Mechanics of Materials 131 (2019) 158–168

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Mechanics of Materials
journal homepage: www.elsevier.com/locate/mechmat

Research paper

Hot deformation behavior of Mg-8Li-3Al-2Zn-0.2Zr alloy based on T

constitutive analysis, dynamic recrystallization kinetics, and processing map
Yuehua Sun, Richu Wang, Jian Ren, Chaoqun Peng, Yan Feng
⁎

School of Materials Science and Engineering, Central South University, Changsha 410083, China

ARTICLE INFO ABSTRACT

Keywords: The hot deformation behavior of as-homogenized Mg-8Li-3Al-2Zn-0.2Zr alloy was investigated by compression
Mg-Li alloy test at 473–623 K/0.001–1 s−1. The relationship of flow stress, temperature, strain rate, and strain is represented by
Flow behavior the Zener-Hollomon parameter including Arrhenius term, and the average activation energy of deformation is cal-
Constitutive equation culated as 107.55 kJ·mol−1. The dynamic recrystallization (DRX) kinetics model of Mg-8Li-3Al-2Zn-0.2Zr alloy
Dynamic recrystallization
is established as XDRX = 1 exp[ 0.2413( * c )1.7875]. The microstructure evolution indicates that DRX process is
Kinetics model
Processing map retarded in α-Mg phase because of the preferred DRX of β-Li phase and the spheroidization of α-Mg phase
leading to a decrease in DRX driving force of α-Mg phase. The processing map at strain of 0.7 exhibits a region of
discontinuous DRX occurring at 573–623 K with strain rate of 0.001–0.01 s−1 and 523 K with stain rate of 0.001
s−1, which are the optimum parameters of hot working for optimizing the workability and microstructure of Mg-
8Li-3Al-2Zn-0.2Zr alloy.

1. Introduction further improved by optimizing deformation processing. Processing

map based on dynamic material model (DMM) is an effective tool to
Mg-Li alloys, as one kind of the lightest metal structural materials, optimize deformation processing and control microstructure. Thus, it is
show a great potential in fields of aerospace, military, medical instru- necessary to study the DRX behavior and microstructure evolution of
ment, and 3C industry because of their low density, high specific Mg-Li alloys during hot deformation, and construct the processing maps
strength and stiffness, good damping, and excellent electromagnetic for them. Karami and Mahmudi (2012, 2014) studied the hot shear
shielding (Cui et al., 2011; Fei et al., 2005; Wu et al., 2014). The ad- deformation behavior of Mg-Li-Zn alloys by shear punch test.
dition of Li reduces the lattice constant ratio (c/a) of magnesium, Yang et al. (2016) investigated the hot deformation behavior of as-ex-
leading to a decrease in critical resolved shear stresses (CRSSs) of slip truded Mg-9Li-3Al-2.5Sr alloy by hot compression test and identified
systems and more slip systems being activated at room temperature the optimum conditions for hot working. Chen et al. (2011) constructed
(Dong et al., 2014). Mg-Li alloys with different Li contents exhibit three the processing map for as-extruded Mg-7.8Li-4.6Zn-0.96Ce-0.85Y-0.3Zr
types of microstructures: α-Mg single-phase (<5.7 wt.%), α-Mg and β- alloy and observed the microstructure evolution in different domains.
Li dual-phase (5.7 − 10.3 wt.%), and β-Li single-phase (>10.3 wt.%) Xu et al. (2015) established the DRX kinetics model for Mg-9.15Li-
(Xu et al., 2015). Dual-phase Mg-Li alloys possess a superior combi- 3.23Al-1.18Nd alloy, and the results revealed that DRX could easily
nation of strength and ductility, accordingly draw more and more at- occur in β-Li phase but was retarded in α-Mg phase. Sivakesavam and
tention (Zhao et al., 2016a). However, the disadvantages of dual-phase Prasad (2002) studied the hot deformation behavior of Mg-11.5Li-1.5Al
Mg-Li alloys limit their extensive application, such as relatively low alloy and identified the superplasticity domain in processing map oc-
strength, poor thermal stability, and inferior corrosion resistance. curring at 673 K/0.001 s−1. However, there are few systematic re-
Plastic deformation is a simple and effective approach to enhance searches about the hot deformation behavior of Mg-8Li-3Al-2Zn-0.2Zr
the mechanical properties of alloys and extend their application. Mg-Li (LAZ832-0.2Zr) alloy based on constitutive analysis, DRX evolution,
alloys as typical wrought Mg alloys are prone to undergo DRX during hot and processing map.
deformation due to low stacking fault energy and wide extended dis- LAZ832-0.2Zr alloy possesses duplex structure (α-Mg and β-Li) and
location, which can surely affect their microstructures and mechanical presents high strength and good ductility. Al and Zn are added to im-
properties (Ion et al., 1982). In addition, the properties of alloys can be prove the strength of alloy due to the large solid solubility in Mg matrix.

