Critical review of superplastic magnesium alloys with emphasis on tensile elongation behavior and deformation mechanisms

H.T.Jeong, W.J.Kim

Department of Materials Science and Engineering, Hongik University, Sangsu-dong 72-1 Mapo-gu, Seoul 121-791, South Korea

Abstract

Keywords: Magnesium alloys; Superplastic; Grain size; Secondary phase; Grain boundary sliding.

1.Introduction

Superplasticity is a phenomenon in which fine-grained materials exhibit a large tensile elongation-to-failure of 400%or more at high temperatures (typically over 0.5Tm, whereTmis the melting temperature) in the practically useful strain rate range for plastic deformation (between 10-4and 1 s-1)[1–5].Superplasticity-related research started since 1934 with a finding of superplasticity in Pb-Sn alloys [6], and the research has been extended to a variety of materials, including ceramics [2,3,7–9].Superplasticity has been used commercially in aviation, automobile, medical, and sports fields to fabricate complicated components with near-net shapes, and aluminum alloys and titanium alloys have been most widely used for commercial purposes [1–3].In general, to achieve superplasticity, two basic conditions should be satisfied [1–3].First, grain boundary sliding (GBS) should occur as a dominant deformation mechanism, and for this mechanism to be operative, the material needs to have small grains with typical sizes of 10 μm or less and a high fraction of high-angle grain boundaries because GBS is favored to occur along disordered high-angle grain boundaries under stress.Second, for GBS to continue to be active throughout deformation, the presence of a proper amount of thermally stable secondary phase particles, which can inhibit rapid grain coarsening duringheating and deformation, is important.Besides the amount of secondary phase, the morphology, size and distribution of the secondary phase are important because they can also strongly affect the static and dynamic grain growth rates [10–12].

Conventional superplasticity occurs in the strain rate range between 10-4–10-3s-1at temperatures above 0.5Tm[3–5].For productivity and energy saving purposes, it is advantageous for superplasticity to occur at lower temperatures and faster deformation rates.There are two special types of superplasticity that have attracted the attention of researchers.Lowtemperature superplasticity (LTS) represents superplasticity at low temperatures below 0.5Tm[13,14].LTS is advantageous because low-temperature superplastic deformation reduces the energy consumption for heating and increases the lifetime of forming tools.High-strain-rate superplasticity (HSRS) represents superplasticity at high strain rates above 10-2s-1and is of great technological interest for the rapid shape forming of engineering materials [9].

Magnesium alloys have been widely used as structural materials because of their light weight and excellent specific strength [15–17].To date, a variety of magnesium alloys have been developed and studied for superplasticity [18–274].There are several review papers on the superplasticity of magnesium alloys, but these papers are focused either on the superplasticity of Mg alloys processed by a specific method or the investigated data are not extensive [275–280].In the present review paper, the effect of grain size and secondary phase on the superplasticity and superplastic deformation mechanisms of magnesium alloys were examined by reviewing and analyzing the data from the academic papers(related to superplasticity of pure Mg, Mg alloys and Mg composites)published from the time when superplasticity was firstly reported on magnesium alloys.To understand the effect of the secondary phase on superplasticity,the amount and type of the major secondary phase in each alloy were calculated using the JMATPro software, which is a simulation software that can calculate a wide range of material properties for multicomponent alloys as a function of temperature[281,282].Furthermore, the critical conditions for achieving LTS and HSRS for magnesium alloys were proposed based on the deformation mechanism maps constructed for Mg alloys, and the result was compared with the experimental data and discussed.

2.History of superplastic Mg alloys

In this study, among the papers that reported superplasticity of magnesium alloys from 1975 to the present, the papers showing tensile elongations of 400% or more are regarded as the papers that reported superplasticity, and the papers showing tensile elongations of 300–400% are regarded as the papers that reported quasi-superplasticity.A reason for taking an elongation of 400% for the minimum elongation for superplasticity is that a coarsegrained solid solution alloy can exhibit tensile elongations of 200～300% when the solute drag creep mechanism dominates plastic flow [3].The papers that reported superplasticity of Mg alloys are divided into five categories in the present study, reporting conventional superplasticity,LTS,HSRS,LTS/HSRS(achievement of LTS and HSRS from the same sample but under different strain-rate and temperature conditions) and LTS+HSRS (simultaneous achievement of LTS and HSRS from the same sample at the same strainrate and temperature condition).

Fig.1.The number of publications on superplastic Mg alloys as a function of year.

Fig.1 shows the number of publications on superplastic Mg alloys as a function of year.From 1975 to recent days,257 papers have been published.Out of 257 papers, the numbers of papers on LTS and HSRS are 44 and 44, respectively.The number of papers that reported HSRS/LTS is 12.The papers that reported LTS+HSRS are only 3.The first report of quasi-superplasticity in Mg alloys was made in 1975 by Kaibyshev et al [18].They reported obtaining a tensile elongation of 320% at a strain rate of 10-3s-1from MA-8 alloy (Mg-Mn-Ce alloy).The first report on the superplasticity of Mg alloys was from cast Mg-16.2 wt.% Ca alloys composed of fine eutectic lamellar structures(50%α-Mg and 50%Mg2Ca) in 1984 [20].The sample showed refinement of the cast structure during tensile deformation, and a tensile elongation of 418% was obtained at 2.4 × 10-3s-1and 773 K.The first report on HSRS was from the same alloy subjected to hot forging.The hot forged Mg-16.2 wt.%Ca alloy showed a tensile elongation of 900% at a strain rate of 1.6 × 10-2s-1, but information regarding the tensile curves and grain size after hot forging was not provided.In 1995, Mabuchi et al [26].reported HSRS by showing a tensile elongation of 560% at 1.7 × 10-2s-1and 573 K from an extruded AZ91 alloy with a small grain size of 1.2 μm.The first paper that reported LTS was from a fine-grained Mg-9 wt% Li alloy(composed of 71% BCCβphase and 29% HCPαphase)prepared by foil metallurgy (cold rolling plus press bonding) in 1990 [22].The sample with a grain size of 5.9 μm showed a tensile elongation of 445% at 10-3s-1and 473 K.The first report on LTS/HSRS was made by Watanabe et al[49].from a powder-metallurgy processed ZK61 alloy (powder sintering plus extrusion) with a very small grain size of 0.65 μm.The alloy exhibited a tensile elongation of 560%at 10-4s-1and 448 K and a tensile elongation of 438% at 10-1s-1and 573 K.Report on LTS+HSR was firstly made from the severe plastic deformation (SPD)-processed AZ91 with nanoscale grains in 2015 where a tensile elongation of 590% was obtained at 10-2s-1and 473 K [200].

