Effects of Yttrium Addition on Bending Deformation Behavior of Magnesium Single Crystals

Abstract

Pure magnesium and Mg–Y alloy single crystals were subjected to three-point bending tests to investigate the effect of crystal orientation and yttrium on bending deformation behavior. Specimens whose neutral planes are parallel to (0001) and neutral axes are [$11\bar{2}0$] deformed due to basal slips, displaying a gull-shape. Their bending yield stresses increased by addition of yttrium and were controlled by the shear stress on the basal plane. Conversely, neutral planes parallel to ($1\bar{1}00$) and neutral axes are [$11\bar{2}0$] resulting in specimens deformed due to {$10\bar{1}2$} twins occurred at the compression side, basal slips within the twins and finally showed a V-shape. In Mg–Y alloys, first order pyramidal ⟨c + a⟩ slips (FPCS) and {$10\bar{1}1$}-{$10\bar{1}2$} double twins were also activated in the tension area. Their bending yield stresses and bending ductility increased by yttrium addition. Strain induced by {$10\bar{1}1$}-{$10\bar{1}2$} double twins at the tension side was very low. FPCS was found to be activated by addition of yttrium and to increase bending ductility.

 

This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 84 (2020) 344–351.

Fig. 13 Optical micrographs of (a) 0.15Y-E1 after yielding, (b) basal slips within {$10\bar{1}2$} twins in compression area and (c) slip lines caused by FPCS and twins in tension area.

1. Introduction

Magnesium (Mg) is an attractive metal for use in transport equipment as it is the lightest structural metal and has a high specific strength. The main deformation mechanism of Mg with a hexagonal close-packed structure are {0001}⟨$11\bar{2}0$⟩ basal slip¹⁾ and {$10\bar{1}2$} twin¹⁾ since their critical resolved shear stresses (CRSSs) are low. However, basal slips never occur when the loading axis is perpendicular or parallel to basal planes. In the same way, when compression or tension loads are perpendicular or parallel to basal planes, {$10\bar{1}2$} twins never occur. This indicates a strong dependence of Mg deformation behavior on crystal orientation.

Bending deformation is an important process for producing various industrial products from metal sheets. Bending deformation involves compressive and tensile stresses simultaneously loaded in sheets. Hence, a strong dependence on crystal orientation is expected to occur in bending deformation of Mg. Kitahara et al.²⁾ performed three-point bending tests of pure Mg single crystals and reported that specimens whose neutral planes are parallel to basal planes mainly deformed due to basal slips, while specimens whose neutral planes are perpendicular to basal planes mainly deformed due to {$10\bar{1}2$} twins. Thus, pure Mg single crystals show a strong dependent on crystal orientation in bending deformation.

Recently, the addition of rare earth elements to Mg has been studied to improve mechanical properties of Mg alloys. Sandlöbes et al.³⁾ performed tensile tests of Mg–3 mass%Y alloy polycrystals at room temperature, reporting that yttrium addition increased Mg ductility approximately five times. Miura et al.⁴⁾ performed compression tests of Mg–1.0 at%Y alloy single crystals and reported that CRSS for basal slip increased by yttrium addition. Furthermore, Mineta et al.⁵⁾ performed compression tests of Mg–0.8 at%Y alloy single crystals and reported that CRSS for {$10\bar{1}2$} twins increased by yttrium addition. Those studies suggest that bending deformation behavior of Mg–Y differs from that of pure Mg. To elucidate this, we subjected pure Mg and Mg–Y alloy single crystals with different yttrium contents and two different crystal orientations to three-point bending tests to investigate crystal orientation dependence and effects of yttrium addition on the bending deformation behavior of Mg.

