformation to failure at (**a**) room temperature and at (**b**) 150, (**c**) 200, and (**d**) 250 ◦C under various strain rates.

#### *3.3. Microstructure after Deformation*

The microstructural changes observed after the elongation to failure tests are shown in Figures 9 and 10. The sample tested at room temperature shows a deformed microstructure with some signs of twinning inside the relatively large unrecrystallized grains. This is despite the initial texture in which the majority of grains have a basal-type texture. However, it should be mentioned that the micrograph was taken near the fracture. Thus, some instabilities due to necking could occur, which could have led to the twinning behavior (see Figure 9). Moreover, due to the initial texture with some off-basal texture components, the activation of {1012} extension twins was feasible. At elevated temperatures (see Figure 10), the micrographs show a fine-grained structure, especially above 200 ◦C. At a temperature of 150 ◦C, the grain was refined as the strain rate decreased. A very different behavior was observed at 200 ◦C, since the smallest grain size was found at the highest strain rate. It is clearly observed that the dynamic recrystallization process was present as the strain rate decreased, obtaining a homogeneous microstructure at 250 ◦C and 10−<sup>4</sup> s<sup>−</sup>1. Despite the coarser grain size in comparison to samples deformed at higher strain rates at 250 ◦C, this sample achieved the highest ductility in this study.

Figure 11 exhibits an inverse pole figure map and respective local texture of a sample deformed at 250 ◦C and a strain rate of 10−<sup>4</sup> s<sup>−</sup>1. Despite the fact that a high elongation to fracture was reached and that a significant dynamic recrystallization took place, the deformation texture shared many similarities with the initial texture; i.e., it retained the majority of grains oriented near the 1010 pole with no obvious development of the 1121 texture component. However, an important texture-weakening was observed, most likely because of the combined activity of dynamic recrystallization and the activation of grain boundary sliding (GBS).

**Figure 9.** Microstructure obtained near the fractured zone after tensile test at room temperature and strain rate of 10−<sup>3</sup> s<sup>−</sup>1.

**Figure 10.** Microstructures obtained near the fractured zone after tensile tests at different temperatures and strain rates.

**Figure 11.** Inverse pole figure map and respective local texture measured near the fracture of a sample deformed at 250 ◦C and a strain rate of 10−<sup>4</sup> s<sup>−</sup>1.

#### *3.4. Zener–Hollomon Parameter*

In order to analyze the different values of mechanical properties obtained after the tensile tests, the Zener–Hollomon parameter was calculated for this alloy. The determination of this value (*Z*) was based on the study carried out by Liu et al. [25], according to the following equation:

$$Z = \dot{\varepsilon} \cdot \exp\left(\frac{Q}{RT}\right) = A \cdot \left(\sinh(\alpha \sigma)\right)^n \tag{1}$$

where *<sup>Z</sup>* is the temperature-compensated strain rate (i.e., the Zener–Hollomon parameter); . *ε* is the strain rate; *Q* is the activation energy; R is the gas constant; T is the absolute temperature; and *A*, *α*, and *n* are material constants. It was assumed that the relationship of the Zener–Hollomon parameter and the steady-rate stress were suitable for Equation (1). The values of *A*, y, and *n* can be obtained from the plot of ln(sin*h*(*ασ*)) versus ln*Z*. However, the values of *α* and *Q* must be determined before the values of *A* and *n* are fixed. The approximate value of *α* is determined as follows.