Fig.2.A diagram showing the contribution of each country to the publications for superplasticity of Mg materials: (a) 1991～2000, (b) 2001～2010, (c)2011–2020 and (d) 1975～2021.

Fig.3.A diagram showing the contribution of each alloy or each alloy system to the publications for superplasticity of Mg materials: (a) 1991～2000, (b)2001～2010, (c) 2011–2020 and (d) 1975～2021.

Study on superplastic Mg alloys started to increase rapidly from 1995, and the peak was reached in 2007 and to the present day, active research is ongoing.Interest in LTS and HSRS has increased with time due to the development of SPD methods for effectively refining the grain size of ingotprocessed Mg alloys and the development of Mg-RE alloy systems containing secondary phases with high thermal stability.

Fig.2 is a diagram showing the contribution of each country to the publication for superplasticity of Mg materials.Countries that made a major contribution were China, Japan,South Korea, the USA and Taiwan.In the period of 1991–2000, the country that contributed the most was Japan, accounting for 80% of the total papers.In the period of 2011–2020, the country that contributed the most was China.

Fig.3 is a diagram showing the contribution of each alloy or each alloy group to the publication of superplasticity of Mg materials.The main constituent elements of the alloys are informed in Table 1.In the period of 1991–2000,AZ91 alloys,Mg composites and ZK60 alloys were primarily studied.In the period of 2001–2010, studies on AZ31 alloys were most extensive,and research on Mg-RE alloys started and expanded yearly.In the period of 2011–2020, the AZ alloys and Mg-RE alloys were the major alloys for study.Studies on the development of new Mg alloys containing elements such as Ca, Sn, and Ga had also started and increased with time.In the total period of 1975–2021, AZ series alloys and Mg-RE alloys were most extensively studied.

3.Grain sizes of superplastic Mg alloys

Fig.4(a) shows the grain sizes (initial grain sizes before superplastic deformation) of superplastic Mg alloys or Mg alloy groups listed in Table 1.Each alloy (group) was categorized into one prepared by non-SPD methods including conventional methods such as rolling and extrusion and powder-metallurgy methods (consolidation of atomized powders (or ribbons) by hot extrusion or rolling), and the other prepared by SPD methods, such as equal channel angular pressing (ECAP), high pressure torsion (HPT), high-ratio differential rolling (HRDSR) and friction stirring process (FSP).The alloys prepared by conventional methods have a widergrain size range (0.7–19 μm) than those prepared by the SPD methods (0.1–11.4 μm).The alloys prepared through powder metallurgy processes have very small grain sizes(0.15–6 μm)comparable to or even smaller than the grain sizes of the alloys prepared by the SPD methods.From Fig.4(a),it is noted that the minimum grain size for superplasticity of Mg alloys is about 10–20 μm, which is similar to that for other superplastic metals [1].Fig.4.(b) shows the average grain sizes of the alloys processed by non-SPD and SPD methods, which were calculated based on the data presented in Fig.4(a).The difference in average grain size between the alloys prepared by the SPD and conventional methods is relatively large in AZ31 and AZ61 with small fractions of secondary phase particles (β-Mg17Al12), while the difference in average grain size is small in AZ91 and Mg-RE alloys with high fractions of secondary phase particles.This is because when an alloy has a high volume fraction of hard particles, the efficiency of grain refinement during thermo-mechanical working is high (since large particles promote dynamic recrystallization and fine particles inhibit grain growth after dynamic recrystallization (DRX)),such that sufficiently fine grains can be readily achieved even through conventional methods.The Mg composites with high fractions of reinforcement also have very small grains.

Table 1The Mg alloys and Mg alloy systems for studied for superplasticity.