2. Experimental Procedures

Mg–0.20 at%Y and Mg–0.29 at%Y alloy ingots were prepared by casting using a high-frequency induction heating vacuum furnace. Pure Mg and Mg–(0.07∼0.25) at%Y alloy single crystals were grown using Mg of 99% purity or more and Mg–Y alloy ingots and high-purity graphite crucibles by the Bridgeman method. Chemical compositions of Mg–Y alloy single crystals were analyzed by inductively coupled plasma atomic emission spectrometry. Single crystals were crystallographically analyzed using the X-ray back reflection Laue method and were cut into cubic specimens using a non-distortion cutting machine with nitric acid. The cubic specimens were chemically polished to be cuboid specimens of approximately 3 × 3 × 25 mm³ using a chemical polishing solution (HNO₃:H₂O₂:C₂H₅OH = 5:7:20). The cuboid specimens underwent eight thermal annealing cycles to remove dislocations and sub-grain boundaries introduced by cutting and polishing in an argon atmosphere. During thermal cycle annealing, the specimens were annealed at 673 K. The temperature was then increased up to 723 K. The holding time at each temperature was 3.6 ks, and the heating and cooling rates were 6.9 × 10⁻³ K/s. Figure 1 shows schematic illustrations of two types of single crystals with different crystal orientations for bending tests. Kitahara et al.²⁾ employed specimens whose neutral planes and axes are parallel to (0001) and [$11\bar{2}0$] and named them B specimen. B specimen was also used for comparison. In addition, specimens whose neutral planes and axes are parallel to ($1\bar{1}00$) and [$11\bar{2}0$] were also employed and are named E specimen in this study. Figure 2 shows a photograph of the three-point bending device used in this study. The radii of the loading and supporting pins were R₁ = 2.0 mm and R₂ = 2.5 mm, respectively. Two different supporting spans, L, were used: 14 mm and 16 mm to compare bending behavior of Mg–Y and pure Mg single crystals. Kitahara et al.²⁾ employed L = 14 mm, R₁ = 1.0 mm and R₂ = 2.0 mm for pure Mg single crystals. When the supporting span was 14 mm, specimens collide with the three-point bending device at displacements exceeding approximately 3 mm. Therefore, a 16 mm supporting span was also employed in this study. Three-point bending tests were carried out at room temperature. The loading rate was 1.67 × 10⁻² mm/s. Bending stress σ and bending strain ε were calculated from eq. (1) and (2).   

\begin{equation} \sigma = (3PL)/(2bh^{2}) \end{equation} (1)

  

\begin{equation} \varepsilon = (6dh)/L^{2} \end{equation} (2)

where P is the load, and b and h are the width and height of the specimens, respectively. Table 1 shows specimen names, composition, dimensions and span. Slip lines and twins were observed with an optical microscope and a CCD camera. Twins were crystallographically identified using FE-SEM/EBSD.

Fig. 1

Schematic illustrations of two types of single crystals with different crystal orientations for bending tests.

Fig. 2

Photograph of three-point bending device used in this study.

Table 1 Specimen names, composition, dimensions, span and bending properties of B and E specimens of pure Mg and Mg–Y alloy single crystals.

3. Results and Discussion

3.1 Bending deformation behavior of B specimens

Figure 3 shows typical bending stress-bending strain curves of B specimens. The arrows in Fig. 3 indicate bending yield stresses σ_y. In this study, σ_y is defined as bending stress at ε = 0.02%. Both σ_y and ε_B, the bending strains when cracks initiated of B specimens are shown in Table 1. Figure 4 shows the relationship between yttrium content and σ_y of B specimens. σ_y of 0.07Y and pure Mg single crystals were approximately identical, while 0.15Y showed higher values. σ_y and profiles of bending stress-bending strain curves were found to be independent of supporting spans and radii of loading and supporting pins. After yielding, all the specimens showed linear work hardening, and the work hardening rate increased by yttrium addition. Bending tests were carried out until ε = 30∼35%, at which point specimens collided with the bending device, but not all of the specimens fractured. It was therefore found that a minimum of 0.15 at%Y addition increases σ_y and the work hardening rate of Mg after yielding. Figures 5(a) and (c) show Mg-B2 and 0.15Y-B2 specimens after bending tests. Figure 5(b) and (d) show optical micrographs of the enlargement of tension areas, surrounded by white lines. Both Mg-B2 and 0.15Y-B2 specimens showed a gull-shape, and a few {$10\bar{1}2$} twins were observed beneath the loading pin, as shown in Fig. 5(a) and (c). On the other hand, uniform slip lines along basal planes between the supporting pins were observed, causing deformation of both Mg-B2 and 0.15Y-B2 specimens. 0.07Y specimen showed the same deformation behavior. Here, the cause of basal slip activation cannot be explained by the bending yield stress as the Schmid factor for basal slip in B specimens is 0. Kitahara et al.²⁾ have reported that bending yield stresses were determined by shear stress parallel to basal planes in three-point bending tests of pure Mg single crystals whose neutral plane is parallel to basal planes. Thus, the shear yield stress parallel to basal planes τ_y of B specimens were calculated using eq. (3).   

\begin{equation} \tau_{y} = P/(2bh) \end{equation} (3)

Fig. 3

Bending stress-bending strain curves of B specimens.

