Formation mechanism of large grains inside annealed microstructure of GH4169 superalloy by cellular automation method

1. Introduction

Because of their good corrosion, fatigue resistance and prominent high-temperature characteristics, Ni-based superalloys are the desired materials of some key components in energy and aerospace industries [1]. In order to make the thermal forming process, it is necessary to study the hot deformation behaviors of materials [2]. Therefore, a lot of studies have been done on the hot deformation behaviors and microstructural evolutions of some Ni-based superalloys, such as Ni-20.0 Cr-2.5 Ti-1.5 Nb-1.0 Al alloy [3], Ni-20.0 Cr-2.5 Ti-1.5 Nb-1.0 Al superalloy [4], Ni-42.5 Ti-3Cu alloy [5], Alloy 617 [6], Nimonic 263 alloy [7], W-S-W superalloy [8], Nimonic 80 A [9], C276 [10], X-750 [11], Inconel 600 [12], Inconel 625 [13], Incoloy 901 [14], GH738 [15], K417 G [16], GH4698 [17] and GH4169 (Inconel 718) [18,19]. Among the above typical superalloys, GH4169 superalloy is the most widely used one. The flow behaviors of GH4169 superalloy were widely investigated by Lin et al. [18,19]. To obtain the optimal processing parameters, the processing maps of this superalloy were established by Wen et al. [20] and He et al. [21]. Chen et al. [22] studied the deformation characteristics of superalloy IN718 by developing a new flow stress model, and the intrinsic workability was evaluated through the generation of three-dimensional (3D) processing maps. In addition, the dynamc recrystallization (DRX) behavior of GH4169 superalloy was also investigated by Chen et al. [23,24], and an improved DRX kinetics model was established. It was found that the complete DRX needs relatively large strains for the material. Therefore, the mixed grains are easily obtained due to incompletely DRX for hot die forgings. The mixed grains inside forgings seriously deteriorate the mechanical properties. Therefore, they need to be eliminated. In authors’ previous work [25], it was found that the heterogeneous deformed microstructure was replaced by the relatively homogeneous recrystallized grains through an annealing treatment at the temperature of 980 °C and time of 10 min for a pre-participated GH4169 superalloy. However, there are still some relatively large grains in the annealed microstructures. Moreover, the mechanisms for the formation of coarse grains are still unclear.

The cellular automation (CA) model is an efficient tool to study the recrystallization behavior of alloys [26,27]. Up to now, many studies on the recrystallization behaviors have been done by CA method. Svyetlichnyy [28] presented a three-dimensional frontal cellular automaton (FCA)-based model for modelling microstructural evolution. Meanwhile, Svyetlichnyy [29] established a 3D CA model to simulate the grain refinement. A 3D cellular automaton model for dendritic growth in multi-component alloys was developed by Zhang et al. [30]. Goetz et al. [31,32] developed a CA model to accurately describe the microstructural evolution in a single-phase alloy. Timoshenkov et al. [33] and Chen et al. [34] established different CA models to study the DRX behavior of C-Mn micro-alloyed steel and AZ31B magnesium alloy, respectively. Chen et al. [35] simulated the microstructural evolution and plastic flow characteristics of a Ni-based superalloy by coupling the DRX with the two-dimensional (2D) cellular automaton (CA). Salehi et al. [36] evaluated the static recrystallization kinetics of steels through a coupled CA model. Li et al. [37] investigated the recrystallization behavior of a nickel-based superalloy by CA method, and found that there is a significant difference in the kinetics of recrystallization between the dendritic arms and interdendritic regions. Schäfer et al. [38] established a CA model to predict the microstructure, texture and kinetics during non-isothermal heat treatments. Han et al. [39,40] simulated the grain growth behavior by CA method. In addition, Zheng et al. [41,42] established a CA model to simulate the phase transformation behavior in a cold-rolled dual-phase steel during intercritical annealing. Li et al. [43] and Song et al. [44] simulated the phase transformation from β to αin TA15 alloy by CA method. The 2D CA models are simple and less time consuming. Microstructural evolution is the three-dimensional problem and the results obtained by 2D CA cannot always be directly transferred to a real 3D process. However, the 3D models require significantly more memory and time for the calculation [45].

In the study, some new annealing experiments to hot deformed specimens were firstly done to study the microstructural evolution of GH4169 superalloy during annealing treatment. Then, a CA model was established to further investigate the mechanisms of grain evolution.