4.Tensile elongation behavior of superplastic Mg alloys

Fig.5(a)-(l) shows the strain rate-temperature map where the tensile elongation data of the pure Mg, AZ series alloys(AZ31,AZ61 and AZ91),Mg-RE alloys(Mg-Gd,ZW(K)and WE), ZK alloys (ZK60 and ZK61), Mg-Li alloys, modified composition Mg alloys and Mg composites are plotted.Depending on the elongation value range, different symbol colors were used: as the tensile elongation value increased, the color approached red.The data are divided into two groups:one group is the samples prepared by non-SPD methods (including conventional methods (rolling/extrusion) and powdermetallurgy methods), and the other group is prepared by SPD methods.For all the pure and Mg alloys, it is apparent that the materials processed by SPD and the powder-processed materials exhibit larger tensile elongations than the materials prepared by conventional methods.Fig.6.shows the strain rate-temperature map, where the superplastic elongation data of the AZ series, Mg-RE, ZK and Mg-Li alloys and Mg composites are plotted for direct comparison.Here, the size of symbol represents the amount of tensile elongation, while the color represents the alloy type.From Figs.5 and 6, the followings are informed.For the pure Mg, superplasticity has not been reported so far[235,283,284].Somekawa and Mukai[283]reported the obtainment of the maximum elongation of 230% from the extruded pure Mg with a grain size of 1.2 μm at 10-5s-1and room temperature.Later, Figueiredo et al[235].showed that the pure magnesium processed by HPT with a grain size of 320 nm could exhibit quasi-superplasticity(an elongation of 310%) at 10-4s-1and room temperature.Increasing the temperature to 373 K decreased the tensile elongation due to rapid grain growth (to 950 nm) in the absence of secondary phase particles [235].Zeng et al [285].showed that cold rolled pure Mg sheet with a micron grain size exhibited excellent formability in folding and unfolding process due to activation of grain boundary sliding.For the AZ31 alloys, the alloys processed by SPD exhibited larger elongations than the alloys prepared by conventional methods,especially at temperatures above 573 K in the strain rate range between 10-4and 10-2s-1.The cast AZ31 alloy processed by ECAP (processed at 423 K) with a bimodal grain structure(large grains having sizes of ～16.5 μm and small grains having sizes of ～0.50 μm) (#1) where Mg17Al12phase particles with ～10 μm and Al8Mn5particles with 1–2 μm were uniformly dispersed in the matrix exhibited a large elongation of 1210% at 10-4s-1and 623 K [124].The authors attributed this result to the significance of the bimodal microstructure where the larger grains have ability to more easily accommodate grain boundary sliding through intragranular slip.For the conventionally processed AZ31B alloy with a grain size of 12.5 μm (#2), which was provided by Magnesium Elektron LTD., exhibited HSRS by showing a tensile elongation of 650% at high strain rates of 1 s-1and 723 K [249].This rather surprising result was attributed to grain refinement caused by the occurrence of extensive dynamic recrystalliza-tion (DRX) during tensile deformation.The AZ31 alloy processed by high pression torsion (#3), having extremely small grain sizes of 110 nm, exhibited LTS by showing a tensile elongation of 400% at 10-4s-1and 423 K [208].When the testing temperature was increased from 423 to 523 K,however, the tensile elongation decreased to 300% at 10-4s-1.Inspection showed that the ultrafine grains of ～200 nm remained at a temperature of 423 K, but there was a large increase in grain size to 3 μm at 523 K, indicating that the ultrafine-grained microstructure in the AZ31 alloy is unstable at high temperatures.The AZ31 sample processed by extrusion and ECAP (8 passes at 473 K) with a grain size of 0.7 μm (#4) also exhibited LTS by showing an elongation of 460% at 10-4s-1and 423 K [82].Compared with the SPD-processed AZ31 alloy, the SPD-processed AZ61 alloy with having a larger amount ofβ-Mg17Al12phase particles showed a better LTS.The AZ61 alloy processed by ECAP (4 passes at 473 K on the extruded material) with the grain size of 0.62 μm (#5) exhibited LTS by showing an elongation of 1320% at 3.3 × 10-4s-1and 473 K [92].For the AZ61 alloys processed by conventional methods, the warm rolled AZ61 with the grain size of 16 μm (#6) exhibited HSRS by showing a 400% at 10-2s-1and 673 K [53].The grain refinement by DRX was observed in the -gauge region during tensile deformation at the corresponding condition, as in the AZ31 alloy with the coarse grains (#2).The AZ61 alloy processed by HRDSR (#7) [179], whereβ-Mg17Al12particles(70 nm) were preferentially located at the grain boundariesover the ultrafine-grained matrix with a grain size of 1.1 μm,exhibited HSRS/LTS by showing an elongation of ～570% at 10-2s-1and 523-553 K and an elongation of 510% at 3.3× 10-4s-1and 473 K.The AZ91 alloys showed better superplasticity than the AZ61 alloys.The AZ91 alloy processed by HPT (N=10 cycles) at room temperature (#8), having a nanoscale grain size and a high-volume fraction of nanosizedβ-phase particles, showed excellent HSRS with an elongation of 860% at 10-2s-1and 573 K [200]and LTS with an elongation of 760%at 10-4s-1and 423 K.At 473 K at 10-2s-1,the same sample also showed HSRS+LTS by showing an elongation of 590% at 10-2s-1and 473 K.This excellent superplasticity of the HPT-processed AZ91 alloy over a wide range of strain rates and temperatures was attributed to the highly increased thermal stability of the ultrafine-grained microstructure due to the presence of a high volume fraction of fineβ-phase particles obtained through the HPT process.The AZ91 alloy processed by hot extrusion at 573 K (#9),having a grain size of 1.2 μm, exhibited HSRS by showing elongation of 560% at 1.7 × 10-2s-1and 573 K [26].The SPD-processed AZ151 alloy exhibited even better superplasticity than the SPD-processed AZ91 alloys.The SPDprocessed AZ151 alloy with a grain size of 2.8 μm, which was processed by reciprocating extrusion where repetitive extrusion was applied for 10 passes at 598 K, exhibited superb HSRS by showing a large elongation of 1610% at 10-2s-1and 598 K [72].This result could be attributed to the presence of a very high-volume fraction of theβ-phase (34%),which greatly stabilized the fine-grained structure during superplastic deformation.

