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Effect of aluminum or zinc solute addition on enhancing impact fracture toughness in Mg–Ca alloys
Acta Materialia 104 (2016) 283e294
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Effect of aluminum or zinc solute addition on enhancing impact fracture toughness in MgeCa alloys Takayuki Hase a, Tatsuya Ohtagaki a, Masatake Yamaguchi b, Naoko Ikeo a, Toshiji Mukai a, * a b
Department of Mechanical Engineering, Kobe University, 1-1 Rokkodai-cho, Kobe 657-8501, Japan Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 July 2015 Received in revised form 19 November 2015 Accepted 23 November 2015 Available online xxx
We measured the impact toughness of three alloys (Mg, Mg-0.3 at%Ca-0.6 at%Zn, and Mg-0.3 at%Ca-0.6 at %Al) by the impact three-point bending test. The plastic deformability and impact toughness were higher in the ternary alloys than in pure Mg. The generalized stacking fault energy and grain boundary cohesive energy were estimated by first-principles calculations for Mg, binary MgeCa, ternary MgeCaeZn, and ternary MgeCaeAl alloys. The calculation results agreed with the trend in the experimental results. We suggest that addition of Ca along with Zn or Al reduced plastic anisotropy and strengthened the grain boundaries, leading to higher in impact toughness of Mg alloys. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Impact fracture toughness MgeCa alloy Solute segregation First-principles calculation Generalized stacking fault energy Crack propagation
1. Introduction Reducing the weight of vehicles is important for minimizing their environmental load. Mg alloys, which less dense than steel or Al alloys, have been investigated for use in structural components to reduce the weight of vehicles such as automobiles, planes, and high-speed trains [1,2]. However, the poor ductility of Mg alloys at room temperature and their flammability are obstacles to their practical use. The addition of rare earth elements can improve the mechanical properties of Mg alloys [3e10]. It is reported that Y addition improves the deformability and fracture toughness of Mg alloys [11e13], and that Ca addition improves their flame-resistance [14,15]. For commercial use, however, it is desirable that Mg alloys be improved without the use of rare earth elements. Several studies have reported Mg alloys with increased mechanical strength, ductility, and fracture toughness [16e19]. Somekawa et al. reported that the fracture toughness of extruded MgeCaeZn alloys is higher than that of conventional Mg alloys [20], but there are few studies on impact toughness of such ternary alloys, which is
* Corresponding author. E-mail address: [email protected] (T. Mukai). http://dx.doi.org/10.1016/j.actamat.2015.11.045 1359-6454/© 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
important for structural members in vehicles. Recent firstprinciples studies have achieved atomic-scale estimation of the mechanical properties of Mg alloys [21e25]. Yasi et al. evaluated the solid solution strengthening effects of 29 types of solute atoms in Mg alloys [26], and Yuasa et al. investigated the effects of solute atoms on the stretch formability of MgeCaeZn alloys [27e29]. However, further studies of the mechanical properties of ternary Mg alloys are required. In this work, the impact three-point bending test using three elastic bars was performed to evaluate the energy absorption of three alloys (Mg, Mg-0.3 at% Ca-0.6 at%Zn, and Mg-0.3 at%Ca-0.6 at %Al), and the effects of the solute elements on the impact toughness of the alloys were investigated. Moreover, first-principles calculations were performed to obtain the generalized stacking fault energy (GSFE) [30] and grain boundary cohesive energy (2gint ) [31] in Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. From the GSFE calculations, dislocation mobility and relative critical resolved shear stress (CRSS) were estimated. We investigated the effects of Ca combined with a Zn or Al solute on dislocation slip and plastic deformation behavior in Mg alloys by comparing the calculated GSFEs of the Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. The effects of the Ca, Zn, and Al solute atoms on grain boundary strength were estimated from calculated 2gint values. Our
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experimental and calculation results show improved impact toughness of the ternary Mg alloys. 2. Modeling of deformation and fracture 2.1. Electronic structure calculation First-principles calculations were performed with the Vienna Ab-initio Simulation Package [32,33], which uses plane-wave density-functional code. We used projector augmented-wave potentials and the PerdeweBurkeeErnzerhof generalized gradient approximation (GGA) exchange-correlation potential for Mg and all solutes [34,35]. The plane-wave cutoff was set to 360 eV with MethfesselePaxton smearing of 0.2 eV. The Brillouin zone was sampled with a MonkhorstePack k-point mesh (specific values for each geometry are given in Section 2.2 and 2.3). The atomic geometry was relaxed until the atomic forces were less than 0.01 eV/Å and the total energy change was less than 1 105 eV/atom by the quasi-Newton method. 2.2. GSFE calculations To investigate the deformation behavior of Mg alloys, we calculated the GSFEs for the basal, prismatic, first-order pyramidal, and second-order pyramidal planes. We used the following calculation models (Fig. 1): for basal slip, a Mg supercell with 13 ð0 0 0 2Þ plane layers (k-point mesh of 5 5 1) containing 117 atoms; for prismatic slip, a Mg supercell with 24 ð1 0 1 0Þ plane layers (k-point mesh of 4 4 1) containing 144 atoms; for the first-order pyramidal plane, a Mg supercell with 13 (1 0 1 1) plane layers (kpoint mesh of 3 4 1) containing 156 atoms; for second-order
Fig. 2. Calculation model for determining the most stable configuration in ternary MgeCaeX (X: Zn, Al) alloys.
pyramidal plane, a Mg supercell with 21 (1 1 2 2) plane layers (kpoint mesh of 4 3 1) containing 169 atoms. All the calculation models had a vacuum gap of 15 Å between the periodically repeated slabs. GSFE was calculated by displacing the upper half of the supercell relative to the bottom half. The atoms were free to relax along only the normal direction of the slip plane. The GSFE calculations were carried out for the Mg, binary MgeCa, ternary MgeCaeZn, and ternary MgeCaeAl alloys. The most stable configurations of Ca, Zn, and Al, were investigated using a 4 4 3 supercell containing 96 atoms, as shown in Fig. 2. One of the six Mg atoms in the MgeCa alloy (Sites 1e6) was substituted with Zn or Al. The most stable configuration was estimated from the binding energy of Ca and Zn or Al. The binding energy Ebind ðCa XÞ was calculated by
Fig. 1. Calculation models for GSFE of (a) the basal, (b) the prismatic, (c) the first-order pyramidal, and (d) the second-order pyramidal slips. The dashed lines indicate the slip plane of each slip system. The blue and gray spheres are Ca and Zn or Al, respectively. The red frames indicate the calculation areas for the two-dimensional variations in GSFE.
T. Hase et al. / Acta Materialia 104 (2016) 283e294
Ebind ðCa XÞ ¼ Efor Esol ðCaÞ Esol ðXÞ
(1)
Here, X is Zn or Al; Efor is the formation energy, which is the energy gain to form the geometry; and Esol is the solution energy, which is the energy gain from dissolving one solute atom into Mg. Efor was calculated by
Efor ¼ Etot NMg Mg þ NCa Ca þ NX X NMg Eatom ðMgÞ NCa Eatom ðCaÞ NX Eatom ðXÞ
(2)
Here, Etot ðNMg Mg þ NCa Ca þ NX XÞ is the total energy of the ternary Mg alloy supercell, Eatom is the energy per atom of each element, and N is the number of atoms of each element contained in the supercell. Esol of Ca was calculated by
Esol ðCaÞ ¼ Etot NMg Mg þ NCa Ca NMg Eatom ðMgÞ NCa Eatom ðCaÞ
Esol of Zn or Al was calculated in the same way. The configuration in which the binding energy Ebind ðCa XÞ was lowest was considered the most stable configuration of Ca and the third element. 2.3. Calculation of grain boundary cohesive energy The RiceeWang model proposes a theoretical relationship between changes in microscale electronic structure and macroscale grain boundary strengthening or decohesion [36]. In the model, the ideal work of interfacial separation (2gint ) is the main factor in grain boundary strengthening. 2gint can be calculated as the difference between twice the fracture surface energy (2gs ) and the grain boundary energy (gGB ). 2gint corresponds to the minimum required energy to form two fracture surfaces by dividing the grain boundary.