2. Materials and experiments

A commercial GH4169 superalloy was used. The size of specimens is Ø10 mm × 15 mm. Before testing, all the specimens were solution-treated (T = 1040 °C, t = 0.75 h). Moreover, some of the solution treated specimens were aged at 900 °C for 12 h or 24 h and then quenched in water again to obtain different contents of δ phase (V_δ). The values of V_δ for aged 12 h and 24 h are 12.75% and 16.69%, respectively. The detailed experimental scheme is shown in Fig. 1. The other details of the experiments can be found in Ref. [25].

3. Experimental results and discussion

Fig. 2(a) shows the typical microstructure of GH4169 superalloy after hot deformation (V_δ is 16.69%, aged 24 h). The grain size is heterogeneous due to the incomplete DRX. Obviously, it needs a larger strain to obtain a complete DRX, which is often difficult to achieve in die forging. This is because the deformation is seriously uneven for most of forgings. For some regions with large strain, the DRX fraction may be 100%, and the initial coarse grains were replaced by small DRX grains. However, the DRX fraction in the regions with small strain will be far less than 100%, just like the microstructure shown in Fig. 2(a). Therefore, it is so important to make these mixed grains become fine grains through an annealing treatment. Fig. 2(b, c and d) displays the annealed microstructures of deformed specimens for which the annealing temperature is 980 °C and the holding time is 10 min. The difference between them is the initial V_δ in matrix. The initial V_δ for Fig. 2(b, c and d) is 0% (solution treated), 12.75% (aged 12 h) and 16.69% (aged 24 h), respectively. From Fig. 2(b, c and d), it can be found that the deformed mixed grains were fully replaced by recrystallization grains for all cases. Moreover, the effect of initial V_δ on annealing recrystallization is large. From Fig. 2(b), it can be found that the sizes of recrystallized grains are very large. The size of recrystallized grains decreases with the increase of V_δ, as shown in Fig. 2(c). Moreover, the grains obviously become fine when the initial V_δ is increased to 16.69%, as shown in Fig. 2(d) [25]. It indicates that the annealing treatment can effectively refine the deformed mixed grains when an appropriate annealing parameter is applied.

From Fig. 2(d), a phenomenon can be found that the grain size is different in different regions. In some regions, the grain size is relatively large and about 20-35 μm, while in some regions the grains are very fine, as shown in Fig. 3. It is a strange phenomenon. It would be so good if all grains were refined just like the regions with fine grains. To achieve the goal, it is necessary to understand the annealing recrystallization behavior firstly, especially the reasons for the formation of coarse grains. In this study, the CA simulations were carried out to analyze annealing recrystallization behavior. Compared to the traditional CA model, the effects of δ phase on the annealing recrystallization need to be considered. The development of CA model will be discussed in detail in Section 4.

4. Establishment of CA model

4.1. Dissolution kinetics of δ phase in GH4169 superalloy during annealing

To understand the effects of δ phase on the annealing recrystallization, it is necessary to establish the dissolution kinetics of δ phase during annealing treatment. The fraction of δ phase is closely related to the annealing time (t) and temperature (T). Therefore, the kinetic model can be expressed as:

V_s=V_r(1-exp(-αtⁿ)) (1)

where V_r and V_s are the volume fraction of δ phase before and after annealing treatment, respectively; α and n are the material constants associated with annealing temperature; t is the annealing time (unit: min).

Therefore, the volume fraction of δ phase dissolved during annealing treatment (X_δ) can be calculated as:

X_δ=1-$\frac{V_{s}}{V_{r}}$ (2)

Eq. (1) can be changed as:

ln(-ln(1-$\frac{V_{s}}{V_{r}}$))=nlnt+lnα (3)

Eq. (4) can be obtained by plugging Eq. (2) into Eq. (3):

ln(-lnX_δ)=nlnt+lnα (4)

To obtain the values of α and n, the microstructures of annealing samples with different annealing time at different temperatures were observed, and X_δ were obtained by statistics. The values of α and n were obtained by the linear fitting method, as listed in Table 1.

4.2. Nucleation of annealing recrystallization

The process of annealing recrystallization includes the nucleation and grain growth. There are a large number of fine subgrains after deformation. These subgrains may grow in the subsequent annealing process, and will become the recrystallization nucleus if their sizes are large enough to overcome the capillary pressure [46]. Because the sizes of subgrains are smaller than that of CA cell, it is impossible to simulate the real nucleation process [47]. Therefore, the nucleation rate used in the CA model is constant. According to the experimental results, the values of nucleation rate at different deformation conditions were determined.