⁎
Corresponding author.
E-mail address: fengyanmse@csu.edu.cn (Y. Feng).

https://doi.org/10.1016/j.mechmat.2019.02.005
Received 11 August 2018; Received in revised form 16 November 2018
Available online 13 February 2019
0167-6636/ © 2019 Elsevier Ltd. All rights reserved.
Y. Sun, et al. Mechanics of Materials 131 (2019) 158–168

Zr is used as a grain refiner to further enhance the strength and improve phase are smooth and round, and AlLi particles are mainly distributed
the microstructure. In this work, the hot deformation behavior of in β-Li phase and along the phase interfaces. The AlLi particle with
LAZ832-0.2Zr alloy was studied by hot compression test. Using true micro-nano scale observed in the top right corner of Fig. 1(a) is larger
stress-strain data, constitutive equation and DRX kinetics model were than the AlLi nano-phase in TEM image reported by Tang et al. (2017),
established to describe the flow behavior and predict the DRX volume which might be the result of slow solidification rate and long-time
fraction, respectively. It is aimed to investigate the hot workability of homogenization at elevated temperature. The volume fraction of each
LAZ832-0.2Zr alloy combined with processing map and microstructure phase counted by image analyzer is about 68% α-Mg, 28% β-Li, and 4%
evolution to optimize the deformation process and determine the fea- AlLi. In the alloy, no compounds containing Zn and Zr elements are
sible processing parameters. found. Therefore, it can be considered that all Zn and Zr atoms exist in
the matrix in the form of solid solution.
2. Experimental procedures Fig. 2 depicts the true stress-strain curves under uniaxial compression
of as-homogenized LAZ832-0.2Zr alloy measured at different tem-
The material used in this study was prepared by mixing and melting peratures and strain rates. The flow stress of all curves increases sharply
pure Mg (>99.9 wt.%), pure Li (>99.9 wt.%), pure Al (>99.9 wt.%), with increasing true strain and reaches a peak value at early stage, then
pure Zn (>99.9 wt.%), and Mg-Zr (30 wt.%) master alloy, and then gradually decreases to a steady state. These curves are typical DRX
poured into a stainless steel mold. The preparation procedure was curves which consist of three stages: work hardening, softening, and
carried out in a vacuum induction furnace under pure argon atmo- steady. Work hardening, as a result of dislocation multiplication, pile-
sphere. The cast ingot with a diameter of 80 mm and a length of up, and tangle, is the main deformation mechanism before the occur-
120 mm was homogenized at 553 K for 24 h and then cooled to room rence of DRX. When the true strain increases to the critical strain (ɛc),
temperature. the dislocation rearrangement and counteraction of unlike dislocation
The chemical composition and density of as-homogenized alloy, result in DRX. The slopes of curves decrease with increasing strain and
listed in Table 1, were determined by inductively coupled plasma the flow stresses decrease after peak stress, which indicates that DRX
atomic emission spectroscopy (ICP-AES) and electronic density balance gradually intensifies. In this stage, work hardening is partially offset by
(AEL-200) using Archimedes method, respectively. Microstructure was the softening caused by DRX. The steady state of curves in the end is the
observed with an optical microscope (OM, Leica-DM6000M), a scan- result of balance between work hardening effect and softening effect,
ning electron microscope (SEM, Quanta-200), a transmission electron indicating that the alloy is recrystallized completely. In addition, the
microscope (TEM, Tecnai G20ST), and a scanning electron microscope stress-strain curves at low strain rates (such as 0.01 and 0.001 s−1)
(SEM, EVO MA 10) equipped with an electron backscatter diffraction exhibit a fluctuation behavior caused by the continuous alternations
(EBSD) system. The samples for OM observation were polished and between dynamic recrystallization and work hardening. Obviously,
etched with a mixture solution containing 1 g oxalic acid, 1 mL acetic temperature and strain rate have a great effect on the flow behavior of
acid, 1 mL nitric acid (68 wt.%), and 120 mL deionized water. The LAZ832-0.2Zr alloy, and the flow stress increases significantly with
samples for TEM and EBSD were prepared using an ion beam thinner (Gatan increasing strain rate and decreasing temperature. LAZ832-0.2Zr alloy
691), and the step size of EBSD mapping is 1.0 μm. Phase analysis was with a density of 1.509 g·cm−3 possesses lower peak stresses during hot
carried out with a D/Max 2500 X-ray diffractometer (XRD) using deformation compared with other Mg alloys like AZ80 (Quan et al.,
monochromatic Cu Kα radiation at a step size of 0.02° and a scan rate of 2011) and Mg-rare earth alloys (Li et al., 2010). They approximately
4°/min. reach their peaks at 110 MPa and 280 MPa, respectively, at 623 K/1
Cylindrical specimens for hot compression tests, with 10 mm in s−1. But LAZ832-0.2Zr alloy reaches its peak around 70 MPa, which is
diameter and 15 mm in height, were machined from the as-homo- ascribed to the existence of β-Li phase leading to the reduction of de-
genized alloy. Isothermal hot compression tests were performed on a formation resistance.
thermo-mechanical simulator (Gleeble-3180). The compression tests
were performed at 473–623 K/0.001–1 s−1. Prior to compression, the 3.2. Constitutive equation of LAZ832-0.2Zr alloy
specimens were heated to the predetermined temperature at a heating
rate of 10 K s−1, and held for 10 min to obtain a uniform and stable Based on the true stress-strain curves shown in Fig. 2, there is an
temperature. Subsequently, the specimens were compressed to a true interaction relationship among deformation temperature (T), strain rate
strain of about 0.7, and immediately followed by water quenching to ( ), strain (ɛ), and flow stress (σ). Constitutive equation is an appro-
keep the deformed microstructure. priate tool for describing the flow behavior of metal materials involving
the abovementioned parameters. In this work, the hyperbolic sine func-
3. Results and discussion tion is used to describe the flow behavior of LAZ832-0.2Zr. The Zener-
Holloman parameter (Z) can effectively represent the combined effect
3.1. Microstructure and flow behavior of LAZ832-0.2Zr alloy of temperature and strain rate on flow stress, and determine the de-
formation activation energy (Q) which is an important material para-
Fig. 1 shows the microstructure and XRD pattern of as-homogenized meter for determining the critical conditions of DRX initiation. Here,
LAZ832-0.2Zr alloy. It can be seen from Fig. 1(a) that the alloy is the effect of strain on flow stress is considered by associating the
composed of α-Mg, β-Li, and AlLi phases, which is consistent with the temperature-independent constants with strain. The predicted results
XRD result shown in Fig. 1(b). According to the previous researches considering strain are more consistent with the experimental data than
(Zhao et al., 2016a, 2016b), the light gray region is α-Mg phase, the those obtained by only using peak stresses to calculate model para-
dark gray region is β-Li phase, and the white spherical particles are AlLi meters (Lin et al., 2010). In Zener-Holloman model, the relations
particles. After homogenization treatment, the boundaries of α-Mg among Z, Q, , T, and σ at different stress levels are usually expressed as
follows (Shalbafi et al., 2017):
Table 1
Chemical composition and density of the experimental alloy.
A1 n < 0.8
Q
Z = exp = A2 exp( ) > 1.2
Alloy Actual composition (wt. %) Density (g·cm−3) RT
A [sinh( )]n for all (1)
Li Al Zn Zr Mg