2gint ¼ 2gS gGB
which atoms are randomly arranged. However, it is difficult to model the structure of such grain boundaries. Instead, to calculate 2gint we used a model with a {1 1 2 1} symmetrically tilted grain boundary, which has a high grain boundary energy [40,41] and approximates the random grain boundaries in Mg. Fig. 7 shows the calculation model for 2gint (k-point mesh of 7 4 1). Hereinafter, this model is called “the GB model”. The GB model contains 76 atoms and a 15 Å vacuum gap between periodically repeated slabs. In this work, 2gint was calculated as the energy difference per unit area between the total energy of the model containing two fracture surfaces (Etot ðFSÞ) and the total energy of the GB model (Etot ðGBÞ).
2gint ¼ (3)
285
Etot ðFSÞ Etot ðGBÞ AGB
Etot ðFSÞ is the total energy of the system in which two fracture surfaces is introduced along the grain boundary with segregated solutes. The distance between the two surfaces are about 15 Å. We calculated 2gint for several types of assumed fracture surfaces, and chose the one with having the lowest 2gint as the fracture surface that was most likely to form. The segregated solutes appear on the two fracture surfaces. 2gint was calculated for models of Mg, MgeCa, MgeCaeZn, and MgeCaeAl. The most stable segregation site for Ca atoms was identified by the segregation energy, Eseg ðCaÞ, which is obtained from
0 Eseg ðCaÞ ¼ Etot GB þ NMg Mg þ NCa Ca Etot GB þ NMg Mg 0 NMg Eatom ðMgÞ NCa Eatom ðCaÞ þ NMg NCa Esol ðCaÞ
(4)
Yamaguchi et al. referred to 2gint as the “grain boundary cohesive energy”, and presented a mechanism of grain boundary decohesion caused by the grain boundary segregation of impurity atoms in bcc Fe and fcc Ni systems [37e39]. In the present study, we estimated 2gint for Mg, MgeCa, MgeCaeZn, and MgeCaeAl and estimated the effects of the addition of Ca and Zn or Al on grain boundary strength. Actual materials contain mainly random grain boundaries in
(5)
(6) 0 MgÞ NMg
Here, Etot ðGB þ is the total energy of the “clean” GB model with no solute segregation. As shown in Fig. 3, one of four Mg atoms in the clean GB model (Sites 1e4) was substituted with Ca. The site at where Eseg ðCaÞ is the lowest was identified as the most stable segregation site of the Ca atom. Next, the most stable configuration of the third element, Zn or Al, was determined from the total segregation energy of Ca and the third element, Eseg ðCa XÞ:
Fig. 3. The {1 1 2 1} tilt grain boundary model for calculating the grain boundary cohesive energy, 2gint . The green dashed line near the grain boundary region indicates the charge density observation plane.
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Fig. 4. Optical micrograph and inverse pole figure maps and IPF of the initial microstructures of Mg, Mg-0.3at.%Ca-0.6at.%Zn, and Mg-0.3at.%Ca-0.6at.%Al.
Eseg ðCa XÞ ¼ Etot GB þ NMg Mg þ NCa Ca þ NX X 0 0 Etot GB þ NMg Mg þ NMg NMg Eatom ðMgÞ NCa Eatom ðCaÞ NX Eatom ðXÞ NCa Esol ðCaÞ NX Esol ðXÞ (7) One of seven Mg atoms in Sites 1e8 excluding the segregation site of the Ca atom was substituted with Zn or Al. The configuration in which Eseg ðCa XÞ was the lowest was identified as the most stable configuration of Ca and Zn or Al. 3. Experimental methods 3.1. Materials The materials examined in this study were Mg, Mg-0.3 at%Ca0.6 at%Zn, and Mg-0.3 at%Ca-0.6 at%Al alloys, extruded at temperatures of 419, 673, and 623 K, respectively. Fig. 4 shows the microstructures of the materials. Impact toughness was estimated by using a three-point bending sample of width 5 mm and thickness 2.5 mm. A V-notch was machined perpendicular to the extruded
Fig. 5. Dimensions of the specimen for the impact three-point bending test.
direction in the extrusions. Fig. 5 shows the configuration and dimensions of the three-point bending specimen. 3.2. Impact toughness testing Fig. 6 shows a schematic of the setup for the three-point bending test [42,43]. The test was performed with one incident bar, two transmission bars, two absorbers, and one striker bar with lengths of 1295, 1095, 400, and 420 mm, respectively. The incident bar, two transmission bars, and two absorbers were made of SKD 11 tool steel with a diameter of 8 mm. The striker bar was made of brass with a diameter of 8 mm. The contact end of incident bar and two transmission bars formed a diagonal hammer and anvil for Charpy impact testing [44]. Two strain gauges were mounted on the surface of each of the incident bar and the two transmission bars at fixed positions 400 mm from the ends in contact with the specimen. The output voltage of the strain gauges was measured with an oscilloscope, and the propagation of stress waves through the incident bar and transmission bars was monitored. Fig. 7 shows equilibrium of forces between the incident bar and two transmission bars. Based on the principles of one-dimensional elastic wave propagation, the displacement rates of the tips of the incident bar, u_ i , and the two transmission bars, u_ t , are expressed as [45].
Fig. 6. Schematic illustration of the impact three-point bending apparatus [43].
T. Hase et al. / Acta Materialia 104 (2016) 283e294
u_ i ¼ cb ð εi þ εr Þ
(8)
u_ t ¼ cb εt
(9)
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Here, Cb is the propagation speed of the elastic wave through the elastic bars, and εi , εr , and εt are the incident, reflected, and transmitted stress waves, respectively. The relative displacement _ is expressed by rate of the incident bar and the transmission bars, u, the following equation.
u_ ¼ u_ i u_ t ¼ cb ð εi þ εr þ εt Þ
(10)
The transmitted waves from the two transmission bars were monitored, and the average of the displacement rate of transmission bars 1 and 2 was treated as the displacement rate of the transmission bars, u_ t . Thus, u_ is expressed by
u_ ¼ u_ i u_ t ¼ cb
εi þ εr þ
εt1 þ εt2 2
(11)
The load of each elastic bar is expressed as
Pi ¼ Ai Ei ðεi þ εr Þ Pt1 ¼ At1 Et1 εt1 Pt2 ¼ At2 Et2 εt2
Fig. 8. Variations in the loadedisplacement curves for Mg, Mg-0.3%Ca-0.6%Zn, and Mg-0.3%Ca-0.6%Al. The bold and dashed arrows indicate the displacements for the crack initiation point and the crack propagation to 0.4 mm, respectively.
(12)
For each elastic bar, P is the load applied, A is the cross-sectional area, and E is the Young’s modulus. The load applied to the specimen is assumed to be balanced. From Eq. 12,
Pi ¼ Pt1 þ Pt2 Ai Ei ðεi þ εr Þ ¼ At1 Et1 εt1 þ At2 Et2 εt2
(13)
The incident bar and the transmission bars in this work are made of the same material and have the same cross-sectional area. Eq. 13 can be rewritten as
εi þ εr ¼ εt1 þ εt2 0εr ¼ εi þ εt1 þ εt2
(14)
By substituting εr in Eq. 14 for that in Eq. 11, the relative _ can be expressed as displacement rate, u,
c u_ ¼ b f 4εi þ 3ðεr þ εt Þg 2
(15)
The relative displacement, u, is obtained as an integrated value _ is time-integrated. in which the relative displacement rate, u,
Z u¼
cb f 4εi þ 3ðεr þ εt Þgdt 2
In this study, the deformation and crack propagation behaviors of the specimen were observed by a high-speed camera with a sampling time of 4 ms. The load applied to the specimen was obtained as the sum of the loads via the two transmission bars (Eq. 12). The displacement of the specimen, u, was obtained from Eq. 16. From the area of the loadedisplacement curve, the absorbed energy per unit area of the specimen was evaluated, and the opening displacement of the Vnotch of the specimen was measured by using the high-speed camera images.
