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.,1,Dynamic recrystallization behavior of a typical nickel based superalloy during hot deformation,一种典型的镍基高温合金热变形中的动态再结晶行为,.,2,.,3,Abstract,Based on the conventional DRX kinetics model, the volume fractions of DRX are rstly estimated. Results show that there is an obvious deviation between the experimental and pre-dicted volume fractions of DRX when the forming temperature is below 980 . Therefore, the segmented models are proposed to describe the kinetics of DRX for the studied superalloy.,分段建立动态再结晶百分数方程,首次建立镍基高温合金动态再结晶百分数方程,.,4,Abstract,Comparisons between the experimental and predicted results indicate that the proposed segmented models can give an accurate and precise estimation of the volume fractions of DRX for the studied superalloy. In addition, the optical observation of the deformed microstructure conrms that the dynamically recrystallized grain size can be well characterized by a power function of ZenerHollumon parameter,建立的再结晶方程与实验结果具有一致性,动态再结晶晶粒尺寸可以用Z参数方程表示,.,5,Introduction,Over the last decades, some efforts have been made on the DRX behaviors of various metals or alloys 1542. In order to control the microstructure and mechanical properties, it is essential to quantify the volume fractions of DRX. The Avrami equation 15is often used to evaluate the softening fractions induced by static recrystallization (SRX), meta-dynamic recrystallization (MDRX) and dynamic recrystallization (DRX). Chen et al. 16 and QuanMomeni and Dehghani 18 developed Mandal et al. 19,20 investigated Ebrahimi et al. 22 studied. Yin al.23investigated. Zeng et al.27 studied the hot deformation.首先介绍，过去的几十年不同学者研究了各种金属的动态再结晶行为，Avrami方程常被用作评估再结晶的软化机制。其中参考文献1618研究了42CrMo钢的动态再结晶行为以及再结晶方程1920探索了奥氏体不锈钢的再结晶组织演化机制、原理以及动力学。23通过物理核验和有限元探索了GCr15钢微观组织演化，用公式表达了奥氏体晶粒长大和动态再结晶。27建立了钛铝合金动态再结晶百分数的Avrami方程预测动态再结晶百分数,.,6,Introduction,Due to the different precipitation phases, together with their changeable shapes and distributions, the hot deformation behaviors of nickel-based superalloys are generally complex. In recent years, some investigations on the hot deformation behaviors of nickel-based superalloys have been carried out 4759. Li et al. 47 and Guo et al. 48 studied the microstructural evolution of Inconel 625 superalloy, and conrmed that the continuous dynamic recrystallization (CDRX) Wang et al. 49discussed the microstructural evolution Wen et al. 50 and Cai et al. 51investigated. Ning et al. 52 studied . Also, Ning et al. 53 constructed Also, Lin et al. 55 studied 由于镍基高温合金热变形过程中的不同析出相分布以及尺寸的变化，使合金的热变形行为变得复杂。By the nite-element (FE) method, the microstructural evolution of the nickel-based superalloys were also simulated by other researchers 5759,研究了625高温合金前期的变形阶段是连续动态再结晶起主要软化作用而不不连续动态再结晶在后变形阶段是主要软化机制,718高温合金动态再结晶形核机制对温度很敏感,建立镍基高温合金热加工图研究热变行为,研究了FGH4096高温合金锻造过程中的热变形行为，并建立成形温度和速率中现象学本构模型来表述稳态应力,其他学者运用有限元方法，模拟了镍基高温合金的微观组织演化,.,7,Introduction,However, there is still less concern about the evaluation of softening fractions induced by DRX for nickel-based superalloys. Due to the signicant effects of DRX on the hot deformation behavior, as well the microstructures and mechanical properties of nickel-based structure parts, it is necessary to accurately estimate the volume fractions of DRX during the hot deformation.,Identify a Gap,.,8,2. Materials and experiments,52.82Ni18.96Cr5.23Nb3.01Mo1.00Ti0.59Al0.01Co0.03C(bal.)Fe.Six different forming temperatures (920, 950, 960, 980, 1010, and1040) and four different strain rates (0.001, 0.01, 0.1, and 1 s -1 ) were used in hot compression tests, and the