LAZ832-0.2Zr 8.04 3.02 1.98 0.17 Bal. 1.509 Where Z is Zener-Holloman parameter and its physical meaning is
the deformation rate factor of temperature compensation, is strain

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Fig. 1. (a) Microstructure and (b) XRD pattern of as-homogenized LAZ832-0.2Zr alloy.

Fig. 2. True stress-strain curves of LAZ832-0.2Zr alloy deformed to a strain of 0.7 at temperatures of (a) 473 K, (b) 523 K, (c) 573 K, and (d) 623 K with different
strain rates.

rate (s−1), Q is deformation activation energy (kJ·mol−1), R is universal Taking the natural logarithm of Eq. (1), and then Eq. (3) is obtained:
gas constant (R = 8.314 J·mol−1·K−1), T is deformation temperature
(K), σ is true stress (MPa), A1, A2, A, n′, β, α, and n are temperature- lnA1 + n ln < 0.8
Q
independent material constants, and the relationship among n′, β, and α lnZ = ln + = lnA2 + > 1.2
RT
can be expressed as Eq. (2). lnA + nln [sinh( )] for all (3)

= By assuming that deformation activation energy (Q) is not a func-

n (2) tion of temperature (T), the material constants n′, β, and n can be

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defined by the following equations.

ln
n =
ln T (4)

ln
=
T (5)

ln
n=
ln[sinh( )] T (6)
If strain rate ( ) is a constant, the deformation activation energy (Q)
can be calculated by Eq. (7).

ln[sinh( )]
Q = R· n· = R ·n· B
()
1
T (7)

The discrete flow stress data at strains ranging from 0.05 to 0.69 Fig. 4. Relationship between ln Z and ln [sinh(ασ)] at a strain of 0.05.
with an interval of 0.04 are used to calculate the above mentioned
parameters. Here, taking a strain of 0.05 as an example to introduce the and strain rates are calculated using Eq. (1) by considering , Q, R, and
evaluation process of material constants. Fig. 3 presents the relationship T. The relationship between ln Z and ln [sinh(ασ)] at strain of 0.05 is
between (a) ln and σ, (b) ln and lnσ, (c) ln and ln[sinh(ασ)], (d) ln described in Fig. 4. The data are fitted by linear regression, and the
[sinh(ασ)] and 1000/T at strain of 0.05, and the slopes of corresponding slope (4.9598) and intercept (17.4009) represent n and ln A at strain of
lines represent β, n′, n, and B, respectively. The mean values of slopes 0.05, respectively.
are taken to evaluate the values of β, n′, n, and B, which are 0.1217,
7.0122, 5.0373, and 2.4155, respectively. According to Eq. (2) and ln Z = lnA + nln[sinh( )] (8)
Eq. (7), the values of α and Q at strain of 0.05 can be calculated as
0.0174 and 101.1614 kJ·mol−1, respectively. To describe the flow behavior of LAZ832-0.2Zr alloy accurately, the
The parameters A and n in hyperbolic sine function can be obtained effect of strain on flow stress is considered by assuming that the ma-
from Eq. (8). At a given strain, 16 values of Z at various temperatures terial constants (α, Q, n, and ln A) are polynomial functions of strain.

