热锻非连续变形过程微观组织演变的元胞自动机模拟
|
摘要
金属的微观组织是决定其宏观力学性能的主要因素，在热锻过程中，金属的微观组织会发生动态回复、动态再结晶、静态回复和静态再结晶等一系列变化，形成新的晶粒。在材料成分一定的条件下，影响晶粒演化的外部因素是温度、应变和应变速率。因此，如何通过控制热锻成形中的温度、变形量和变形速度，来达到控制微观组织及产品力学性能的目的，近年来已成为热锻成形中的热点研究问题，在大锻件成形中尤其如此，乃至于成性的重要性远大于成形。通过一定条件下的物理实验实测结果，建立微观组织演变的唯象数学模型，进而用来预报热成形过程的微观组织演变，是目前热锻成形中的常用研究方法，但这种研究思路只适用于变形比较简单、变形次数少的热成形过程。大锻件的成形一般是多个道次，每个道次包含多次压下，属于增量成形过程。每次压下中和相邻两次压下之间锻件可能发生完全或不完全动态再结晶、亚动态再结晶和静态再结晶，部分晶粒得到细化，应变能降低或消失，而未发生再结晶的晶粒则仍然保留高应变能，这种变形能的差异导致在随后的变形中再结晶驱动力不同，微观组织演变非常复杂，依靠实验方法建立的唯象组织演变模型已无法描述这样复杂的晶粒演变过程。本论文以典型能源大锻件材料为研究对象，探讨更能反映物理本质的微观组织演变建模方法。实际上，材料的位错密度是联系宏观变形过程与微观组织演变之间的桥梁，变形导致材料的位错密度增加，当位错能增加到一定程度时将导致再结晶发生，再结晶后的晶粒位错密度急剧降低，并在新的变形中再逐步累积和循环。根据“应变-位错密度-再结晶-流变应力”之间的宏微观相互影响规律，本文旨在建立包含“变形-回复-动态再结晶-亚动态再结晶和静态再结晶”各过程在内的微观组织演变元胞自动机（Cellular Automaton, CA）模拟方法，并与热成形过程宏观有限元模拟相结合，实现大锻件成形过程微观组织演变的预报。为此开展了以下主要研究工作：
在Gleeble-3500热模拟实验机上，对典型大锻件材料进行了等温压缩实验。研究了不同应变速率和变形温度条件下材料流变规律与动态再结晶行为；根据经典应力-位错关系和动态再结晶动力学方程，分别对加工硬化-动态回复和动态再结晶两阶段建立了流变应力模型；同时从实验获得的高温流变应力曲线中提取了建立CA模型所需的材料特性参数。
基于晶粒长大的热力学机制、曲率驱动机制和能量耗散机制，制定了能够反映晶粒长大物理机制的元胞转变规则，建立了模拟晶粒正常长大的CA模型。采用该模型模拟了高温奥氏体化晶粒正常长大过程，分析了晶粒正常长大过程CA模拟结果的形态学、动力学和拓扑学等典型特征。
基于位错驱动的形核条件和晶粒长大动力学理论，建立了模拟动态再结晶过程的CA模型（DRX-CA Model）。DRX-CA模型综合考虑了位错密度的演变、再结晶形核及晶粒长大等一系列过程，同时考虑了合金元素及第二相粒子对再结晶的影响。应用所建立的DRX-CA模型预测了典型大锻件材料30Cr2Ni4MoV低压转子钢在不同应变、变形温度、应变速率和初始晶粒尺寸条件下动态再结晶行为，检验了DRX-CA模型对典型实验特征的预测能力。
为了反映晶粒形状变化对再结晶形核与晶粒长大的影响，建立了包含晶粒拓扑变形技术在内的CA模型。该模型采用既相互关联又各自独立的两套坐标系，即物质坐标系和元胞坐标系，来描述材料动态变形中的再结晶形核与晶粒长大过程。其中物质坐标系用于描述晶粒的变形，晶粒形状及尺寸随着应变的发展而发生改变；元胞坐标系用于描述晶粒的形核和长大，元胞尺寸不发生改变，同时其转变规则也与不变形时相同，从而保证了新晶粒的等轴长大。通过对比采用晶粒拓扑变形技术的CA模拟结果、传统CA方法的模拟结果和金相实验结果，检验了包含晶粒拓扑变形技术的CA模型描述晶粒演化的准确性。
建立了包含动态再结晶、亚动态再结晶和静态再结晶的多次非连续热变形过程的微观组织演变CA模拟模型，该模型以位错密度为基本变量，通过追踪非连续热变形过程中元胞内位错密度的变化，模拟复杂再结晶过程中微观组织的演变。采用该方法对典型大锻件材料30Cr2Ni4MoV低压转子钢四个道次热压缩过程微观组织演变进行了模拟。在此基础上，将有限元计算与CA模拟方法相集成，定义了CA计算时宏观热变形参数的更新规则，通过软件用户子程序开发，建立了预报热锻非连续热变形微观组织演变的多尺度数字化仿真系统，对典型大锻件成形工艺-多道次平砧拔长宏观物理场量和微观组织演变进行了多尺度数字化仿真，模拟结果对锻造工艺的优化提供了指导。
研究结果表明，CA模拟结果比较准确地再现了温度、应变和初始晶粒度对晶粒演化过程的影响规律，CA模拟给出的晶粒尺寸及形貌与金相实验结果接近一致，根据CA模拟得到的位错密度而计算的流变应力曲线和实验条件下的流变应力曲线吻合良好，证明了以位错密度为基本变量追踪变形历史的CA模拟方法的预测结果符合材料热变形过程中的宏微观演变特征，可以用于模拟非连续热变形过程复杂再结晶微观组织的演变。将宏观有限元计算与微观组织CA模拟相集成，可以对热锻非连续变形过程宏观物理量场和晶粒演变进行多尺度数字化仿真，研究结果给出了多道次热变形的晶粒演化状态，根据模拟结果可为优化大锻件非连续热变形的锻造工艺提供指导。
The prediction and control of microstructure evolution in heavy forgings during discontinuoushot deformation play a key role in improving the mechanical properties of heavy forgings. Heavyforging process usually consists of multi-pass and each pass consists of multiple reductions, so it is atypical process of incremental bulk forming. During multi-pass deformation, different parts of theforging at different time will stay in two states: deformation and non-deforamtion. Different statesinclude different mechanisms. Both incomplete and complete dynamic recrystallization (DRX) occurin the deformation state. In non-deforamtion state, incomplete DRX will result in meta-dynamicrecrystallization (MDRX) and static recrystallization (SRX). Complete DRX will result in graingrowth. The complicated recrystallization behavior leads to the non-uniform distribution of storedenergy among individual grains and within grain interiors. However, it is difficult to conceive atraditional phenomenological model to describe the complicated recrystallization processes.Therefore, it is highly necessary to develop a new algorithm that better reflects the physical behaviorobserved in heavy forging production. According to the micro-and macroscopic relationship among“strain, dislocation density, DRX and flow stress”, a mesoscale Celullar Automon (CA) model isdeveloped to predict the microstructure evolution for typical heavy forged materials during heavyforging production, during which DRX, SRX and MDRX may occur. The main research content is asfollows:
The compression tests are conducted with Gleeble-3500thermo-mechaincal simulator to studythe DRX behavior and rheological regularity of LP and HP-IP rotor steels at various temperaturesand strain rates. Based on trandional stress-dislocation relation and kinematics of DRX, the flowstress constitutive equations of the work hardening-dynamical recovery period and dynamicalrecrystallization period are established to accurately describe the relationships of the flow stress,strain rate and temperature of LP and HP-IP rotor steels. More importantly, the necessaryexperimental data for the estabilishment of the CA model is abtained by conducting these physicsexperiments.
The CA model based on the curvature-driven mechanism, thermodynamic driving mechanismand lowest energy principle has been developed to simulate normal grain growth during high-temperature austenitizing for LP rotor steel. In this model, the morphology, grain size distribution,topological aspects and local kinetics of austenite grain growth are annlyzed under differenttemperatures and calculation time, i.e.CAS.
The DRX-CA model coupling foundamental metallurgical principles has been developed topredict microstructure evolution during DRX in heavy forged materials. The evolution of dislocationdensity, DRX nucleation and grain growth are under consideration. At the same time, the effects ofalloying elements and the second-phase particles on the recyrstallization nucleation and growth arealso taken into account in the developed DRX-CA model. In order to examine the prediction performance, DRX behavior of LP rotor steel is simulated under different strains, deformationtemperatures, strain rates and initial grain sizes.
The effect of deformation on grain surface area per unit volume and edge length per unit volumeis another issure in DRX. During deformation, the dislocation density increases gradually and whenit reaches a critical density, new nucleus will appear on the grain boundaries and grow with themodel of equiaxed growth. This growth relies on the difference of dislocation density between thedynamic recrystallized grains and deformed grains. When the dislocation density in the new dynamicrecrystallized grains reaches the critical density again, the next round of DRX occurs. Thecompression only occurs on the grains that have not completed the DRX in each round. To describethe compression effect more accurately, an update CA model is propsed in which a cellularcoordinate system and a material coordinate system are establishe separately. The cellular coordinatesystem remains unchangeable, but the material coordinate system and the corresponding grainboundary shape will change with deformation. The simulation results show that the topologydeformation has an accelerated affect on the rate of DRX. The results also indicate that the averagegrain size exhibits a slight decreas because of the effect of topology deformation on therecrystallized grain growth. The average grain size is closer to the experimental results using thetopological CA model with a comparison of the conventional CA simulation.
On the basis of the topological CA model, a mesoscale CA model is established to simulatemicrostructure evolution during discontinuous hot deformation for LP rotor steel. The model has thecapability of tracking the deformation history of each cell with dislocation density being an internalvariable, and accurately describes even complex recrystallization process. To examine the validity ofthe developed CA model, we attempted to apply the mesoscale simulation method to four-pass hotdefroamtion for LP rotor steel. The multi-scale simulation platform for prediction the microstructureevolution during discontinuous hot deformation is established by coupling FEM method and CAmethod. Bsed on the established simulation platform for microstructure evolution, numericalsimulations for stretching process with multi-stroke and multi-pass are performed. It proveides anovey way for investigating the microstructure evolution during the complicated recrystallizationprocesses observed in heavy forging production on a multi-scale.