(16)
Fig. 7. Equilibrium of forces between the incident bar and two transmission bars.
4. Experimental results Fig. 8 shows the loadedisplacement curves of Mg, Mg-0.3%Ca0.6%Zn, and Mg-0.3%Ca-0.6%Al. Solid arrows indicate the crack initiation point and dashed arrows indicate the crack propagation point at 0.4 mm, which were determined from the high-speed camera images. The amount of energy absorption per unit area, E, for each material was evaluated by
E¼
1 Bb0
Z Pdd
(17)
Here, b0 is the original ligament width, B is the thickness of the specimen, P is the load applied to the specimen, and d is the displacement. The integration term is the area under the loadedisplacement curve. The absorbed energy per unit area from the load starting point to the crack initiation point, and that from the crack initiation point to the crack propagation point at 0.4 mm, were evaluated by Eq. 17. Fig. 9 shows the variation in the absorbed energy of each material. The ternary alloys had the same level of energy absorption by crack initiation, and this level was greater than that of Mg. The amount of energy absorbed by crack initiation indicates how difficult crack initiation is, so these results suggest that the addition of Ca and the third element suppressed the initiation of cracks in Mg. The plastic blunting capability at the crack tip was estimated from the measurements of the V-notch opening displacement. Fig. 10 and Table 1 show the relative V-notch opening displacement at crack initiation. Both the ternary alloys had greater relative opening displacement than Mg, suggesting that
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Mg-Ca-Zn Mg-Ca-Al
0 -0.04
B Binding energy E
bind
(Caa-X) (eV V)
0.04
-0.08 -0.12 -0.16 Site 1 Site 2 Site 3 Site 4 Site 5 Site 6
Fig. 11. Variations of binding energy, Ebind ðCa XÞ, in the ternary Mg alloys.
Fig. 9. Absorbed energy per unit area by crack initiation (hatching) and by crack propagation below 0.4 mm (solid) of Mg, Mg-0.3%Ca-0.6%Zn and Mg-0.3%Ca-0.6%Al.
5. Discussion the addition of Ca and Zn or Al increased the plastic blunting at the crack tip in Mg alloys. Direct comparison of the amount of energy absorption of the crack at less than 0.4 mm indicates that the energy absorption was highest in Mg-0.3% Ca-0.6%Al, followed by Mg-0.3%Ca-0.6%Zn and Mg. These results suggest that the addition of Ca and Zn or Al suppressed the propagation of cracks in Mg alloys and that the Mg0.3% Ca-0.6% Al alloy was the most resistant to crack propagation among the materials tested in this study.
5.1. Effect of the solute on plastic deformation behavior Fig. 11 shows the calculation results for Ebind ðCa XÞ. Site 4 had the lowest value in both the MgeCaeZn alloy and the MgeCaeAl alloy. Therefore, Site 4 was identified as the most stable configuration for Zn or Al. We used the ternary Mg alloy model with Zn or Al located at the Site 4 for our GSFE calculations. Figs. 12 and 13 show the calculated two-dimensional variations of GSFE (g-surface) for the basal and prismatic planes. The calculation area is indicated by the red frame in the calculation model of
Fig. 10. Experimental measurement of V-notch opening displacement.
Table 1 Experimental V-notch opening displacement.
Mg Mg-0.3%Ca-0.6%Zn Mg-0.3%Ca-0.6%Al
Origin (mm)
Crack initiation (mm)
Relative opening displacement (%)
0.539 0.513 0.486
0.601 0.614 0.600
11.5 19.7 23.5
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Fig. 12. Variations of the two-dimensional g-surface for the basal plane in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys.
each slip system in Fig. 1. For these calculations, cutoff energies of 210e276 eV were applied and the atomic geometry was relaxed until the total energy change was less than 1.0 103 eV/atom. Slip
deformation is likely to occur in the direction of the lower GSFE. For the basal slip (Fig. 12), the calculation results suggest that slip is likely to occur in the [1 0 1 0] direction, which is the Shockley
Fig. 13. Variations of the two-dimensional g-surface for the prismatic plane of the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys.
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Fig. 14. Variations of one-dimensional GSFE for (a) the basal slip system and (b) the prismatic slip system in the Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys.
partial dislocation for the basal slip in the presented materials. The calculation results also suggest that after the occurrence of slip in the [1 0 1 0] direction, the slip is likely to occur in the [1 1 0 0] direction. Thus, the g-surface indicates that the basal slip easily occurs the direction of Shockley partial dislocation rather than the direction of the perfect dislocation. Calculating the onedimensional variations of GSFE in the basal plane along the [1 0 1 0] and [1 1 0 0] directions, confirmed that the maximum value of the GSFE (unstable stacking fault energy, gus ) along each direction was equivalent in all the materials considered in this study. Therefore, the dislocation mobility in the basal plane can be investigated by calculating GSFE along [1 0 1 0]. Fig. 14(a) shows one-dimensional variations of GSFE in the basal plane along the [1 0 1 0]. The fault vector was varied from h i 0.0b to 1.0b in 0.1b steps. Here, b is the Burgers vectors a0 1 0 1 0 . The calculated g-surface for the prismatic plane (Fig. 13) shows that dislocation slip is likely to occur in the ½1 1 2 0 direction, which is direction of the perfect
dislocation for the prismatic slip in all materials in this study. The calculated one-dimensional variations of GSFE for the prismatic slip are shown in Fig. 14(b). Here, Burgers vectors b is a0 ½1 1 2 0. The one-dimensional variations of GSFE of the basal and prismatic slips in Mg, binary MgeCa, and ternary MgeCaeZn alloys have also been calculated by Yuasa et al. [27]. Our calculation results agree well with previous calculations, and suggest that the effects of alloying Al on the basal and prismatic slips in MgeCa alloy are similar to the effects of alloying Zn. In Mg, ductility is primarily achieved by activating the slip involving the <0 0 0 1> component. We calculated GSFE for the first and second-order pyramidal planes (Figs. 15 and 16, respectively). The calculated g-surface for the first-order pyramidal plane indicates that the minimum energy path (green vector, Fig. 15(a)) to achieve slip differs from the ideal {1 0 1 1} <1 1 2 3> Burgers vector (wide white arrow, Fig. 15(a)) among the materials examined in this study. The g-surface of the first-order
Fig. 15. The variations of the two-dimensional g-surface for the first-order pyramidal plane in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys. The green vector in (a) indicates the minimum energy path, which forms the {1 0 1 1}<1 1 2 3> dislocation.
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Fig. 16. Variations of the two-dimensional g-surface for the second-order pyramidal plane in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys. The green vector in (a) indicates the minimum energy path, which forms the {1 1 2 2}<1 1 2 3> dislocation.