The hot working favored the power law at high stress levels, and the equation is presented as follows:

$$Z \approx A\_1 \sigma^{n\prime} \tag{2}$$

The favored equation is the exponent law at low stress levels, which is given by

$$Z \approx A\_2 \exp(\beta \sigma) \tag{3}$$

Assuming the value of *n* = *n*, the approximate value of *n* can be taken as the slope of the plot of ln*<sup>σ</sup>* versus ln. *ε* at low stress levels. It can be seen by comparing Equation (1) with Equation (3) that *A* = *A*2/2*<sup>n</sup>* and the value of *α* = *β*/*n*. The values of *A*<sup>2</sup> and *β* can be determined according to the *<sup>σ</sup>* versus ln. *ε* plot at high stress levels. It should also be noted that *σ* can be referred to as the peak stress *σ<sup>p</sup>* [26], which is easier to obtain; therefore, it is the stress used in this study. The value of *Q* is calculated in the following equation:

$$Q = R \left[ \frac{\partial \ln \left( \sinh \left( a \sigma\_p \right) \right)}{\partial (1/T)} \right]\_{\dot{\varepsilon}} \cdot \left[ \frac{\partial \ln \dot{\varepsilon}}{\partial \ln \left( \sinh \left( a \sigma\_p \right) \right)} \right]\_T \tag{4}$$

On the right-hand side of the above equation, the first term represents the slope of the ln sin*h ασ<sup>p</sup>* versus 1/*T* plot, called q1, while the second term represents the reciprocal value of inclination of the ln sin*h ασ<sup>p</sup>* versus ln. *ε* plot, called 1/q2.

The exact values of *A* and *n* are obtained from the plot ln sin*h ασ<sup>p</sup>* versus ln*Z*, being the relationship of *σ<sup>p</sup>* and *Z* as follows:

$$
\ln(Z) = \ln(A) + n \cdot \ln\left(\sinh\left(\alpha \sigma\_p\right)\right) \tag{5}
$$

In this way, the approximate values of *n* and *β* are estimated from Figure 12a,b, respectively. So, the value of *α* is 0.0056. On the other side, q1 and 1/q2 are obtained from Figure 12c,d, respectively. As a result, the average value of *Q* is 466.1 kJ/mol. Now, substituting *<sup>Q</sup>*, R, T, and . *ε* in Equation (1), the values of ln*Z* can be obtained, which are in the range of 50 to 250. Finally, the exact values of *A* and *n* are obtained from the ln sin*h ασ<sup>p</sup>* versus ln*Z* plot (see Figure 12d), where *n* is 84.81 and ln *A* is 58.52.

**Figure 12.** Schematic of the dependence of the peak stress on temperature and strain rate. Plots of (**a**) ln*σ<sup>p</sup>* versus ln. *ε*, (**b**) *σp* versus ln. *<sup>ε</sup>*, (**c**) ln(*sinh*(*ασp*)) versus 1/*T*, (**d**) ln(*sinh*(*ασp*)) versus ln. *ε*, and (**e**) ln(*sinh*(*ασp*)) versus ln*Z*.

The calculation of the activation energy allows an estimation of the deformation mechanism that predominates during the deformation under different conditions of strain rate and temperature. Based on the obtained average activation energy of 466.1 kJ/mol through the range of strain rates and temperature, the dominant deformation mechanism in the present alloy is grain boundary sliding (GBS) [27].

Another way to establish the dominant deformation mechanism involved in this alloy is through the method developed by Kim et al. [3,4].

Several criteria must be met to expect the material to behave superplastically [28], and this alloy meets some of the requirements. For example, it has a fine and stable microstructure at the end of the tensile test at 250 ◦C and 10−<sup>4</sup> s−<sup>1</sup> with an average grain size of ~4 μm, and there is the presence of second-phase particles that inhibit grain growth. On the other hand, superplastic materials generally exhibit high values of strain rate sensitivity "*m*" during stress–strain tests [27–29], which is expressed by the following equation [8,28,30]:

$$
\sigma = k \dot{\varepsilon}^m \tag{6}
$$

where <sup>σ</sup> is the true flow stress, k is a constant, and . *ε* is the strain rate. Metals normally exhibit *m* < 0.2 and superplastic alloys commonly have values of *m* > 0.33. However, the commercial ZK60 alloy of this study that obtained 464% elongation atfracture has a value of *m* = 0.29.

Bussiba et al. [31] reported an elongation of 220% at a strain rate of 1 × 10−<sup>5</sup> s−<sup>1</sup> in a ZK60 alloy with a value of *m* = 0.2; they concluded that grain boundary sliding (GBS) was the dominant deformation mechanism.