Research results show that the impact of the law of temperature, strain rate and intial grain sizeon grain evolution is revealed by CA simulation. Using the developed CA model, the relationshipbetween the flow stress, volume fraction recrystallized and recrystallized grain size and thethermomechanical parameters is established. By comparison of the simulated results by the CAmodel with the flow stress and metallographs from the experiment, it is obviously seen that thesimulation results closely resemble the experimental results. It is proved that the developed CAmodel accurately reflects the interaction mechanism between micro and macro evolution. Therefore,this model can then be used to simulate the microstructure evolution during the discontinuousforming processes. Multi-scale digital simulation can be achieved to predicte the evolution of themacro-physical fields and mesoscopic grain during discontinuous hot forging by coupling mesoscopic CA model with macro-scale finite element analysis. It shows that, based on the multi-scale simulation platform, the optimum forging method can be designed.
在Gleeble-3500热模拟实验机上，对典型大锻件材料进行了等温压缩实验。研究了不同应变速率和变形温度条件下材料流变规律与动态再结晶行为；根据经典应力-位错关系和动态再结晶动力学方程，分别对加工硬化-动态回复和动态再结晶两阶段建立了流变应力模型；同时从实验获得的高温流变应力曲线中提取了建立CA模型所需的材料特性参数。
基于晶粒长大的热力学机制、曲率驱动机制和能量耗散机制，制定了能够反映晶粒长大物理机制的元胞转变规则，建立了模拟晶粒正常长大的CA模型。采用该模型模拟了高温奥氏体化晶粒正常长大过程，分析了晶粒正常长大过程CA模拟结果的形态学、动力学和拓扑学等典型特征。
基于位错驱动的形核条件和晶粒长大动力学理论，建立了模拟动态再结晶过程的CA模型（DRX-CA Model）。DRX-CA模型综合考虑了位错密度的演变、再结晶形核及晶粒长大等一系列过程，同时考虑了合金元素及第二相粒子对再结晶的影响。应用所建立的DRX-CA模型预测了典型大锻件材料30Cr2Ni4MoV低压转子钢在不同应变、变形温度、应变速率和初始晶粒尺寸条件下动态再结晶行为，检验了DRX-CA模型对典型实验特征的预测能力。
为了反映晶粒形状变化对再结晶形核与晶粒长大的影响，建立了包含晶粒拓扑变形技术在内的CA模型。该模型采用既相互关联又各自独立的两套坐标系，即物质坐标系和元胞坐标系，来描述材料动态变形中的再结晶形核与晶粒长大过程。其中物质坐标系用于描述晶粒的变形，晶粒形状及尺寸随着应变的发展而发生改变；元胞坐标系用于描述晶粒的形核和长大，元胞尺寸不发生改变，同时其转变规则也与不变形时相同，从而保证了新晶粒的等轴长大。通过对比采用晶粒拓扑变形技术的CA模拟结果、传统CA方法的模拟结果和金相实验结果，检验了包含晶粒拓扑变形技术的CA模型描述晶粒演化的准确性。
建立了包含动态再结晶、亚动态再结晶和静态再结晶的多次非连续热变形过程的微观组织演变CA模拟模型，该模型以位错密度为基本变量，通过追踪非连续热变形过程中元胞内位错密度的变化，模拟复杂再结晶过程中微观组织的演变。采用该方法对典型大锻件材料30Cr2Ni4MoV低压转子钢四个道次热压缩过程微观组织演变进行了模拟。在此基础上，将有限元计算与CA模拟方法相集成，定义了CA计算时宏观热变形参数的更新规则，通过软件用户子程序开发，建立了预报热锻非连续热变形微观组织演变的多尺度数字化仿真系统，对典型大锻件成形工艺-多道次平砧拔长宏观物理场量和微观组织演变进行了多尺度数字化仿真，模拟结果对锻造工艺的优化提供了指导。
研究结果表明，CA模拟结果比较准确地再现了温度、应变和初始晶粒度对晶粒演化过程的影响规律，CA模拟给出的晶粒尺寸及形貌与金相实验结果接近一致，根据CA模拟得到的位错密度而计算的流变应力曲线和实验条件下的流变应力曲线吻合良好，证明了以位错密度为基本变量追踪变形历史的CA模拟方法的预测结果符合材料热变形过程中的宏微观演变特征，可以用于模拟非连续热变形过程复杂再结晶微观组织的演变。将宏观有限元计算与微观组织CA模拟相集成，可以对热锻非连续变形过程宏观物理量场和晶粒演变进行多尺度数字化仿真，研究结果给出了多道次热变形的晶粒演化状态，根据模拟结果可为优化大锻件非连续热变形的锻造工艺提供指导。
The prediction and control of microstructure evolution in heavy forgings during discontinuoushot deformation play a key role in improving the mechanical properties of heavy forgings. Heavyforging process usually consists of multi-pass and each pass consists of multiple reductions, so it is atypical process of incremental bulk forming. During multi-pass deformation, different parts of theforging at different time will stay in two states: deformation and non-deforamtion. Different statesinclude different mechanisms. Both incomplete and complete dynamic recrystallization (DRX) occurin the deformation state. In non-deforamtion state, incomplete DRX will result in meta-dynamicrecrystallization (MDRX) and static recrystallization (SRX). Complete DRX will result in graingrowth. The complicated recrystallization behavior leads to the non-uniform distribution of storedenergy among individual grains and within grain interiors. However, it is difficult to conceive atraditional phenomenological model to describe the complicated recrystallization processes.Therefore, it is highly necessary to develop a new algorithm that better reflects the physical behaviorobserved in heavy forging production. According to the micro-and macroscopic relationship among“strain, dislocation density, DRX and flow stress”, a mesoscale Celullar Automon (CA) model isdeveloped to predict the microstructure evolution for typical heavy forged materials during heavyforging production, during which DRX, SRX and MDRX may occur. The main research content is asfollows:
The compression tests are conducted with Gleeble-3500thermo-mechaincal simulator to studythe DRX behavior and rheological regularity of LP and HP-IP rotor steels at various temperaturesand strain rates. Based on trandional stress-dislocation relation and kinematics of DRX, the flowstress constitutive equations of the work hardening-dynamical recovery period and dynamicalrecrystallization period are established to accurately describe the relationships of the flow stress,strain rate and temperature of LP and HP-IP rotor steels. More importantly, the necessaryexperimental data for the estabilishment of the CA model is abtained by conducting these physicsexperiments.