4.3. Growth of grains

The migration of grain boundaries is the main growth way of grain nuclei during annealing treatment. The velocity of grain boundary migration (V^s) is in direct proportion to the driving pressure (Ps) [48]:

V^s=M^sP^s (5)

where M^s is the recrystallized grain boundary migration rate related to the grain boundary misorientation (θ). It can be expressed as [49]:

M^s=M₀(1-exp(-5$(\frac{θ}{θ_{0}})^{4}$)) (6)

where M₀represents the mobility of high-angle boundaries, θ0is the critical value to define the types of grain boundaries, and θ₀=15o.

The grain boundary migration is essentially a thermal diffusion process. For pure metals, M0can be expressed as [50]:

M₀=$\frac{D}{kT}$ (7)

where Tis the deformation temperature (K), k is the Boltzmann's constant, D is the grain boundary diffusion factor, andD=hD_0bexp($\frac{-Q_{b}}{RT}$), in which h represents the thickness of grain boundary, D0bis the self-diffusion coefficient of grain boundary, R is the ideal gas constant,Q_b is the activation energy for grain boundary diffusion.

For alloys, the solute drag effect produced by the solute elements should be taken into account. Therefore, M₀ for alloys should be expressed as [51]:

M₀=$\frac{D}{kT\Gamma}$ (8)

where Γis the value of dissolved atoms per unit area of grain boundaries. Γ can be calculated by:

$\Gamma=\frac{4\sqrt{2}C_{s}}{a^{2}}exp(\frac{E}{RT})$ (9)

where a represents the lattice parameter,C_s is the concentration of solute atoms, E is the binding energy between solute elements and grain boundary. Therefore, M₀ can be represented as:

M₀=$\frac{a}{4\sqrt{2}C_{s}}\frac{hD_{0b}}{kT}exp(\frac{-(Q_{b}+E)}{RT})$ (10)

For the studied alloy, according to the existing research [27], the values of M₀at different temperatures are listed in Table 2.

The content of solute element changes during annealing treatment because of the change of solute drag effect resulted from the dissolution of δ phase. The content of solute element increases with the decrease in V_δ. Therefore, the drag effect becomes strong with the decreasingV_δ. Thus, the correction of grain boundary migration rate is achieved by adding a correction coefficient (f₁(V_δ)) related toV_δ. Therefore, M^scan be expressed as:

M^s=(1+f₁(V_δ))M₀(1-exp(-5$(\frac{θ}{θ_{0}})^{4}$)) (11)

Generally, the driving pressure (P^s) is mainly provided by the grain boundary and stored energy. The stored energy refers to the energy generated by the accumulation of dislocations near the grain boundaries, while the other is the energy of dislocation, which is a part of the grain boundaries [52].

The relationship between the driving pressure ($P^{s}_{S}$) provided by the stored energy and the dislocations density difference on the both sides of grain boundary (Δρ) can be expressed as [53]:

$P^{s}_{S}$ =τΔρ (12)

where τis the dislocation line energy, andτ=0.5μb². μandbrepresent the shear modulus and the Burger's vector, respectively.

The other driving pressure ($P^{s}_{G}$) is the product of grain boundary curvature (κ) and grain boundary energy (γ), and can be expressed as [54]:

$P^{s}_{G}$=γκ (13)

γ can be calculated by [55]:

$γ=\begin{cases}γ_{0}& \text θ≥θ_{0}\\γ_{0}\frac{θ}{θ_{0}}(1-ln(\frac{θ}{θ_{0}}))& \text θ＜θ_{0}\end{cases}$(14)

where γ₀ is the high-angle boundary energy which can be calculated by [56]:

γ₀= $\frac{μbθ_{0}}{4π(1-ν)}$ (15)

where νis the Poisson ratio.

κcan be approximated by [57],

κ=$\frac{C_{k}}{C_{d}}\frac{Kink-N^{k}_{i}}{N^{k}+1}$ (16)

where C_dis the size of cell, Cd=2 μm,C_kis a topological parameter, C_k=1.28. $N^{k}_{i}$ the number of cell of which the state is the same as that of central cell i in the statistical area. N^kis the number of neighboring cells that include both first and second one, and N=24. Kinkis the number of the cells of which the state is the same as those of central cell i in the statistical area while the grain boundary is straight. The difference between $N^{k}_{i}$ and Kink represents the degree to which the current grain boundary deviates from the straight grain boundary.