nal deformation degree was 70%. Then, the deformed specimens were sliced along the compression axis section for microstructural analysis. After polished mechanically and etched in a solution consisting of HCl(100 ml) + CH 3 CH 2 OH (100 ml) + CuCl 2 (5 g) at room temperature for 35 min, the exposed surfaces were observed by optical microscope (OM).The average grain size was evaluated by the linearintercept method, according to the standard ASTM: E112-12,计算晶粒尺寸的方法,.,9,3. Results and discussion,3.1. Hot deformation behavior,3.2.1. Calculation of dynamically recrystallized volume fraction,3.2.2. Calculation of e0.5,3.2.4. Determination of material parameter n d,3.2.3. Determination of the critical strain,3.2. Conventional DRX kinetics model,3.3. The segmented kinetics models for dynamic recrystallization,3.4. Microstructural evolution and dynamic recrystallization,.,10,3.2. Conventional DRX kinetics model,再结晶百分数,再结晶百分数为50%的应变,临界应变,.,11,3.2.1. Calculation of dynamically recrystallized volume fraction (X drx ),通过数学模型对应力应变曲线外延，得到回复曲线,从而得出某一应变下的再结晶百分数,饱和应力sat,稳态应力ss,.,12,3.2.5. Verication of conventional DRX kinetics model,实线为预测结果，点为实验结果，因此具有良好的一致性,.,13,3.2.4. Determination of material parameter n d,已知某一应变下的再结晶百分数，50%再结晶百分数的应变，临界应变，从而通过公式就行线性拟合出参数nd,.,14,4. Conclusions,The dynamic recrystallization behavior of a typical superalloy is investigated. Firstly, the conventional kinetic equations are developed to evaluate the volume fractions of DRX. However, the model cannot well describe the dynamic recrystallization behavior of thestudied superalloy when the forming temperature is below 980 C.The main reason is that the dynamic recrystallization process is slow under the low forming temperature. Therefore, the segmented DRX kinetics models are proposed. A good agreement be-tween the experimental and predicted results shows that the established segmented models are able to describe the dynamic recrystallization behavior of the studied superalloy. The effects offorming temperature, strain rate on DRX grain size are signicant.Under high forming temperatures and low strain rates, the dynam-ically recrystallized grain easily coarsens. The grain size of complete DRX in the studied superalloy can be well characterized bythe power function of ZenerHollomon parameter.,.,15,Evolution of grain renement degree induced by dynamic recrystallization for Nimonic 80A during hot compression process and its FEM analysis,80A镍铬钛合金热压缩过程动态再结晶引起的晶粒细化程度演化以及有限元分析,.,16,.,17,Abstract,a series of isothermal hot compression tests were conducted with the height reduction range of 10%-60% under the strain rate range of 0.01-10 s and the temperature range of 1237e1523 K on a Gleeble-3500 thermo-mechanical physical simulator. The onset strains of DRX initiation ( c) were identied by - curves (strain hardening rates curves) and their derivative. Then the dynamic recrystallization kinetics model and the dynamic recrystallization grain size model were established based on the results from thermal simulation experiments and metallographic analysis.,10%-60%的压下量，应变速率为0.01-10s-1,通过-曲线得出临界应变，建立动态再结晶方程，晶粒尺寸方程,.,18,Abstract,After that, the grain renement degrees of the specimens were proposed and calculated, then the effects of temperature, strain rate and deformation degree on the grain renement degree were discussed through the metallographs over a wide range of temperatures and strain rates. Finally, the developed models were applied in the nite element simulation model, which implies a good application prospect of the theoretical