The CA model based on the curvature-driven mechanism, thermodynamic driving mechanismand lowest energy principle has been developed to simulate normal grain growth during high-temperature austenitizing for LP rotor steel. In this model, the morphology, grain size distribution,topological aspects and local kinetics of austenite grain growth are annlyzed under differenttemperatures and calculation time, i.e.CAS.
The DRX-CA model coupling foundamental metallurgical principles has been developed topredict microstructure evolution during DRX in heavy forged materials. The evolution of dislocationdensity, DRX nucleation and grain growth are under consideration. At the same time, the effects ofalloying elements and the second-phase particles on the recyrstallization nucleation and growth arealso taken into account in the developed DRX-CA model. In order to examine the prediction performance, DRX behavior of LP rotor steel is simulated under different strains, deformationtemperatures, strain rates and initial grain sizes.
The effect of deformation on grain surface area per unit volume and edge length per unit volumeis another issure in DRX. During deformation, the dislocation density increases gradually and whenit reaches a critical density, new nucleus will appear on the grain boundaries and grow with themodel of equiaxed growth. This growth relies on the difference of dislocation density between thedynamic recrystallized grains and deformed grains. When the dislocation density in the new dynamicrecrystallized grains reaches the critical density again, the next round of DRX occurs. Thecompression only occurs on the grains that have not completed the DRX in each round. To describethe compression effect more accurately, an update CA model is propsed in which a cellularcoordinate system and a material coordinate system are establishe separately. The cellular coordinatesystem remains unchangeable, but the material coordinate system and the corresponding grainboundary shape will change with deformation. The simulation results show that the topologydeformation has an accelerated affect on the rate of DRX. The results also indicate that the averagegrain size exhibits a slight decreas because of the effect of topology deformation on therecrystallized grain growth. The average grain size is closer to the experimental results using thetopological CA model with a comparison of the conventional CA simulation.
On the basis of the topological CA model, a mesoscale CA model is established to simulatemicrostructure evolution during discontinuous hot deformation for LP rotor steel. The model has thecapability of tracking the deformation history of each cell with dislocation density being an internalvariable, and accurately describes even complex recrystallization process. To examine the validity ofthe developed CA model, we attempted to apply the mesoscale simulation method to four-pass hotdefroamtion for LP rotor steel. The multi-scale simulation platform for prediction the microstructureevolution during discontinuous hot deformation is established by coupling FEM method and CAmethod. Bsed on the established simulation platform for microstructure evolution, numericalsimulations for stretching process with multi-stroke and multi-pass are performed. It proveides anovey way for investigating the microstructure evolution during the complicated recrystallizationprocesses observed in heavy forging production on a multi-scale.
Research results show that the impact of the law of temperature, strain rate and intial grain sizeon grain evolution is revealed by CA simulation. Using the developed CA model, the relationshipbetween the flow stress, volume fraction recrystallized and recrystallized grain size and thethermomechanical parameters is established. By comparison of the simulated results by the CAmodel with the flow stress and metallographs from the experiment, it is obviously seen that thesimulation results closely resemble the experimental results. It is proved that the developed CAmodel accurately reflects the interaction mechanism between micro and macro evolution. Therefore,this model can then be used to simulate the microstructure evolution during the discontinuousforming processes. Multi-scale digital simulation can be achieved to predicte the evolution of themacro-physical fields and mesoscopic grain during discontinuous hot forging by coupling mesoscopic CA model with macro-scale finite element analysis. It shows that, based on the multi-scale simulation platform, the optimum forging method can be designed.
引文
ANDERSON M P, SROLOVITZ D J, GREST G S.1984. Computer simulation of grain growth-.Kinetics[J]. Acta Metallurgica,32(5):783-791.
AUSTIN R A, MCDOWELL D L.2011. A dislocation-based constitutive model for viscoplasticdeformation of fcc metals at very high strain rates[J]. International Journal of Plasticity,27:1-24.
BARIANI P, BRUSCHI S, DAL NEGRO T.2000. A new constitutive model for hot forging of steeltaking into account the thermal and mechanical history[J]. Annals of CIRP,49:195-198.
BARKóCZY P, ROóSZ A, GEIGER J.2003. Simulation of recrystallization by cellular automatonmethod [J]. Mater Sci Forum,414-415:359-364.
BATE P S, HUTCHINSON W B.2005. Grain boundary area and deformation[J]. Scripta Material,52(3):199-203.
BAUDIN T, JULLIARD F, PAILLARD P, PENELLE R.2000. Simulation of primaryrecrystallization from TEM orientation data[J]. Scripta Materialia,43(1):63-68.