Fig. 4

Relationship between bending yield stress σ_y and yttrium content of B specimens.

Fig. 5

Optical micrographs of (a) Mg-B2 and (c) 0.15Y-B2 after yielding; the enlargement of tension areas with basal slips surrounded by white lines are shown in (b) and (d).

Figure 6 shows the relationship between τ_y and yttrium content of B specimens. Reported CRSSs for basal slip of pure Mg¹⁾ and Mg–1.0 at%Y⁴⁾ single crystals are also shown in Fig. 6. CRSS for basal slip was assumed to be proportional to the amount of yttrium addition; the relationship is indicated by the dashed line in Fig. 6. τ_y increased with increasing yttrium content and mostly conformed to the dashed line. Therefore, σ_y would increase since CRSS for basal slip increased due to yttrium addition. In addition, pure Mg single crystals of B specimens have been reported to show a gull-shape since tilt boundaries formed above in supporting pins due to pile up of basal dislocations.²⁾ The cause of Mg–Y alloy single crystals apparently displaying a gull-shape, as shown in Fig. 5(c), would likely be the same.

Fig. 6

Relationship between shear yield stress on basal planes τ_y and yttrium content of B specimens.

3.2 Bending deformation behavior of E specimens

Figure 7 shows typical bending stress-bending strain curves of E specimens. Vertical arrows in Fig. 7 indicate crack initiation points. Serrations were observed on bending stress-bending strain curves of all the specimens until approximately ε = 4% after yielding. After that, work hardening rates rapidly rose to approximately ε = 8%, after which cracks initiated. Also, the bending deformation behavior of E specimens was independent of supporting spans, similar to B specimens. σ_y and ε_B of E specimens are summarized in Table 1. Figure 8 shows changes in σ_y and ε_B as a function of yttrium content of E specimens. σ_y of 0.07Y and pure Mg single crystals were approximately identical; however, σ_y increased with increasing yttrium content exceeding 0.15 at%, as shown in Fig. 8(a). ε_B also increased by yttrium addition, as shown in Fig. 8(b). Therefore, σ_y and ε_B of Mg increase by yttrium addition in E specimens.

Fig. 7

Bending stress-bending strain curves of E specimens.

Fig. 8

Changes in (a) bending yield stress σ_y and (b) bending ductility ε_B, as a function of yttrium content of E specimens.

Figure 9 shows optical micrographs of Mg-E3 and 0.25Y-E1 beneath the loading pin at yielding. In both specimens, twinning occurred at the compression side near the loading pin, and their tips reached the tension area. The twins were geometrically analyzed and identified to be {$10\bar{1}2$} twins. Thus, E specimens were found to yield due to {$10\bar{1}2$} twins. 0.07Y and 0.15Y, lower yttrium content, also yielded due to {$10\bar{1}2$} twins. Here, Kitahara et al.²⁾ observed that twins reaching tension area in the bending tests of pure Mg single crystals and proposed the movement of the neutral plane. In addition, the movement of the neutral plane during the bending deformation has been reported in AZ31 alloys polycrystals.⁶⁾ Figure 10 shows a schematic illustration of bending deformation of E specimens at yielding considering the movement of the neutral plane. Assuming that the height of specimens h changes to be h′ by the movement of the neutral plane, bending stresses at the compression side σ_c and the tension side σ_t were calculated from eq. (4) and (5),   

\begin{equation} \sigma_{c} = MN_{c}/I \end{equation} (4)

  

\begin{equation} \sigma_{t} = MN_{t}/I \end{equation} (5)