Fig. 3. Relationship between (a) ln and σ, (b) ln and ln σ, (c) ln and ln [sinh(ασ)], (d) ln [sinh(ασ)] and 1000/T at a strain of 0.05.

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Fig. 5. Relationship between true strain and various constants: (a) α, (b) ln A, (c) n, and (d) Q.

The evaluation of values for α, Q, n, and ln A at various strains are reduces the amount of flow stress necessary for deformation and de-
obtained by using the corresponding flow stress to repeat the above creases the deformation activation energy. The lower deformation ac-
evaluation procedure, and the relationship between these material tivation energy (95 kJ·mol−1) of Mg-11.5Li-1.5Al alloy provides potent
constants and strain is shown in Fig. 5. It is recognized that six-order evidence that β-Li phase can decrease the deformation activation en-
polynomial fits well on the calculated values of these constants. The ergy (Sivakesavam and Prasad, 2002). However, Wei et al. (2015) and
expressions are shown in Eqs. (9)–(12), and the coefficients of poly- Xu et al. (2015) reported that Mg-9Li-3Al-2Sr-2Y alloy and Mg-9Li-3Al-
nomial functions for α, Q, n, and ln A are listed in Table 2. The average 1Nd alloy possessed higher deformation activation energy, and they
deformation activation energy of as-homogenized LAZ832-0.2Zr alloy were 112.306 kJ·mol−1 and 126.9285 kJ·mol−1, respectively. The
is calculated as Q = 107.55 kJ·mol−1 which is smaller than those of Mg strengthening phases (such as Al2Y, Al4Sr, Al2Nd, and Al11Nd3) hinder
(134 kJ·mol−1) (Sivakesavam and Prasad, 2002), AZ31B (158.7323 the movement of dislocations and increase the deformation resistance
kJ·mol−1) (Liu et al., 2011), AZ80 (215.82 kJ·mol−1) (Quan et al., of alloy during hot deformation. Thus, the deformation activation en-
2011), and Mg-2.0Zn-0.3Zr-0.9Y alloy (236.2 kJ·mol−1) (Lv et al., ergies of these alloys are improved compared with LAZ832-0.2Zr alloy.
2014). The addition of Li decreases the c/a axial ratio of Mg lattice
= 6 + 5 + 4 + 3 + 2 + + (9)
resulting in more slip systems to be actuated. Especially when Li con- 1 2 3 4 5 6 7

tent is between 5.7 wt.% and 10.3 wt.%, Mg-Li alloy is composed of α- Q = Q1 6 + Q2 5 + Q3 4 + Q4 3 + Q5 2 + Q6 + Q7 (10)
Mg and β-Li phases. The existence of β-Li phase in LAZ832-0.2Zr alloy
n = n1 6 + n2 5 + n3 4 + n4 3 + n5 2 + n6 + n7 (11)

Table 2 ln A = A1 6 + A2 5 A3 4 + A4 3 A5 2 + A6 + A7 (12)
Coefficients of the polynomial functions.
Taking the inverse function of Eq. (1), and the flow stress can be
α Q n lnA expressed as Eq. (13). The material constants (α, Q, n, and ln A) at
α1 = −0.5528 Q1 = −12,896.89 n1 = −51.28 A1 = −2547.20 different strains are calculated using Eqs. (12)–(15), and the predicted
α2 = 1.2706 Q2 = 31,539.38 n2 = 142.61 A2 = 6253.01 flow stresses are obtained by substituting the strain rate, temperature,
α3 = −1.1673 Q3 = −30,417.44 n3 = −126.87 A3 = −6054.11 strain, and calculated constants into Eq. (13). That is, 31 parameters need
α4 = 0.5176 Q4 = 14,625.46 n4 = 26.65 A4 = 2923.77 to be determined for this constitutive function and they are strain rate,
α5 = −0.1110 Q5 = −3629.98 n5 = 18.83 A5 = −729.58
temperature, strain, and the 28 coefficients listed in Table 2. Fig. 6 illus-
α6 = 0.0177 Q6 = 441.71 n6 = −9.61 A6 = 89.07
α7 = 0.0166 Q7 = 84.42 n7 = 5.37 A7 = 14.25 trates the comparison between measured and predicted flow stresses at
various temperatures and strain rates. The proposed constitutive

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Fig. 6. Comparison between measured and predicted flow stresses by using Zener-Hollomon model at temperatures of (a) 473 K, (b) 523 K, (c) 573 K, and (d) 623 K.

et al., 2015; He et al., 2013). The comparison between experimental

and predicted flow stresses combined with R and AARE is shown in
Fig. 7. High correlation coefficient (R = 0.9974) indicates that a good
correlation is obtained between the predicted and the experimental
flow stresses. The average absolute relative error is only 3.37% for all
deformation conditions, which demonstrates that the developed con-
stitutive equation has a high accuracy in predicting flow stresses. These
statistical analyses reveal a good predictability of the developed con-
stitutive equation for LAZ832-0.2Zr alloy.
1