BAUDIN T, SOLAS D, ETTER A L, CECCALDI D, PENELLE R.2004. Simulation of primaryrecrystallization from TEM observations and neutron diffraction measurements[J]. ScriptaMaterialia,51:427-430.
BLAZ L, SAKAI T, JONAS J J.1983. Effect of initial grain size on dynamic recrystallization ofcopper[J]. Metal Science,17(12):609-616.
BUSSO E P.1998. A continuum theory for dynamic recrystallization with microstructure-relatedlength scales. Internation Journal of Plasticity,14(4-5):319-353.
COLAS R.1996. A model for the hot deformation of low-carbon steel[J]. Journal of MaterialsProcessing Technology,62(1-3):180-184.
CHUA L O, YANG L.1988. Cellular neural networks: Applications[J]. IEEE Transaction CircularSystem,35:1273-1290.
CHUNG J S, HWANG S M.1998. Application of a genetic algorithm to process optimal design innon-isothermal metal forming[J]. Jounal of Materials Processing Technology,80-81:136-143.
陈文.2011.增量体积成形数值模拟技术及其在多道次拔长工艺设计中的应用[D].上海:上海交通大学博士学位论文.
崔忠圻.1989.金属学及热处理[M].北京:机械工业出版社.
崔振山,陈文,陈飞,张效迅.2010.大锻件控性锻造过程的计算机模拟技术[J].机械工程学报,46(11):2-8.
崔振铎,刘华山.2010.金属学及热处理[M].长沙:中南大学出版社.
DAVIES C H J.1995. The effect of neighbourhood on the kinetics of a cellular automatonrecrystallization model[J]. Scripta Metallurgical et Materialia,33(7):1139-1143.
DAVIES C H J.1997. Growth of nuclei in a cellular automaton simulation of recrystallization[J].Scripta Materialia,36(1):35-40.
DAVIES C H J.1999. The cellular automaton simulation of static recrystallization in cold-rolledAA1050[J]. Scripta Materialia,40(10):1145-1150.
邓小虎.2009.金属热变形及焊缝凝固过程的元胞自动机模拟[D].大连:大连理工大学博士学位论文.
DEHGHAN-MANSHADI A, BARNETT M R, HODGSON P D.2008a. Hot deformation andrecrystallization of austenitic stainless steel: Part. Dynamic recrystallization[J]. Metallurgicaland Materials Transactions A,39:1359-1370.
DEHGHAN-MANSHADI A, BARNETT M R, HODGSON P D.2008b. Hot deformation andrecrystallization of austenitic stainless steel: Part П. Post-deformation recrystallization[J].Metallurgical and Materials Transactions A,39:1371-1381.
丁汉林.2007. AZ91镁合金高温变形行为的实验研究与数值模拟[D].上海:上海交通大学博士学位论文.
丁恒敏.2005.铸造合金的微观组织模拟—几种方法关键技术的研究[D].武汉:华中科技大学博士学位论文.
DING R, GUO Z X.2001. Coupled quantitative simulation of microstructural evolution and plasticflow during dynamic recrystallization[J]. Acta Materialia,49:3163-3175.
DING R, GUO Z X.2002. Microstructural modeling of dynamic recrystallization using an extendedcellular automaton approach[J]. Computational Materials Science,23:209-218.
DOHERTY R D, HUGHES D A, HUMPHREYS F J, JONAS J J, JUUL JENSEN D, KASSNER M E,KING W E, MCNELLEY T R, MCQUEEN H J, ROLLETT A D.1997. Current issues inrecrystallization: a review[J]. Materials Science and Engineering A,238:219-274.
DERBY B, ASHBY M F.1987. On dynamic recrystallization[J]. Scripta Metallurgica,21:879-884.
EBRAHIMI R, ZAHIRI S H, NAJAFIZADEH A.2006. Mathematical modeling of the stress-straincurves of Ti-IF steel at high temperature[J]. Journal of Materials Processing Technology,171:301-305.
ELWAZRI A M, ESSADIQI E, YUE S.2004a. Kinetics of static recrystallization in microalloyedhypereutectoid steels[J]. ISIJ International,44(1):162-170.
ELWAZRI A M, ESSADIQI E, YUE S.2004b. Kinetics of metadynamic recrystallization inmicroalloyed hypereutectoid steels[J]. ISIJ International,44(4):744-752.
FAN D, GENG C W, CHEN L-Q.1997a. Computer simulation of topological evolution in2-D graingrowth using a continuum diffuse-interface field model[J]. Acta Materialia,45(3):1115-1126.
FAN D, CHEN L–Q.1997b. Computer simulation of grain growth using a continuum field model[J].Acta Materialia,45:611-622.
FAN X G, YANG H.2011. Internal-state-variable based self-consistent constitutive modeling for hotworking of two-phase titanium alloys coupling microstructure evolution[J]. International Journalof Plasticity,27:1833-1852.
冯海林.2007.生物病毒复杂系统定性仿真研究[D].合肥:中国科学技术大学博士学位论文.
FRISCH U, HASSLACER B, POMEAU Y.1986. Lattice gas automata for the Navier-Stokesequation[J]. Physical Review Letter,56:1505-1508.
GAO J, THOMPSON R G.1996. Real time-temperature models for Monte Carlo simulations ofnormal grain growth[J]. Acta Materialia,44(11):4565-4570.
GARDNER M.1970. Mathematical Games: The fantastic combinations of John Conway’s newsolitaire game “life”[J]. Scientific American:120-123.
