2018 Volume 59 Issue 1 Pages 66-71
The hardness and tensile properties of Mg-La-Zr alloys with various lanthanum contents were investigated, and the microstructures of the alloys were examined. The microstructure was composed of fine globular primary α-Mg grains and eutectic areas. The values of yield stress and modulus of the eutectic were, respectively, about 3 times and 1.7 times higher than those of the primary α-Mg. The increase in the yield stress of the alloys with less than 1.2%La is due to a rapid increase in coverage of the α-Mg grain boundary by the eutectic. As the increment in the grain boundary coverage decreases with lanthanum content, the composite strengthening (composite materials effect) starts to play a more significant role in increasing yield stress. As the grain boundary coverage reaches a plateau at about 2%La, further increase in the yield stress is mainly due to the composite strengthening, the effect of which is dependent on the volume fraction of eutectic. During tensile-testing at 150℃, the alloys with higher lanthanum content exhibited dual yield points, the first from yielding of the primary α-Mg, followed by the higher-yield point associated with the eutectic. This suggests that composite strengthening is in effect.
This Paper was Originally Published in Japanese in J. JILM 66 (2016) 647–651.
Among the practical metals, magnesium (Mg) has the lowest density and can be applied in various fields, particularly in vehicles, as one method of protecting the global environment.
Adding rare earth (RE) elements to Mg alloys can improve the strength and creep resistance1). Particularly, heavy RE elements such as yttrium (Y), gadolinium (Gd), and dysprosium (Dy), which have high solid solubilities in Mg, are of use in solid solution strengthening and precipitation hardening. Excellent heat-resistant Mg alloys with these elements have also been fabricated2). Another report states that trace amounts of cerium (Ce) can improve the formability of Mg3). In addition, RE elements have low toxicity to living organisms and have recently attracted attention as alloying elements for biodegradable Mg-based materials4). However, the effect of REs on Mg alloys varies widely.
Even before individual RE was technically available, REs have been used in the form of Mischmetal for Mg alloys5). In particular, because the presence of RE elements does not inhibit crystal grain refinement by zirconium(Zr), the Mg–RE–Zr system has been studied in casting, and several WE-series and other Mg alloys have been developed.
Lanthanum (La), a light RE, has very limited solubility in Mg and hence it does not contribute to age-hardening6,7). Generally, the contribution of La to creep resistance is also considered to be less than those of Ce and praseodymium (Pr)7,8). However, among the light REs, La has the lowest density; it is also inexpensive and easy to handle. In addition, a eutectic reaction is attained by the addition of a small amount of La, which forms the thermally stable intermetallic compound of Mg12La. When Zr is added as well, the primary α-Mg dendrite crystals are transformed to fine spherical crystals which are surrounded by eutectic areas, forming a uniformly solidified structure9).
The mechanical properties of Mg–La–Zr alloys are affected by the hard eutectic phase9,10). Because the eutectic forms a three-dimensional networked-structure in the alloy, recent research using 3D structural observation11) has been conducted. However, the influence of the eutectic on the mechanical properties is not fully known.
In this study, we report on the yielding behavior as influenced by the eutectic of Mg–La–Zr alloys from the perspective of the microstructure and mechanical properties.
Mg–La–Zr alloys containing 0 to 4.2%La were prepared from 99.92%Mg, 99.9%La, and Mg– 33%Zr master alloy (all in mass%). The addition amount of Zr was set to 1.5%. Tensile tests were performed at room temperature and 150℃, in accordance with JIS Z 2241 and JIS G 0567, respectively. In both cases, the specimens were made in accordance with JIS 14 A, with a parallel part of 6 mm in diameter and a gauge length of 30 mm. An initial strain rate was set to 5.5 × 10−4 s−1.
The Vickers hardness and Young's modulus of the primary α-Mg and the eutectic phase were estimated using a nano-indentation tester (HM 500, manufactured by Fischer)12,13). The test load was 25 mN, and the indenter was a Vickers indenter shaped as a square pyramid. For each sample, the microstructure was observed with an optical microscope and a field-emission scanning electron microscope (FE-SEM; acceleration voltage 10 kV).
The constituent phases of the Mg–La–Zr alloy are primary crystalline α-Mg and the eutectic (αMg + Mg12La). Figure 1 shows a back-scattered electron image of the Mg–La–Zr alloys; the darker regions that appear in spherical morphology are the primary α-Mg crystals, while those that appear in white are eutectic areas, surrounding the primary α-Mg crystals and forming a network pattern. In addition, the area ratio increases with increasing La content.
Backscattered SEM micrographs of as-cast Mg-La-Zr alloys, showing primary α-Mg crystals (dark) and eutectic areas (light).