Where M is the bending moment, I is the moment of inertia of area, and N_c is the distance between the compression side and the neutral plane, and N_t is the distance between the tension side and the neutral plane, respectively. N_c and N_t can be expressed by eq. (6) and (7), respectively.   

\begin{equation} N_{c} = 0.5h + xh \end{equation} (6)

  

\begin{equation} N_{t} = 0.5h - xh \end{equation} (7)

Where x is the ratio of the movement of the neutral plane to h. Considering the movement of the neutral plane, σ_c and σ_t can be expressed as eq. (8) and (9).   

\begin{align} \sigma_{c}&=(PL/4)(12/b\{2(0.5h+xh)\}^{3})(0.5h+xh)\\ &=\sigma/(1+2x)^{2} \end{align} (8)

  

\begin{align} \sigma_{t}&=(PL/4)(12/b\{2(0.5h+xh)\}^{3})(0.5h-xh)\\ &=\{\sigma(1-2x)\}/(1+2x)^{3} \end{align} (9)

Here, CRSS for {$10\bar{1}2$} twin τ_twin was calculated using the bending yield stress at the compression side σ_cy obtained from eq. (8) and Schmid factor for {$10\bar{1}2$} twin. Figure 11 shows the relationship between τ_twin and yttrium content. Reported CRSSs for {$10\bar{1}2$} twin of pure Mg¹⁾ and Mg–Y alloy⁷⁾ single crystals are also shown in Fig. 11. Assuming that CRSS for {$10\bar{1}2$} twin is proportional to the amount of yttrium addition, the relationship is indicated by the dashed line in Fig. 11. τ_twin increased with increasing yttrium content and were almost on the dashed line. Therefore, σ_y of E specimens would increase since CRSS for {$10\bar{1}2$} twin increased due to yttrium addition.

Fig. 9

Optical micrographs of the center area of (a) Mg-E3 and (b) 0.25Y-E1 beneath the loading pin at yielding.

Fig. 10

Schematic illustration of bending deformation mechanism of E specimens at yielding.

Fig. 11

Relationship between τ_twin for {$10\bar{1}2$} twin and yttrium content in E specimens.

Figure 12(a), Fig. 13(a) and Fig. 14(a) show optical micrographs of Mg-E3, 0.15Y-E1 and 0.25Y-E1 after yielding. The dashed lines in figures indicate the region where {$10\bar{1}2$} twins were observed. Different from B specimens, many {$10\bar{1}2$} twins occurred at the compression side and propagated to the tension area between supporting pins, resulting in that E specimens finally showed a V-shape. However, the area fraction of {$10\bar{1}2$} twins decreased by yttrium addition. Such decrease in {$10\bar{1}2$} twin activity by yttrium addition has been reported in indentation tests of both pure Mg and Mg–Y alloy single crystals⁸⁾ and tensile tests of Mg–Y alloy polycrystals.⁹⁾ Many slip lines were observed in {$10\bar{1}2$} twins, as shown in Fig. 12(b), Fig. 13(b) and Fig. 14(b). These slip lines are expected to be caused by (0001) [$\bar{2}110$] basal slips based on geometrical relationship between the crystal orientation of twins and the angle of the slip lines. Furthermore, angles between the directions of σ - [0001] and σ - [$\bar{2}110$] in the twins are 31° and 60°, respectively. Thus, the Schmid factor for basal slip against bending stress is 0.43, and basal slips would thus be activated in the {$10\bar{1}2$} twins. In addition, twins which morphologically differ from {$10\bar{1}2$} twins and slip lines were observed in the tension area of 0.15Y and 0.25Y, as shown in Fig. 13(c) and Fig. 14(c). Slip lines tilted by approximately 60° from [$11\bar{2}0$] on (0001) indicate that first order pyramidal ⟨c + a⟩ slips (FPCS) were activated. Figure 15 shows a SEM image and an IPF map of twins occurring in the tension area of 0.15Y-E1. The crystal orientation relationship between the matrix and the band twins crossing {$10\bar{1}2$} twins was approximately 38° around ⟨$11\bar{2}0$⟩. Here, basal planes rotate about 37.55° around ⟨$11\bar{2}0$⟩ due to {$10\bar{1}1$}-{$10\bar{1}2$} twins (double twins).¹⁰⁾ Therefore, twins in the tension area were identified to be double twins.