GEIGER J, ROóSZ A, BARKóCZY P.2001. Simulation of grain coarsening in two dimensionas bycellular-automaton[J]. Acta Materialia,49:623-629.
GOETZ R L, SEETHARAMAN V.1998a. Static recrystallization kinetics with homogeneous andheterogeneous nucleation using a cellular automata model[J]. Metallurgical and MaterialsTransactions A,29:2307-2321.
GOETZ R L, SEETHARAMAN V.1998b. Modeling dynamic recrystallization using cellularautomata[J]. Scripta Materialia,38:405-413.
GOTTSTEIN G, MARX V, SEBALD R.2000. Integration of physically based models into FEM andapplication in simulation of metal forming processes[J]. Modelling and Simulation in MaterialsScience and Engineering,8(6):881-891.
关小军,焦宪友,周家娟,张继祥,刘运腾,申孝民,麻晓飞.2007.单一晶粒长大过程的元胞自动机模拟[J].中国有色金属学报,17(5):699-703.
管靖.2008.锻造成形过程微观组织优化设计方法研究[D].济南:山东大学博士学位论文.
郭娟,王艳敏,李卫,吴迪,赵宪明.2009.静态再结晶过程的元胞自动机模拟(Ⅰ)-微观组织演化和动力学研究[J].大型铸锻件,1:20-24.
郭娟,贺艺,许艺萍,吴迪,赵宪明.2009.静态再结晶过程的元胞自动机模拟(Ⅱ)-晶粒尺寸和边数的变化[J].大型铸锻件,2:4-7.
HEDLUND G A.1969. Endomorphisms and automorphisms of the shift dynamical system[J].Theory of Computing systems,3(4):320-375.
HE Y Z, DING H L, LIU L F, SHIN K.2006. Computer simulation of2D grain growth using acellular automata model based on the lowest energy principle[J]. Materials Science andEngineering A,429:236-246.
HESSELBARTH H, GOBEL I.1991. Simulation of recrystallization by cellular automata[J]. ActaMetallurgica et Materialia,39(9):2135-2143.
HESSELBARTH H, KAPS L, HAESSNER F.1993. Two dimensional simulation of therecyrstallization kinetics in the case of inhomogeneously stored energy[J]. Materials ScienceForum,317:113-115.
花福安,杨院生,郭大勇,董文辉,胡壮麒.2004.基于曲率驱动机制的晶粒生长元胞自动机模型[J].金属学报,40(11):1210-1214.
HUANG S Q, YI Y P, LIU C.2009. Investigation of dynamic recrystallization for aluminium alloy7050forging using cellular automaton [J]. Journal of Central South University of Technology(English Edition),16(1):18-24.
黄光晓.2009.外汇市场复杂性及人工外汇市场研究[D].厦门:厦门大学博士学位论文.
HUMPHREYS F J, HATHERLY M.1995. Recrystallization and related annealing phenomena[M].Elsevier Science, Oxford, UK.
IVASISHIN O M, SHEVCHENKO S V, VASILIEV N L, SEMIATIN S L.2006. A3-D Monte-Carlo(Potts) model for recrystallization and grain growth in polycrystalline materials[J]. MaterialScience and Engineering A,433:216-232.
JANG Y-S, KO D-C, KIM B-M.2000. Application of the finite element method to predictmicrostructure evolution in the hot forging of steel[J]. Journal of Processing Technology,101:85-94.
JANSSENS K G F, RAABE D, KOZESCHNIK E, MIODOWNIK M A, NESTLER B.2007.Computational materials engineering: an introduction to microstructure evolution[M]. ElsevierAcademic Press, ISBN:978-0-12-369468-3.
JANSSENS K G F.2010. An introductory review of cellular automata modeling of moving grainboundaries in polycrystalline materials[J]. Mathematics and Computers in Simulation,80(7):1361-1381.
焦宪友,关小军,刘运腾,关宇昕,张继祥，申孝民,麻晓飞.2005.基于元胞自动机法的晶粒长大模拟[J].山东大学学报(工学版),35(6):24-28.
姜锐.2003.交通流复杂动态特性的微观和宏观模式研究[D].合肥:中国科学技术大学博士论文.
江志松.2001.元胞自动机的语法复杂性[D].苏州:苏州大学博士学位论文.
金宁.1990.大锻件孔隙性缺陷的压合与焊合规律的研究及高温栅的研究[D].北京:清华大学博士学位论文.
金泉林.1994.一个新的动态再结晶过程的分析模型[J].塑性工程学报，1(1):3-14.
JING Z Y, CUI Z S.2010. Investigation on strain dependence of dynamic recrystallization behaviorusing an inverse analysis method[J]. Materials Science and Engineering A,527:3111-3119.
金朝阳.2010.基于反分析方法的低碳钢动态再结晶行为数值模拟[D].上海:上海交通大学博士学位论文.
KARHAUSEN K, KOPP R.1992. Model for ingegrated process and microstructure simulation in hotforming[J]. Steel Research,63:247-256.
KAZEMINEZHAD M, TAHERI A K, TIEU A K.2006. Utilization of the finite element and MonteCarlo model for simulating the recrystallization of inhomogeneous deformation of copper[J].Computational Materials Science,38(4):765-773.
KIM S-I, YOO Y C.2001. Dynamic recrystallization behavior of AISI304stainless steel[J].Materials Science and Engineering A,311:108-113.