H. Watanabe [24] demonstrated a superplastic behavior in a conventional ZK60 alloy by reporting an elongation greater than 400% during tension in the temperature range from 200 to 225 ◦C and strain rates from 2.6 × 10−<sup>6</sup> to 3 × 10−<sup>5</sup> s−<sup>1</sup> with values of *m* = 0.5.

For the determination of the deformation mechanism that predominates during deformation, a deformation mechanism map (DMM) created by Kim et al. [3] was used, since this is valid for magnesium alloys in general, according to the author mentioned. The calculation of the activation energy allows for an estimation of the deformation mechanism that predominates during the deformation under different conditions of strain rate and temperature.

It was observed that the deformation mechanisms that were activated during tensile tests for ZK60 alloys were dislocation glide and grain boundary sliding (GBS), depending on the test conditions. As the stress decreased (at lower strain rates), the grain boundary sliding (GBS) was activated.

Although the DMM created by Kim et al. [3] did not correspond to that of the ZK series alloys, it provided a close estimate for magnesium-based alloys in general.

It can be established that as ln *Z* decreases, the elongation to fracture will increase with a concomitant decrease of the peak stress (see Figure 13). A similar case was reported by Victoria-Hernández et al. [32]. For an AZ31 alloy with a ductility above ~400%, ln *Z* was 19, while for an AZ61 alloy with a ductility above 500%, ln *Z* had a value of 28—much lower values when compared to the alloys studied in this work. On the other hand, the maximum stress values are much higher in this work when compared to the study by Victoria-Hernández et al. [32], due to the strengthening effect of the alloying elements where Zr played an important role in controlling the grain size even after the occurrence of dynamic recrystallization.

**Figure 13.** Tensile strength and elongation to failure versus ln*Z*plot.

#### **4. Conclusions**

A homogeneous and refined microstructure with a grain size of 4 ± 2 μm was obtained after conventional thermomechanical treatment and attributed to the amount of zirconium. The overall texture results show the development of the conventional basal texture where most of the basal planes are aligned parallel to ED. The texture component 1211 was observed parallel to the extrusion direction; this type of texture is commonly observed in Mg alloys with rare earth (RE) additions. However, it did not seem to play a significant role during further tensile deformation at room temperature and after tensile tests at elevated temperatures. There was no strengthening of the aforementioned pole, even in the case of a sample deformed under a superplastic regime.

The commercial ZK60 alloy showed excellent ductility at 250 ◦C at three different strain rates, especially at the slowest strain rate (10−<sup>4</sup> s<sup>−</sup>1). This alloy was able to present a superplastic behavior, as it achieved a peak elongation of 464%, which is explained due to the combined effect of dynamic recrystallization and the likely activation of GBS. The latter mechanism was believed to be dominant during tests at 250 ◦C temperature and slow strain rates. As calculated, the activation energy indicates the feasible activation of this mechanism. Furthermore, the texture-weakening effect found in the sample deformed under a superplastic regime suggests the dominant activation of this deformation mechanism. By increasing the strain rate or reducing the temperature, the dominant deformation mechanism seemed to change to dislocation glide.

**Author Contributions:** Conceptualization, J.V.-H. and C.P.-T.; methodology, J.V.-H. and C.P.-T.; formal analysis, C.P.-T. and D.H.-S.; investigation, C.P.-T.; writing—original draft preparation, M.A.G.- B.; writing—review and editing, M.A.G.-B. and D.H.-S.; visualization, M.A.G.-B..; supervision, D.H.- S.; project administration, D.L. and J.V.-H.; funding acquisition, D.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Data supporting reported results can be shared on a reasonable request to corresponding authors.

**Acknowledgments:** C.P.-T. is grateful for the fruitful discussions with J. Bohlen during his research stay at HZG. C.P.-T. also acknowledges the economic support (Becas Mixtas) of CONACyT-Mexico for his research stay in Germany. The technical support of Y. Shin and A. Reichert at HZG is gratefully acknowledged.