Table 2 Calculated unstable stacking fault energy of Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys for the basal, prismatic, first-order pyramidal, and second-order pyramidal slips. Model
gus (basal) (J/m2)
gus (prism) (J/m2)
gus (pyramidal I) (J/m2)
gus (pyramidal II) (J/m2)
Mg MgeCa MgeCaeZn MgeCaeAl
0.085 0.073 0.079 0.077
0.232 0.164 0.153 0.152
0.380 0.377 0.365 0.368
0.515 0.520 0.491 0.505
pyramidal plane for Mg has also been calculated by Nogaret et al. [46] and Zu et al. [47] by density functional theory and molecular dynamics calculations. In this study, the calculation results show that the minimum energy path of the {1 0 1 1}<1 1 2 3> slip in Mg is almost consistent with previous calculations, and suggest that the path is unchanged even after alloying Ca in combination with Zn or Al. The calculated g-surface for the second-order pyramidal
plane, on the other hand, indicates that the dislocation slip easily occurs on the slip plane along the {1 1 2 2}<1 1 2 3> direction in all the materials studied here. The calculated unstable stacking fault energy gus along the minimum energy path of each slip system for the present materials is shown in Table 2. Direct comparison of the variations in gus revealed that the first-order pyramidal slip is more easily activated
seg
Segregation energy E (Ca) (eV)
0.2 0 -0.2 -0.4 -0.6 -0.8
Site 1
Site 2
Site 3
Site 4
Fig. 17. Variations of segregation energy, Eseg ðCaÞ, in the MgeCa alloy.
Fig. 18. Variations of total segregation energy, Eseg ðCa XÞ, in the ternary Mg alloy.
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T. Hase et al. / Acta Materialia 104 (2016) 283e294 Table 3 Calculated 2gint for the Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. Model
2gint (J/m2)
Mg MgeCa MgeCaeZn MgeCaeAl
1.162 1.267 1.272 1.299
than the second-order pyramidal slip for all the materials. As shown in the table, the addition of the Ca atom reduced the unstable stacking fault energy gus of the basal, prismatic, and firstorder pyramidal slips. However, the addition of Zn or Al increased gus of the basal slip, but reduced gus of the prismatic and first-order pyramidal slips. In particular, although the reducing ratio of gus for the first-order pyramidal slip in the ternary alloys was small, gus of the prismatic slip was markedly reduced by the alloying. The value of gus in the second-order pyramidal slip was largest in the MgeCa alloy, followed by the Mg, MgeCaeAl, and MgeCaeZn alloys. No variation in the second-order pyramidal slip was evident in our calculations. Pei et al. have reported a similar trend in MgeY alloy, where the minimum energy path of the second-order pyramidal slip is complicated and the effect of alloying yttrium is unclear [48]. Further investigation is required in order to understand the energy path along the second-order pyramidal slip in Mg. Because gus indicates the difficulty of the dislocation slip, the magnitude relation of gus corresponds to that of CRSS. Therefore, the calculated gus implies that the addition of Ca and Zn or Al activates non-basal slip, especially the prismatic slip, and relatively reduces the plastic anisotropy of Mg. This trend agrees with the experimental results for the relative opening displacement (Table 1). Taken together, these results suggest that the reduction of plastic anisotropy in Mg by addition of Ca and Zn or Al, alleviates the stress concentration in the alloy and increases its plastic deformability.
2gint for Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. The calculation results of 2gint indicate that Ca and Zn or Al are grain boundary strengthening elements for Mg. In particular, Al is a more effective than Zn as a third element for strengthening the grain boundary. Fig. 19 shows that charge density near the grain boundary region indicated by the green dashed line in Fig. 3. The contour map in Fig. 19 shows the calculated number of charges in a cube with side length equal to the Bohr radius. Fracture can be regarded as the breaking of atomic bonds, that is, as changes in electronic structure. As the electronic structure becomes more difficult to change, the metal material becomes less likely to fracture. Many electron orbitals are occupied where the charge density is high and the electronic structure is difficult to change. This means that increasing charge density strengthens atomic bonding and increases resistance to the fracture. The contour map of charge density indicates that the Mg alloys with higher 2gint values had higher charge density in the grain boundary region. Therefore, we suggest the increased charge density in the grain boundary region induced the increase in 2gint and strengthened the grain boundaries. Fig. 20 shows that the relationship between 2gint and absorbed energy per unit area after crack propagation to 0.4 mm. The absorbed energy after the crack propagation to 0.4 mm is correlated to grain boundary cohesive energy 2gint (Fig. 19). In addition, fractography by scanning electron microscopy revealed that the addition of Ca solute together with Zn or Al strengthened the grain boundary of Mg and suppressed intergranular fracture. Intergranular fracture along grain boundaries was observed in the Mg sample, but ductile dimples were found in the ternary alloys after the impact three-point bending tests. For the ternary alloys, the fracture mode in the experimental results agrees well with the enhanced cohesive energy at grain boundaries in the calculation results. Therefore, we conclude that the solute addition of Ca together with Zn or Al can enhance the grain boundary strength and effectively improve the impact toughness of Mg. Furthermore, our results suggest that MgeCaeAl alloys are promising Mg alloys with high deformability and toughness.
5.2. Effect of the solute on crack propagation
6. Summary
Fig. 17 shows the calculation results for Eseg ðCaÞ. Sites 1 and 3 are equivalent segregation sites. Site 1 is the most stable segregation site of the Ca atom. Fig. 18 shows the calculation results for Eseg ðCa XÞ. Site 2 had the lowest value of Eseg ðCa XÞ in both the MgeCaeZn alloy and the MgeCaeAl alloy, and it was identified as the most stable site for Zn or Al. Therefore, the MgeCa model with a Ca atom segregated at Site 1, and the ternary Mg model with Zn or Al segregated at Site 2 were used to calculate the grain boundary cohesive energy 2gint in this study. Table 3 shows the variations in
To clarify the effect of adding Ca and Zn or Al to Mg, impact toughness testing and first-principles calculations of GSFE and 2gint in Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys were conducted. The results are summarized as follows. (i) The impact toughness test showed that energy absorption was improved by adding Ca and Zn or Al. For crack initiation, the absorbed energy was higher in both the ternary Mg alloys than in Mg. The amount of energy absorption from the
Fig. 19. Charge density near the grain boundary region in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, (d) MgeCaeAl alloys.
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Fig. 20. Variation of the absorbed energy per unit area after the crack propagation to 0.4 mm E0:4 and grain boundary cohesive energy 2gint .
crack initiation by crack propagation below 0.4 mm was the highest in Mg-0.3%Ca-0.6%Al, followed by Mg-0.3%Ca-0.6%Zn and Mg. (ii) Calculations of GSFE for the basal, prismatic, first-order pyramidal, and second-order pyramidal slips demonstrated that the alloying of Mg with Ca and Zn or Al resulted in activation of non-basal slip, especially, the prismatic slip. However, measurements of the V-notch opening displacement in impact toughness testing indicated that plastic blunting was increased in the ternary Mg alloys. This suggests that reducing the plastic anisotropy alleviated the stress concentration in the ternary alloys and increased their plastic deformability. (iii) Calculations of the grain boundary cohesive energy, 2gint , showed that adding Ca and Zn or Al strengthened the grain boundary in Mg alloys. The magnitude relation of the grain boundary cohesive energy corresponded to that of the energy absorbed in crack initiation by crack propagation below 0.4 mm during impact toughness testing. These results therefore suggest that the energy absorption during crack propagation is increased in the ternary Mg alloys by the addition of Ca and Zn or Al strengthening the grain boundaries. Our results suggest that MgeCaeAl alloys are promising candidates for high-toughness Mg alloys. Acknowledgments This work was supported in part by JSPS KAKENHI Grant No. 25246012 and the Light Metals Education Foundation, Japan. References [1] T. Mukai, Materials technology for weight reduction~possibility of magnesium alloys~, Mater. Jpn. 43 (2004) 810e814. [2] H. Mori, K. Fujino, K. Kurita, Y. Chino, N. Saito, M. Noda, H. Komai, H. Obara, Application of the flame-retardant magnesium alloy to high speed rail vehicles, Mater. Jpn. 52 (2013) 484e490. [3] E.A. Ball, P.B. Prangnell, Tensile-compressive yield asymmetries in high strength wrought magnesium, Scr. Metall. Mater. 31 (1994) 111e116. [4] T. Mohri, M. Mabuchi, N. Saito, M. Nakamura, Microstructure and mechanical properties of a Mg-4Y-3RE alloy processed by thermo-mechanical treatment, Mater. Sci. Eng. A 257 (1998) 287e294.