KIM S-I, LEE Y, LEE D L, YOO Y C.2003. Modeling of AGS and recrystallized fraction ofmicroalloyed medium carbon steel during hot deformation[J]. Materials Science and EngineeringA,355:384-393.
KONG L X, HODGSON P D, WANG B.1999. Development of constitutive models for metalforming with cyclic strain softening[J]. Journal of Materials Processing Technology,89-90:44-45.
KOPP R, CHO M L, SOUZA M D.1987. Multi-level simulation of metal-forming processes[J].Advanced Technology of Plasticity,24-28:1229-1234.
KREMEYER K.1998. Cellular automata investigations of binary solidification[J]. Journal ofComputational Physics,142(1):243-262.
KUGLER G, TURK R.2004. Modeling the dynamic recrystallization under multi-stage hotdeformation[J]. Acta Materialia,52:4659-4668.
KUMAR M, SASIKUMAR R, KESAVAN NAIR P.1998. Competition between nucleation and earlygrowth of ferrite from austenite-studies using cellular automaton simulations[J]. Acta Materialia,46:6291-6303.
LAASRAOUI A, JONAS J J.1991a. Recrystallization of austenite alter deformation at hightemperature and strain rates-analysis and modeling[J]. Metallurgical Transaction A,22(7):151-160.
LAASRAOUI A, JONAS J J.1991b. Prediction of steel flow stresses at high temperature and strainrates[J]. Metallurgical and Materials Transactions A,22(7):1545-1558.
LANGTON C.1986. Studying artificial life with cellular automata[J]. Phisica D: NonlinearPhenamena,22(1-3):120-149.
兰勇军.2005.低碳钢奥氏体-铁素体相变介观模拟计算[D].沈阳:中国科学院金属研究所博士学位论文.
LEE B H, REDDY N S, YEOM J T, LEE C S.2007. Flow softening behavior during hightemperature deformation of AZ31Mg alloy[J]. Journal of Materials Processing Technology,187-188:766-769.
LEE M G, LIM H, ADAMS B L, HIRTH J P, WAGONER R H.2010. A dislocation density-basedsingle crystal constitutive equation[J]. International Journal of Plasticity,26(7):925-938.
李殿中,杜强,胡志勇.1999.金属成形过程组织演变的Cellular Automaton模拟技术[J].金属学报,35:1201-1205.
李恒德.编著.2002.材料科学与工程国际前沿[M].山东:山东科学技术出版社.
LI D Z, XIAO N M, LAN Y J, ZHENG C W, LI Y Y.2007. Growth modes of individual ferrite grainsin the austenite to ferrite transformation of low carbon steels[J]. Acta Materilia,55:6234-6249.
LI M Q, CHEN D J, XIAOG A M.2002. An adaptive prediction model of grain size for the formingof Ti-6Al-4V alloy based on fuzzy neural networks[J]. Journal of Materials Technology,123:377-381.
LI M Y, KANNATEY E.2002. Monte Carlo simulation of Heat-Affected zone microstructure inLaser-Beam-Welded Nickel sheet[J]. Welding Journal,3:37-44.
李强.2004.凝固过程枝晶演变的数值模拟研究[D].沈阳:中国科学院金属研究所博士学位论文.
李晓丽.2005.钛合金高温变形时跨层次模型及数值模拟[D].西安:西北工业大学博士学位论文.
刘国权,王浩,岳景朝.2008.晶粒、细胞或皂泡的三维多面体模型评述[J].第十二届中国体视学与图像分析学术会议,34-37.
刘志勇,许庆彦,柳百成.2007.枝晶生长的介观尺度三维数值模拟[J].清华大学学报(自然科学版),47(8):1253-1258.
李才伟.1997.元胞自动机及复杂系统的时空演化模拟[D].武汉:华中科技大学博士学位论文.
刘建生,郭会光,孙捷先.1997.刚粘塑性有限元软件TRORM2及应用[J].太原重型机械学院学报,18(3):255-259,268.
LIU Y, BAUDIN T, PENELLE R.1996. Simulation of normal grain growth by cellular automata[J].Scripta Materialia,34(11):1679-1683.
LIU J, CUI Z S, LI C X.2008a. Modelling of flow stress characterizing dynamic recrystallization formagnestium alloy AZ31B[J]. Computational Materials Science,41:375-382.
刘娟.2008b.镁合金锻造成形性研究及数值模拟[D].上海:上海交通大学博士学位论文.
LIU Y, BAUDIN T, PENELLE R.1996. Simulation of normal grain growth by cellular automata[J].Scripta Materialia,34(11):1679-1683.
LIN Y C, CHEN M S, ZHONG J.2008. Effect of temperature and strain rate on the compressivedeformation behavior of42CrMo steel[J]. Journal of Materials Processing Technology,205:308-315.
LIN Y C, CHEN M S.2009. Numerical simulation and experimental verification of microstructureevolution in a three-dimensional hot upsetting process[J]. Journal of Materials ProcessingTechnology,209:4578-4583.
刘助柏,李纬民.1994a.新FM锻造法[J].机械工程学报,30(4):79-82.
刘助柏.1994b.平砧拔长矩形截面毛坯的新理论[J].机械工程学报,30(5):47-49.
卢瑜,张立文,邓小虎,裴继斌,王赛,张国梁.2007.纯铜动态再结晶过程的元胞自动机模拟[J].金属学报,44(3):292-296.