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

#### **References**


## *Article* **Fatigue Properties of AZ31B Magnesium Alloy Processed by Equal-Channel Angular Pressing**

**Ryuichi Yamada 1,\*, Shoichiro Yoshihara <sup>2</sup> and Yasumi Ito <sup>1</sup>**


**Abstract:** A stent is employed to expand a narrowed tubular organ, such as a blood vessel. However, the persistent presence of a stainless steel stent yields several problems of late thrombosis, restenosis and chronic inflammation reactions. Biodegradable magnesium stents have been introduced to solve these problems. However, magnesium-based alloys suffer from poor ductility and lower than desired fatigue performance. There is still a huge demand for further research on new alloys and stent designs. Then, as fundamental research for this, AZ31 B magnesium alloy has been investigated for the effect of equal-channel angular pressing on the fatigue properties. ECAP was conducted for one pass and eight passes at 300 ◦C using a die with a channel angle of 90◦. An annealed sample and ECAP sample of AZ31 B magnesium alloy were subjected to tensile and fatigue tests. As a result of the tensile test, strength in the ECAP (one pass) sample was higher than in the annealed sample. As a result of the fatigue test, at stress amplitude *σa* = 100 MPa, the number of cycles to failure was largest in the annealed sample, medium in the ECAP (one pass) sample and lowest in the ECAP (eight passes) sample. It was suggested that the small low cycle fatigue life of the ECAP (eight passes) sample is attributable to severe plastic deformation.

**Keywords:** magnesium alloy; fatigue; equal-channel angular pressing; grain refinement; S–N curve; stent

#### **1. Introduction**

Ischaemic heart disease is the world's biggest killer, accounting for a combined 9.4 million deaths in 2016 [1]. This disease has remained the leading cause of death glob-ally in the last 15 years [1]. A stent, as a countermeasure against ischaemic heart disease, is employed to expand a narrowed tubular organ, such as a blood vessel. A stent is a tiny tube that a doctor places in an artery or duct to help keep it open and restore the flow of bodily fluids in the area. Stents help relieve blockages and treat narrow or weakened arteries. Despite this, the persistent presence of a metallic stent yields several problems of late thrombosis, restenosis and chronic inflammation reactions. Conventionally, an austenite-based stainless steel that is a general stainless steel, such as SUS316, SUS316 L, etc., is used for the material of a stent for vasodilatation [2]. Once the stainless steel stent is implanted, it will remain in an artery permanently because of its excellent corrosion resistance. In some cases, restenosis may occur [3]. Restenosis is when too much tissue grows around the stent. This could narrow or block the artery again. In general, a stent should be removed within 6 to 9 months. Stent removal surgery is expensive and physically demanding for the patient. Biodegradable magnesium stents have been introduced to solve these problems. There is still a huge demand for further research on new alloys and stent design [4,5]. Ideally, implanted stents can maintain their mechanical integrity during the healing of the vessel wall and then dissolve after healing. The mechanical strength and properties of magnesium are suitable for biodegradable implants, especially for stent

**Citation:** Yamada, R.; Yoshihara, S.; Ito, Y. Fatigue Properties of AZ31B Magnesium Alloy Processed by Equal-Channel Angular Pressing. *Metals* **2021**, *11*, 1191. https:// doi.org/10.3390/met11081191

Academic Editor: Sangbong Yi

Received: 30 June 2021 Accepted: 22 July 2021 Published: 26 July 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