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Full length article
Effect of aluminum or zinc solute addition on enhancing impact fracture toughness in MgeCa alloys Takayuki Hase a, Tatsuya Ohtagaki a, Masatake Yamaguchi b, Naoko Ikeo a, Toshiji Mukai a, * a b
Department of Mechanical Engineering, Kobe University, 1-1 Rokkodai-cho, Kobe 657-8501, Japan Center for Computational Science and e-Systems, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 July 2015 Received in revised form 19 November 2015 Accepted 23 November 2015 Available online xxx
We measured the impact toughness of three alloys (Mg, Mg-0.3 at%Ca-0.6 at%Zn, and Mg-0.3 at%Ca-0.6 at %Al) by the impact three-point bending test. The plastic deformability and impact toughness were higher in the ternary alloys than in pure Mg. The generalized stacking fault energy and grain boundary cohesive energy were estimated by first-principles calculations for Mg, binary MgeCa, ternary MgeCaeZn, and ternary MgeCaeAl alloys. The calculation results agreed with the trend in the experimental results. We suggest that addition of Ca along with Zn or Al reduced plastic anisotropy and strengthened the grain boundaries, leading to higher in impact toughness of Mg alloys. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Impact fracture toughness MgeCa alloy Solute segregation First-principles calculation Generalized stacking fault energy Crack propagation
1. Introduction Reducing the weight of vehicles is important for minimizing their environmental load. Mg alloys, which less dense than steel or Al alloys, have been investigated for use in structural components to reduce the weight of vehicles such as automobiles, planes, and high-speed trains [1,2]. However, the poor ductility of Mg alloys at room temperature and their flammability are obstacles to their practical use. The addition of rare earth elements can improve the mechanical properties of Mg alloys [3e10]. It is reported that Y addition improves the deformability and fracture toughness of Mg alloys [11e13], and that Ca addition improves their flame-resistance [14,15]. For commercial use, however, it is desirable that Mg alloys be improved without the use of rare earth elements. Several studies have reported Mg alloys with increased mechanical strength, ductility, and fracture toughness [16e19]. Somekawa et al. reported that the fracture toughness of extruded MgeCaeZn alloys is higher than that of conventional Mg alloys [20], but there are few studies on impact toughness of such ternary alloys, which is
* Corresponding author. E-mail address: [email protected] (T. Mukai). http://dx.doi.org/10.1016/j.actamat.2015.11.045 1359-6454/© 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
important for structural members in vehicles. Recent firstprinciples studies have achieved atomic-scale estimation of the mechanical properties of Mg alloys [21e25]. Yasi et al. evaluated the solid solution strengthening effects of 29 types of solute atoms in Mg alloys [26], and Yuasa et al. investigated the effects of solute atoms on the stretch formability of MgeCaeZn alloys [27e29]. However, further studies of the mechanical properties of ternary Mg alloys are required. In this work, the impact three-point bending test using three elastic bars was performed to evaluate the energy absorption of three alloys (Mg, Mg-0.3 at% Ca-0.6 at%Zn, and Mg-0.3 at%Ca-0.6 at %Al), and the effects of the solute elements on the impact toughness of the alloys were investigated. Moreover, first-principles calculations were performed to obtain the generalized stacking fault energy (GSFE) [30] and grain boundary cohesive energy (2gint ) [31] in Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. From the GSFE calculations, dislocation mobility and relative critical resolved shear stress (CRSS) were estimated. We investigated the effects of Ca combined with a Zn or Al solute on dislocation slip and plastic deformation behavior in Mg alloys by comparing the calculated GSFEs of the Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. The effects of the Ca, Zn, and Al solute atoms on grain boundary strength were estimated from calculated 2gint values. Our
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experimental and calculation results show improved impact toughness of the ternary Mg alloys. 2. Modeling of deformation and fracture 2.1. Electronic structure calculation First-principles calculations were performed with the Vienna Ab-initio Simulation Package [32,33], which uses plane-wave density-functional code. We used projector augmented-wave potentials and the PerdeweBurkeeErnzerhof generalized gradient approximation (GGA) exchange-correlation potential for Mg and all solutes [34,35]. The plane-wave cutoff was set to 360 eV with MethfesselePaxton smearing of 0.2 eV. The Brillouin zone was sampled with a MonkhorstePack k-point mesh (specific values for each geometry are given in Section 2.2 and 2.3). The atomic geometry was relaxed until the atomic forces were less than 0.01 eV/Å and the total energy change was less than 1 105 eV/atom by the quasi-Newton method. 2.2. GSFE calculations To investigate the deformation behavior of Mg alloys, we calculated the GSFEs for the basal, prismatic, first-order pyramidal, and second-order pyramidal planes. We used the following calculation models (Fig. 1): for basal slip, a Mg supercell with 13 ð0 0 0 2Þ plane layers (k-point mesh of 5 5 1) containing 117 atoms; for prismatic slip, a Mg supercell with 24 ð1 0 1 0Þ plane layers (k-point mesh of 4 4 1) containing 144 atoms; for the first-order pyramidal plane, a Mg supercell with 13 (1 0 1 1) plane layers (kpoint mesh of 3 4 1) containing 156 atoms; for second-order
Fig. 2. Calculation model for determining the most stable configuration in ternary MgeCaeX (X: Zn, Al) alloys.
pyramidal plane, a Mg supercell with 21 (1 1 2 2) plane layers (kpoint mesh of 4 3 1) containing 169 atoms. All the calculation models had a vacuum gap of 15 Å between the periodically repeated slabs. GSFE was calculated by displacing the upper half of the supercell relative to the bottom half. The atoms were free to relax along only the normal direction of the slip plane. The GSFE calculations were carried out for the Mg, binary MgeCa, ternary MgeCaeZn, and ternary MgeCaeAl alloys. The most stable configurations of Ca, Zn, and Al, were investigated using a 4 4 3 supercell containing 96 atoms, as shown in Fig. 2. One of the six Mg atoms in the MgeCa alloy (Sites 1e6) was substituted with Zn or Al. The most stable configuration was estimated from the binding energy of Ca and Zn or Al. The binding energy Ebind ðCa XÞ was calculated by
Fig. 1. Calculation models for GSFE of (a) the basal, (b) the prismatic, (c) the first-order pyramidal, and (d) the second-order pyramidal slips. The dashed lines indicate the slip plane of each slip system. The blue and gray spheres are Ca and Zn or Al, respectively. The red frames indicate the calculation areas for the two-dimensional variations in GSFE.
T. Hase et al. / Acta Materialia 104 (2016) 283e294
Ebind ðCa XÞ ¼ Efor Esol ðCaÞ Esol ðXÞ
(1)
Here, X is Zn or Al; Efor is the formation energy, which is the energy gain to form the geometry; and Esol is the solution energy, which is the energy gain from dissolving one solute atom into Mg. Efor was calculated by
Efor ¼ Etot NMg Mg þ NCa Ca þ NX X NMg Eatom ðMgÞ NCa Eatom ðCaÞ NX Eatom ðXÞ
(2)
Here, Etot ðNMg Mg þ NCa Ca þ NX XÞ is the total energy of the ternary Mg alloy supercell, Eatom is the energy per atom of each element, and N is the number of atoms of each element contained in the supercell. Esol of Ca was calculated by
Esol ðCaÞ ¼ Etot NMg Mg þ NCa Ca NMg Eatom ðMgÞ NCa Eatom ðCaÞ
Esol of Zn or Al was calculated in the same way. The configuration in which the binding energy Ebind ðCa XÞ was lowest was considered the most stable configuration of Ca and the third element. 2.3. Calculation of grain boundary cohesive energy The RiceeWang model proposes a theoretical relationship between changes in microscale electronic structure and macroscale grain boundary strengthening or decohesion [36]. In the model, the ideal work of interfacial separation (2gint ) is the main factor in grain boundary strengthening. 2gint can be calculated as the difference between twice the fracture surface energy (2gs ) and the grain boundary energy (gGB ). 2gint corresponds to the minimum required energy to form two fracture surfaces by dividing the grain boundary.