As shown in Fig. 2, the average Vickers hardness values of the primary α-Mg and eutectic compound are HV 47 and HV 152, respectively. The average contact pressure $P_{m}$ (load/projected impression area) by the indenter relates proportionally to the yield stress $\sigma_{y}$, i.e., $ P_{m} \propto \sigma _{y} $14). Because the Vickers hardness is defined as the load divided by the impression surface area, HV = 0.927 $P_{m}$ is obtained by converting the impression surface area into the projected impression area15). In addition, the proportionality of HV and $P_{m}$ indicates that the yield stress of the eutectic compound at room temperature is estimated to be approximately three times that of primary α-Mg. As shown in Fig. 3, the Young's modulus is 30 GPa for primary α-Mg and 52 GPa for the eutectic. Defining the Young's moduli of the primary α-Mg and eutectic as $E_{m}$ and $E_{e}$, respectively, the relationship $E_{e}/E_{m} = 1.73$ is obtained. Generally, the reliability of measured (absolute) values obtained by nano-indentation testing is insufficient. However, comparing relative values is a well-established test method16). Therefore, in this study, we considered the relative value of the Young's modulus, defined by the ratio $E_{e}/E_{m}$.
Micro-Vickers hardness values of α-Mg and eutectic phases.
Values of Young's Modulus of α-Mg and eutectic estimated from hardness tests.
From the hardness test results shown in section 3.1, the stress–strain curve of the Mg–La–Zr alloy is schematically depicted in Fig. 4. The stress–strain curve of the alloy is located between those of the primary α-Mg and eutectic, as shown by the broken line in the figure. In this study, it is assumed that the strain in the tensile direction of each phase is equal to the yield stress. Therefore, the influence on the yield behavior of the eutectic is investigated based on the rule of mixtures with the stress.
Diagram describing the composite-strengthening effect for Mg-La-Zr alloys.
In Fig. 4, yield occurs when the primary α-Mg, a soft phase, reaches the yield stress $\sigma_{y(m)}$. Therefore, the following equation holds:
| \[ \sigma_{y} = \sigma_{e} f + \sigma_{y(m)} (1 - f) \] | (1) |
In addition to providing composite reinforcement17), the eutectic obstructs dislocation movement by covering the surface of primary α-Mg, thereby strengthening the α-Mg phase. This is referred to as strengthening by grain boundary covering18). For the yield stress of ${\sigma_{y(m)}}'$, the following eq. (2) is derived using the crystal grain size $d$ and the grain boundary covering ratio $\xi$ of the hard phase:
| \[ {\sigma_{y(m)}}' = \sigma_{o} + K \sqrt{(r_{e} - r_{m}) \xi + r_{m}} d^{-1/2}. \] | (2) |
Here, $\xi$ is the ratio of the length over which the eutectic covers the primary α-Mg crystal to the peripheral length of the α-Mg crystal. $\sigma_{o}$ and $K$ are constants, and $r$ is the slip resistance. If $r_{e}$ is the slip resistance of the primary α-Mg/eutectic boundaries and $r_{m}$ is the slip resistance of the primary α-Mg/α-Mg boundaries, $r_{e}$ and $r_{m}$ are respectively expressed as follows:
| \[ r_{e} = \{Gb/(1 - \nu)\pi\} \tau_{e},\ r_{m} = \{Gb/(1 - \nu)\pi\} \tau_{m} \] | (3) |
Here, to facilitate understanding and assuming that while $f$ remains constant, the strengthening by the grain boundary coverage is in effect, we find the relationship, shown in Fig. 5, between the strengthening by grain boundary covering and composite reinforcement. The yield stress of the primary α-Mg shifts in the direction of the arrow in the figure owing to the strengthening effect of the grain boundary covering. By assuming that the yield stress ${\sigma_{y(m)}}'$ is reached at strain $\varepsilon '$, the influence of the composite reinforcement with this state as a reference is considered. Then, eq. (1) becomes
| \[ {\sigma_{y}}' = {\sigma_{e}}' f + {\sigma_{y (m)}}' (1 - f), \] | (4) |
Relationship between composite-strengthening ($\varDelta \sigma_{c}$) and strengthening by grain-boundary coverage ($\varDelta \sigma_{y(m)}$).