application. Magnesium is bi-ocompatible because it is essential for several biological reactions and as a co-factor for enzymes. However, magnesium degradation is accelerated in chloride-abundant en-vironments, such as human body fluids. Therefore, magnesium must be modified to improve its corrosion resistance. In addition, magnesium-based alloys suffer from poor ductility [6] and lower than desired fatigue performance. Further, the great success of stents in treating cardiovascular disease is undermined by their long-term fatigue failure. Pulsatile pressure and repetitive mechanical forces within the coronary artery may result in fatigue fracture after stent implantation, particularly in patients with complex coronary disease [7]. It has also been reported that stents implanted near the heart have a higher probability of fatigue failure. In this research group, it has been found that the corrosion rate of magnesium alloy becomes larger under pulsating flow [8]. If the fatigue properties can be improved, there is a possibility of reducing the corrosion rate. These aspects make fatigue properties an important attribute of cardi-ovascular stents. In this study, we focused on the possibility of improving the strength and fatigue properties simultaneously by grain refinement. Then, as fundamental re-search for this, AZ31 B magnesium alloy has been investigated for the effect of equal-channel angular pressing on tensile and fatigue properties.

#### **2. Materials and Methods**

#### *2.1. Specimens*

The chemical composition (in mass %) of the AZ31 B magnesium alloy made by MACRW Co., Ltd. (Shizuoka, Japan) used in this study is listed in Table 1. The AZ31 B alloy was hot extruded to a rod with a diameter of 6 mm and then cut into pieces with a length of 60 mm. ECAP was conducted on the as-extruded material through a die with an internal angle *ϕ* of 90◦ between the vertical and horizontal channels and a curvature angle *ψ* of 90◦ (Figure 1). As a lubricant, we used molybdenum disulphide (MoS2) manufactured by Sumico Lubricant Co., Ltd. (Tokyo, Japan). Conditions of ECAP are presented in Table 2. ECAP was conducted for 1 pass and 8 passes, which creates an equivalent strain of 0.91 during one passage through the die as shown in Equation (1) [9].

$$\varepsilon\_{N} = \left(\frac{N}{\sqrt{3}}\right) \left[2\cot\left\{\left(\frac{\varrho}{2}\right) + \left(\frac{\psi}{2}\right)\right\} + \psi \text{cosec}\left\{\left(\frac{\varrho}{2}\right) + \left(\frac{\psi}{2}\right)\right\}\right] \tag{1}$$

*ε<sup>N</sup>* is the strain of the material after ECAP for *N* passes and *N* is extrusion pass number. For comparison, the annealed sample for AZ31 B consisted of hold for 1 h at 450 ◦C, furnace cooling. ECAP-8 was used because the maximum number of passes that would not cause cracking under the conditions of this experiment was 8 passes. Furthermore, ECAP-8 p samples were found to have inferior fatigue properties compared to annealed samples [10]. ECAP-1 p was also added to investigate the effect of reducing the number of passes for ECAP. Three distinct kinds of test pieces, i.e., ECAP-1 p, ECAP-8 p and annealed, had commonly equiaxed microstructures (Figure 2). The average grain sizes of annealed and ECAP-8 p samples were confirmed by optical microscope observation to be 40 μm and 6–7 μm, respectively. ECAP-1 p had a bimodal structure, and it was determined that accurate grain size could not be calculated from the average grain size. It was the optical microscope structure in which coarse grains of 30–40 μm and fine grains of less than 10 μm were mixed.