The second phases have different influences on recrystallization according to their sizes [58,59]. For the second phases with large size, the high dislocation density around them can promote the nucleation of recrystallized grains. While the fine second phases will limit the growth of grains. The pinning effects of δ phase on the migration of grain boundaries can be expressed as [60]:

P_z=$\frac{3V_{d}γ}{2d_{δ}}$ (17)

where d_δis the equivalent radius of δ phase.

Therefore, the driving pressure of aged GH4169 superalloy (P^s) can be evaluated by Eq. (18) or (19) according to its neighboring cells, respectively.

P^s=$P^{s}_{S}$-P_z=τΔρ-$\frac{3V_{d}γ}{2d_{δ}}$ (18)

P^s=$P^{s}_{G}$-P_z=$\frac{3V_{d}γ}{2d_{δ}}$ (19)

4.4. Nucleation rate of aged GH4169 superalloy

The nucleation rate of solution-treated GH4169 superalloy can be described by [61]:

$\dot{N}^{s}$=$C^{s}_{1}$(G-G₀)^{$C^{s}_{2}$}exp($\frac{Q^{s}_{n}}{RT}$) (20)

where $C^{s}_{1}$, $C^{s}_{2}$ and $ Q^{s}_{n}$ represent the material parameters, G represents the stored energy induced by deformation, andG=τρ₁, G0is the energy needed for the start of annealing recrystallization. For the studied alloy, according to the existing research [27], the material parameters in Eq. (20) are 994, 5.42 and 669,289 J/mol, respectively. Considering the accelerating effects of δ phase on the nucleation, the nucleation rate of aged GH4169 superalloy can be described by:

$\dot{N}^{s}$=(1+f₂(V_δ)) $C^{s}_{1}$ (G-G₀)^{$C^{s}_{2}$}exp($\frac{Q^{s}_{n}}{RT}$) (21)

where f₂(V_δ)is the correction coefficient related to V_δ.

4.5. Procedures of simulation

The CA method can describe a physical system through dispersing the time and space [62]. The space is discretized into cells which have a group of state variables. The states of cell i at timet+Δt can be expressed as:

S^t+Δt(i)=f(S^t(i),S^t(N(i))) (22)

where f represents the transform rules, Δt is the time step, S^t(N(i)) is the states of neighboring cells at time t,S^t+Δt(i) and S^t(i)represent the states of cell iat time t+Δt andt, respectively.

In this paper, According to Kugler’s method [63], the time step is defined as the ratio between the cell size and maximum migration speed of grain boundary. The time step (Δt) can be calculated as$Δt=\frac{C_{d}}{V_{max}}=\frac{C_{d}}{MτΔρ}$. The value used in the simulation should be less than it. The relationship between the flow stress and dislocation density can be expressed by Eq. (23). For the newly-created grain nucleus, the dislocation density reduces from an initial value ρ_I to a lower valueρ_y. The dislocation densities ρ_y and ρ_I can be calculated from the measured yield stress (σ_y) and the stress before unloading (σ_I), respectively.

$σ=αμb\sqrt{ρ}$ (23)

where αis material constant, μis shear modulus and b is the distance between adjacent atoms in the slip direction.

The simulations were carried out in a grid with 460 × 460 square cells. There are six state variables in each cell, i.e., the precipitated phase state, recrystallization number, grain orientation, grain number, distance variable and dislocation density variable. The precipitated phase state variable is used to distinguish the precipitated phase from the matrix. In this simulation, 0 represents the matrix cell while 1 denotes δ phase. The explanation for the others state variable can be found in Ref. [27]. The nucleation of static recrystallization is assumed to occur on grain or phase boundaries. In each time step, the number of grain nuclei ($N^{s}_{n}$) can be obtained by calculating the product of $\dot{N}^{s}$, Δt and the total area of grain and phase boundaries (S). The probability for nucleation ($P^{s}_{n}$) was obtained by $P^{s}_{n}= N^{s}_{n}/ N^{s}_{pg}. N^{s}_{pg}$ represents the number of cells belong to the phase and grain boundaries. The selected cell will be treated as a recrystallized grain nucleus if $P^{s}_{n}$ is larger than the random number created by computer. Once the nucleation is successful, the dislocation density of the selected cell reduces to a lower value. For a cell located on the phase or grain boundaries, if all the neighboring cells represent recrystallization grains, the driving pressure $P^{s}_{G}$ takes effect; otherwise, the driving pressure $P^{s}_{S}$ takes effect.