calculation.,通过金相观察研究了温度，应变速率和变形程度对晶粒细化的影响,得出的再结晶方程代入到有限元软件中，具良好的预测前景,.,19,1. Introduction,As for the nickel-based alloy with low stacking fault energy, DRX is prone to occur and predominant in strain softening mechanisms resulting in grain renement（因为镍基合金是底层错能金属，倾向于发生动态再结晶以及在晶粒细化方面作为主要的软化机制）for the products of Nimonic 80A, in order to control microstructure evolution and further insuring mechanical property by regulating process parameters, it is signicant to analyze the evolution of grain size by establishing DRX kinetics & grain size model, and further developing their applications with nite element method (FEM),因为温度，应变速率，应变对晶粒尺寸具有重要影响，因此有必要建立数学模型，用有限元方法进行分析,.,20,1. Introduction,Over the last few decades, considerable researches have focused not only on detecting and analyzing the phase microstructures of materials which undergo DRX during deformation but also on modelling the DRX kinetics of alloys 14,15. Wang et al.16 identied Baohui Tian et al17. distinguished Quan et 18al.measured Such works concentrated on recognizing DRX grains and analyzing micro-mechanisms during a hot deformation process. Then the most serious issue is how to apply the theoretical results iAt present, nite element method (FEM) with thermal-mechanical-microstructure dynamic coupling supplies an effective at form practical applications. Li et al. established math ematical models to predict DRX, DRV and grain size evolution of plastic mold steel (SDP1) 19. These works built the DRX kinetics models, but few analyzed the variety of grain size induced by DRX along with processing parameters.,通过金相观察和EBSD技术得出718高温合金两种形核机制，并表述了动态再结晶形核过程,利用X射线技术和透射电镜研究了80A合金的位错密度和位错亚结构，得到80A合金的动态再结晶和动态回复行为下的微观组织,测量了80A合金的晶粒尺寸和细晶所占的比例，得出80A合金主要软化机制是动态再结晶,.,21,2. Materials and experiments,sixteen samples were compressed to the xed true-strain of 0.916 (the height reduction of 60%) with four different strain rate of 0.01s-1 0.1s-1 1s-1 10s-1 sand four different temperatures of 1273 K, 1323 K, 1373 K, 1423 K. In addition, ve specimens were deformed with the true-strain of 0.105, 0.223, 0.357,0.511, 0.693 (height reduction of 10%, 20%, 30%, 40%, and 50%) The true stress and truestrain were derived from the nominal stress-strain data according to the following formulas:,取样于压缩后样品的中心位置抛光，用HCl(100ml ) H2SO4(5ml)CuSO4(5g)室温下进行腐蚀60s,.,22,3. Results and discussion,3.1. Modelling of DRX kinetics,3.1.1. Initiation of DRX c,3.1.2. Quantizing the values of Xdrx and ,3.1.3. DRX kinetics models,.,23,4. The evolution law of grain renement degree,80A合金变形速率为0.01s-1，60%变形量（a）1273 K (b) 1323 K;(c) 1373 K; (d) 1423 K.,动态再结晶晶粒几乎都在晶界处产生，除了某些大变形区域外仍然有许多原始形态，愈多的“项链”组织就代表着产生了愈多的再结晶晶粒，当温度达到1373K甚至是1423K时，晶粒长大并逐渐均匀化,.,24,4. The evolution law of grain renement degree,80A合金变形温度为1373k，60%变形量（a） 0.01s-1 (b)0.1s-1 (c)1s-1 (d)10s-1,大量的孪晶界转变成具又锯齿状晶界的再结晶晶粒，并且所有试样都完成了动态再结晶。应变速率为0.01时，晶粒细小且均匀，这是由于较低的应变速率提供了足够的时间进行能量聚集，高应变速率下晶粒来不及完成再结晶,.,25,5. FEM analysis on grain renement induced by DRX,晶粒尺寸在试样内是分布不均匀的，最大均匀尺寸分布在试样上表面和下表面的中心区域，最小晶粒尺寸分布在试样的中心区域，这是由于变形中的温度，应变，应变速率分布不均匀。模拟结果这些区域尺寸分别为17.2um,15.9um,11.9um而观测区域的统计结果为12.5um，10.9um，8.7um,由此可知建立的动态再结晶模型可以输入到有限元软件中预测镦粗过程的微观组织演化.,fig15.Prediction of grain size under the deformation condition of (a) T =1373 K，=0.1，strain=0.357。（b）T =1373 K，=0.1，strain=0.916 (c) T =1373 K，=1，strain=0.916,.,26,6. Conclusions, The DRX kinetics and grain size models were established according to the basic stress-strain data and metallographs of samples obtained from a series of isothermal compressions with height reduction of 60% over temperature range of 1273e1423 K and strain rate range of 0.01-10 s .