**Table 1.** Composition of the specimens in mass %. Bai. in Mg is an abbreviation for balance.


**Figure 1.** Schematic diagram of ECAP processing.



**Figure 2.** Optical micrographs of AZ31 B alloy. (**a**) Annealed, (**b**) ECAP-1 p and (**c**) ECAP-8 p.

#### *2.2. Experimental Procedure*

From the hot-extruded rod or ECAPed sample, tensile and fatigue test pieces were produced by machining. The gauge length and diameter of tensile and fatigue test pieces were 15 mm and 3 mm, respectively. The round-rod test pieces were turned on a lathe and manually mechanically polished and buffed to a mirror finish. The tensile test was carried out on one specimen of each type at an initial strain rate of 1.5 × 10−<sup>3</sup> s−<sup>1</sup> at room temperature. ECAP and tensile tests were performed by an Autograph AG-250 kNG, a precision universal tensile tester manufactured by SHIMADZU CORPORATION (Kyoto, Japan). Fatigue test was carried out on one specimen of each type in a sinusoidal stress wave of a frequency of 30 Hz with a stress ratio of R (= Kmin/Kmax) = 0.1 at room temperature, followed by fractographic observation by a scanning electron microscope (SEM, JSM-7100 F by JEOL Ltd., Tokyo, Japan). The fatigue testing machine was an ElectroPuls E10000 Linear-Torsion all-electric dynamic test instrument manufactured by INSTRON Japan (Kanagawa, Japan). Residual stress measurement was carried out by X-ray diffraction (XRD, SmartLab by Rigaku Corporation, Tokyo, Japan) on the gripping surface of the test piece after the fatigue test. XRD was employed to measure the residual stress of the rods, in which Cr Kα radiation was used as the X-ray source. X-ray generator was attached by a collimator, which could carry out the incident beam of 1 mm spot sizes.

#### **3. Experimental Results**

#### *3.1. Tensile Test*

Figure 3 shows nominal stress vs. strain curves for the three specimens. Strength in the ECAP-1 p sample was higher than in the annealed sample. The tensile strength of ECAP-1 p was 321 MPa, which was slightly improved by about 1.2 times compared to the annealed sample. In contrast, elongation to failure was larger in the ECAP-8 p sample than in the annealed sample. In spite of processing more, ECAP-8 p had lower tensile strength and lower yield strength than ECAP-1 p. The elongation to failure of ECAP-8 p was 23%, which was improved by about 1.4 times compared to the annealed sample. Tensile properties obtained from tensile tests for the three specimens are summarized in Table 3.

**Figure 3.** Nominal stress vs. strain curves for annealed, ECAP-1 p and ECAP-8 p samples of AZ31 B alloy.


**Table 3.** Tensile properties (ultimate tensile strength *σu*, yield strength *σy*, elongation to failure *δ*) of AZ31B alloy.

#### *3.2. Fatigue Test*

As a result of the fatigue test in Figure 4, at stress amplitude *σ<sup>a</sup>* = 100 MPa number of cycles to failure was largest in the annealed sample, medium in the ECAP-1 p sample and lowest in the ECAP-8 p sample. At stress amplitude *σ<sup>a</sup>* = 80 MPa, the number of cycles to failure was largest in the ECAP-1 p sample, medium in the annealed sample and lowest in the ECAP-8 p sample. It was confirmed that grain refinement improved fatigue life at low stress amplitude. When the stress amplitude *σ<sup>a</sup>* exceeds 80 MPa, the annealed sample has the best fatigue properties and the ECAP-8 p sample has the worst fatigue properties, suggesting that among tensile properties, strength is more effective in improving fatigue properties than ductility. And since the fatigue properties of the annealed sample are superior to those of the ECAP-1 p sample, it is suggested that increasing the yield strength rather than the tensile strength is effective in improving the fatigue properties.

**Figure 4.** S–N curves for annealed, ECAP-1 p and ECAP-8 p samples of AZ31 B alloy.

Figure 5 shows the SEM images of fracture surface at stress amplitude *σ<sup>a</sup>* = 100 MPa. From this, many fatigue crack initiation sites were located at each fracture surface. In all fracture surfaces, the crack growth area extends radially from the starting point of the fracture indicated by the arrow to the area delineated by the dashed line. In ECAP-1 p and ECAP-8 p, which are shown in Figure 5b,c, the crack growth areas from different fracture initiation points overlap each other. In ECAP-8 p, which had a large number of passes, the number of starting points for fracture was four, which was larger than the two in ECAP-1 p, suggesting early fatigue fracture. In the annealed sample, the starting points of the destruction overlap, however they are not completely connected. Therefore, it is inferred that the fatigue life of ECAP-1 p and ECAP-8 p was reduced by the sudden decrease in the cross section of the parallel section of the fatigue specimen when the crack growth areas overlapped each other. Although it is qualitative, the crack growth area ratio is larger in the annealed and ECAP-1 p sample than in ECAP-8 p. Therefore, it is possible that the crack growth area ratio of the fracture surface increases with the superior fatigue property.