5. CA simulation results and discussion

5.1. Determination of the correction coefficient of the nucleation rate and migration rate of grain boundary

The correction coefficients f1(V_δ) and f2(V_δ) represent the effect of δ phase on the recrystallized grain boundary migration rate and nucleation rate, respectively. In the study, it is assumed that the relationship between the correction coefficients and Vδis linear to simplify the simulation, i.e. f₁(V_δ)=k₁ V_δ and f₂(V_δ)=k₂ V_δ. The values of k₁ and k₂ were obtained by reiterative testing and modification. It is found that the errors between the experimental and simulated average grain sizes are relatively small when f₁(V_δ)=0.3 V_δand f₂(V_δ)=5 V_δ, as shown in Fig. 4. The average absolute relative error (AARE) is calculated by Eq. (24). AARE is 5.82%. This indicates that there is a small error between the experimental and simulated average grain sizes.

AARE(%)=$\frac{1}{N}\sum_{i=1}^{N}|\frac{E_{i}-P_{i}}{E_{i}}|$×100 (24)

where E_i and P_i are the experimental and simulated average grain sizes, respectively. N is the number of average grain sizes samples.

Then, that f₁(V_δ)=0.3 V_δand f₂(V_δ)=5V_δwere used in the CA simulation. Fig. 5 illustrates the experimental and simulated microstructures at different annealing conditions. It can be found that CA simulation can well reproduce the experimental results, which furtherly verify the reliability of the parameters of CA model. In addition, it can be found that there is a large difference in microstructures between the specimens with different annealing parameters. As shown in Fig. 5(a, b and g), the final average grain size increases with the increase of annealing temperature. This is because the migration of grain boundaries increases with increasing temperature. By comparing to the Fig. 5(e, k and l), it is found that the grain size for the specimen without aging is much larger than those with aging. This is because δ phase promotes the recrystallization nucleation by increasing possible sites, and provides a pinning effect on the growth of grains.

5.2. Evolution of average dislocation density in annealing process

Fig. 6 shows the evolution of average dislocation density ($\bar{ρ}$) in annealing process with different pre-deformations. It can be found that the value of $\bar{ρ}$decreases rapidly at the beginning of annealing. This is because a lot of SRX nuclei were produced near the initial gain boundaries when the dislocation density (ρ) exceeds a critical value for nucleation (ρ0), which consumes lots of dislocations. The relationship between the flow stress and dislocation density can be expressed by Eq. (23). The critical stress for DRX nucleation can be obtained from the stress-strain curve. Then the critical dislocation density for DRX nucleation (ρ0) can be calculated. In addition, the growth of DRX nuclei and grains also results in the decrease of dislocation density [35]. However, it is found that there is no significant change in the drop rate of $\bar{ρ}$ when its value is lower thanρ0. This is because there are a lot of unstable recrystallized grains which consume a large amount of dislocations in the process of growth. But the change of $\bar{ρ}$ becomes slower and slower as the annealing time further increases, and the value of $\bar{ρ}$ tends to a constant when the annealing time is large. In addition, it can be found from Fig. 6 that the time for $\bar{ρ}$ decreasing to ρ0 is 385 s in the case that the true strain is 0.69. However, there are still some initial grains at the time (the white grain in Fig. 7). All the initial grains were replaced by recrystallized one at the time of 600 s. The sizes of grains become uniform, but the average grain size increases. The change rate of $\bar{ρ}$ sharply decreases at the annealing time of 600 s. It indicates that the difference of dislocation density becomes small. The driving pressure ($P^{s}_{G}$) will play a major role in the grain growth after the time. Compared to Han’ work [39] in which only the curvature driven subgrain growth mechanism was considered during SRX, two driving pressures ($P^{s}_{S}$ and $P^{s}_{G}$) for the grain growth are considered in this study. It is because there is still some deformation energy before annealing, and the value of $P^{s}_{S}$ is much larger than that of $P^{s}_{G}$ [54]. Therefore, according to the obtained dislocation evolution curve and microstructure, the optimal annealing process parameters can be predicted through CA simulation.