通过应力应变曲线建立动态再结晶动力学模型和晶粒尺寸模型 A concept was introduced and calculated to reveal the evolution of grain renement degree induced by DRX. then the effects of temperature, strain rate and deformation degree on the grain renement degree were analyzed through the metallographs, it is found that the grain renement degree increased with the increase temperature, increase strain rateand increase deformation degree to a certain extent.在一定程度上随着温度，应变速率增加晶粒细化程度增加,.,27,The developed DRX kinetics and grain size models were applied in the nite element model, and the simulation processes under different deformation conditions were conducted. The numerical results shows a good application prospect of theoretical models.得出的动态再结晶方程和晶粒尺寸模型输入到有限元软件中。在理论模型中可得到良好应用。,6. Conclusions,.,28,Simulation on dynamic recrystallization behavior of AZ31 magnesium alloy using cellular automaton method coupling LaasraouiJonas model,采用元胞自动机结合LaasraouiJonas位错密度模型模拟AZ31 镁合金的动态再结晶行为,.,29,.,30,The dynamic recrystallization (DRX) process of AZ31 magnesium alloy including microstructure and dislocation density evolution during hot compression was simulated by adopting the cellular automaton (CA) method coupling the LaasraouiJonas model (LJ model). 采用元胞自动机结合 LaasraouiJonas 位错密度模型(LJ 模型)模拟 AZ31 镁合金在动态再结晶过程中的位错密度和微观组织演化。,Abstract,.,31,Abstract,The reliability of simulation depended on the accuracy of the hardening parameter, the recovery parameter and the strain rate sensitivity in the LJ model. The hardening parameter was calculated in terms of the LJ model and the KocksMecking model (KM model), and then the recovery parameter and the strain rate sensitivity were obtained by using the equation of steady state flow stress for DRX. Good agreements between the simulations and the experimental observations were achieved. LJ 模型中的硬化参数、回复参数和应变速率灵敏系数决定模拟的准确性。在目前的研究中，基于 LJ 模型和 KocksMecking 模型(KM 模型)求解硬化参数；采用动态再结晶中的稳态应力公式求解回复参数和应变速率灵敏系数。结果表明：模拟结果与实验结果一致。,.,32,The main characteristics of DRX may be summarized as follows: 1) A critical value of dislocation density is required for onset of DRX; 2) The recrystallized grains (R-grains) are equiaxed and the average grain size stays same at a given deformation condition; 3) Preexistent grain boundaries (GBs) are usually nucleation sites 68.Since it is difficult to study the microstructural evolution characteristics during grain growth by physical experiments, computer simulations have been used by many researchers 9. Up to now, various approaches have been proposed to simulate DRX, such as the Monte Carlo (MC) method and the cellular automaton (CA) method. The MC method has been widely adopted to study microstructural evolution, for instance, normal grain growth, grain growth with second-phase particles, and recrystallization 10.,1. Introduction,动态再结晶主要特点 (1)动态再结晶开始时的临界位错密度值（2）在同样的变形条件下再结晶晶粒等轴且平均尺寸相同（3）晶界处常常是形核位置,蒙特卡洛法和元胞自动机法被用作模拟动态再结晶。蒙特卡洛法广泛应用于晶粒生长，晶粒同第二相粒子生长，动态再结晶,.,33,However, grain growth kinetics during DRX was not simulated by these simulations, due to the limitations of the MC method. The CA method is algorithm that represents discrete spatial and temporal evolution of complex systems by applying local or global deterministic or probabilistic transformation rules to the location of a lattice. This method did not consider the hot-deformation parameters (e.g. temperature and strain rate), their effects on DRX process (e.g. nucleation, volume fraction and average dynamically R-grain sizes), and the relationship between the nucleation sites and the dislocation density distribution. Compared with the MC method simulations, the CA