Activation of non-basal ＜c+ a＞slip in multicomponent Mg alloys

Hyo-Sun Jng ,Jong-Kwn Lee, ,Antonio Jo?o Seco Ferreir Tpi, ,Nck Joon Kim ,Byeong-Joo Lee,?

a Department of Materials Science and Engineering,Pohang University of Science and Technology (POSTECH),Pohang 37673,Republic of Korea

bGraduate Institute of Ferrous Technology,Pohang University of Science and Technology (POSTECH),Pohang 37673,Republic of Korea

Abstract Activating non-basal ＜c+a＞slip is a key method to improve room temperature ductility and formability of Mg alloys.However,the detailed criterion for activation of the ＜c+a＞slip in multicomponent Mg alloys,which can be utilized in commercial Mg alloys,requires further understanding.The present authors investigated the mechanism and criterion using a molecular statics simulation on dislocation behaviors in multicomponent Mg alloys.We found that if multicomponent Mg alloys have an equivalent dislocation binding intensity to associated binary Mg alloys that are optimized to minimize the critical resolved shear stress anisotropy and thus activate the ＜c+a＞slip,then the critical resolved shear stress anisotropy between slip systems of the multicomponent Mg alloys can also be minimized,resulting in activation of the ＜c+a＞slip.The activation is maximized in multicomponent Mg alloys when alloying a large amount of weak dislocation binding elements.It was confirmed through experiments that the multicomponent Mg alloys satisfying the above criterion show higher room-temperature tensile elongation and formability than other alloys.

Keywords: Mg-Zn-Ca alloy;Molecular statics simulation;Ductility;Formability.

1.Introduction

Magnesium (Mg) is the lightest structural metal and has been attracting attention as a part material for reducing the weight of automobiles and aircrafts [1,2].However,such applications remain limited due to its poor ductility and formability at room temperature (RT) [3,4].These poor mechanical properties originate from the hexagonal close-packed (hcp)crystal structure of Mg,which involves fewer slip systems than face-centered-cubic or body-centered-cubic structures.

One promising way to improve the poor mechanical properties of Mg is to activate non-basal＜c+a＞slip [5],and considerable efforts have been made to do it at RT.One of the proposed methods is to reduce theI1stacking fault energy (SFE).TheI1stacking faults can act as a nucleation source of＜c+a＞dislocations[6],which can be facilitated by reducing theI1SFE [7].Previous studies have reported that yttrium (Y) reduces theI1SFE,thus facilitating the＜c+a＞slip activation [8].Based on this finding an yttrium similarity index (YSI) has been devised to fine alloying elements such as Y that can reduce theI1SFE in a short time [9].This method accurately predicts the＜c+a＞slip activation in binary Mg alloys containing rare earth elements (REEs),and Mg-0.90Al-0.06Ca (at%) alloy [3].However,it cannot explain the＜c+a＞slip activation in binary Mg alloys containing non-RE elements,in particular,Mg-Al [10] and Mg-Zn alloys [11].Another method is to reduce the cross slip energy barrier of＜c+a＞dislocations [7,12].This method is based on the characteristic that pure Mg generally exhibits a pyramidal-to-basal (PB) transition of＜c+a＞dislocations and the PB transition transforms the dislocation core structures from glissile pyramidal to sessile basal.The immobile sessile dislocations result in poor ductility of pure Mg.If the cross slip energy barrier can be reduced by alloying,the Mg alloy would show accelerated cross slip,causing the cross slip-rate to exceed the PB transition rate and then activating the＜c+a＞slip.This method can predict the ductility improvement in Mg-REE alloys and some dilute Mg-Al-Ca-Mn and Mg-Zn-X (X=Mn,Zr,and Gd) alloys [7,12],but it cannot explain the ductility improvement in Mg-Al [10] and Mg-Zn [11] solid solutions,which are the basic alloys constituting the ternary and quaternary Mg alloys to which the method is applied.

Here,our group has suggested a new mechanism for activation of the＜c+a＞slip by alloying solute elements[10,13].The solute atoms form stronger solute-dislocation binding and solid solution strengthening on basal slip planes than on nonbasal slip planes due to their different dislocation core structures.This dissimilar solute effect reduces the inherent large critical resolved shear stress(CRSS)anisotropy between basal and non-basal slip systems,creating a suitable environment to activate the＜c+a＞slip [14].The solute-dislocation binding originates from the difference in atomic size between the solute element and Mg.Therefore,any alloying element with an atomic size difference from Mg can activate the＜c+a＞slip,if the alloying amount is carefully controlled depending on the size of the solute-dislocation binding.This mechanism has been applied to Mg binary alloys containing elements with a size-mismatch in previous works [10,13,15,16] to confir its validity.These works report that the new mechanism successfully explains the＜c+a＞slip activation in Mg-Y and Mg-Nd alloys containing REEs[10,13]as well as Mg-Al,Mg-Ca,Mg-Li,and Mg-Zn alloys containing non-REEs [10,15,16].Furthermore,it can predict the optimum content of those elements to maximize the＜c+a＞slip activation;the predictions are similar to the finding of other experiments [10,17-19].