=
1
ln
Z
1
n
+
Z
2
n
+1 =
1
ln
exp ( )
Q( )
RT
n( )

A A ( ) A( )

+
exp ( ) Q( )
RT
n( )

+1
Fig. 7. Comparison between measured and predicted flow stresses combined A( )
with correlation coefficient (R) and average absolute relative error (AARE). (13)

equation gives a good estimate of the flow stress for LAZ832-0.2Zr alloy 3.3. DRX kinetics model of LAZ832-0.2Zr alloy
under most deformation conditions, except for a few points that deviate
from their experimental values. The lubrication condition between During hot deformation process, dislocations continuously multiply
sample and mold, change in effective contact area caused by upsetting, and accumulate with increasing strain in work hardening stage. When
and inhomogeneous deformation caused by uniaxial compression might the dislocation density increases to a certain degree that at a critical
be the reasons of deviation between estimated stress and experimental strain, the stored energy is sufficient to induce DRX and the deforma-
stress. Correlation coefficient (R) and average absolute relative error tion enters into the softening stage. In this stage, DRX gradually in-
(AARE) are used to quantify the predictability of constitutive equation, tensifies and its volume fraction increases as the strain increases. When
and their calculation equations are described in some references (Wei work hardening and softening achieve a balance, the flow stress keeps

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Y. Sun, et al. Mechanics of Materials 131 (2019) 158–168

Fig. 8. (a) Relationship between θ and σ at 623 K and 0.001 s−1, and (b) (∂θ/∂σ) versus σ plots at 623 K and different strain rates.

constant and the deformation comes to a steady stage in which the alloy the strain rate increases. For a given strain rate, the strain required for
is completely recrystallized. To quantitatively describe the DRX evo- same XRD volume fraction increases as the deformation temperature
lution of LAZ832-0.2Zr alloy, DRX kinetics model is used to predict the decreases. This phenomenon indicates that the DRX process of LAZ832-
volume fraction of DRX and expressed as follows (Lv et al., 2014): 0.2Zr alloy is delayed distinctly at high strain rates and low deforma-
n tion temperatures. The effect is attributed to the reduced mobility of
XDRX = 1 exp k c
grain boundaries with increasing strain rate and decreasing deforma-
* (14) tion temperature. Therefore, the alloy cannot recrystallize completely
Where XDRX is volume fraction of DRX, ɛ is true strain, ɛc is critical when deformed at low temperatures and high strain rates (such as at
strain for the initiation of DRX, ɛ* is the strain for maximum softening 200 °C, 250 °C/1 s−1, 250 °C/0.1 s−1, and 300 °C/1 s−1), and the DRX
rate, and k and n are material constants. volume fraction tends to be less than 1.
d
Fig. 8(a) depicts the relationship between θ ( = d is strain hard- It is known that the DRX behavior of alloy is closely related to de-
−1
ening rate) and σ at 623 K and 0.001 s . The stress σc (corresponding formation mechanism and microstructure evolution. For Mg alloys with
to ɛc) is the critical stress for DRX and σ* (corresponding to ɛ*) is the low stacking fault energy, their wide extended dislocations are difficult
stress for maximum softening rate. The stress σsat is the saturation stress to escape from nodes and dislocation networks or to neutralize the
and its value is evaluated by the intersection point of tangent σc and unlike dislocations by climbing and cross-slipping (Ion et al., 1982).
= 0 . σsat represents the dislocation density in the most work-hardened Thus, dislocations accumulate at grain boundaries, twin boundaries,
grains and the driving force for the continuation of DRX (Feng et al., and second-phase particles during continuous hot deformation, leading
2014). The peak stress (σp) is defined as the stress at = 0 , and σss is the to an increase in dislocation density and stored energy. When the stored
steady state stress (corresponding to ɛss). The strain ɛ* is defined as the energy increases to the amount required for DRX, DRX process occurs.
strain at which the value of θ reaches the negative peak. The critical It has been reported that DRX formed in twins is the main mechanism of
strain (ɛc) is obtained when the value of ( / ) reaches the DRX for Mg alloys with inferior workability (such as Mg-Zn-Zr alloy)
minimum value, and the relationship between ( / ) and σ at 623 K especially under high strain rates and low temperatures (Lv et al., 2014;
is shown in Fig. 8(b). The critical strains of DRX at 623 K with strain Wu et al., 2010), while DRX formed at grain boundaries and second-
rates of 0.001, 0.01, 0.1, and 1 s−1 are 0.01707, 0.02655, 0.03611, and phase particles is the main mechanism of DRX for Mg alloys with good
0.06837, respectively. To calculate the material constants k and n, it is workability (such as Mg-Al-Zn alloy) especially under low strain rates
indispensable to identify the deformation conditions ( XDRX = 1) that and high temperatures (Quan et al., 2011). Compared with other Mg
correspond to flow stress at the steady state. The DRX volume fraction alloys, LAZ832-0.2Zr alloy exhibits a lower critical strain (ɛc) for DRX
can also be expressed using stress as follows: and a similar DRX behavior to Mg-Al-Zn alloy, which might be inter-
preted by microstructure evolution and deformation mechanism. The
2 2
XDRX = sat microstructure of LAZ832-0.2Zr alloy deformed at 473 K and 1 s−1 is
sat
2
ss
2
(15) shown in Fig. 10(a). It can be seen that both α-Mg and β-Li phases are
Combining Eq. (14) and Eq. (15), the material constants k and n can elongated perpendicular to the compression direction, and β-Li phases
be calculated as −0.2413 and 1.7875, respectively. Therefore, the DRX partly exhibit a chain microstructure. Lots of fine grains with wavy and
kinetics model of as-homogenized LAZ832-0.2Zr alloy is expressed by ill-defined grain boundaries are found in the spindly β-Li phases,
the following equation: showing a typical continuous DRX feature. The grain boundaries are
formed via dislocation rearrangement, so they are deformed and
c
1.7875
curved. Usually, continuous DRX occurs in the deformed region with
XDRX = 1 exp 0.2413
* (16) high dislocation density, and is favored at low temperatures
(Sakai et al., 2009). All α-Mg phases maintain the elongated micro-
On the basis of Eq. (16), the effect of deformation temperature, structure without fine DRX grains, only a very small number of shear
strain rate, and strain on DRX volume fraction is shown in Fig. (9). The bands are observed in α-Mg phases. Thus, DRX of β-Li phase is the main
DRX kinetics of as-homogenized LAZ832-0.2Zr alloy is represented in softening mechanism under this deformed condition. During hot de-
terms of S-shaped curves. During hot deformation process, DRX occurs formation, plastic deformation occurs first in β-Li phase because its
when the strain reaches the critical strain. After that, the DRX volume strength is lower than that of α-Mg phase. The dislocation movement in
fraction increases and then reaches a constant value of 1 as the strain β-Li phase is hindered and limited by second-phase particles and phase
increases to complete the DRX process. For a given deformation tem- interfaces, leading to an increase in stored energy of β-Li phase and an
perature, the strain required for same XRD volume fraction increases as