5.3. Analysis for the formation of coarse grains during annealing

As shown in Fig. 5, compared to the initial grains, the sizes of grains after the annealing treatment become more uniform and smaller. However, there are still some coarse grains after a fully recrystallization. Generally, it is believed that the occurrence of the coarse grains owes to the lack of a second-phase pinning in the alloy with the second phase. But there are no enough δ phases in the region with fine grains as well. Therefore, the reason for the occurrence of coarse grains may be other factors. Song et al. [64] found that the way of grain growth is different at different regions. The grains grow at a normal velocity in the completely recrystallized area, while grow at a higher velocity in the others area due to the stored energy. In this study, there are some small DRX nuclei near the grain boundaries or phase boundaries after deformation. The driving pressure is the interaction of grain boundary energy and deformation energy for these grains during annealing treatment. There is an incubation period for the static recrystallization (SRX). The growth of DRX nuclei and the nucleation of SRX consume most of dislocation energy. Therefore, the driving pressure for SRX nuclei becomes lower, which leads to a lower velocity for SRX grain growth. Thus, the sizes of SRX grains are relatively small. However, the DRX nuclei may rapidly grow during the incubation period of SRX at which the driving pressure is still large, which may be response for the coarse grains.

Fig. 8 shows the simulated microstructures annealed at 980 °C with different time (The red represents the DRX grains produced in the deformation process, and the green denotes the SRX grains in annealing process). It can be found that the original DRX nuclei begin to grow at the early stage of annealing and the grain size is larger than that of the others. It indicates that the reason for the formation of coarse grains is that DRX nuclei formed in hot deformation have a high growth rate in annealing treatment. Fig. 9 shows the evolution of dislocation density distribution in annealing treatment. It can be found that there are a lot of regions with high dislocation density in the early stage of annealing, as shown in Fig. 9(a and b). With the increase of annealing time, the area of high dislocation density gradually decreases due to the nucleation and grain growth, as shown in Fig. 9(c). With the further increase of annealing time, the area of high dislocation density gradually decreases and then disappears, as shown in Fig. 9(d-f). There are two driving pressures for grain growth [52]. i.e., $P^{s}_{G}$ and $P^{s}_{S}$. In the early stage of annealing, there is a large difference in dislocation density between the DRX and deformed grains. Therefore, the driving pressure $P^{s}_{S}$plays a major role in the growth of DRX nuclei. Thus, these DRX grains grow with a high velocity. When the annealing time reaches 600 s, the difference in dislocation density between the recrystallization grains and the initial one becomes small. It indicates that the driving pressure for grains grow is changed gradually from $P^{s}_{S}$ to $P^{s}_{G}$. In the late stage of annealing treatment, there is only a little difference in dislocation density between the SRX and DRX grains and initial one. It is $P^{s}_{G}$rather than $P^{s}_{S}$ plays a major role in the growth of grains. Based on the analysis above, it can be concluded that the reason for the occurrence of coarse grains is that the DRX grain nuclei grow with a higher velocity at the early stage of annealing. Han et al. [40] studied the grain growth kinetics in the presence of second phase particles by a CA mode, and found that second phase particles has a significant effect on the final limiting grain size. Similar conclusions have been obtained in this paper. But in Han’ studies [40], the second-phase particles were treated as inert particles that do not evolve during grain growth. However, the δ phase will evolve during grain growth in this study. Hence, the CA model considered the effects of δ phase on the nucleation and growth of grains is more accurate. Meanwhile, the way to avoid the occurrence of the coarse grains by increasing V_δbefore annealing may be feasible considering the pinning effects of δ phase on the grain growth.

6. Conclusions

The microstructural evolution of GH4169 superalloy during annealing treatment was investigated by experiments and cellular automation simulation. Some important conclusions are listed as follows:

(1)A CA model which can take the effects of δ phase on the annealing recrystallization into account was developed to study the recrystallization behavior and analyze the reasons for the formation of coarse grains during annealing treatment.

(2)Based on CA simulation, the reasons for the formation of coarse grains were found. It was found that the coarse grains results from the fast growth of DRX grain nuclei at the early stage of annealing because the high initial dislocation density can provide a large drive force.

(3)The average dislocation density decreases rapidly at the early stage of annealing due to the nucleation of SRX and growth of DRX grains. Moreover, the drop rate of dislocation density does not significantly change until the recrystallization fully complete.

Acknowledgements

This work was supported by the Hunan Provincial Natural Science Foundation of China (No. 2017JJ3380), the National Natural Science Foundation of China (No. 51775564), the State key Laboratory of High Performance Complex Manufacturing (No. zzyjkt2014-01), the Open-End Fund for the Valuable and Precision Instruments of Central South University (No. CSUZC201821), Hebei Iron and Steel Joint Funds (No. E2015209243), and the Fundamental Research Funds for the Central Universities of Central South University (No. 153711025).

The authors have declared that no competing interests exist.

---