The applicability of the new mechanism,however,has only been proved for binary Mg alloys.Commercial Mg alloys generally contain two or more alloying elements to enhance hardness [20,21],corrosion resistance [22,23],or creep resistance [24,25],depending on their usage.For this reason,it is necessary to confir whether this mechanism can apply to multicomponent Mg alloys.If the application is possible,the optimum content of alloying elements to maximize the＜c+a＞slip activation should also be confirmed This can be done by calculating the CRSS of basal and non-basal slip systems of multicomponent Mg alloys,confirming that their CRSS anisotropy between slip systems can be reduced,and identifying the composition that minimizes the CRSS anisotropy most efficiently .

The purpose of the present study is to confir whether the＜c+a＞slip activation mechanism established in binary Mg alloys can be extended to multicomponent Mg alloys and to determine the optimum content of alloying elements to maximize the＜c+a＞slip activation.The investigated multicomponent Mg alloy is the Mg-Zn-Ca ternary alloy,one of the representative commercial Mg alloys.For the investigation,we firs determined the optimum binary content of Zn and Ca to maximize the＜c+a＞slip activation in individual binary Mg alloys using a molecular statics (MS) simulation.To optimize the binary content of Zn more precisely,an experiment to evaluate the tensile property of Mg-Zn alloys was carried out.We then confirmed that the CRSS anisotropy of the ternary alloy can be reduced as in the binary alloys with optimum content once the ternary composition was adjusted to maintain equivalent dislocation binding intensity to the optimum binary alloys.The optimum ternary Mg alloy was predicted to contain a large amount of relatively weak binding element that stably activates the＜c+a＞slip.The simulation results were validated by our experiment in which a Mg-Zn-Ca alloy satisfying the aforementioned criterion for activating the＜c+a＞slip showed higher ductility and formability than other alloys.

2.Methods

2.1.Computational procedure

The CRSS of basal slip systems with simple dislocation structures can be obtained from experiments or first-principle calculations.However,the CRSS of non-basal slip systems,especially that of a pyramidal II slip system,is difficult to obtain from the above-mentioned methods due to the similarity in orientations between twin systems and slip systems[26] and the asymmetric dislocation structures [13].This difficult can be resolved by a large-scale atomistic simulation based on (semi-)empirical interatomic potentials.The atomistic simulation can deal with complex systems including the pyramidal II slip system,and the CRSS of basal and nonbasal slip systems can be calculated through an MD (molecular dynamics) or MS (molecular statics) simulation for the dislocation gliding.Thus,we used the atomistic simulation to calculate the CRSS values of basal and non-basal slip systems of Mg alloys.

This simulation requires interatomic potentials for relevant systems.We used the second nearest-neighbor modified embedded-atom method (2NN MEAM) [27,28] potential for the Mg-Zn-Ca ternary system developed by Jang et al.[29].This potential reproduces thermodynamic and structural properties of the Mg-Zn-Ca alloy system reasonably well.Furthermore,the potential closely reproduces the generalized SFE (GSFE),which is known to be related to deformation behaviors of metallic alloys,on basal,prismatic,pyramidal I,and pyramidal II slip planes [29].Interatomic potentials for the constituent unary and binary alloy systems,that is,the 2NN MEAM potentials for pure Mg [30],Mg-Zn [31],and Mg-Ca [32] binary systems,are also reported to accurately reproduce the fundamental material properties of the relevant systems including the GSFE on basal and non-basal slip planes [31-34].In particular,the pure Mg potential is reported to accurately reproduce the core structures of edge and screw dislocations on pyramidal II planes,in good agreement with DFT calculations[35].The Mg-Zn potential is also known to exhibit good reproducibility in the binding energy between an edge dislocation and a Zn atom on basal plane,similar to DFT [36] and model calculations [37],as listed in Table 1 [15].

Table 1Peak values of binding energy between an edge dislocation and a Zn atom on basal plane according to the present 2NN MEAM potential,in comparison with DFT and model calculations.The unit of binding energy is eV.

Table 2Calculated CRSS ratio between non-basal slip modes and the basal slip mode in Mg-0.1,0.3,0.5,and 1.0 at% Zn alloys.The non-basal slip modes denote the prismatic slip,pyramidal II slip in the positive direction,and pyramidal II slip in the negative direction.