Fig.5.Strain rate-temperature maps where the tensile elongation data of the SPD- and nonSPD-processed (a) pure Mg (b) AZ31, (c) AZ61, (d) AZ91, (e)ZK60 and ZK61, (f) Mg-Gd, (g) ZW(K), (h) WE, (i) Mg-RE (Mg-Gd+ZW(K)+WE), (j) Mg-Li, (k) Modified commercial Mg alloys and (l) Mg composites.A green vertical line at 10-2 s- 1 and a pink horizonal line at 473 K in each map represent the boundary for LTS and HSRS, respectively.Symbol color represents tensile-elongation (ef (%)) range:: 100%≤ef<200%.: 200%≤ef<300%.: 300%≤ef<400%.: 400%≤ef<600%.: 600%≤ef<800%. 800%≤ef<1000%.: 1000%≤ef<1200%.: 1200%≤ef.

Fig.5.Continued

Fig.5.Continued

Fig.6.The strain rate-temperature map where the superplastic elongation data of the AZ series alloys, Mg-RE, ZK series alloys, Mg-Li alloys and Mg composites are plotted together for direct comparison.

The ZK60 alloys exhibit LTS superior to the AZ alloys.The ZK60 alloy processed by ECAP at 473 K (#10), having a grain size of ～0.8 μm, exhibited very large elongations of 2000–3000% at 10-4s-1and 473 K [136].The ZK60 alloy processed by HRDSR with a grain size of ～1.1 μm and 10–50 nm sized Mg(Zn, Zr)2phase particles (#11) exhibited HSRS at 553–573 K by showing elongations of 470–930% at 10-2s-1and ～500% at 10-1s-1[152].Powder metallurgy-processed ZK61 alloy exhibited excellent superplasticity comparable to the superplasticity of the same alloy processed by SPD methods.For example, the ZK61 alloy fabricated through powder metallurgy(using rapidly solidified powder and extrusion at 523 K with a high reduction ratio of 100:1) with a grain size of 0.65 μm and particles with an average size of 25 nm (#12) [49]exhibited HSRS/LTS by showing an elongation of 440% at 10-1s-1and 573 K and an elongation of 560% at 10-4s-1and 448 K.

The Mg-RE alloys exhibit enhanced superplasticity compared with the AZ and ZK alloys in the high temperature range above 573 K by showing better conventional superplasticity and HSRS.The Mg-RE alloys, however, exhibit notably poorer LTS.The superplastic Mg-RE alloys can be classified into three groups: (1) Mg-Gd base alloys with the LPSO, Mg-Y or Mg-Gd compounds, (2) ZW and ZWK alloys with the I or LPSO phase, and (c) WE alloys with the Mg41RE5phase.For the Mg-Gd based alloys, the Mg-9.4Gd-4.1Y-1.2Zn-0.4Zr alloy processed by friction stir processing(FSP) with a fine grain size of ～3 μm and LPSO phase uniformly distributed within the grains (#13) exhibited superior HSRS at 623–773 K with a maximum elongation of 3570%at 3 × 10-2s-1and 698 K [176].This excellent superplasticity was attributed to the thermally stable fine microstructure.For the ZW and ZWK alloys, the powder metallurgy processed Mg97Zn1Y2alloy with the grain size of 100-200 nm and LPSO and Mg24Y5particles (#14) exhibited HSRS by showing an elongation of 780% at 6 × 10-2s-1and 623 K [51].The chip/ribbon-consolidated Mg97Zn1Y2alloys fabricated from twin-roll-cast sheets and melt-spun ribbons(#15), having the LPSO phase and the grain size of 0.5–1 μm, also exhibited excellent HSRS at 673 K [251].Lee and Kim [257]reported that the Mg-1.7Y-9.5Zn-0.4Zr alloy processed by HRDSR (#16), having the ultrafine grains (～1 μm)on which highly refined I phase particles were uniformly dispersed, exhibited LTS by showing tensile elongations of 570–720% at 10-3s-1and 473 K.Interestingly, this is the only case where LTS has been reported for the Mg-RE alloys.For the WE alloys, the ECAP processed Mg-4Y-3.2RE-0.41Zr-0.15Li (WE43) with the grain size of 340 nm (#17) exhibited HSRS by showing an elongation of ～1230% at 10-2s-1and 623-673 K [260].Moreover, large elongations of 800–1000% were obtained at a higher strain rate of 10-1s-1.The microstructure remained fine-grained even after large deformation at 723 K, indicating that enhanced HSRS is due to the excellent thermal stability of the ultrafine-grained microstructure.The Mg-3.8Y-2.6RE-0.45Zr alloy processed by the conventional method (prepared through hot extrusion at a ratio of 100:1 at 673 K) (#18), having a very small grain size of 1.5 μm and fine (0.2–0.5 μm) spherical precipitates of Mg11NdY2, was also capable of exhibiting excellent HSRS by showing an elongation of 1180% at 4 × 10-2s-1and 673 K [36].

While the ZK60 series alloys exhibit excellent LTS near 473 K, the Mg-Li alloys with dual phases (BCC+HCP phases) exhibit excellent LTS even far below 473 K.This enhanced LTS is considered to occur as grain boundary diffusivity in theβ-phase (BCC) is considerably higher than the grain boundary diffusivity in theα-phase (HCP) such that grain boundary sliding is active alongβ/βandα/βbound-aries even at low temperatures.An Mg-8Li alloy containing 50 vol.% of the Mg-richα-phase and 50 vol.% of the Lirichβ-phase processed by HPT at room temperature (#19),having a grain size of 500 nm, exhibited LTS by showing an elongation of 400% at 323 K and an elongation of 700% at 373 K at a strain rate of 10-3s-1[205].Edalati et al [230].showed that when the Mg-8Li alloy was subjected to HPT for many turns (N= 200 cycles) at room temperature, the alloy had an extremely small grain size of 240 nm and exhibited LTS by showing an elongation of 440% at room temperature (300 K) at 10-3s-1(#20).Using the multimode deformation process method by using a combination of both extrusion and rolling, a Mg-8Li-5Zn alloy with a grain size less than 2.8 μm (#21) was fabricated,and this material exhibited LTS by showing an elongation of 720% at 10-3s-1and 423 K and 1400% at 10-3s-1and 473 K [238].The same material also exhibited LTS+HSRS by showing a tensile elongation of 620% at 10-2s-1at 473 K.

