Microstructure Evolution and Grain Growth Model of AZ 31 Magnesium Alloy under Condition of Isothermal

Microstructure evolution of AZ31 magnesium alloy in annealing process had been investigated by experiment study at heating temperature range of 150C–450C and holding time range of 15min–60min. The effects of heating temperature and holding time on grain growth had been analyzed. The results presented that the grain size tends to grow up with the increase of holding time at a certain temperature. At a certain holding time, the grain size increased firstly and then decreased at the heating temperature range of 150–250C. And when heating temperature is higher than 250C, the grain grows up gradually with the increase of heating temperature. The grain growth model of AZ31 Mg alloy has been established by regression based on the experimental data at temperature of 250–450C, 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.


Introduction
Deformation mechanism of magnesium alloy sheet is glide in base surface and twin in taper surface.The important contribution of twin deformation to plastic deformation is to change the grain orientation and is advantageous to start nonbasal slip system and improve the capability of plastic deformation [1].With rolling deformation at low temperature of magnesium alloy sheet, a very high intensity of basal texture formed in the rolling direction.The texture hindered starting the basal slip system in low temperature and affected the forming performance of the magnesium alloy sheet [2].Secondary twin of magnesium alloy promotes effectively the nucleation of recrystallization and grain refinement significant.When the driving force of recrystallization is large enough, the matrix will annex surrounding tensile twinning, at the same time, and texture is induced to change.The texture of matrix orientation is strengthened, and texture of tensile twinning orientation weakened gradually [3].The annealing processes operating in hot-deformed magnesium alloy with continuous dynamic recrystallized grain structures can be mainly controlled by grain coarsening without texture change [4].The annealing texture with grown grains retained hot deformation texture without emerging or strengthening other components [5].When AZ31 magnesium alloy deformed by uniaxial compression at 400 ∘ C and a strain rate of 0.3 s −1 , many extension twins appeared, and some of the selected twins obeyed a Schmid factor criterion [6].The effect of grain boundary misorientation (h) on twinning in a Mg AZ31 alloy is investigated, and the results present that twin nucleation and propagation are favored at low misorientation (h), and it reveals non-Schmid effects [7].Considering the microstructure evolution of friction stir welding (FSW) of AZ91 magnesium alloy, a model is established based on the combination of cellular automaton, and it considered the ability of presented model in demonstrating the nucleation and grain growth stages during dynamic recrystallization (DRX) [8].The recrystallization volume fraction and grain size of martensitic stainless steel during hot forging process of turbine blade have been analyzed by numerical simulation, and the optimum hot forging process for complex forging parts was obtained [9].Based on measurements of deposit  size and shape in the various experiments, a semiempirical model of 420 and 4140 steel is presented, which predicts the trend in deposit sizes for various processing parameters [10].
The goal of this paper is to study the variation law of grain size of AZ31 magnesium alloy during heating process and to put forward the grain growth model of AZ31 magnesium alloy under the isothermal condition.And calculation accuracy of the model would be analyzed.

Experiments
Experiment material is AZ31 magnesium alloy sheet, and the thickness is 7 mm.Heating temperature is 150 ∘ C-450 ∘ C, and holding time is 10 min-60 min.The test plane of microstructure and grain size is transverse direction plane (TD plane) (transverse direction).Original microstructure of AZ31 magnesium alloy is uniform and isometric crystal, shown in Figure 1(a), where the grain size is 20.08 m.Methods for measuring the grain size was Scanning Electron Microscope (SEM), Transmission Electron Microscope (TEM), and X-Ray Diffraction (XRD).

Experiment Results and Analysis
The microstructure of AZ31 magnesium alloy at different heating temperature is shown in Figure 1.Original microstructure of AZ31 magnesium alloy is shown in Figure 1(a).When heating temperature is less than 250 ∘ C, grain size grows slowly.When heating temperature is higher than 300 ∘ C, it is obvious that the grain size grows significantly with the increase of heating temperature, as seen in Figure 3(a).When heating temperature is 450 ∘ C, the microstructure of AZ31 magnesium alloy at different holding time is shown in Figure 2. It is obvious that grain size grows significantly with the increase of holding time, as seen in Figure 3(b).
Influence of deformation temperature and holding time on grain size of AZ31 magnesium alloy is shown in disappearing, recrystallization grain nucleation, large grain of original microstructure, and fine recrystallization grain.When heating temperature is higher than 200 ∘ C, the rate of recrystallization nucleation is higher than growth rate, which led to grain size decrease after recrystallization.When heating temperature is higher than 250 ∘ C, the grain size grew quickly with the increase of heating temperature and holding time.