Fig. 12

Optical micrographs of (a) Mg-E3 after yielding and (b) enlargement of basal slips within {$10\bar{1}2$} twins in the compression area.

Fig. 13

Optical micrographs of (a) 0.15Y-E1 after yielding, (b) basal slips within {$10\bar{1}2$} twins in compression area and (c) slip lines caused by FPCS and twins in tension area.

Fig. 14

Optical micrographs of (a) 0.25Y-E1 after yielding, (b) basal slips within {$10\bar{1}2$} twins in compression area and (c) slip lines caused by FPCS and twins in tension area.

Fig. 15

(a) SEM image and (b) IPF map of twins occurred at tension area of 0.15Y-E1.

Figure 16 shows schematic illustrations of bending deformation mechanism in E specimens. In pure Mg single crystals, a neutral plane would be located at the tip of {$10\bar{1}2$} twins generated at the compression side (Fig. 16(a)), while in Mg–Y alloy single crystals, a neutral plane would be located between {$10\bar{1}2$} twins generated at the compression side and double twins generated at the tension side (Fig. 16(b)). Therefore, the position of neutral plane, xh, was investigated through in-situ observation of twins on the specimen surface during bending tests. Figure 17 shows the relationship between the position of neutral plane and bending strain beneath the loading pin in E specimens. 0.5h and 1.0h in Fig. 17 correspond to the center and bottom edge of specimens, respectively. The movement of neutral plane in Mg–Y alloy single crystals was found to be smaller than that of pure Mg single crystals. Yttrium addition was thus found to increase the activation stress of {$10\bar{1}2$} twins, inhibiting occurrence of {$10\bar{1}2$} twins. As a result, double twins and FPCS became more easily activated in the tension area, resulting in the short length of {$10\bar{1}2$} twins, and the movement of neutral planes diminished in Mg–Y single crystals.

Fig. 16

Schematic illustrations of bending deformation mechanism in E specimens of (a) Pure Mg and (b) Mg–Y alloy.

Fig. 17

Relationship between the position of neutral plane and bending strain beneath the loading pin in E specimens.

In order to elucidate the deformation mechanism of Mg–Y alloy single crystals in the tension area, contribution of double twins and FPCS to bending deformation was investigated. First, the elongation of the specimen length due to the double twins δ was investigated. The strain due to double twins is calculated using eq. (10),¹¹⁾ assuming that the shear deformation due to twins is equivalent to the slip deformation.   

\begin{equation} \delta = \sqrt{1 + 2\varepsilon'\cos\varphi_{0}\cos \lambda_{0} + \varepsilon'^{2}\cos^{2}\varphi_{0}} \end{equation} (10)

Where ε′ is the shear strain induced by double twins, and φ₀ and λ₀ are angles between the loading direction before deformation and the normal direction of the twin planes and between the loading direction before deformation and the shear direction of the twins, respectively. Crystal orientation relationship between basal planes and the matrix is 56.17° around ⟨$11\bar{2}0$⟩¹⁰⁾ since double twins formed through {$10\bar{1}2$} twinning within {$10\bar{1}1$} twins. Thus, φ₀ and λ₀ are 109.86° and 13.03°, respectively. The shear strain induced by double twins ε′ is 0.04.¹²⁾ Based on these values and eq. (10), assuming that the entire tension side of the specimen deforms due to double twins, the elongation of the tension side estimated to be 1.32% in [$11\bar{2}0$]. Second, the fraction of double twins at the tension side of Mg–Y alloy single crystals was investigated. The fraction of double twins was defined as the twin width of double twins at the tension side of the specimen divided by the length between supporting pins. The strain caused by double twins ε_DT is determined by multiplying the fraction of double twins by 1.32%. Furthermore, bending strain at the tension side ε_t, was estimated considering the movement of the neutral plane. ε_t when the height of the specimen is h′ can be calculated by replacing h with h′ in eq. (2). However, since the actual distance between the tension side and the neutral plane N_t is 0.5h − xh, ε_t can be expressed as eq. (11).   

\begin{align} \varepsilon_{t} &= \{(6dh')/L^{2}\}\times \{(0.5h-xh)/(h'/2)\} \\ &= 12d(0.5h-xh)/L^{2} \end{align} (11)