Figure 6 depicts the stress–strain curves at room temperature of some Mg–La–Zr alloys. In the curves shown, the yield points are clear in all cases except the 4.2 La sample. The 0.5 La curve is obtained from this experiment, while the others are quoted from Ref. 19). Figure 7 shows the relationship between the La content and yield stress. For 4.2 La, the offset 0.2% proof stress value is plotted. For alloys containing La, the crystal grain size is uniform at approximately 20 μm, permitting investigation of the yield behavior as affected by the eutectic phase. However, the average grain size of the 0 La alloy reaches 47 μm,9), and the influence of grain size on yield stress cannot be ignored. Therefore, this data point was excluded. In Fig. 7, the differences in the yield stress between subsequent pairs of alloys are of different orders: for example, $\varDelta \sigma_{y} = 23\,{\rm MPa}$ between 0.5 La and 1.6 La, but $\varDelta \sigma_{y} = 8\,{\rm MPa}$ between 1.6 La and 2.6 La. Because the difference in the La content is approximately 1% between each composition, $\varDelta \sigma_{y}$ differs greatly over the composition range of La.
Example of engineering stress-strain curves at room temperature for Mg-La-Zr alloys. All the curves except for 0.5%La are from Ref. 19.
Diagram showing values of yield stress and the contributing-strengthening mechanism with respect to lanthanum content. Range: (a) strengthening by grain boundary coverage; (b) strengthening both by grain boundary coverage and composite-strengthening; and (c) composite-strengthening.
Figure 8 shows the relationships between La contents $x$ (mass%) and grain boundary coverage $\xi$ (%), and between La contents and eutectic volume fraction $f$ (%). The eutectic volume fraction is calculated from the eutectic area fractions of a plurality of polished surfaces20). The solid line in the figure is based on the regression curve. The relation between $x$ and $\xi $ is $\xi = 87.8 - 87.6 (0.145)^{x}$, and the relationship between $x$ and $f$ is expressed as $f = 5.08x$. As shown in Fig. 8, an increase in the value of $\xi$ becomes small after about 1.6La. For example, for samples containing 1.6La and 2.6La, the value of $\xi$ is 82 and 86%, respectively. Because $\xi$ does not change significantly, it can be determined from eq. (2) that between these compositions, $\sigma_{y(m)} \approx 0$. Generally, for composite materials containing unidirectional continuous-fibers, strengthening effects do not appear when $f<10$%, this is because of the fact that the effects of composite reinforcement can be offset by stress concentration21). For Mg–La–Zr, stress concentration also occurs because of differences in the elastic coefficients of the primary α-Mg and eutectic. Therefore, assuming that the same phenomenon occurs, it is estimated that for La contents up to 2.0% with $f$ = 10%, $\varDelta \sigma_{c} \ll \varDelta \sigma_{y(m)}$. Thus, in the regime between 0 and 2.0 La, $\varDelta \sigma_{y} \approx \varDelta \sigma_{y(m)}$. However, from Fig. 8, the grain boundary coverage $\xi$ reaches 80% at 1.2La and an increase in the value of $\xi$ becomes very small above 1.2La. Therefore, it can be considered $\varDelta \sigma_{y(m)} \approx 0$ beyond 1.2La. Lanthanum contents between 1.2 and 2.0% represent a transitional regime in that contributing strengthening mechanism changes from strengthening by the grain boundary coverage to composite strengthening, and it is estimated that $\varDelta \sigma_{y} \approx 0$. For alloys containing more than 2.0La, the influence of the composite reinforcement becomes dominant, and $\varDelta \sigma_{c} \gg \varDelta \sigma_{y(m)}$. Considering these behaviors and based on eqs. (1) and (2), the changes in yield stress with La content are depicted by the dashed line in Fig. 7. From this figure, it is considered that an increase in yield stress ($\varDelta \sigma_{y} \approx \varDelta \sigma_{y(m)} = 23\,{\rm MPa}$) between 0.5La and 1.6La is mainly due to the strengthening by grain boundary coverage and an increase ($\varDelta \sigma_{y} \approx \varDelta \sigma_{c} = 8\,{\rm MPa}$) between 1.6 La and 2.6La is due to the composite strengthening mechanism. As described above, in the Mg–La–Zr alloy, the strengthening by the grain boundary coverage can be attained by small addition of La approximately 1%, and the yield stress is remarkably increased. For 4.2La, the effect of composite reinforcement is significant.
Change in values of the length fraction of grain boundary coverage by eutectic and volume fraction of eutectic with lanthanum content.
As shown in Fig. 6, at 0.5La, 1.6La and 2.6La, stress reduction and stagnation are observed immediately after yield. This might be due to the elastic energy increase, caused by the strengthening mechanism by the grain boundary coverage, being released by the slippage (yield) of the primary α-Mg crystal and eutectic and then converted into plastic work. However, further consideration is necessary on this point.