**Figure 5.** SEM images of fracture surfaces of annealed, ECAP-1 p and ECAP-8 p samples of AZ31 B alloy at stress amplitude *σa* = 100 MPa. (**a**) Anneal, (**b**) ECAP-1 p, (**c**) ECAP-8 p.

Figure 6 is a SEM image which enlarged fatigue crack initiation sites; fracture surfaces are found mainly to consist of transgranular quasi-cleavage. Annealed and ECAP-1 p samples showed a fracture surface with severe surface undulations as if plastic deformation had occurred to a large extent, which could be seen as twinning. No twinning-like structures were observed in ECAP-8 p. It is inferred that the twinning deformation at the starting point of fracture in the annealed and ECAP-1 p samples resist fatigue fracture and the fatigue life is longer than that of ECAP-8 p.

**Figure 6.** High-magnification SEM images of fracture surfaces of annealed, ECAP-1 p and ECAP-8 p samples of AZ31 B alloy at stress amplitude *σa* = 100 MPa. (**a**) Anneal, (**b**) ECAP-1 p, (**c**) ECAP-8 p.

#### **4. Discussion**

In a related study, it was found that the fatigue properties of Mg–Al alloys decreased as the number of passes in ECAP increased [11]. Although it is AZ80 magnesium alloy, the fatigue properties of the six passes material decreased, and the two passes material was superior in fatigue properties [11]. It has been reported that the fatigue properties of AZ31 magnesium alloy, which is close in composition, were improved by ECAP processing, but the number of passes was small, four passes [12]. Therefore, the decrease in the fatigue properties of ECAP-8 p in the present experimental results may be due to the increase in the number of passes. Residual stress measurement was performed to consider the cause of the deterioration of fatigue properties due to ECAP processing at high stress amplitude (Figure 7). For all three specimens, the residual compressive residual stress after the fatigue test was measured. The annealed sample seems to have had little residual stress before the fatigue test. Since the compressive stress value is lower in the annealed sample, it can be inferred that ECAP-1 p and ECAP-8 p had tensile stress generated by ECAP processing. ECAP-1 p and ECAP-8 p showed tensile residual stress, which increased with the number of passes, and ECAP-8 p was considered to have the earliest fatigue failure. It has also been reported that both strength and elongation can be increased by artificial aging heat treatment after ECAP processing in AZ91 magnesium alloy [13]. As future work, it is necessary to verify whether artificial aging of ECAP-1 p can exceed the fatigue properties of annealed samples. The mechanical properties of ECAP samples with varying number of passes between two and seven should also be continued to be investigated.

#### **5. Conclusions**

The effects of varying the number of passes on tensile and fatigue properties of AZ31 B magnesium alloy under the present experimental conditions were investigated when equalchannel angular pressing was performed. Tensile strength in ECAP-1 p was higher than in the annealed sample. In contrast, elongation to failure was larger in the ECAP-8 p sample than in the annealed sample. From the fatigue test, at stress amplitude *σ<sup>a</sup>* = 100 MPa, number of cycles to failure was largest in the annealed sample, medium in the ECAP-1 p sample and lowest in the ECAP-8 p sample. At stress amplitude *σ<sup>a</sup>* = 80 MPa, number of cycles to failure was largest in the ECAP-1 p sample and medium in the annealed sample. It was found that grain refinement by ECAP was effective in improving fatigue life depending on the value of stress amplitude. Strength is more effective than ductility in improving fatigue properties, and it is considered important to increase the yield strength. It was suggested that the low fatigue life of the ECAP-8 p sample is attributable to tensile residual stress in severe plastic deformation.

**Author Contributions:** Conceptualization, R.Y. and S.Y. and Y.I.; methodology, R.Y.; writing original draft preparation, R.Y.; supervision, R.Y. and S.Y. and Y.I.; project administration, R.Y.; funding acquisition, S.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by JSPS KAKENHI, grant number JP19K04095.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

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

#### **References**


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