Using the above-mentioned interatomic potentials,we conducted an MS simulation to calculate the CRSS of basal,prismatic,and pyramidal II slip planes for the Mg-Zn-Ca alloy.To observe the basal,prismatic,and pyramidal II dislocation behaviors in the simulations,we made a special condition in which only a specific dislocation can be easily activated.The condition could be achieved by artificially introducing a dislocation in perfect crystal samples,as shown in Fig.S1 and giving shear deformation to glide the dislocation.In general,only the intended (introduced) dislocation is observed in those kinds of simulations.However,as already reported in our previous papers [10,13],if the amount of alloying element is large,the core structures can transform into immobile structures and then generate twins on the pyramidal II planes.In the present study,the alloy contents were not that large,so no such a transformation occurred.In order to compare the CRSS results with those for Mg-Zn and Mg-Ca binary alloys,the simulation conditions and sample sizes were the same as those for the binary alloys [10,13,15,16].Each simulation sample involves an edge dislocation in the main slip systems:basal {0001}＜120＞,prismatic{100}＜120＞,and pyramidal II {122}＜123＞.The simulated core structures of the basal,prismatic,and pyramidal II dislocations in pure Mg are shown in Fig.S1.The sample sizes were 32 nm×52 nm×1 nm (79,600 atoms),32 nm×52 nm×1.5 nm (114,624 atoms),and 30 nm×32 nm×2 nm (99,704 atoms),respectively.Rigid strain-controlled loading was applied to create a shear deformation on each slip system and the direction of shear was the slip direction.The stress and strain values of the slip systems were obtained from repeating shear displacement and relaxation.The samples were allowed to relax along the normal direction of slip planes.The strain rate was 6×106s-1for the basal and prismatic slip systems and 1×107s-1for the pyramidal slip system.Since these strain rates used in the present study were too high compared to those in general experiments (order of 10-4-10-2),the simulation was conducted at 0 K to avoid probable artifact that may come from the high strain rates.We believe that the finding obtained from the 0 K simulation would be valid also at RT.This is because it has been revealed that the CRSS values for various alloys decrease monotonically with increasing temperature and the CRSS curves with different compositions do not cross each other during the increase of temperature [37].Therefore,one may expect that the relative effect of alloy content would be maintained between 0 K and RT.The solute atoms are randomly distributed in the samples since we aimed to create a Mg-rich solid solution.To reduce the statistical error due to the distribution of alloying elements in samples,three different solid solution samples were prepared for each composition and labeled sample A,B,and C.An example of the set of basal samples with Mg-0.25Zn-0.05Ca composition is presented in Fig.1.The same simulations were performed independently using the three samples for each composition.The stress-strain curves for these samples were then averaged.The CRSS was define as the average of flow stresses after the dislocation starts gliding.These calculations were conducted by the large-scale atomic/molecular massively parallel simulator (LAMMPS) package [38].The radial cut-off distance was 6.0 °A,which is larger than the second nearest-neighbor distances of Mg,Zn,and Ca.

2.2.Experimental procedure

Tensile tests were performed on Mg-Zn binary alloys at RT to fine the optimum content of Zn to maximize the＜c+a＞slip activation.Mg-xZn (x:0.3,0.5,0.75,and 1.0 at%)alloys were produced by induction melting at 800°C in a graphite crucible under an inert atmosphere of a CO2and SF6mixture and casting in a stainless steel mold.The measured Zn content was 0.284 (0.761),0.495 (1.32),0.783(2.08),and 0.990 (2.62) at% (wt%) for the 0.3,0.5,0.75,and 1.0 at% Zn alloys,respectively.As-cast Mg alloys were homogenized at 400 °C for 12 h and hot-rolled at 250 °C with a total reduction of 13% per pass.The number of passes and the annealing conditions were chosen to obtain alloys with similar grain sizes and texture.Six,seven,eight,and ten reduction passes were performed for the 0.3,0.5,0.75,and 1.0 at% Zn alloys,respectively.The final annealing of these alloys was carried out at 300 °C (0.3 and 0.5 at% Zn alloys)or 400 °C (0.75 and 1.0 at% Zn alloys) for 1 h,followed by water quenching.The obtained grain sizes were 19.75,17.24,20.00,and 22.73 μm for the 0.3,0.5,0.75,and 1.0 at% Zn alloys,respectively.A linear intercept method was used to measure the average grain size.Tensile properties were measured at RT using fla tensile specimens with a gauge length of 12.5 mm,a gauge width of 5 mm,and a gauge thickness of 1 mm at a strain rate of 6×10-4s-1.The tensile loading direction was parallel to the rolling direction (RD).The crystallographic texture of the alloys was analyzed on the midsection of the specimens using Co Kαradiation.Pole fig ures were obtained from five different planes,{10.0},{00.2},{10.1},{10.2},and {10.3} plane,using a Schulz reflection method,and the XRD data were processed using TexTool v.3.3 software.

Fig.1.Central part of the basal samples with Mg-0.25Zn-0.05Ca composition.Colors represent the element type of atoms (Gray:Mg,Blue:Ca,Red:Zn).To distribute the element type by coloring,the coordination number analysis was not applied.Instead,the location of the edge dislocation was indicated by the yellow mark.