The new (modified) Mg alloys containing Sn, Mn, Ga or Ca elements and other commercial Mg alloys have been developed and studied for superplasticity.Among those alloys,the Mg-8.3Al-8.1Ga alloy produced by the powder metallurgy method (#22), having a grain size of 2 μm and particles of Mg17Al12and Mg5Ga2, exhibited excellent HSRS by showing a maximum elongation of 1080% at 10-2s-1and 573 K [30].The friction stir processed AM60 (Mg-Al-Mn) alloy with the grain size of 2.5 μm (#23) exhibited HSRS/LTS by showing an elongation of 830% at 573 K and 10-2s-1and an elongation of 550% at 10-4s-1and 473 K [99].

Most of the Mg composites exhibit quasi-superplasticity,though their grain sizes are pretty small (Fig.4(b)).The doubly extruded ZK60 alloy composite containing 17 vol % SiC particles with a grain size of 1.7 μm (#24) exhibited HSRS by showing tensile elongations of 450% at 10-1s-1and 623 K [37].When the strain rate decreased below 10-1s-1, however, the extruded ZK60 alloy composite suddenly lost superplasticity.The AZ61 Mg-based composites with up to 10%SiO2nano particles with a size of 20 nm processed by fourpass FSP (#25), having grain sizes of 0.8–2.0 μm , exhibited HSRS by showing a tensile elongation of ～450% at 10-2–3× 10-1s-1and 573–673 K [90].Overall, the superplasticity of Mg composites is inferior to the superplasticity of the alloys because of poor interfacial bonding issue.

5.Effect of secondary phase on superplasticity of Mg alloys

Fig.7(a)-(c) shows the plot of tensile elongations vs.temperature for each alloy or each alloy group (that exhibited superplasticity) constructed to examine the effect of the secondary phase on tensile elongation.The presence of a proper amount of secondary phase at high temperature is important because this affects thermal stability of fine grains, which is crucial for the achievement of good superplasticity [1].The range of tensile elongation values obtained from the related references is indicated by a vertical line (reflecting the effects of strain rate and grain size on tensile elongation), and the average of the elongation values is indicated by a symbol superimposed on the line.The major equilibrium secondary phase of which type and amount as a function of temperature was calculated by using the JMatPro software, and its amount was plotted as a function of temperature.For the same alloy group with different chemical compositions, the amount of major phase was calculated based on the composition of each alloy using the software and then averaged.For the AZ series alloys, the major secondary phase isβ-Mg17Al12,and its amount decreases with increasing temperature because the maximum solute solubility of Al in Mg increases with increasing temperature [286].The addition of 1% Zn to Mg-Al alloys, which helps to refine the cast microstructure and overcome the harmful corrosive effect of iron impurity [287,288],does not change the amount ofβ-Mg17Al12according to the calculation by the JMatPro software.For the AZ31, AZ61,AZ91 and AZ151 alloys, the Mg17Al12phase disappears at 476.8 K, 581.5 K, 652.8 K and 704.3 K, respectively.In the temperature range between 373 K and 640 K, the AZ alloy with a higher volume fraction of Mg17Al12exhibits larger elongations.Above 673 K, however, the elongation difference between the AZ31, AZ61 and AZ91 alloys greatly diminishes, which can be attributed to the dissolution of Mg17Al12.However, the AZ31 alloy still exhibits large elongations up to 1000% at 723 K (with an average elongation of 500%)despite the dissolution of Mg17Al12at a much earlier temperature (476.8 K).Fine dispersion of Al-Mn compounds over the matrix [124], which is predicted to stably exist up to 873 K (see the inserted graph in (a)), may importantly contribute to the thermal stability of fine microstructures of AZ31 alloys at high temperatures.For the ZK60 and ZK61 alloys,the maximum tensile elongation and the average elongation values gradually decrease with increasing temperature following the trend of the amount of MgZn that continuously decreases with increasing temperature.It is worthwhile to note that for the superplastic ZK60 and ZK61 alloys, metastable MgZn2phase particles have been more frequently observed than the equilibrium MgZn phase particles [168,269].For the Mg-RE alloys, the major secondary phases, such as LPSO, I,W and Mg41RE5,are predicted to be stable up to temperatures higher than 773 K, and even at 773 K, the 2–5 wt.% amounts of secondary phases still exist.Note that the tensile elongations of the Mg-RE alloys are notably larger than the tensile elongations of the AZ and ZK alloys in the temperature range between 573 and 773 K, and the tensile elongations of the Mg-RE alloys tend to increase with increasing temperature in this temperature range, where the AZ and ZK alloys show the opposite trend (Fig.7(d)) Fig.8.shows the plot of tensile elongations vs.fractions of major secondary phase (wt.%) at 673 K constructed based on Fig.7(d).As seen,the WE alloys with Mg41RE5phase, the ZW(K) alloys with the I phase and the Mg-Gd and ZW(K) alloys with the LPSO phase, which have much larger secondary phase amounts (8-17 wt.%) than the AZ and ZK alloys (less than 1 wt.%), exhibit larger elongations than the AZ and ZK alloys.The Mg-Gd and ZW(K)alloys with the LPSO phase, which have the largest amountof the secondary phase among the investigated Mg-RE alloys,exhibit the largest tensile elongations.The presence of a large amount of thermally stable secondary phases at high temperatures in the Mg-RE alloys explains why the Mg-RE alloys show superplasticity superior to the AZ and ZK alloys above 673 K.

