-
Research ArticleMicrostructure Evolution and Grain Growth Model
ofAZ31 Magnesium Alloy under Condition of Isothermal
Zhongtang Wang,1 Lingyi Wang,2 and Lizhi Liu3
1School of Material Science and Engineering, Shenyang Ligong
University, Shenyang 110159, China2Shenyang Institute of
Technology, Liaoning, Fushun 113122, China3Brilliance Auto R and D
Center (BARC), Shenyang 110141, China
Correspondence should be addressed to Zhongtang Wang;
[email protected]
Received 8 October 2015; Revised 26 November 2015; Accepted 10
December 2015
Academic Editor: Pradeep Lancy Menezes
Copyright © 2015 Zhongtang Wang et al. This is an open access
article distributed under the Creative Commons AttributionLicense,
which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properlycited.
Microstructure evolution of AZ31 magnesium alloy in annealing
process had been investigated by experiment study at
heatingtemperature range of 150∘C–450∘C and holding time range of
15min–60min. The effects of heating temperature and holding timeon
grain growth had been analyzed. The results presented that the
grain size tends to grow up with the increase of holding timeat a
certain temperature. At a certain holding time, the grain size
increased firstly and then decreased at the heating
temperaturerange of 150–250∘C. And when heating temperature is
higher than 250∘C, the grain grows up gradually with the increase
of heatingtemperature. The grain growth model of AZ31 Mg alloy has
been established by regression based on the experimental data
attemperature of 250–450∘C, and the relative error between model
calculation results and experimental results is less than
19.07%.Activation energy of grain growth of AZ31 magnesium alloy
had been determined.
1. Introduction
Deformation mechanism of magnesium alloy sheet is glidein base
surface and twin in taper surface. The importantcontribution of
twin deformation to plastic deformation isto change the grain
orientation and is advantageous to startnonbasal slip system and
improve the capability of plasticdeformation [1].With rolling
deformation at low temperatureof magnesium alloy sheet, a very high
intensity of basaltexture formed in the rolling direction. The
texture hinderedstarting the basal slip system in low temperature
and affectedthe forming performance of the magnesium alloy sheet
[2].Secondary twin of magnesium alloy promotes effectively
thenucleation of recrystallization and grain refinement
signif-icant. When the driving force of recrystallization is
largeenough, the matrix will annex surrounding tensile twinning,at
the same time, and texture is induced to change. Thetexture of
matrix orientation is strengthened, and textureof tensile twinning
orientation weakened gradually [3]. Theannealing processes
operating in hot-deformed magnesiumalloy with continuous dynamic
recrystallized grain structures
can be mainly controlled by grain coarsening without
texturechange [4].The annealing texture with grown grains
retainedhot deformation texture without emerging or strengthen-ing
other components [5]. When AZ31 magnesium alloydeformed by uniaxial
compression at 400∘C and a strain rateof 0.3 s−1, many extension
twins appeared, and some of theselected twins obeyed a Schmid
factor criterion [6].The effectof grain boundary misorientation (h)
on twinning in a MgAZ31 alloy is investigated, and the results
present that twinnucleation and propagation are favored at
lowmisorientation(h), and it reveals non-Schmid effects [7].
Considering themicrostructure evolution of friction stir welding
(FSW) ofAZ91 magnesium alloy, a model is established based on
thecombination of cellular automaton, and it considered theability
of presented model in demonstrating the nucleationand grain growth
stages during dynamic recrystallization(DRX) [8]. The
recrystallization volume fraction and grainsize of martensitic
stainless steel during hot forging processof turbine blade have
been analyzed by numerical simulation,and the optimum hot forging
process for complex forgingparts was obtained [9]. Based on
measurements of deposit
Hindawi Publishing CorporationIndian Journal of Materials
ScienceVolume 2015, Article ID 897686, 6
pageshttp://dx.doi.org/10.1155/2015/897686
-
2 Indian Journal of Materials Science
50𝜇m
(a)
50𝜇m
(b)
50𝜇m
(c)
50𝜇m
(d)
50𝜇m
(e)
50𝜇m
(f)
50𝜇m
(g)
50𝜇m
(h)
Figure 1: Microstructure of AZ31 Mg alloy at different heating
temperature and holding time 45min (a, original; b, 150∘C; c,
200∘C; d, 250∘C;e, 300∘C; f, 350∘C; g, 400∘C; h, 450∘C).