For experiments on Mg-Zn-Ca ternary alloys,Mg-0.61 at% Zn-0.08 at% Ca (Mg-1.62 wt% Zn-0.13 wt%Ca) and Mg-0.61 at% Zn-0.12 at% Ca (Mg-1.62 wt%Zn-0.20 wt% Ca) alloys were produced by ingot casting.As-cast Mg alloys were homogenized at 430 °C for 24 h and hot-rolled at 400 °C with a total reduction of 15% per pass.The number of passes was eight.The final annealing of these alloys was carried out at 350 °C (Mg-0.61Zn-0.08Ca) or 400 °C (Mg-0.61Zn-0.12Ca) for one hour,followed by water quenching.To investigate the stretch formability of the specimens,an Erichsen test was carried out at RT.Disc shape specimens with 50 mm diameter were machined from the rolled sheet and were subsequently annealed.The blank holder force,punch speed,and diameter were 10 kN,6 mm/min,and 20 mm,respectively.Silicon oil was used as a lubricant.Other experimental conditions were the same as those for the Mg-Zn binary alloys.

3.Results and discussion

We examined whether the＜c+a＞slip activation mechanism established for binary Mg alloys can be extended to ternary Mg alloys.The Mg-Zn-Ca alloy,one of the representative commercial Mg alloys,was chosen as a model alloy system to investigate whether its CRSS anisotropy among slip systems can be reduced when alloying amounts are carefully added depending on the size of solute-dislocation binding.Determining the appropriate content of individual alloying elements requires information on the optimum content of Zn and Ca that maximize the＜c+a＞slip activation in individual binary alloys,i.e.,the Mg-Zn and Mg-Ca alloys,respectively.This information can be obtained by simulating dislocation behaviors in Mg-Zn and Mg-Ca binary alloys.

3.1.Optimum alloy content in Mg-Zn and Mg-Ca binary alloys

According to our previous works [10,15],Zn and Ca differ from Mg in atomic size and are bound to dislocations,as presented in Fig.S2.Due to this binding,the addition of these solutes increases the CRSS of the slip systems.As shown in Fig.2,the amount of CRSS increment in each slip system is different,which arises from the structural complexity of the dislocation cores of the three slip systems.During the gliding,basal and prismatic dislocations with simple cores maintain their core structures and thereby are strongly pinned to solute atoms.However,the complex core of the pyramidal II dislocation changes sporadically during the gliding.This change can cause local relaxation of the solute-dislocation binding energy;atoms in the pyramidal II plane thus may have a relatively lower pinning force to dislocations during gliding relative to the static state calculations as shown in Fig.S2.As a result,the CRSS anisotropy among slip systems is reduced by the alloying.Despite the similar CRSS anisotropy reduction,the amounts of alloying elements,Zn and Ca,to maximize the reduction are different.The CRSS anisotropy of Mg-Zn alloys is minimized in a rather wide range of 0.3-1.0 at% Zn addition (Fig.2a).According to the result given in Table 2,the Mg-0.3,0.5,and 1.0 at% Zn alloys all show relatively low CRSS anisotropy compared to the Mg-0.1 Zn alloy.Among them,the Mg-0.5Zn alloy shows the lowest CRSS anisotropy between the basal and pyramidal slips.On the other hand,that of Mg-Ca alloys is minimized with the addition of 0.1 at% Ca (Fig.2b).This difference is due to the size of solute-dislocation binding;Zn pins the dislocations weakly while Ca pins them strongly.This strong binding of Ca readily increases the CRSS of the slip systems,which narrows the range of the alloying amount that can minimize the CRSS anisotropy.The optimum binary content of Ca thus can be anticipated to be around 0.1 at%.However,because of the relatively weak binding,the pinning effect of Zn changes rather smoothly with the alloying amount and the range of optimum alloying amount of Zn is 0.3-1.0 at%.

Fig.2.Simulated stress-strain curves of (a) Mg-Zn [15] and (b) Mg-Ca alloys on basal,prismatic,and pyramidal II planes.“Positive’’ (‘‘negative’’) denotes the shear stress that causes tension (compression) along the c-axis direction.

This wide range makes it difficult to determine the optimum alloy content of Zn using a simulation only.In order to confir the improvement of the ductility of Mg-Zn alloys in the above composition range and to determine the optimum binary content of Zn,we performed a tensile test on Mg-Zn alloys containing 0.3-1.0 at% Zn.To clearly observe its effect on the increment of the ductility due to the＜c+a＞slip activation,we attempted to make the grain size and texture in the Mg-Zn alloy samples similar to each other.The obtained grain size of the Mg-Zn alloys was 17.24-22.73 μm.These alloys also showed similar strong basal textures (Fig.3a).Fig.3b shows that all alloys exhibit improved ductility compared to pure Mg,which shows 3-12% tensile elongation after rolling and annealing [11,17].The number of tensile samples,the standard deviation of elongation values,and details of the tensile test of the Mg-Zn alloys are available in the supplementary material.This experimental result is consistent with the simulation results.Among these alloys,the Mg-0.5 at% Zn alloy showed the highest elongation in experiments and the minimum CRSS anisotropy between basal and pyramidal II slips in simulation.Therefore,0.5 at% Zn was finally selected as the optimum binary content to maximize the＜c+a＞slip,for the subsequent simulations on ternary alloys.