Fig.7.Plot of tensile elongations and amount of major secondary phase as a function of temperature for superplastic (a) AZ, (b) ZK, and (c) Mg-RE alloys and (d) overlap of all the alloys for direct comparison.An inset in (a) shows the amount of minor Al-Mn compound phases as a function of temperature.

Fig.8.Plot of tensile elongations vs.fractions of major secondary phase(wt.%) for the AZ, ZK, and Mg-RE alloys at 673 K.

Besides to the amount of secondary phase, the size of secondary phase and the interfacial characteristics between secondary phase and matrix are important for achieving good superplasticity.There is little deformation incompatibility between the LPSO phase and the Mg matrix [176]and coherent interface forms between I-phase and the Mg matrix [90,289].Therefore, the Mg alloys with LPSO and I phase particles are more resistant to deformation-induced cavitation caused by decohesion of secondary phase/Mg matrix interface during grain boundary sliding, thereby producing a better superplasticity.Sufficient refinement of secondary phase is, however,required even in LPSO and I phase [180,183,252]because when the particle size is large, cavitation is promoted due to development of high stress concentration at the secondary phase/Mg matrix interface and grain growth rate is high due to a weak pinning effect of coarse particles.According to the microstructural study by transmission electron microscopy, the SPD-processed Mg alloys such as AZ (AZ31/AZ61/AZ91),ZK60, Mg-Gd based, ZW(K) and WE alloys, which exhibited excellent LTS, HSRS or LTS/HSRS, had the particles of 100–400 nm sizeβ-Mg17Al12[175,179,188,198,200,218,226,246],10–50 nm size MgZn2[152,165,168,207,209,224,229], 50–100 nm size LPSO [176,183,193,251], 100–1000 nm size I [170,204,252,257]and 100–400 nm size Mg-Y-RE compounds [201,202,260]in their microstructures prior to superplastic deformation.The poorer superplasticity of the Mg-RE alloys compared to the AZ and ZK alloys at low temperatures (Fig.5) may be also due to the presence of high volume fractions of secondary phase in the Mg-RE alloys.This is because the interface between matrix and secondary phaseprovides nucleation sites for cavities during superplastic deformation, especially at low temperatures where high stress develops at interfaces.

Fig.9.The Qc values of the AZ31, AZ91, ZK60 and Mg-Gd alloys calculated by using Eq.(2).

6.Deformation mechanisms of superplastic Mg alloys

High-temperature plastic flow of pure metals and alloys at steady state has been depicted by the following equation[1–3]:

whereQcis the activation energy for superplastic flow,Ris the gas constant,Tis the absolute temperature,Eis the elastic modulus,σis the flow stress, ˙εis the strain rate andAis the material constant.From Eq.(1),theQcvalue can be measured at a givenusing the following equation:

Fig.9 shows theQcvalues of the AZ31, AZ91, ZK60 and Mg-Gd alloys calculated by using Eq.(2).In plotting the curves, the raw data of strain rate and flow stress were extracted from the strain rate change tests provided in the related papers [40,44,53,54,61,70,78,100,105,116,120,134,135,144,168,173,179,187,190,198,218,228,257,258,290,291,292,293]and their flow stresses were divided by the elastic modulus for pure Mg (E= 42.9(1 - 5.3 × 10-4(T- 300))GPa[294]).For theQcvalues of the AZ and ZK60 alloys, 76%of the total measurements are in the range between 60 and 93 kJ/mole, where 93 kJ/mole indicates the activation energy for grain boundary diffusion (Qgb) of pure Mg [295], while 15% of the total measurements from Mg-RE alloys belong to this range.In the range between 98 and 135 kJ/mole,where 135 kJ/mole indicates the activation energy for lattice diffusion in Mg (QL) [295], 17% of the total measurements for the AZ series and ZK60 alloys and the ZW and ZWK alloys with W or I phase reside.In the range between 135 and 180 kJ/mole, Mg-Gd alloys with LPSO and WE alloys with Mg41RE5reside.This result indicates that most of the AZ and ZK60 alloys show an activation energy for plastic flow close toQgb, and some are betweenQgbandQL.However, theQcvalues of Mg-RE alloys, especially Mg-Gd and WE alloys, are apparently larger than those for the AZ and ZK60 alloys.These results are in agreement with the results obtained from the hot compression tests, where the activation energies for plastic flow for Mg-RE alloys were measured to be higher than the activation energies for plastic flow for pure Mg [296–298], confirming that theQgbandQLvalues of the Mg-RE alloys are larger than those of the AZ and ZK60 alloys.