Figure 18 shows the relationship between ε_DT and ε_t of Mg–Y alloy single crystals; ε_t was calculated using both eq. (11) and the results of Fig. 17. ε_DT was approximately 0.35% when ε_t was even 25.5%, indicating that the strain induced by double twins is very low relative to the bending strain at the tension side. Here, basal slips may be activated in double twins due to the orientation rotation. However, Ando et al.¹²⁾ reported that cracks within double twins initiated by stress concentration caused by pile-up of dislocations near the twin interfaces due to basal slips in double twins may occur. In other words, basal slips within double twins may cause crack initiation. In this study, double twins were observed at approximately ε = 13% and cracks along the twins at ε = 17% in 0.07Y. While double twins occurred at approximately ε = 5%, no cracks were observed up to approximately ε = 20% in 0.15Y and 0.25Y. Here, many slip lines caused by FPCS were observed in the matrix of 0.15Y and 0.25Y, as shown in Fig. 13(c) and Fig. 14(c). Therefore, the stress concentration at the interface of double twins would be relieved by many FPCS activations around double twins, resulting in no visible cracks immediately after the formation of double twins in 0.15Y and 0.25Y. Thus, FPCS likely contributes to the deformation in the tension area in Mg–Y alloy single crystals.

Fig. 18

Relationship between strain induced by double twins and bending strain at the tension side of E specimens.

Figure 19 shows bending stress-bending strain curves and σ_t calculated using both eq. (9) and the results in Fig. 17 of Mg-E3 and 0.25Y-E1. Broken horizontal lines in Fig. 19 indicate activation stress of FPCS in [$11\bar{2}0$] calculated from CRSSs for FPCS of pure Mg¹³⁾ and Mg–0.6 at%Y (0.6Y).¹⁴⁾ Activation stress of FPCS was found to be independent of yttrium addition, as shown in Fig. 19. Here, σ_t of 0.25Y was larger than that of pure Mg, increasing at ε = 11%∼15%, which was close to the activation stress of FPCS. In addition, no slip lines cause from FPCS were observed at ε = 10.7%; however, FPCS was activated at ε = 14.6% or more. Thus, yttrium addition appears to decrease the difference between bending stress at the tension side and activation stress of FPCS and thus decreases {$10\bar{1}2$} twinning activity; consequently, movement of the neutral plane is reduced and the bending stress at the tension side increases accordingly. This results in an increase in bending ductility as FPCS is activated.

Fig. 19

Bending stress – bending strain curves of (a) Mg-E3 and (b) 0.25Y-E1. Closed circle indicate bending stress at the tension side σ_t. Broken horizontal lines indicate activation stress of FPCS in pure Mg¹³⁾ and Mg–0.6 at%Y.¹⁴⁾

4. Conclusions

Three-point bending tests of pure Mg and Mg–(0.07∼0.25) at%Y alloy single crystals were carried out to investigate the effect of crystal orientation and yttrium addition on bending deformation behavior.

1. (1)    B specimens whose neutral planes are parallel to (0001) and neutral axes are [$11\bar{2}0$] deformed due to basal slips and showed a gull-shape. In addition, the 0.15 at% yttrium addition did not change the bending deformation behavior. Bending yield stresses of B specimens increased by 0.15 at% yttrium content since CRSS for basal slip increased with yttrium addition.
2. (2)    E specimens whose neutral planes are parallel to ($1\bar{1}00$) and neutral axes are [$11\bar{2}0$] yielded due to {$10\bar{1}2$} twins occurred at the compression side. Bending yield stress of E specimens increased with increasing yttrium addition since CRSS for {$10\bar{1}2$} twins increased by yttrium addition. Bending ductility also increased by yttrium addition. In pure Mg, {$10\bar{1}2$} twins and basal slips within the twins were activated; however, in Mg–Y alloys, first order pyramidal ⟨c + a⟩ slips (FPCS) and double twins were also activated in the tension area, and the bending ductility increased mainly by FPCS activation.

Acknowledgements

This study was financially supported by “The Amada Foundation (Grant Number AF-2018016)”. The authors are very grateful for the supports.

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