Fig.3.(a) Pole figure of basal {00.2} planes and (b) tensile stress-strain curves at room temperature of annealed Mg-0.3 Zn,Mg-0.5 Zn,Mg-0.75 Zn,and Mg-1.0 Zn (at%) alloys.

3.2.Optimum alloy content in Mg-Zn-Ca ternary alloys

In the present study,we sought to confir whether the non-basal＜c+a＞slip activation mechanism established for binary Mg alloys is applicable to multicomponent Mg alloys.For this,we firs had to determine the optimum content of alloying elements,Zn and Ca,that minimize the CRSS anisotropy between slip systems of the Mg-Zn-Ca ternary alloy,based on the information on the optimum alloy content in each binary alloy.We assumed that once a ternary alloy has an equivalent dislocation binding intensity to the associated binary Mg alloys with optimum content,the CRSS anisotropy of this alloy would then be minimized.This was a simple assumption that borrows the concept of “equivalence” which is widely used.That is,it was thought that the effect of 0.5 Zn on the dislocation binding and resultant CRSS would be similar to that of 0.1Ca.The effect of 0.25 Zn was thought to be equivalent to that of 0.05Ca,and the Mg-0.25Zn-0.05Ca alloy was expected to show a similar CRSS anisotropy to the Mg-0.5Zn or Mg-0.1Ca alloy.Since the binding intensity of Zn and that of Ca were different,we normalized the alloy content by dividing the individual alloy contentby the optimum binary content

It was assumed that ternary alloys with compositions that satisfy the following condition have the equivalent dislocation binding intensity to the associated binary alloys with optimum alloy content:

There are various combinations of the alloy content that satisfy Eq.(2).To investigate the effect of individual elements on the CRSS anisotropy reduction,the following three cases with different ratios between the amount of alloying elements were considered:(1) containing a larger amount of weaker dislocation binding element Zn;(2) containing the same amount of weaker and stronger dislocation binding elements Zn and Ca;and (3) containing a larger amount of stronger dislocation binding element Ca.The selected ratios between the amounts of alloying elements for the three cases and the resultant alloy compositions are listed in Table 3.To evaluate the reduction of CRSS anisotropy in these three cases,we conducted an MS simulation in a similar manner to the Mg binary alloys.The simulated stress-strain curves of the ternary Mg alloys show that the CRSS anisotropy between basal and non-basal slip systems is minimized in all the Mg-Zn-Ca ternary alloys considered,regardless of the composition (Fig.4a).As a means to confir the validity of our assumption for the ternary alloy composition with an equivalent binding intensity,as given in Eq.(2),we further examined the slip behavior of a ternary alloy that does not satisfy the criterion given in Eq.(2).As such an alloy,we chose the Mg-0.5Zn-0.1Ca alloy containing the optimum binary content for both Zn and Ca.As expected,the CRSS for the non-basal＜c+a＞slip increased a lot as well as the basal slip,and thus the CRSS anisotropy was not reduced(Fig.4b).From these results,we could conclude that once the amount of individual alloys elements is carefully adjusted to have a dislocation binding intensity equivalent to that of the associated binary Mg alloys with optimum content,theCRSS anisotropy between slip systems also can be minimized in ternary alloys.It was further confirmed that the non-basal＜c+a＞slip activation mechanism established for binary Mg alloys is applicable to ternary Mg alloys.

Table 3The content ratios of Zn and Ca and resultant ternary compositions of the Mg-Zn-Ca alloys for three cases.

Fig.4.Simulated stress-strain curves of (a) Mg-Zn-Ca alloys with equivalent dislocation binding intensity and (b) Mg-0.5Zn-0.1Ca alloy on basal,prismatic,and pyramidal II planes.