Grain Growth Model
According to the relevant references, grain growth tendency of magnesium alloy is in agreement with that of austenite.The austenitic grain growth model could be used to study grain growth tendency of magnesium alloy [11,12].Grain growth model of austenitic materials which is proposed by Sellars and Whiteman [13] is shown as follows: In that,  is ultimate grain size (m),  0 is original grain size (m),  is heating temperature (K),  is holding time (min), R is gas constant (8.314J/(mol⋅K)),  is activation energy of grain growth (J/mol), and , , ,  are coefficients, being related to materials, determined by test data.
According to (1), there will be obtained equation of   +  =   0 + ( +   )exp(−/).According to experience, for AZ31 magnesium alloy, the value of  is greater than 1.5, Indian Journal of Materials Science the value of  is greater than 1.0, the grain size is greater than 2 m, and the value of  (holding time) is greater than 15 min.In order to calculate the coefficients  and  easily, the equation   +  =   0 + ( +   )exp(−/) could be simplified as (2).A new type model of grain growth of AZ31 magnesium alloy had been put forward, shown as follows: In that, coefficients (, , , ) cannot be determined by linear regression method.Coefficients (, , , ) are determined in the following steps: (1) Given  value ( = 0.25, 0.50, 1.0, 1.5, 2.0, 2.5, . ..), coefficients (, , ) could be determined by test data and each  value.
(2) For given  value (e.g.,  = 0.25), when holding time () is constant, according to (2),  value could be determined by In that,  = ([ln(  −   0 )]/(1/))|  .According to the test data presented by Figure 3(c), curves of ln(  −   0 ) and 1/ could be drawn at different heating temperature, similar to Figure 5(a), and the gradient of the curve is the value .Then the value  could be determined by (3).
According to the test data presented in Figure 3(b), curves of ln(  −   0 ) and ln could be drawn at different holding time, similar to Figure 5(b), and the gradient of the curve is the value .According to the value of , , and , the value of  could be calculated by (2).
Corresponding to each  value, the sum of relative error square between the values of , , and  and the average value of them is objective function (()).The curve of () versus  could be drawn, as seen in Figure 4.The equation of () could be obtained, as seen in (5).When () is minimum, then  value is the optimization value.The optimal value of  is 1.683:  () = 17.67891 − 24.01221 + 11.74168 2 − 2.11678 3 + 0.12054 4 + 0.00699 5 . (5) When  is 1.683, the curves of ln(  −   0 ) and 1/ could be drawn at different heating temperatures, as shown in Figure 5(a).The curves of ln(  −   0 ) and ln could be drawn at different heating temperatures, as shown in Figure 5(b).

Indian Journal of Materials Science
According to (2)-( 4), the values of  and  and  should be calculated accurately.The results are that  is 33112 J/mol,  is 1.030, and  is 3766.978.The linear correlation coefficient is 97.181%-99.585%.Under the isothermal condition, the grain growth model of AZ31 magnesium alloy is shown as follows:  1.683 = 20.08 1.683 + 3766.978

Conclusions
(1) The grain size tends to grow up with the increase of holding time at a certain temperature.The grain size increased firstly and then decreased at the temperature range of 150-250 ∘ C at a certain holding time.
The grain grows up gradually with the increase of temperature when the heating temperature is higher than 250 ∘ C.
(2) For AZ31 magnesium alloy sheet, activation energy of grain growth () is 33112 J/mol.Under the condition of isothermal, grain growth model of AZ31 magnesium alloy had been put forward.
(3) The grain growth model of AZ31 Mg alloy has been established by regression based on the experimental data at temperature range of 250-450 ∘ C. The relative error between model calculation and experimental results is less than 19.07%.

Figure 3 :
Figure 3: Effect of heating temperature and holding time on grain size of AZ31 Mg alloy (a, grain size (150-450 ∘ C); b, grain size versus holding time; c, grain size versus heating temperature).

Figure 4 :Figure 5 :
Figure 4: Relation of sum of error's square of , , and  with  value.

Figure 6 :
Figure 6: Comparison of calculated and experimental results (  , calculated results;   , experimental results) (a, experiment results versus calculated results; b, different heating temperature, holding time 15 min; c, heating temperature 300 ∘ C, different holding time).
Relative error between model calculation and experimental results is less than 11.05%.When heating temperature is 300 ∘ C, comparison of calculated and experimental results is shown in Figure6(c).Relative error between model calculation and experimental results is less than 10.00%.