The constitutive equation that describes the superplastic flow for pure Mg and Mg alloys can be expressed using the effective diffusivity,D∗e f f, as follows [299]:

wherek3is a constant,for pure Mg [295]andfor pure Mg [295],[299],δ= 2b[299]andb= 321 pm for pure Mg [295].Fig.10(a) shows the plot for thefor the AZ, ZK and ZW(K)alloys, having the similar activation energies for plastic flow compared with the pure Mg, where the strain rate and flow stress data are from the strain rate change tests [22,23,40,44,53,54,59,61,70,104,105,116,120,134,135,137,152,168,173,179,190,198,218,290,291,292,293,300,301,302,303,304].The data for the various alloys tend to merge to a common line, but thevalues of the SPD-processed materials are obviously smaller than thevalues for nonSPD-processed alloys when compared at a givenThis difference possibly results from the use of the initial grain size for plotting the data of the SPD-processed Mg alloys because the SPD-processed materials often have a high fraction of nonequilibrium grain boundaries and a large grain boundary area such that they have a high driving force for grain growth compared to nonSPD-processed alloys.Therefore,rapid grain growth, at least during the initial testing period including the sample heating and holding time, is inevitable in the SPD-processed materials.For the AZ, ZK and ZW(K)alloys, when the grain sizes approximately 3.7 times larger than the initial grain sizes are used, the data for the nonSPDand SPD-processed alloys can be well correlated into a single curve.Fig.10.(b) shows the plot where the data for the nonSPD-processed alloys are plotted together for comparison.The fitting quality for the nonSPD-processed Mg-Gd and WE alloys is not bad, although they have largerQLandQgbvalues than those of pure Mg.The fitting quality for the nonSPD-processed Mg-Li alloys is also not so bad,considering the presence of the BCC phase in the Mg-Li alloys withQLandQgbvalues different from those of pure Mg.The plot informs the following.First, thek3value (in Eq.(3)) for the nonSPD-processed AZ, ZK and ZW(K)alloys are very similar to 1.63 × 108.Second, thek3values for the Mg-Gd and WE alloys are smaller than thek3values of the AZ, ZK and ZW(K) alloys, while thek3values for Mg-Li alloys are larger than thek3values of the AZ, ZK and ZW(K) alloys.Third, among the Mg-RE alloys, thek3value of the WE alloys is smallest (1.0 × 106), and thek3value of the ZW alloys is largest (3.0 × 107).Fourth, at a given temperature and strain rate, the flow stress is highest in the WE alloy, while the flow stress is lowest in the Mg-Li alloys.

Fig.10.(a) Plot for the vs. for the AZ, ZK and ZW(K) alloys.(b) Plot for thevs. for the various alloys processed by non-SPD methods.

7.Deformation mechanism maps for superplastic Mg alloys

During deformation at high temperatures, various deformation mechanisms simultaneously operate and compete with one another [305–308].Table 2 shows the list of equations for grain boundary sliding (GBS), which are grain sizedependent, and slip creep, which are grain size-independent.Thekivalues for Harper-Dorn creep [309], dislocation climb creep [310]and GBS [311,312]are the phenomenological equations obtained from the fitting result for the experimental data of many materials.Thekivalues for Mg alloys for dislocation climb creep and GBS that were analyzed by Kim et al[308].based on the experimental data of AZ alloys available up to the year 2001 are also provided in the table.Thek3, k4andk5values forDL-, Dp-andDgbcontrolled GBS mechanisms determined based on the data of the AZ, ZK and ZW(K) alloys shown in Fig.10 and the relationship ofk4= 50 ×k3[308]andk5= (2xπ)×k3[308]are 1.63 ×108, 8.15 × 109and 1.02 × 107, respectively, and these values are listed in Table 2.The newly measuredk3value is not much different from thek3value measured in the previous work [308]but is smaller.

Under the assumption that different creep mechanisms simultaneously operate and compete with one another, the total strain rate(˙εtotal)is determined by adding the strain rates calculated by the different constitutive creep equations:

Table 2The constitutive equations and the material constants used for the construction of the deformation mechanism and processing maps for AZ, ZK and ZW(K) alloys: (1) ki is the material constant, and (2) DL, Dgb and Dp are the lattice diffusivity,grain-boundary diffusivity and pipe diffusivity, respectively.

Figs.11(a)-(d) show the plots ofcalculated using Eq.(4) for the HPT-processed pure Mg with the grain size of 950 nm at 373 K [235], the rolled AZ31 alloy with the grain size of 6.7 μm at 673 K [120], the HRDSR-processed AZ91 alloy with the grain size of 1.5 μm at 573 K [218],and the extruded ZK60 alloy with the grain size of 3.3 μm at 673 K [38].Thecurves depict the experimental data reasonably well in the wide range of temperatures and grain sizes.The fitting result indicates that theDgb-controlled GBS orDL-controlled GBS dominates plastic flow where superplasticity is observed.As temperature increases, the contribution ofDL-controlled GBS increases and the superplastic strain-rate regime extends to a higher strain rate.

Deformation mechanism maps(DMMs)are graphical models that inform the dominant deformation mechanism for a given metallic material under different grain sizes, strain rates and temperature conditions, and they propose the conditions under which the deformation mechanism dominates over the other deformation mechanisms [305–308].The dominant deformation mechanism can be determined by finding the deformation mechanism that has the highest contribution to the total strain rate () calculated by Eq.(4).Fig.12.shows the DMM for the AZ,ZK and ZW(K)alloys plotted as a function of grain size and strain rate at different temperatures.At 473 K,the transition fromDgb-GBS(grain-boundary-diffusion controlled grain boundary sliding) toDp-DCC (pipe-diffusion controlled dislocation climb creep) occurs at a grain size of 6 μm at 10-4s-1, and as the strain rate increases, the critical grain size for the transition from Dgb-GBSto Dp-DCC decreases.At 573 K, the regime for DL-DCC (lattice-diffusion controlled dislocation climb creep) develops at low strain rates, and this regime expands as the temperature increases further.The regime for DL-GBS (lattice-diffusion controlled grain boundary sliding) appears at 573 K, and this regime expands as the temperature increases further.