Then,a question arises which alloy can be chosen as the alloy with the most optimum content among the three alloys shown in Table 3 and Fig.4a.We define the optimum alloy as one that exhibits high ductility (reduction of the CRSS anisotropy) most stably,that is,with the least statistical fluctuation.It should be noted here that the results presented in Fig.4 were the average of three independent simulations.The stability or statistical fluctuation was checked by comparing the simulated stress-strain curves of the three independent slip samples with different solute distributions for each composition,assuming that the alloy with the minimum fluctuation among the samples would show the most stable slip behavior.This comparative simulation was performed for the ternary alloys listed in Table 3.The results for the basal and non-basal slip systems are presented in Fig.5.One can notice that the curves from the individual samples show more similar slip behaviors as the alloying amount of the weak binding element Zn increases,and the similarity is maximized in the Mg-0.40Zn-0.02Ca alloy among the three alloys.This phenomenon arises from the dependence of the effect of the solute distribution on the curve on the dislocation binding intensity of each solute atom.As mentioned earlier,the dislocation binding intensity of Ca is strong.The resultant stressstrain behavior would be more sensitive to the distribution of Ca atoms;when the samples contain more Ca atoms,i.e.the Mg-0.10Zn-0.08Ca alloy,the stress-strain curve of each sample thus varies largely depending on its solute (Ca) distribution.However,in the case of Zn,the element with relatively weak dislocation binding,the effect of the solute distribution on the stress-strain curve would be relatively small.Therefore,alloying a large amount of weak binding element causing less variation would be beneficial for stable activation of the non-basal＜c+a＞slip in ternary Mg alloys.

Fig.5.Simulated stress-strain curve for each sample of Mg-Zn-Ca alloys on (a) basal,(b) prismatic,and pyramidal II planes in (c) negative and (d) positive directions.

3.3.Experimental verification of the ternary alloy design scheme

The ultimate purpose of the present study is to obtain a guideline for designing multicomponent Mg alloys with improved RT ductility and formability.According to the present simulations,the optimum binary content of Zn and Ca to maximize the＜c+a＞slip activation in each binary alloy is 0.5 at% and 0.1 at%,respectively.In the case of the Mg-Zn-Ca ternary alloy,when the weak binding element Zn is used as the main alloying element,its CRSS anisotropy is expected to be reduced stably.Considering that these results were obtained from 0 K simulations,the optimum content should be set slightly higher in real experiments at RT.This is because the strength of the solute-dislocation binding and the increase of CRSS would be mitigated at RT due to the thermal activation.In the present work,the guideline for the determination of the optimum alloy content was that the CRSS on the pyramidal plane should not increase compared to that of pure Mg and the CRSS on the basal plane should be as close to that of the pyramidal plane as possible.The optimum content of Zn determined by this guideline was 0.5 at%.Alloys with higher Zn content were not selected because the CRSS on the pyramidal plane was expected to increase over that of pure Mg as shown in Fig.2.However,it could be well expected that at finite temperatures,with more active local relaxations,the CRSS on the pyramidal plane would not increase that strictly as shown in the 0 K simulation,over that of pure Mg.This means that even when larger than 0.5 at% Zn is alloyed the CRSS on the pyramidal plane may not increase over the pure Mg value and the optimum Zn content may be larger than the simulated value,0.5 at%,at RT.Because there is no information for the difference in the optimum alloy content between 0 K and RT,it was decided to compare the experimental tensile test results with the simulation.Although the Mg-0.5Zn alloy showed the largest ductility,it could be expected that the Mg-1.0Zn alloy could also yield equally good ductility at RT.Therefore,the intermediate content,0.75 at%,was selected as the optimum Zn content for experiments at RT.The ratio of the optimum Zn content between RT and 0 K,1.5,was applied also to the Mg-Ca alloys.Thus,the optimum content of Ca in the experimental Mg-Ca alloy was chosen to be 0.15 at%.The validity of this empirically determined coefficient value of 1.5 needs to be confirmed in the long term through future simulations and experimental studies.The alloying element ratio showing the most stable CRSS anisotropy reduction in Fig.5 corresponds to case 1 in Table 3,=0.8:0.2,hereafter designated as“Zn:Ca=8:2”.We applied the same ratio to the optimum content of Zn and Ca in our experiments.The resultant alloy composition was Mg-0.6Zn-0.03Ca.

It should be mentioned here that the Mg-Zn binary alloy could be considered to be an extreme example of a ternary alloy containing Zn as the main alloying element.The Mg-Zn alloy shows good RT ductility [11,17,39],but exhibits poor RT formability,similar to pure Mg [40,41].In industrial applications,the formability is equally important to the ductility.Previous studies report that the poor formability of the Mg-Zn alloy can be improved greatly by adding a small amount of Ca [41-44].For these reasons,the Ca-containing ternary Mg-Zn-Ca alloy was chosen to be the optimum alloy.However,the optimum alloy content of Ca should be considered in more detail because Ca is known to exhibit a relatively high segregation tendency on grain boundaries (GBs)[44].Although the mechanism has not been fully understood,this GB segregation is recognized to greatly affect the texture evolution and RT formability [44,45].This means that when 0.03 at% Ca is added because of the GB segregation,the amount of Ca actually dissolved in the matrix can be smaller than the initially designed amount and may be insufficient to minimize the CRSS anisotropy.This has led the present authors to assume that the Ca content of the optimum ternary alloy may need to be slightly higher than 0.03 at%.To estimate the amount of Ca segregating to GB,we calculated the Ca amount when the grain size of the Mg matrix is about 20 μm,which is a similar condition of the present experiment,and the Ca atoms film the 10% of the GB.The detailed calculation process is available in the supplementary material,and the finally obtained amount of Ca segregating on GB was 11.8 atomic ppm.To this value,considering the amount of Ca consumed due to precipitates and inclusions which can occur in experiments,we set the 0.01 at% Ca (100 atomic ppm)as the compensation amount for the optimum composition.Thus,0.04 at% was finally selected as the optimum Ca content in the real experimental ternary alloy,Mg-0.6Zn-0.04Ca.This alloy was expected to exhibit both good RT ductility and formability in our experiments.