3.3 Yield behavior at 150℃Figure 9 shows the stress–strain curves of Mg–La–Zr alloys at 150℃. At 2.3 La and 4.1 La, two yield points are observed, as indicated by arrows ① and ② in the figure. From Fig. 5, the stress of ① and ② correspond to ${\sigma_{y}}'$ and eutectic yield, respectively. The presence of yield ②, which indicates that the eutectic shares some of the load, suggests the composite strengthening. However, in Fig. 9, only one yield point is observed for the stress–strain curves of 0.5La and 0.85La. Therefore, they probably yielded when the load stress $\sigma$ reached ${\sigma_{y(m)}}'$. The yield condition at this point is $\sigma = {\sigma_{y}}' = {\sigma_{y(m)}}'$. The sharp decrease in yield point is attributed to the relief of the elastic energy increase induced by the covered grain boundary strengthening during yield, as occurs at room temperature.
Example of engineering stress-strain curves at 150℃ for Mg-La-Zr alloys.
As can be seen from Fig. 8, the values of $\xi$ for 2.3La and 4.1La are nearly equal. Therefore, from eq. (2), the values of ${\sigma_{y(m)}}'$ for 2.3La and 4.1La are considered equal. As shown in Fig. 9, the stress ${\sigma_{y}}'$ at point ① is 80 MPa for 2.3La and 89 MPa for 4.1La. Furthermore, assuming that the relationship $E_{e}/E_{m} = 1.73$ holds at 150℃, the following equation:
| \[ {\sigma_{y}}' = {\sigma_{y(m)}}' \{1 + 0.73f\} \] | (5) |
The active slip systems of Mg increase at 150℃. Therefore, when the load stress $\sigma$ exceeds ${\sigma'_{y}}$ (①), slip deformation in primary α-Mg begins first with simultaneous plastic relaxation. Therefore, the gradient of the stress–strain curve also changes at this point. When the composite reinforcement is active, slip deformation in the primary α-Mg is significantly restrained by the eutectic. However, if the bond between primary α-Mg and eutectic is strong, yield is suppressed by the increase in active slip systems. Therefore, through the elastically deforming eutectic, slip further progresses independently in each primary α-Mg grain. In this case, as the plastic strain increases, dislocations accumulate in the primary α-Mg/eutectic boundaries, and internal compressive stress fields are formed in the primary α-Mg grains, while tensile stress fields are formed in eutectic. As a result, in the stress range between ① and ② in Fig 9, work hardening is accelerated within primary α-Mg, resulting in a high increase in the gradient of the stress–strain curve. When $\sigma$ reaches ②, the entire eutectic region reaches the yield stress, triggering slips through multiple primary α-Mg grains. In addition, the plastic relaxation resulting from these actions again causes decreases in the slope of the stress–strain curve. Therefore, the two yield points ① and ②, which were not seen at room temperature, are clearly observed at 150℃.
As described above, for Mg–La–Zr alloys reinforced by the eutectic, the plastic deformation of the primary α-Mg occurs before yield begins in the eutectic region. Because of this, caution is required when analyzing the initial plastic deformation behavior at elevated temperatures.
In this study, we investigated the contributing effects of the eutectic in Mg–La–Zr alloys on the yielding behaviors based on the microstructure and mechanical properties, and obtained the following conclusions.
(1) At room temperature, the eutectic yield stress is approximately three times greater than that of the primary α-Mg. In addition, for the Young's moduli $E_{m}$ and $E_{e}$ of the primary α-Mg and eutectic, respectively, the relationship $E_{e}/E_{m} = 1.73$ is obtained.
(2) The yield stress of the Mg–La–Zr alloy is increased by strengthening by grain boundary covering and by composite reinforcement. Each strengthening mechanism requires separate analysis; the former is dependent on the grain boundary coverage by the eutectic, while the latter is dependent on the eutectic volume fraction.
(3) For La contents up to 1.2%, strengthening mechanism by grain boundary covering dominates, while for La contents above 2.0%, the yield stress increases by the composite strengthening mechanism. However, the range between 1.2 to 2.0 La represents a transition region from the strengthening by grain boundary covering to composite strengthening mechanism, and the increase in yield stress is stagnant in this range.
(4) The yield behaviors of Mg–La–Zr alloys at 150℃ generally follow the equation ${\sigma_{y}}' = {\sigma_{e}}' f + {\sigma_{y(m)}}' (1 - f)$. Yield is initiated when the stress occurring in the primary α-Mg reaches the yield stress ${\sigma_{y(m)}}'$. In addition, at 150℃, the active slip systems are increased compared to those at room temperature. Therefore, plastic deformation of the primary α-Mg progresses while the eutectic deforms elastically. Therefore, in the stress–strain curve at elevated temperature, two yield points, one from the primary crystal α-Mg and the other from the eutectic, are observed separately.
The partial financial support provided by the Light Metal Educational Foundation, Inc. is gratefully acknowledged.