50𝜇m
(a)
50𝜇m
(b)
50𝜇m
(c)
50𝜇m
(d)
Figure 2: Microstructure of AZ31 at different holding time
(heating temperature 450∘C) (a, 15min; b, 30min; c, 45min; d,
60min).
size and shape in the various experiments, a semiempiricalmodel
of 420 and 4140 steel is presented, which predicts thetrend in
deposit sizes for various processing parameters [10].
The goal of this paper is to study the variation law of
grainsize of AZ31 magnesium alloy during heating process and toput
forward the grain growthmodel ofAZ31magnesiumalloyunder the
isothermal condition. And calculation accuracy ofthe model would be
analyzed.
2. Experiments
Experiment material is AZ31 magnesium alloy sheet, and
thethickness is 7mm. Heating temperature is 150∘C–450∘C, andholding
time is 10min–60min. The test plane of microstruc-ture and grain
size is transverse direction plane (TD plane)(transverse
direction). Original microstructure of AZ31 mag-nesium alloy is
uniform and isometric crystal, shown inFigure 1(a), where the grain
size is 20.08 𝜇m. Methods formeasuring the grain size was Scanning
Electron Microscope(SEM), Transmission Electron Microscope (TEM),
and X-Ray Diffraction (XRD).
3. Experiment Results and Analysis
The microstructure of AZ31 magnesium alloy at differ-ent heating
temperature is shown in Figure 1. Originalmicrostructure of AZ31
magnesium alloy is shown in Fig-ure 1(a). When heating temperature
is less than 250∘C, grainsize grows slowly. When heating
temperature is higher than300∘C, it is obvious that the grain size
grows significantly withthe increase of heating temperature, as
seen in Figure 3(a).When heating temperature is 450∘C, the
microstructure ofAZ31 magnesium alloy at different holding time is
shown inFigure 2. It is obvious that grain size grows significantly
withthe increase of holding time, as seen in Figure 3(b).
Influence of deformation temperature and holding timeon grain
size of AZ31 magnesium alloy is shown in Fig-ure 3(a).The grain
size increased firstly and then decreased atthe temperature range
of 150–250∘C at a certain holding time.The grain grew gradually
with the increase of temperaturewhen the heating temperature is
higher than 250∘C. Whenheating temperature is lower than 200∘C, the
grain sizehad a tendency to grow, because of the twin gradually
-
Indian Journal of Materials Science 3
Gra
in si
ze (𝜇
m)
15min
30min
45min
60min
20
40
60
80
200 250 300 350 400 450150Heating temperature (∘C)
(a)
250∘C300∘C350∘C
400∘C450∘C
20
40
60
80
Gra
in si
ze (𝜇
m)
30 45 6015Holding time (min)
(b)
15min
30min
45min
60min
20
40
60
80
Gra
in si
ze (𝜇
m)
300 350 400 450250Heating temperature (∘C)
(c)
Figure 3: Effect of heating temperature and holding time on
grain size of AZ31Mg alloy (a, grain size (150–450∘C); b, grain
size versus holdingtime; c, grain size versus heating
temperature).
disappearing, recrystallization grain nucleation, large grainof
original microstructure, and fine recrystallization grain.When
heating temperature is higher than 200∘C, the rateof
recrystallization nucleation is higher than growth rate,which led
to grain size decrease after recrystallization. Whenheating
temperature is higher than 250∘C, the grain size grewquickly with
the increase of heating temperature and holdingtime.
4. Grain Growth Model
According to the relevant references, grain growth
tendencyofmagnesium alloy is in agreementwith that of
austenite.Theaustenitic grain growth model could be used to study
graingrowth tendency of magnesium alloy [11, 12]. Grain growth
model of austeniticmaterials which is proposed by Sellars
andWhiteman [13] is shown as follows:
𝑑𝑛
= 𝑑𝑛
0
+ 𝐴𝑡exp (− 𝑄𝑅𝑇) ,
𝑑 = 𝐵𝑡𝑚exp(− 𝑄
𝑅𝑇) .