To evaluate the validity of the above guideline for the alloy design of Mg alloys,it was necessary to confir experimentally whether the designed Mg-0.6Zn-0.04Ca alloy could show improved ductility and formability compared to pure Mg and also to Mg-Zn-Ca ternary alloys with different compositions.A great amount of effort had been made during our experiments to create the Mg-0.6Zn-0.04Ca alloy.Unfortunately,to us,it was so difficult to control the Ca content precisely and eventually we failed to fabricate the Mg-0.6Zn-0.04Ca alloy.Thus,we tried to fine the information of this alloy from previous studies,and then found an experiment with a similar composition,Mg-0.57Zn-0.04Ca (Mg-1.52Zn-0.066Ca) in at% (wt%),reported by Chino et al.[41-43].This group have studied Mg alloys for a long time and have published many papers [41-43,46-49],so we thought that the result of them is reliable and utilized it in our study,although it may not be solid evidence to prove the Mg-0.6Zn-0.04Ca alloy because of the difference in the processing condition.This alloy shows 23-30% tensile elongation,73-120 MPa yield strength (YS),and an 8.2 mm index of Erichsen(IE)value[41-43].The ductility was improved compared to pure Mg (3-12% tensile elongation [11,17]),and its IE value was the highest among Mg-Zn-Ca alloys reported in the literature [41-43,47].To further investigate the effect of Ca content,we casted Mg-Zn-Ca alloys containing different amounts of Ca,the element that greatly influences the＜c+a＞slip activation.The cast compositions were Mg-0.61Zn-0.08Ca and Mg-0.61Zn-0.12Ca,hereafter designated as Mg-0.6Zn-0.08Ca and Mg-0.6Zn-0.12Ca,respectively.Both cast alloys contained a higher amount of Ca than the designed alloy with 0.04 at% Ca and thus were predicted to have lower ductility and formability than the Mg-0.6Zn-0.04Ca alloy.

Fig.6.Calculated isothermal sections of the Mg-Zn-Ca system near Mg rich corner at 300,350,400,and 450 °C.Filled circle:Mg-0.61Zn-0.08Ca alloy.Open circle:Mg-0.61Zn-0.12Ca alloy.

The process temperature for the Mg-0.6Zn-0.08Ca and Mg-0.6Zn-0.12Ca alloys was chosen so that the two alloys form a Mg-rich solid solution single-phase microstructure,considering that the present mechanism is based on the solutedislocation interaction in the solid solution matrix.This temperature was determined through a thermodynamic calculation for the Mg-Zn-Ca system at 300-450 °C using the FactSage program.The calculation showed that both alloys form a solid solution at temperatures above 350 °C (Fig.6).To make their grain size similar,the Mg-0.6Zn-0.08Ca and Mg-0.6Zn-0.12Ca alloys were annealed at 350 °C and 400 °C,respectively.Their average grain sizes were 21.70 and 22.50 μm,respectively,which were smaller than that of the Mg-0.57Zn-0.04Ca alloy,32 μm [41-43].The optical microscope (OM)images in Fig.7a and b show that some inclusion particles were formed in both alloys.However,the amount of the inclusion was small so that the inclusion particles would not have a decisive effect on the deformation behavior of the alloys.The cast alloys exhibited similar weakened basal texture after rolling and annealing (Fig.7c and d).The tensile (along the rolling direction) and Erichsen tests show that the Mg-0.6Zn-0.08Ca alloy has a higher tensile elongation and IE value (31% and 8.00 mm) at RT than the Mg-0.6Zn-0.12Ca alloy (26% and 7.28 mm),as presented in Fig.8.This means that 0.12 at% Ca was too much,compared to 0.08 at% Ca in terms of ductility and formability.The properties of the cast alloys could also be compared with those of the reference alloy(Mg-0.57Zn-0.04Ca [41-43]),although the differences in the experimental conditions between the two works (rolling vs.extrusion and rolling,etc.) would have to be taken into account.The ductility of the present cast alloys (26-31% along the rolling direction) was comparable to or higher than that of the reference alloy (23-30%,23% along the rolling direction,but perpendicular to the extrusion direction).However,the stretch formability (IE value)of the present,high Ca-containing alloys with 7.28-8.0 mm was lower than that of the reference alloy with 8.2 mm.Considering that the grain size of the present alloys with 21.70-22.50 μm was smaller than that of the reference alloy with 32 μm,which would be an advantage to the present alloys for ductility and also the formability [49],one can conclude that low content of Ca below 0.08 at% and close to 0.04 at%would be beneficial for both the ductility and formability of the Mg-Zn-Ca alloys.