2gint ¼ 2gS gGB
which atoms are randomly arranged. However, it is difficult to model the structure of such grain boundaries. Instead, to calculate 2gint we used a model with a {1 1 2 1} symmetrically tilted grain boundary, which has a high grain boundary energy [40,41] and approximates the random grain boundaries in Mg. Fig. 7 shows the calculation model for 2gint (k-point mesh of 7 4 1). Hereinafter, this model is called “the GB model”. The GB model contains 76 atoms and a 15 Å vacuum gap between periodically repeated slabs. In this work, 2gint was calculated as the energy difference per unit area between the total energy of the model containing two fracture surfaces (Etot ðFSÞ) and the total energy of the GB model (Etot ðGBÞ).
2gint ¼ (3)
285
Etot ðFSÞ Etot ðGBÞ AGB
Etot ðFSÞ is the total energy of the system in which two fracture surfaces is introduced along the grain boundary with segregated solutes. The distance between the two surfaces are about 15 Å. We calculated 2gint for several types of assumed fracture surfaces, and chose the one with having the lowest 2gint as the fracture surface that was most likely to form. The segregated solutes appear on the two fracture surfaces. 2gint was calculated for models of Mg, MgeCa, MgeCaeZn, and MgeCaeAl. The most stable segregation site for Ca atoms was identified by the segregation energy, Eseg ðCaÞ, which is obtained from
0 Eseg ðCaÞ ¼ Etot GB þ NMg Mg þ NCa Ca Etot GB þ NMg Mg 0 NMg Eatom ðMgÞ NCa Eatom ðCaÞ þ NMg NCa Esol ðCaÞ
(4)
Yamaguchi et al. referred to 2gint as the “grain boundary cohesive energy”, and presented a mechanism of grain boundary decohesion caused by the grain boundary segregation of impurity atoms in bcc Fe and fcc Ni systems [37e39]. In the present study, we estimated 2gint for Mg, MgeCa, MgeCaeZn, and MgeCaeAl and estimated the effects of the addition of Ca and Zn or Al on grain boundary strength. Actual materials contain mainly random grain boundaries in
(5)
(6) 0 MgÞ NMg
Here, Etot ðGB þ is the total energy of the “clean” GB model with no solute segregation. As shown in Fig. 3, one of four Mg atoms in the clean GB model (Sites 1e4) was substituted with Ca. The site at where Eseg ðCaÞ is the lowest was identified as the most stable segregation site of the Ca atom. Next, the most stable configuration of the third element, Zn or Al, was determined from the total segregation energy of Ca and the third element, Eseg ðCa XÞ:
Fig. 3. The {1 1 2 1} tilt grain boundary model for calculating the grain boundary cohesive energy, 2gint . The green dashed line near the grain boundary region indicates the charge density observation plane.
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Fig. 4. Optical micrograph and inverse pole figure maps and IPF of the initial microstructures of Mg, Mg-0.3at.%Ca-0.6at.%Zn, and Mg-0.3at.%Ca-0.6at.%Al.
Eseg ðCa XÞ ¼ Etot GB þ NMg Mg þ NCa Ca þ NX X 0 0 Etot GB þ NMg Mg þ NMg NMg Eatom ðMgÞ NCa Eatom ðCaÞ NX Eatom ðXÞ NCa Esol ðCaÞ NX Esol ðXÞ (7) One of seven Mg atoms in Sites 1e8 excluding the segregation site of the Ca atom was substituted with Zn or Al. The configuration in which Eseg ðCa XÞ was the lowest was identified as the most stable configuration of Ca and Zn or Al. 3. Experimental methods 3.1. Materials The materials examined in this study were Mg, Mg-0.3 at%Ca0.6 at%Zn, and Mg-0.3 at%Ca-0.6 at%Al alloys, extruded at temperatures of 419, 673, and 623 K, respectively. Fig. 4 shows the microstructures of the materials. Impact toughness was estimated by using a three-point bending sample of width 5 mm and thickness 2.5 mm. A V-notch was machined perpendicular to the extruded
Fig. 5. Dimensions of the specimen for the impact three-point bending test.
direction in the extrusions. Fig. 5 shows the configuration and dimensions of the three-point bending specimen. 3.2. Impact toughness testing Fig. 6 shows a schematic of the setup for the three-point bending test [42,43]. The test was performed with one incident bar, two transmission bars, two absorbers, and one striker bar with lengths of 1295, 1095, 400, and 420 mm, respectively. The incident bar, two transmission bars, and two absorbers were made of SKD 11 tool steel with a diameter of 8 mm. The striker bar was made of brass with a diameter of 8 mm. The contact end of incident bar and two transmission bars formed a diagonal hammer and anvil for Charpy impact testing [44]. Two strain gauges were mounted on the surface of each of the incident bar and the two transmission bars at fixed positions 400 mm from the ends in contact with the specimen. The output voltage of the strain gauges was measured with an oscilloscope, and the propagation of stress waves through the incident bar and transmission bars was monitored. Fig. 7 shows equilibrium of forces between the incident bar and two transmission bars. Based on the principles of one-dimensional elastic wave propagation, the displacement rates of the tips of the incident bar, u_ i , and the two transmission bars, u_ t , are expressed as [45].
Fig. 6. Schematic illustration of the impact three-point bending apparatus [43].
T. Hase et al. / Acta Materialia 104 (2016) 283e294
u_ i ¼ cb ð εi þ εr Þ
(8)
u_ t ¼ cb εt
(9)
287
Here, Cb is the propagation speed of the elastic wave through the elastic bars, and εi , εr , and εt are the incident, reflected, and transmitted stress waves, respectively. The relative displacement _ is expressed by rate of the incident bar and the transmission bars, u, the following equation.
u_ ¼ u_ i u_ t ¼ cb ð εi þ εr þ εt Þ
(10)
The transmitted waves from the two transmission bars were monitored, and the average of the displacement rate of transmission bars 1 and 2 was treated as the displacement rate of the transmission bars, u_ t . Thus, u_ is expressed by
u_ ¼ u_ i u_ t ¼ cb
εi þ εr þ
εt1 þ εt2 2
(11)
The load of each elastic bar is expressed as
Pi ¼ Ai Ei ðεi þ εr Þ Pt1 ¼ At1 Et1 εt1 Pt2 ¼ At2 Et2 εt2
Fig. 8. Variations in the loadedisplacement curves for Mg, Mg-0.3%Ca-0.6%Zn, and Mg-0.3%Ca-0.6%Al. The bold and dashed arrows indicate the displacements for the crack initiation point and the crack propagation to 0.4 mm, respectively.
(12)
For each elastic bar, P is the load applied, A is the cross-sectional area, and E is the Young’s modulus. The load applied to the specimen is assumed to be balanced. From Eq. 12,
Pi ¼ Pt1 þ Pt2 Ai Ei ðεi þ εr Þ ¼ At1 Et1 εt1 þ At2 Et2 εt2
(13)
The incident bar and the transmission bars in this work are made of the same material and have the same cross-sectional area. Eq. 13 can be rewritten as
εi þ εr ¼ εt1 þ εt2 0εr ¼ εi þ εt1 þ εt2
(14)
By substituting εr in Eq. 14 for that in Eq. 11, the relative _ can be expressed as displacement rate, u,
c u_ ¼ b f 4εi þ 3ðεr þ εt Þg 2
(15)
The relative displacement, u, is obtained as an integrated value _ is time-integrated. in which the relative displacement rate, u,
Z u¼
cb f 4εi þ 3ðεr þ εt Þgdt 2
In this study, the deformation and crack propagation behaviors of the specimen were observed by a high-speed camera with a sampling time of 4 ms. The load applied to the specimen was obtained as the sum of the loads via the two transmission bars (Eq. 12). The displacement of the specimen, u, was obtained from Eq. 16. From the area of the loadedisplacement curve, the absorbed energy per unit area of the specimen was evaluated, and the opening displacement of the Vnotch of the specimen was measured by using the high-speed camera images.
