Research Article Microstructure Evolution and Grain Growth ...Research Article Microstructure...

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,


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).

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).


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).

References

[1] G. Chen, C. Yang, and C. Huang, “Investigation of the twinningin plastic deformation of magnesium alloy,” Materials Review,vol. 20, no. 8, pp. 107–114, 2006 (Chinese).

[2] P. Yang, Y. Hu, and F. Cui, “Texture investigation on thedeformation mechanisms in magnesium alloy AZ31 deformedat high temperature,” Chinese Journal of Materials Research, vol.18, no. 1, pp. 52–59, 2004 (Chinese).

[3] Z. Zeng, Y. C. Xin, and M. Y. Wang, “Influence of twin types onstatic recrystallization of AZ31 magnesium alloy,” Transactionsof Materials and Heat Treatment, vol. 33, no. 8, pp. 33–38, 2011(Chinese).

[4] X. Y. Yang, Y. K. Zhu, H. Miura, and T. Sakai, “Staticrecrystallization behavior of hot-deformed magnesium alloyAZ31 during isothermal annealing,” Transactions of NonferrousMetals Society of China, vol. 20, no. 7, pp. 1269–1274, 2010.

[5] S. Abdessameud, H. Azzeddine, B. Alili, and D. Bradai, “Graingrowth in AZ31 alloy after uniaxial compression,” Transactionsof Nonferrous Metals Society of China (English Edition), vol. 20,no. 12, pp. 2215–2222, 2010.

[6] X. Liu, J. J. Jonas, B. W. Zhu et al., “Variant selection ofprimary extension twins in AZ31 magnesium deformed at400∘C,”Materials Science&EngineeringA, vol. 649, pp. 461–467,2016.

[7] A. Fernández, A. Jérusalem, I. Gutiérrez-Urrutia, and M.T. Pérez-Prado, “Three-dimensional investigation of grainboundary-twin interactions in a Mg AZ31 alloy by electronbackscatter diffraction and continuum modeling,” Acta Mate-rialia, vol. 61, no. 20, pp. 7679–7692, 2013.

[8] P. Asadi, M. K. Besharati Givi, and M. Akbari, “Simulation ofdynamic recrystallization process during friction stir welding ofAZ91 magnesium alloy,” The International Journal of AdvancedManufacturing Technology, 2015.

[9] F. Chen, F. Ren, J. Chen, Z. Cui, and H. Ou, “Microstructuralmodeling and numerical simulation of multi-physical fields formartensitic stainless steel during hot forging process of turbineblade,” The International Journal of Advanced ManufacturingTechnology, 2015.

[10] J. B. Ferguson, B. F. Schultz, A. D.Moghadam, and P. K. Rohatgi,“Semi-empirical model of deposit size and porosity in 420stainless steel and 4140 steel using laser engineered net shaping,”Journal of Manufacturing Processes, vol. 19, pp. 163–170, 2015.

[11] C. J. Simpson, K. T. Aust, andW. C. Winegard, “The four stagesof grain growth,” Metallurgical Transactions, vol. 2, no. 4, pp.987–991, 1971.

[12] G. F. Bolling and W. C. Winegard, “Some effects of impuritieson grain growth in zone-refined lead,” Acta Metallurgica, vol. 6,no. 4, pp. 288–292, 1958.

[13] C. M. Sellars and J. A. Whiteman, “Recrystallization and graingrowth in hot rolling,”Metal Science, vol. 13, no. 3-4, pp. 187–194,1978.

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