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Y. Sun, et al. Mechanics of Materials 131 (2019) 158–168

Fig. 9. Volume fraction of DRX obtained at various strain rates and temperatures: (a) 473 K; (b) 523 K; (c) 573 K; (d) 623 K.

increase in dislocation density at AlLi particles and phase interfaces.

Therefore, DRX process preferentially occurs in β-Li phase, resulting in
a lower critical strain for DRX. The softer β-Li phase reduces the de-
formation resistance of α-Mg phase and makes the deformation of α-Mg
phase more homogeneous, which decreases the dislocation density and
driving force for DRX in α-Mg phase. As a result, the DRX process of α-
Mg phase is retarded in duplex LAZ832-0.2Zr alloy. For LAZ832-0.2Zr
alloy compressed at 473 K and 1 s−1, incomplete DRX occurs in β-Li
phase but no DRX occurs in α-Mg phase, which is well in agreement
with the low DRX volume fraction (about 0.35 at strain 0.7) shown in
Fig. 9(a). The microstructure of LAZ832-0.2Zr alloy deformed at 473 K
and 0.001 s−1 is shown in Fig. 10(b). Compared with Fig. 10(a), the
DRX degree of β-Li phase increases and the interfaces of α-Mg phase
become smooth and round. The enlarged view of rectangular region on
the top displays an isolated DRX α-Mg grain at the trigeminal grain
boundaries of β-Li phase, which indicates that discontinuous DRX occurs
in α-Mg phase under this condition but the amount is very little. It is
believed that spheroidization of α-Mg phase is also a softening me-
chanism besides DRX of β-Li phase. The spheroidization of α-Mg phase
is a result of atomic diffusion, which depends on temperature and time.
Low strain rate provides more time for atomic diffusion and DRX, re-
sulting in the increase of DRX volume fraction and spheroidization of α-
Mg phase. In addition, high temperature is beneficial to atomic diffu-
sion due to high vacancy concentration and increasing diffusible atoms
with high energy. Generally, diffusion is easier to occur along crystal
Fig. 10. Microstructures of specimens deformed to a strain of 0.7 at (a) 473 K/1 defects (such as dislocation, grain boundary, and free surface) at which
s−1, (b) 473 K/0.001 s−1, (c) 573 K/1 s−1, (d) 573 K/0.001 s−1, (e) 623K/1 atoms need lower diffusion activation energy to diffuse. Therefore, the
s−1, and (f) 623 K/0.001 s−1. diffusion of atoms is bound to make the composition more uniform and
eliminate some crystal defects, leading to a decrease in stored energy