(16)
Fig. 7. Equilibrium of forces between the incident bar and two transmission bars.
4. Experimental results Fig. 8 shows the loadedisplacement curves of Mg, Mg-0.3%Ca0.6%Zn, and Mg-0.3%Ca-0.6%Al. Solid arrows indicate the crack initiation point and dashed arrows indicate the crack propagation point at 0.4 mm, which were determined from the high-speed camera images. The amount of energy absorption per unit area, E, for each material was evaluated by
E¼
1 Bb0
Z Pdd
(17)
Here, b0 is the original ligament width, B is the thickness of the specimen, P is the load applied to the specimen, and d is the displacement. The integration term is the area under the loadedisplacement curve. The absorbed energy per unit area from the load starting point to the crack initiation point, and that from the crack initiation point to the crack propagation point at 0.4 mm, were evaluated by Eq. 17. Fig. 9 shows the variation in the absorbed energy of each material. The ternary alloys had the same level of energy absorption by crack initiation, and this level was greater than that of Mg. The amount of energy absorbed by crack initiation indicates how difficult crack initiation is, so these results suggest that the addition of Ca and the third element suppressed the initiation of cracks in Mg. The plastic blunting capability at the crack tip was estimated from the measurements of the V-notch opening displacement. Fig. 10 and Table 1 show the relative V-notch opening displacement at crack initiation. Both the ternary alloys had greater relative opening displacement than Mg, suggesting that
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Mg-Ca-Zn Mg-Ca-Al
0 -0.04
B Binding energy E
bind
(Caa-X) (eV V)
0.04
-0.08 -0.12 -0.16 Site 1 Site 2 Site 3 Site 4 Site 5 Site 6
Fig. 11. Variations of binding energy, Ebind ðCa XÞ, in the ternary Mg alloys.
Fig. 9. Absorbed energy per unit area by crack initiation (hatching) and by crack propagation below 0.4 mm (solid) of Mg, Mg-0.3%Ca-0.6%Zn and Mg-0.3%Ca-0.6%Al.
5. Discussion the addition of Ca and Zn or Al increased the plastic blunting at the crack tip in Mg alloys. Direct comparison of the amount of energy absorption of the crack at less than 0.4 mm indicates that the energy absorption was highest in Mg-0.3% Ca-0.6%Al, followed by Mg-0.3%Ca-0.6%Zn and Mg. These results suggest that the addition of Ca and Zn or Al suppressed the propagation of cracks in Mg alloys and that the Mg0.3% Ca-0.6% Al alloy was the most resistant to crack propagation among the materials tested in this study.
5.1. Effect of the solute on plastic deformation behavior Fig. 11 shows the calculation results for Ebind ðCa XÞ. Site 4 had the lowest value in both the MgeCaeZn alloy and the MgeCaeAl alloy. Therefore, Site 4 was identified as the most stable configuration for Zn or Al. We used the ternary Mg alloy model with Zn or Al located at the Site 4 for our GSFE calculations. Figs. 12 and 13 show the calculated two-dimensional variations of GSFE (g-surface) for the basal and prismatic planes. The calculation area is indicated by the red frame in the calculation model of
Fig. 10. Experimental measurement of V-notch opening displacement.
Table 1 Experimental V-notch opening displacement.
Mg Mg-0.3%Ca-0.6%Zn Mg-0.3%Ca-0.6%Al
Origin (mm)
Crack initiation (mm)
Relative opening displacement (%)
0.539 0.513 0.486
0.601 0.614 0.600
11.5 19.7 23.5
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Fig. 12. Variations of the two-dimensional g-surface for the basal plane in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys.
each slip system in Fig. 1. For these calculations, cutoff energies of 210e276 eV were applied and the atomic geometry was relaxed until the total energy change was less than 1.0 103 eV/atom. Slip
deformation is likely to occur in the direction of the lower GSFE. For the basal slip (Fig. 12), the calculation results suggest that slip is likely to occur in the [1 0 1 0] direction, which is the Shockley
Fig. 13. Variations of the two-dimensional g-surface for the prismatic plane of the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys.
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Fig. 14. Variations of one-dimensional GSFE for (a) the basal slip system and (b) the prismatic slip system in the Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys.
partial dislocation for the basal slip in the presented materials. The calculation results also suggest that after the occurrence of slip in the [1 0 1 0] direction, the slip is likely to occur in the [1 1 0 0] direction. Thus, the g-surface indicates that the basal slip easily occurs the direction of Shockley partial dislocation rather than the direction of the perfect dislocation. Calculating the onedimensional variations of GSFE in the basal plane along the [1 0 1 0] and [1 1 0 0] directions, confirmed that the maximum value of the GSFE (unstable stacking fault energy, gus ) along each direction was equivalent in all the materials considered in this study. Therefore, the dislocation mobility in the basal plane can be investigated by calculating GSFE along [1 0 1 0]. Fig. 14(a) shows one-dimensional variations of GSFE in the basal plane along the [1 0 1 0]. The fault vector was varied from h i 0.0b to 1.0b in 0.1b steps. Here, b is the Burgers vectors a0 1 0 1 0 . The calculated g-surface for the prismatic plane (Fig. 13) shows that dislocation slip is likely to occur in the ½1 1 2 0 direction, which is direction of the perfect
dislocation for the prismatic slip in all materials in this study. The calculated one-dimensional variations of GSFE for the prismatic slip are shown in Fig. 14(b). Here, Burgers vectors b is a0 ½1 1 2 0. The one-dimensional variations of GSFE of the basal and prismatic slips in Mg, binary MgeCa, and ternary MgeCaeZn alloys have also been calculated by Yuasa et al. [27]. Our calculation results agree well with previous calculations, and suggest that the effects of alloying Al on the basal and prismatic slips in MgeCa alloy are similar to the effects of alloying Zn. In Mg, ductility is primarily achieved by activating the
Fig. 15. The variations of the two-dimensional g-surface for the first-order pyramidal plane in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys. The green vector in (a) indicates the minimum energy path, which forms the {1 0 1 1}<1 1 2 3> dislocation.
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Fig. 16. Variations of the two-dimensional g-surface for the second-order pyramidal plane in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, and (d) MgeCaeAl alloys. The green vector in (a) indicates the minimum energy path, which forms the {1 1 2 2}<1 1 2 3> dislocation.
Table 2 Calculated unstable stacking fault energy of Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys for the basal, prismatic, first-order pyramidal, and second-order pyramidal slips. Model
gus (basal) (J/m2)
gus (prism) (J/m2)
gus (pyramidal I) (J/m2)
gus (pyramidal II) (J/m2)
Mg MgeCa MgeCaeZn MgeCaeAl
0.085 0.073 0.079 0.077
0.232 0.164 0.153 0.152
0.380 0.377 0.365 0.368
0.515 0.520 0.491 0.505
pyramidal plane for Mg has also been calculated by Nogaret et al. [46] and Zu et al. [47] by density functional theory and molecular dynamics calculations. In this study, the calculation results show that the minimum energy path of the {1 0 1 1}<1 1 2 3> slip in Mg is almost consistent with previous calculations, and suggest that the path is unchanged even after alloying Ca in combination with Zn or Al. The calculated g-surface for the second-order pyramidal
plane, on the other hand, indicates that the dislocation slip easily occurs on the slip plane along the {1 1 2 2}<1 1 2 3> direction in all the materials studied here. The calculated unstable stacking fault energy gus along the minimum energy path of each slip system for the present materials is shown in Table 2. Direct comparison of the variations in gus revealed that the first-order pyramidal slip is more easily activated
seg
Segregation energy E (Ca) (eV)
0.2 0 -0.2 -0.4 -0.6 -0.8
Site 1
Site 2
Site 3
Site 4
Fig. 17. Variations of segregation energy, Eseg ðCaÞ, in the MgeCa alloy.