(1)
In that, 𝑑 is ultimate grain size (𝜇m), 𝑑0is original grain
size
(𝜇m), 𝑇 is heating temperature (K), 𝑡 is holding time (min),R is
gas constant (8.314 J/(mol⋅K)), 𝑄 is activation energy ofgrain
growth (J/mol), and 𝐴, 𝐵, 𝑛, 𝑚 are coefficients, beingrelated to
materials, determined by test data.
According to (1), there will be obtained equation of 𝑑𝑛 +𝑑 =
𝑑
𝑛
0
+ (𝐴𝑡 + 𝐵𝑡𝑚
)exp(−𝑄/𝑅𝑇). According to experience,for AZ31 magnesium alloy,
the value of 𝑛 is greater than 1.5,
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4 Indian Journal of Materials Science
0
10y(n)
20
30
1 2 3 4 5 60n
Figure 4: Relation of sum of error’s square of 𝑄,𝑚, and 𝐴 with 𝑛
value.
15min 30min45min 60minFitting curve
4
5
6
7
1.4 1.6 2.01.81/T (10−3 K−1)
ln(d
1.683
−d1.683
0)
(a)
523K 573K
623K673K 723KFitting curve
4
5
6
7
3.0 3.5 4.02.5
ln(d
1.683
−d1.683
0)
lnt (min)
(b)
Figure 5: Relation of grain size with heating temperature and
holding time for AZ31 Mg alloy (a, with heating temperature; b,
with holdingtime).
the value of 𝑚 is greater than 1.0, the grain size is
greaterthan 2 𝜇m, and the value of 𝑡 (holding time) is greater
than15min. In order to calculate the coefficients 𝑛 and 𝑚
easily,the equation 𝑑𝑛 + 𝑑 = 𝑑𝑛
0
+ (𝐴𝑡 + 𝐵𝑡𝑚
)exp(−𝑄/𝑅𝑇) could besimplified as (2). A new type model of grain
growth of AZ31magnesium alloy had been put forward, shown as
follows:
𝑑𝑛
= 𝑑𝑛
0
+ 𝐴𝑡𝑚exp(− 𝑄
𝑅𝑇) . (2)
In that, coefficients (𝐴,𝑄, 𝑛,𝑚) cannot be determined bylinear
regression method. Coefficients (𝐴,𝑄, 𝑛,𝑚) are deter-mined in the
following steps:
(1) Given 𝑛 value (𝑛 = 0.25, 0.50, 1.0, 1.5, 2.0, 2.5, . .
.),coefficients (𝐴,𝑄,𝑚) could be determined by test data andeach 𝑛
value.
(2) For given 𝑛 value (e.g., 𝑛 = 0.25), when holding time(𝑡) is
constant, according to (2),𝑄 value could be determinedby
𝑄 = −𝑅 ⋅𝜕 [ln (𝑑𝑛 − 𝑑𝑛
0
)]
𝜕 (1/𝑇)
𝑡
= −𝑅𝑘. (3)
In that, 𝑘 = (𝜕[ln(𝑑𝑛 − 𝑑𝑛0
)]/𝜕(1/𝑇))|𝑡. According to the
test data presented by Figure 3(c), curves of ln(𝑑𝑛 − 𝑑𝑛0
)
and 1/𝑇 could be drawn at different heating temperature,similar
to Figure 5(a), and the gradient of the curve isthe value 𝑘. Then
the value 𝑄 could be determined by(3).
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Indian Journal of Materials Science 5
Expe
rimen
tald
e(𝜇
m)
20
40
60
80
40 60 8020Calculated dc (𝜇m)
(a)
CalculatedExperimental
15
20
25
30
35
40
45
Gra
in si
ze (𝜇
m)
300 350 400 450250Heat temperature (∘C)
(b)
CalculatedExperimental
15
20
25
30
35
40
45
Gra
in si
ze (𝜇
m)
30 45 6015Holding time (min)
(c)
Figure 6: Comparison of calculated and experimental results
(𝑑𝑐
, calculated results; 𝑑𝑒
, experimental results) (a, experiment results versuscalculated
results; b, different heating temperature, holding time 15min; c,
heating temperature 300∘C, different holding time).