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for DRX of α-Mg phase. It can be considered that the spheroidization of with nucleation at original grain boundaries by bulging and grain
α-Mg phase is also a main reason for the delay of its DRX. The alloy growth by grain boundary migration.
deformed at 573 K and 1 s−1 (see Fig. 10(c)) exhibits a similar micro- Additionally, the microstructures of LAZ832-0.2Zr alloy deformed
structure to that deformed at 473 K and 0.001 s−1. Partial DRX occurs under different conditions are observed by TEM. Fig. 12(a) shows a
in β-Li phase and a certain extent of spheroidization occurs in α-Mg large pebble particle with smooth boundary, and the corresponding
phase without DRX grains. Fig. 10(d) illustrates the microstructure at electron diffraction pattern indicates that this particle is AlLi phase.
573 K and 0.001 s−1. β-Li phase is entirely composed of fine equiaxed Fig. 12(b) presents a typical discontinuous DRX grain formed at the
grains with an average size of 3.72 μm, suggesting that β-Li phase un- triple junctions of grain boundaries, and there are no dislocations in the
dergoes complete DRX process under this condition. It can be seen from interior of grain which displays sharp and straight grain boundary. This
the magnification of rectangular region that the DRX grains of β-Li discontinuous DRX grain is confirmed as α-Mg phase by the corre-
phase display well-defined and sharp grain boundaries, exhibiting a sponding electron diffraction pattern. Fig. 12(c) and (d) presents the
typical characteristic of discontinuous DRX. It has been reported that microstructures of β-Li phase obtained under different conditions. At
discontinuous DRX process is favored at high temperatures, and it can 473 K/1 s−1 (Fig. 12(c)), the continuous DRX β-Li grains with irregular
facilitate the migration of grain boundaries and accelerate the diffusion- grain boundaries are formed by merging of adjacent subgrains which
controlled process (Dudova et al., 2010). The spheroidization phe- result from dislocation climbing and dislocation rearrangement.
nomenon of α-Mg phase is more pronounced under this condition due Therefore, the grain boundaries are curved and a small number of
to the high diffusion coefficient at high temperatures and the promotion dislocations appear inside the new DRX grains. At 573 K/0.001 s−1
of discontinuous DRX. Moreover, some DRX grains of α-Mg phase are (Fig. 12(d)), the DRX β-Li grains with sharp and well-defined grain
found at the phase interfaces and the trigeminal grain boundaries of β- boundaries exhibit a typical feature of discontinuous DRX. Based on the
Li. In the microstructure at 623 K and 1 s−1 (see Fig. 10(e)), the β-Li above analysis, the TEM results are consistent with the OM analysis and
phase undergoes complete DRX process and the DRX grains are with an the EBSD analysis.
average size of 2.99 μm. Compared with the microstructure at 573 K
and 1 s−1, the spheroidization and DRX of α-Mg phase at 623 K and 1 3.4. DMM processing map of LAZ832-0.2Zr alloy
s−1 have not changed. This can be explained by the fact that the de-
formation time of alloy is greatly reduced at high strain rates, leading to The processing maps based on DMM model are usually used to
no enough time for atom diffusion and DRX nucleation. Fig. 10(f) de- describe the dynamics of hot deformation, which are obtained by
picts the microstructure at 623 K and 0.001 s−1. The DRX grains of β-Li overlapping a power dissipation map and an instability map. The power
phase have obviously grown up with an average size of 6.74 μm, and α- dissipation map represents the power dissipation caused by micro-
Mg phase undergoes incomplete DRX and obvious spheroidization. structural changes, and its characteristics can be expressed by the ef-
According to Fig. 9, the alloy deformed to a strain of 0.7 at 573 K/0.001 ficiency of power dissipation (η) as follows:
s−1 and 623 K/0.001 s−1 exhibits a complete DRX behavior and the
DRX volume fraction is 1. However, the corresponding microstructures 2m
=
(see Fig. 10(d) and (f)) prove that β-Li phase undergoes complete DRX m+1 (17)
but α-Mg phase undergoes partial DRX, indicating that the DRX grains Where m is the strain rate sensitivity of material and can be calcu-
of α-Mg phase requires a longer time for nucleation and growth. ln
lated by m = ln . In addition, the instability map is developed on the
Fig. 11(a–e) shows the microstructure distribution of α-Mg phase basis of the extremum principle of irreversible thermodynamics, and
under different conditions, in which three types of microstructures, instability parameter (ξ) is used as the criterion of continuous in-
namely recrystallized, substructured, and deformed microstructures, stability for large plastic deformation and expressed as follows
are marked with red, yellow, and green, respectively. Meanwhile, the (Prasad and Seshacharyulu, 1998):
corresponding fractions of three types of microstructures are listed in
Table 3. β-Li phase could not be indexed. The surface with higher Li
content is easily oxidized, which limits the EBSD analysis of β-Li phase. ( )=
ln ( m
m+1 ) +m 0
ln (18)
It can be clearly seen that the fractions of recrystallized region and
substructured region increase with increasing temperature and de- The unstable regions in instability map are evaluated by using in-
creasing strain rate, and the recrystallized fraction of α-Mg phase at stable criterion ξ < 0. The DMM processing map of LAZ832-0.2Zr alloy
623 K/0.001 s−1 reaches up to 11.06%. After hot compression, a great at strain of 0.7 is shown in Fig. 13. The contour numbers represent the
number of low-angle grain boundaries (2°–15°) remarked with white efficiency of power dissipation marked as percent. Domain І corre-
are observed in the original grains of α-Mg phase. These low-angle sponds to the unstable region marked as gray, which occurs at higher
grain boundaries are the result of dislocation accumulation on dis- strain rates (such as 1 s−1 and 0.1 s−1) over a wide temperature range.
location walls, thus they can be regarded as subgrain boundaries. The alloy deformed at 473 K and 1 s−1 shown in Fig. 10(a) exhibits a
Fig. 11(f) depicts the misorientation angle distribution of α-Mg phase non-uniform microstructure with a small amount of shear bands, which
under different conditions. As the temperature increases and the strain belongs to the unstable region (Domain I). At high strain rates, the
rate decreases, the fraction of low-angle grain boundaries obviously stress concentration produced during deformation process cannot be
decreases but that of high-angle grain boundaries (15°–100°) increases released due to short deformation time, leading to microcracks or flow
owing to the DRX process of α-Mg phase. To determine the DRX me- instability. Moreover, shear bands are also responsible for uneven de-
chanism of α-Mg phase, the corresponding enlarged inverse pole figures formation and flow instability. Therefore, the unstable region should be
of local regions remarked with rectangle are shown in Fig. 11(g–i). The avoided during hot deformation. Domain II occurs at 573–623 K/
fine DRX grains are formed along the serrated original grain boundaries 0.001–0.01 s−1 and 523 K/0.001 s−1, with a peak efficiency of about
or at the triple junctions, and these DRX grains exhibit different or- 45% at 623 K/0.001 s−1. According to Fig. 10(d) and (f), the uniform
ientation relationships with their parent grains and adjacent DRX microstructures consist of completely recrystallized β-Li phase, and
grains. In addition, grain boundary bulging can be observed at the obviously spheroidized and recrystallized α-Mg phase. Therefore, Do-
serrated grain boundaries, and the subgrains formed at bulgy grain main II with discontinuous DRX is the preferred region for optimizing
boundaries also possess different orientation from their parent grains. the workability and microstructure of materials. It has been reported
Based on the above analysis and previous researches (Dudova et al., that contour density has a significant effect on the deformation me-
2010; Jiang et al., 2015), the DRX mechanism of α-Mg phase can be chanism of alloy (Meng et al., 2009). The dense contour lines indicate
confirmed as discontinuous DRX which is a traditional DRX process that small changes in deformation parameters result in a large