method is also probabilistic, but relatively flexible in simulating different physical systems and effective in calculation 6.,1. Introduction,元胞自动机法不用考虑热变形参数（温度，应变速率）以及他们对动态再结晶过程的影响（形核，体积分数和平均再结晶晶粒）且不考虑形核点和位错密度分布之间的联系,.,34,1. Introduction,Dislocation density plays a very significant role in nucleation and microstructural evolution of DRX during hot deformation 1. Therefore, many models have been attempted to describe the evolution of dislocation density, such as the LJ model 13, the KM model 14, and the two-parameter model 15. These models, which are internal variable dislocation density models, aim to calculate the flow stress and the evolution of dislocation density during hot deformation process. However, the modified LJ model, which was proposed by GOURDET and MONTHEULLET 2, considers the influence of GB migration on dislocation density. Thus, the modified LJ model has provided a more realistic description of the evolution of dislocation density. Meantime, our previous research 16 has proved that the LJ model is suitable to simulate the dislocation density evolution in detail, and has successfully used the modified LJ model to simulate the microstructural evolution of MgAlCa-based alloy during hot extrusion.,by GOURDET和MONTHEULLET 提出修改后的LJ模型，考虑了晶界的迁移对位错密度的影响，因此修改后的LJ模型对位错密度演化具有可靠描述，同时以往研究已经证明LJ模型适合模拟具体模拟位错密度变化，并且成功的模拟了镁铝合金热挤压过程中微观组织演化,.,35,2 Experimental,Hot compression tests were performed on a Gleeble3500 machine to obtain the stress strain curves over five temperatures ( 300, 350, 400, 450 and 500 C) with five strain rates (0.03, 0.3, 3, 30 and 90 s 1 ) and a strain of 1 to calculate material constants. To study the microstructure of AZ31 magnesium, the cross-sections parallel to compression axis were cut from the deformed specimens and those samples were mounted, polished and etched.,材料常数通过热压缩曲线计算获得,平行于压缩方向进行切样,.,36,3 Modeling,3.1 Dislocation density model,3.2 Model of DRX nucleation and growth,3.3 Cellular automaton method and procedures of simulation,位错密度模型,动态再结晶形核和长大模型,元胞自动机法和模拟程序,第i个晶粒的位错密度,晶界迁移扫过的体积,硬化参数,回复参数,N1：行数N2:列数,Q:通过应力应变曲线获得的激活能,形核率,.,37,4 Results and discussion,Based on the equations mentioned above, the hardening parameter, the recovery parameter and the strain rate sensitivity are determined. The results can be expressed as the following equations:,.,38,4.3 Simulation results and discussion,.,39,4.3 Simulation results and discussion,Compared Fig. 6 with the microstructure under a temperature of 500 C with a strain rate of 0.03 s 1 and a strain of 1 (Fig. 8), the grain size at high temperature is much bigger, due to the higher velocity of GB migration. After comparing the simulated results with the experimental observations, some discrepancies can be observed (Figs. 6, 7 and 8), because of the possible involvement of additive high energy sites for nucleation which has not been taken into account during simulation, such as dislocation tangle and dislocation pining. In general, the simulated results agree well with the experimental findings. It is shown that the simulations of final grain size are in quantitative agreement with the experimental results in Table 3.,对比500应变速率为0.03（图6）和应变速率为1（图8），高温下晶粒尺寸更大，由于更高的晶界移动速度。模拟结果与实验结果相对比有一些差异，是由于额外的能量较高的形核点的参与，模拟中没有考虑这一点，比如位错缠结和位错钉扎，总的来说，模拟结果与实验具有一致性,.,40,5 Conclusions,1) The hardening parameter, which was calculated based on the LJ model and the KM model, was obtained to be 10 13 m 2 . The recovery parameter and the strain rate sensitivity were calculated by using the relationship between flow stress and strain rate at steady state during DRX, and w