Fig.12.The DMMs for the AZ and ZK alloys plotted as a function of grain size (d) and strain rate at different temperatures: (a) 473 K, (b) 573 K, (c)673 K and (d) 773 K.

8.Critical conditions for achieving LTS, HSRS and LTS+HSRS

From the DMMs, the critical grain size at which the transition from GBS (superplastic flow) to DCC (non-superplastic flow) occurs, which differs depending on strain rates, can be estimated.The critical grain sizes determined at two different strain rates of 10-4and 10-2s-1are plotted and the regimes for conventional superplasticity, LTS, HSRS and HSRS+LTS are marked in Fig.13 (a).At 10-4s-1, the transition from Dgb-GBS to Dp-DCC upon increase of grain size occurs below 573 K, while the transition from DL-GBS to DL-DCC occurs above 573 K.As the strain rate increases to10-2s-1, the transition from DL-GBS to DL-DCC is initiated at a higher temperature of 623 K.At a strain rate of 10-4s-1, which is the minimum strain rate for superplasticity in practice, the critical grain size for superplasticity is 0.17 μm at 298 K.Therefore, when the grain size is larger than this, superplastic deformation is predicted to be difficult to obtain at 298 K.As the temperature increases, the critical grain size increases, and at 673 K, the critical grain size is 30.38 μm.At a strain rate of 10-2s-1, the critical grain size decreases to 0.056 μm at 298 K.The critical grain size increases with temperature, and at 673 K, the size is 8.25 μm.The grain sizes at 10-2s-1represent the critical grain sizes for observing HSRS.When the grain size is larger than this, HSRS is predicted not to be obtained.The critical grain size for LTS can be determined by locating the position at 473 K on the curve for 10-4s-1, which is 4.43 μm.When the grain size is smaller than 4.43 μm, LTS can be obtained.The critical grain-size condition for LTS+HSRS is located at 473 K-10-2s-1, which corresponds to 1.55 μm.On the plot of Fig.13(b), the conditions for experimental data (temperature and grain size) where LTS, HSRS and LTS+HSRS were observed are loaded.A reasonably good match between the experimental results and the prediction is observed.Most of the experimental data sitting within the region for LTS+HSRS, however, actually only show LTS.Only the SPD-processed AZ91 alloy [200]exhibits LTS+HSRS.The rare achievement of LTS+HSRS for Mg alloys implies that the retention of grain sizes less than 1 μm during superplastic deformation is very difficult due to rapid grain growth of ultrafine-grained microstructures during sample heating and deformation.Achievement of HSRS is possible even though grain growth occurs to some extent.For example, when the size of ultrafine grains increases by grain growth but remains at smaller than 8.25 μm at 673 K,there is a high chance of achieving HSRS.This critical grain size can increase to as large as 20.33 μm at 773 K.The fine-grained Mg-RE alloys with high fractions of thermally stable compounds satisfy the critical grain-size conditions for HSRS by suppressing rapid grain growth.Note that the datum of pure Mg with a grain size of 320 nm is near the critical grain size for superplasticity at 10-4s-1and 298 K (0.17 μm) but slightly out of the range for superplasticity.This prediction is in good agreement with the experimental result where the pure Mg with the grain size of 320 nm showed quasi-superplasticity at room temperature [235].The current analysis explains why an extremely small grain size is required for superplasticity of pure Mg at room temperature.

Fig.13.(a) The critical grain sizes for the transition from GBS (superplastic flow) to DCC (non-superplastic flow) at two different strain rates of 10-4 and 10-2 s- 1 and the regimes for conventional superplasticity, LTS, HSRS and HSRS+LTS.(b) The experimental data where LTS, HSRS and LTS+HSRS were observed are loaded on the graph of (a).

9.Summaries

The superplastic data of fine-grained Mg alloys studied from 1975 to present were classified into five categories, reporting conventional superplasticity, LTS, HSRS, HSRS/LTS and HSRS+LTS, and their tensile elongation behaviors and deformation mechanisms were analyzed in various ways, and the analysis results were discussed.

1.Most studies on the superplasticity of Mg alloys have focused on AZ series alloys, ZK, Mg-Li and Mg-RE alloys,and recently, Mg-RE alloys have attracted the most attention.

2.SPD-processed Mg alloys have smaller grain sizes than conventionally processed Mg alloys, and thus, the formers exhibit better superplasticity in all types of Mg alloys.The powder-metallurgy processed Mg alloys exhibit superplasticity comparable to or better than the SPD-processed Mg alloys.

3.The ZK60 alloys with finely dispersed particles exhibited excellent LTS, while the Mg-RE alloys with a high fraction of thermally stable particles exhibited excellent HSRS.Mg-Li alloys exhibited LTS even at temperatures far lower than 473 K due to the presence of a high-volume fraction of the BCC phase.For the AZ alloys, as the volume fraction of Mg17Al12phase increased, the LTS and HSRS properties became enhanced.

4.Dgb-GBS andDL-GBS were found to typically operate as the dominant deformation mechanism below ～473 and above ～673 K, respectively, at small grain sizes.

5.Deformation mechanism maps were constructed based on the analysis of the deformation behaviors of superplastic Mg alloys, and based on the results obtained, the critical conditions for achieving LTS,HSRS and HSRS+LTS were determined.According to the prediction, LTS+HSRS is obtainable when the grain size is maintained at ˜1 μm at 473 K during deformation.For this reason, reports on LTS+HSRS in Mg alloys have been rare.

Declaration of Competing Interest

None.

Acknowledgments

This research was financially supported by the National Research Foundation of Korea funded by the Korean government (MSIT) (Project No.NRF 2020R1A4A1018826).

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.