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Fig. 11. (a–e) Microstructure distribution of α-Mg phase under different conditions: (a) 473 K/0.001 s−1; (b) 573 K/0.001 s−1; (c) 623 K/0.001 s−1; (d) 573 K/1 s−1;
(e) 623 K/1 s−1, (f) the misorientation angle distribution of α-Mg phase, and (g–i) the enlarged inverse pole figures of marked regions selected in (b) and (c).

Table 3
Fractions of three types of microstructures of α-Mg phase under different
conditions.
Compression Recrystallized Substructured Deformed
condition fraction (%) fraction (%) fraction (%)

473 K/0.001 s−1 3.16 2.04 94.80

573 K/0.001 s−1 8.20 2.73 89.07
623 K/0.001 s−1 11.06 27.69 61.25
573 K/1 s−1 3.64 2.67 93.69
623 K/1 s−1 5.09 3.76 91.15

fluctuation of power dissipation efficiency, thus the deformation me-

chanism is easy to change and the plastic deformation is unstable.
Therefore, the process parameters need to be strictly controlled during
deformation process in the region with dense contour lines. Domain III
with higher power dissipation efficiency and sparse contour lines is a
feasible region for hot working, in which the flow behavior is relatively
stable and the corresponding deformation mechanism is incomplete
DRX.

4. Conclusions
Fig. 12. TEM images of (a) AlLi particle, (b) α-Mg phase at 473 K/0.001 s−1,
The flow behavior, DRX kinetics, and hot workability of LAZ832- (c) β-Li phase at 473 K/1 s−1, and (d) β-Li phase at 573 K/0.001 s−1.
0.2Zr alloy were investigated by compression test at 473–623 K with
strain rate of 0.001–1 s−1, and the following conclusions can be drawn: alloy at elevated temperatures exhibits a typical DRX characteristic,
and the flow stress decreases with increasing temperature and de-
(1) As-homogenized LAZ832-0.2Zr alloy is composed of α-Mg, β-Li, creasing strain rate.
and AlLi phases, and AlLi particles mainly distribute in β-Li phase (2) The flow stresses of LAZ832-0.2Zr alloy predicted by the developed
and along the phase interfaces. The flow behavior of LAZ832-0.2Zr constitutive equation based on Zener-Hollomon model are in good

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the Central Universities of Central South University (No. 2017zzts005) progress in magnesium-lithium alloys. Int. Mater. Rev. 60, 65–100.
and the Open-End Fund for the Valuable and Precision Instruments of Wei, G., Peng, X., Hadadzadeh, A., Mahmoodkhani, Y., Xie, W., Yang, Y., Wells, M.A.,
Central South University (No. CSUZC201814). 2015. Constitutive modeling of Mg-9Li-3Al-2Sr-2Y at elevated temperatures. Mech.
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the online version, at doi:10.1016/j.mechmat.2019.02.005. Alloys Compd. 639, 79–88.
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