(3) When heating temperature (𝑇) is constant, accordingto (2),𝑚
value could be determined by
𝑚 =𝜕 [ln (𝑑𝑛 − 𝑑𝑛
0
)]
𝜕 (ln𝑡)
𝑇
. (4)
According to the test data presented in Figure 3(b), curves
ofln(𝑑𝑛 − 𝑑𝑛
0
) and ln𝑡 could be drawn at different holding time,similar to
Figure 5(b), and the gradient of the curve is thevalue 𝑚. According
to the value of 𝑛, 𝑄, and 𝑚, the value of𝐴 could be calculated by
(2).
Corresponding to each 𝑛 value, the sum of relative errorsquare
between the values of 𝑄, 𝑚, and 𝐴 and the average
value of them is objective function (𝑦(𝑛)). The curve of
𝑦(𝑛)versus 𝑛 could be drawn, as seen in Figure 4. The equationof
𝑦(𝑛) could be obtained, as seen in (5). When 𝑦(𝑛) isminimum, then 𝑛
value is the optimization value.Theoptimalvalue of 𝑛 is 1.683:𝑦 (𝑛)
= 17.67891 − 24.01221𝑛 + 11.74168𝑛
2
− 2.11678𝑛3
+ 0.12054𝑛4
+ 0.00699𝑛5
.
(5)
When 𝑛 is 1.683, the curves of ln(𝑑𝑛 − 𝑑𝑛0
) and 1/𝑇 couldbe drawn at different heating temperatures, as
shown inFigure 5(a). The curves of ln(𝑑𝑛 −𝑑𝑛
0
) and ln𝑡 could be drawnat different heating temperatures, as
shown in Figure 5(b).
-
6 Indian Journal of Materials Science
According to (2)–(4), the values of 𝑄 and𝑚 and 𝐴 should
becalculated accurately.The results are that𝑄 is 33112 J/mol,𝑚is
1.030, and𝐴 is 3766.978.The linear correlation coefficient
is97.181%–99.585%. Under the isothermal condition, the graingrowth
model of AZ31 magnesium alloy is shown as follows:
𝑑1.683
= 20.081.683
+ 3766.978𝑡1.03exp(−33112.185
𝑅𝑇) . (6)
Comparison of calculated and experimental results is shownin
Figure 6(a). Relative error between model calculation
andexperimental results is less than 19.07%. When holding timeis
15min, comparison of calculated and experimental resultsis shown in
Figure 6(b). Relative error between model cal-culation and
experimental results is less than 11.05%. Whenheating temperature
is 300∘C, comparison of calculated andexperimental results is shown
in Figure 6(c). Relative errorbetween model calculation and
experimental results is lessthan 10.00%.
5. Conclusions
(1) The grain size tends to grow up with the increase ofholding
time at a certain temperature. The grain sizeincreased firstly and
then decreased at the temper-ature range of 150–250∘C at a certain
holding time.The grain grows up gradually with the increase
oftemperature when the heating temperature is higherthan 250∘C.
(2) For AZ31 magnesium alloy sheet, activation energy ofgrain
growth (𝑄) is 33112 J/mol. Under the conditionof isothermal, grain
growth model of AZ31 magne-sium alloy had been put forward.
(3) The grain growth model of AZ31 Mg alloy has beenestablished
by regression based on the experimentaldata at temperature range of
250–450∘C. The relativeerror between model calculation and
experimentalresults is less than 19.07%.
Conflict of Interests
The authors declare that there is no conflict of
interestsregarding the publication of this paper.
Acknowledgments
This project is supported by National Natural Science
Foun-dation of China (Grant no. 51575366) and the Science
andTechnology Bureau of Shenyang City (F14-231-1-32).
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