Fig.7.Optical micrograph images of annealed (a) Mg-0.61Zn-0.08Ca and (b) Mg-0.61Zn-0.12Ca alloys,and pole figure of basal {00.2} planes showing the texture of annealed (c) Mg-0.61Zn-0.08Ca and (d) Mg-0.61Zn-0.12Ca alloys.Scale bar of the optical micrograph images corresponds to 100 μm.

Fig.8.(a) Tensile stress-strain curves at room temperature,and (b) the specimens after Erichsen test of annealed Mg-0.61Zn-0.08Ca and Mg-0.61Zn-0.12Ca alloys.

It has been shown that the activation of the non-basal＜c+a＞slip and resultant improvement of ductility and formability can also be realized in multicomponent Mg alloys,once the alloy composition is carefully controlled so that it has an equivalent dislocation binding intensity to the associated binary Mg alloys optimized to minimize the critical resolved shear stress anisotropy.The activation of the non-basal＜c+a＞slip can occur stably with less statistical fluctuation when alloying a large amount of relatively weak dislocation binding elements.In the case of Mg-Zn-Ca alloys,Zn is such an element with weak dislocation binding.However,a small amount of Ca,an element with a strong segregation tendency,is also necessary to improve the formability as well as the ductility,even though the mechanism for the role of Ca is not clearly known.The alloy we have finally designed that is expected to have both high ductility and formability is the Mg-0.6Zn-0.04Ca (at%) alloy,and it has been experimentally confirmed that the low Ca-containing alloys (0.04-0.08 at%) have higher RT ductility and formability than pure Mg and Mg alloys with a larger amount of Ca.

The present alloy design scheme can serve as a guideline for the design of Mg alloys with improved ductility and formability.Based on the scheme,the followings can be further suggested for an alloy design in a wider range of Mg alloys:First,it may be desirable to further increase the YS while maintaining the already obtained high formability of the Mg-Zn-Ca based alloys.We believe that it is not recommended to increase the Zn content beyond 1 at% and particularly the Ca content to increase the YS,because further increase of this alloy content would not contribute to reducing the CRSS anisotropy and activate the non-basal＜c+a＞slip.Other combinations of elements that do not form a compound with Zn or Ca but form compound phases between themselves instead of being dissolved in the matrix would be highly efficient for strengthening.A recently proposed Mg-3Al-1Zn-1Mn-0.5Ca (wt%) alloy,in which Mn and Al formed strong compound phases without being dissolved in the matrix phase and showed a YS of 219 MPa while maintaining an IE value of 8.0 mm when fabricated through strip casting [45],is a promising candidate for a Mg-Zn-Ca based alloy with improved strength.A more systematic study of the effect of Mn and Al content on the mechanical properties is necessary.Further,as mentioned earlier,since the role of Ca on the texture development and improvement of the formability remains unknown,it would be an important topic of future research to extend the alloy design of RT deformable Mg alloys into a wider range of alloy systems.Finally,it should be noted here that the composition of Mg-0.6Zn-0.04Ca alloy involves a somewhat arbitrary factor;that is,it is based on the simulated alloy composition with the ratio of “Zn:Ca=8:2”.The ratio was arbitrarily selected for the simulation and could be “Zn:Ca=9:1”,for example.The designed alloy in the present scheme thus could have a Ca content smaller than 0.04 at%.An experimental study on the formability of such alloys is strongly recommended because no experimental information is available for Mg-Zn-Ca alloys with a smaller amount of Ca than 0.04 at%.

4.Conclusion

It has been shown that the non-basal＜c+a＞slip can be activated in multicomponent Mg alloys by adjusting the alloy composition so that the alloy can have an equivalent dislocation binding intensity to the associated binary Mg alloys with optimum content.This activation can be stabilized when the weak dislocation binding element is used as the main alloying element.The finally designed alloy composition was Mg-0.6 at% Zn-0.04 at% Ca (Mg-1.6 wt% Zn-0.66 wt% Ca),and it has been experimentally confirmed that alloys containing small amounts of Ca (0.04-0.08 at%) have higher RT ductility and formability than pure Mg and Mg alloy with larger Ca content.The present understanding and alloy design scheme can be extended to a wider range of higher-order Mg alloys,contributing to future designs of new multicomponent Mg alloys with high RT ductility,formability,and other properties all together.

Declaration of Competing Interest

None.

Acknowledgment

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science &ICT(2016R1A2B4006680).

Supplementary materials

Supplementary material associated with this article can be found,in the online version,at doi:10.1016/j.jma.2021.03.007.