Fig. 18. Variations of total segregation energy, Eseg ðCa XÞ, in the ternary Mg alloy.
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T. Hase et al. / Acta Materialia 104 (2016) 283e294 Table 3 Calculated 2gint for the Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. Model
2gint (J/m2)
Mg MgeCa MgeCaeZn MgeCaeAl
1.162 1.267 1.272 1.299
than the second-order pyramidal slip for all the materials. As shown in the table, the addition of the Ca atom reduced the unstable stacking fault energy gus of the basal, prismatic, and firstorder pyramidal slips. However, the addition of Zn or Al increased gus of the basal slip, but reduced gus of the prismatic and first-order pyramidal slips. In particular, although the reducing ratio of gus for the first-order pyramidal slip in the ternary alloys was small, gus of the prismatic slip was markedly reduced by the alloying. The value of gus in the second-order pyramidal slip was largest in the MgeCa alloy, followed by the Mg, MgeCaeAl, and MgeCaeZn alloys. No variation in the second-order pyramidal slip was evident in our calculations. Pei et al. have reported a similar trend in MgeY alloy, where the minimum energy path of the second-order pyramidal slip is complicated and the effect of alloying yttrium is unclear [48]. Further investigation is required in order to understand the energy path along the second-order pyramidal slip in Mg. Because gus indicates the difficulty of the dislocation slip, the magnitude relation of gus corresponds to that of CRSS. Therefore, the calculated gus implies that the addition of Ca and Zn or Al activates non-basal slip, especially the prismatic slip, and relatively reduces the plastic anisotropy of Mg. This trend agrees with the experimental results for the relative opening displacement (Table 1). Taken together, these results suggest that the reduction of plastic anisotropy in Mg by addition of Ca and Zn or Al, alleviates the stress concentration in the alloy and increases its plastic deformability.
2gint for Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys. The calculation results of 2gint indicate that Ca and Zn or Al are grain boundary strengthening elements for Mg. In particular, Al is a more effective than Zn as a third element for strengthening the grain boundary. Fig. 19 shows that charge density near the grain boundary region indicated by the green dashed line in Fig. 3. The contour map in Fig. 19 shows the calculated number of charges in a cube with side length equal to the Bohr radius. Fracture can be regarded as the breaking of atomic bonds, that is, as changes in electronic structure. As the electronic structure becomes more difficult to change, the metal material becomes less likely to fracture. Many electron orbitals are occupied where the charge density is high and the electronic structure is difficult to change. This means that increasing charge density strengthens atomic bonding and increases resistance to the fracture. The contour map of charge density indicates that the Mg alloys with higher 2gint values had higher charge density in the grain boundary region. Therefore, we suggest the increased charge density in the grain boundary region induced the increase in 2gint and strengthened the grain boundaries. Fig. 20 shows that the relationship between 2gint and absorbed energy per unit area after crack propagation to 0.4 mm. The absorbed energy after the crack propagation to 0.4 mm is correlated to grain boundary cohesive energy 2gint (Fig. 19). In addition, fractography by scanning electron microscopy revealed that the addition of Ca solute together with Zn or Al strengthened the grain boundary of Mg and suppressed intergranular fracture. Intergranular fracture along grain boundaries was observed in the Mg sample, but ductile dimples were found in the ternary alloys after the impact three-point bending tests. For the ternary alloys, the fracture mode in the experimental results agrees well with the enhanced cohesive energy at grain boundaries in the calculation results. Therefore, we conclude that the solute addition of Ca together with Zn or Al can enhance the grain boundary strength and effectively improve the impact toughness of Mg. Furthermore, our results suggest that MgeCaeAl alloys are promising Mg alloys with high deformability and toughness.
5.2. Effect of the solute on crack propagation
6. Summary
Fig. 17 shows the calculation results for Eseg ðCaÞ. Sites 1 and 3 are equivalent segregation sites. Site 1 is the most stable segregation site of the Ca atom. Fig. 18 shows the calculation results for Eseg ðCa XÞ. Site 2 had the lowest value of Eseg ðCa XÞ in both the MgeCaeZn alloy and the MgeCaeAl alloy, and it was identified as the most stable site for Zn or Al. Therefore, the MgeCa model with a Ca atom segregated at Site 1, and the ternary Mg model with Zn or Al segregated at Site 2 were used to calculate the grain boundary cohesive energy 2gint in this study. Table 3 shows the variations in
To clarify the effect of adding Ca and Zn or Al to Mg, impact toughness testing and first-principles calculations of GSFE and 2gint in Mg, MgeCa, MgeCaeZn, and MgeCaeAl alloys were conducted. The results are summarized as follows. (i) The impact toughness test showed that energy absorption was improved by adding Ca and Zn or Al. For crack initiation, the absorbed energy was higher in both the ternary Mg alloys than in Mg. The amount of energy absorption from the
Fig. 19. Charge density near the grain boundary region in the (a) Mg, (b) MgeCa, (c) MgeCaeZn, (d) MgeCaeAl alloys.
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Fig. 20. Variation of the absorbed energy per unit area after the crack propagation to 0.4 mm E0:4 and grain boundary cohesive energy 2gint .
crack initiation by crack propagation below 0.4 mm was the highest in Mg-0.3%Ca-0.6%Al, followed by Mg-0.3%Ca-0.6%Zn and Mg. (ii) Calculations of GSFE for the basal, prismatic, first-order pyramidal, and second-order pyramidal slips demonstrated that the alloying of Mg with Ca and Zn or Al resulted in activation of non-basal slip, especially, the prismatic slip. However, measurements of the V-notch opening displacement in impact toughness testing indicated that plastic blunting was increased in the ternary Mg alloys. This suggests that reducing the plastic anisotropy alleviated the stress concentration in the ternary alloys and increased their plastic deformability. (iii) Calculations of the grain boundary cohesive energy, 2gint , showed that adding Ca and Zn or Al strengthened the grain boundary in Mg alloys. The magnitude relation of the grain boundary cohesive energy corresponded to that of the energy absorbed in crack initiation by crack propagation below 0.4 mm during impact toughness testing. These results therefore suggest that the energy absorption during crack propagation is increased in the ternary Mg alloys by the addition of Ca and Zn or Al strengthening the grain boundaries. Our results suggest that MgeCaeAl alloys are promising candidates for high-toughness Mg alloys. Acknowledgments This work was supported in part by JSPS KAKENHI Grant No. 25246012 and the Light Metals Education Foundation, Japan. References [1] T. Mukai, Materials technology for weight reduction~possibility of magnesium alloys~, Mater. Jpn. 43 (2004) 810e814. [2] H. Mori, K. Fujino, K. Kurita, Y. Chino, N. Saito, M. Noda, H. Komai, H. Obara, Application of the flame-retardant magnesium alloy to high speed rail vehicles, Mater. Jpn. 52 (2013) 484e490. [3] E.A. Ball, P.B. Prangnell, Tensile-compressive yield asymmetries in high strength wrought magnesium, Scr. Metall. Mater. 31 (1994) 111e116. [4] T. Mohri, M. Mabuchi, N. Saito, M. Nakamura, Microstructure and mechanical properties of a Mg-4Y-3RE alloy processed by thermo-mechanical treatment, Mater. Sci. Eng. A 257 (1998) 287e294.
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