吕炎编著.1995.锻造工艺学[M].北京:机械工业出版社.
吕炎编著.1999.锻件缺陷分析与对策[M].北京:机械工业出版社.
刘鑫,钟约先,马庆贤,袁朝龙.2010.低压转子钢30Cr2Ni4MoV动态再结晶行为研究[J].中国机械工程,21(5):603-606.
蔺永诚,陈明松,钟掘.2008.42CrMo钢的热压缩流变应力行为[J].中南大学学报(自然科学版),39(3):550-553.
麻晓飞.2008.二相粒子材料再结晶退火的元胞自动机模型及其模拟研究[D].济南:山东大学博士学位论文.
马新武.2002.体积成形过程数值模拟与优化技术及其系统开发研究[D].济南:山东大学博士学位论文.
MARX V, REHER F R, GOTTSTEIN G.1999. Simulation of primary recrystallization using amodified three-dimensional cellular automaton[J]. Acta Materilia,47(4):1219-1230.
毛卫民,赵新兵编著.1994.金属的再结晶与晶粒长大[M].北京:冶金工业出版社.
MCQUEEN H J.1988. Initiating nucleation of dynamic recrystallization, primarily in polycrystals.Materials Science and Engineering A,101:149-160.
MCQUEEN H J, RYAN N D.2002. Constitutive analysis in hot working[J]. Materials Science andEngineering A,322:43-63.
MCQUEEN H J.2004. Development of dynamic recrystallization theory[J]. Materials Science andEngineering A,387-389:203-208.
MECKING H, KOCKS U F.1981. Kinetics of flow and strain-hardening[J]. Acta Metallurgica,29(11):1865-1875.
MISHRA S, DEBROY T.2004. Measurements and Monte Carlo simulation of grain growth in theheat affected zone of Ti-6Al-4V welds[J]. Acta Materialia,52(5):1183-1192.
MUKHOPADHYAY P, LOECK M, GOTTSTEIN G.2007. A cellular operator model for thesimulation of static recrystallization[J]. Acta Materialia,55:551-564.
MULLINS W W.1956. Two-dimension motion of idealized grain boundaries[J]. Journal of AppliedPhysics27:900-904.
NAGATANI T.1993. Jamming transition in the traffic-flow model with two-level crossings. PhysicalReview E,48:3290-3294.
PALMER M, PAJAN K, GLICKSMAN M, FRADKOV V E, NORDBERG J.1995. Two-dimensionalgrain growth in rapidly solidified succinonitrile films[J]. Metallurgical Materials Transactions A,26:1061-1066.
PECZAK P, LUTON M J.1993. The effect of nucleation models on dynamic recrystallization Ι.Homogeneous stored energy distribution[J]. Philosophical Magazine B,68(1):115-144.
PECZAK P, LUTON M J.1994. The effect of nucleation models on dynamic recrystallization Ⅱ.Heterogeneous stored energy distribution[J]. Philosophical Magazine B,70(4):817-849.
PECZAK P.1995. A Monte Carlo study of influence of deformation temperature on dynamicrecrystallization[J]. Acta Metallurgica Et Materialia,43(3):1279-1291.
裴鹿成,王仲奇.1998.蒙特卡洛方法及应用[M].北京:海洋出版社.
POURSINA M, EBRAHIMI H, PARVIZIAN J.2008. Flow stress behavior of two stainless steels: Anexperimental-numerical investigation[J]. Journal of Materials Processing Technology,199:287-294.
曲杰.2004.考虑动态再结晶的粘塑性本构模型的参数识别[D].北京:清华大学博士学位论文.
RAABE D.1999. Introduction of a scalable three-dimensional cellular automaton with aprobabilistic swiching rule for the discrete mesoscale simulation of recrystallization phenomena[J].Philosophical Magazine A,79(10):2339-2358.
RAABE D, BECKER R C.2000. Coupling of a crystal plasticity finite-element model with aprobabilistic cellular automaton for simulation primary static recrystallization in aluminium[J].Modeling and Simulation in Materials Science and Engineering,8:445-462.
RAABE D, SACHTLEBER M, ZHAO Z, ROTERS F, ZAEFFERER S.2001. Micromechanical andmacromechanical effects in grain scale polycrystal plasticity experimentation and simulation[J].Acta Materialia,49:3433-3441.
RAABE D.2002. Cellular automata in materials science with particular reference to recrystallizationsimulation[J]. Annual Review of Materials Research,32:53-76.
RAABE D, ROTERS F, BARLAT F, CHEN L Q.2004. Continuum scale simulation of engineeringmaterials[M]. Wiley-VCH, Weinheim, ISBN:3-527-30760-5.
RAABE D, HANTCHERLI L.2005.2D cellular automaton simulation of the recrystallizationtexture of an IF sheet steel under consideration of Zener pinning[J]. Computational MaterialsScience,34:299-313.
RADHAKRISHNAN B, ZACHARIA T.1995. Monte Carlo simulation of grain boundary pinning inthe weld-heat-affected zone[J]. Metallurgical and Materials Transactions A,26(8):2123-2130.
RADHAKRISHNAN B, SARMA G, ZACHARIA T.1998. Coupled finite element-Monte Carlosimulation of microstructure and texture evolution during thermomechanical processing[J].Proceedings of the TMS Fall Meeting, November,267-278.
READ W T, SHOCKLEY W.1950. Dislocation models of crystal grain boundaries[J]. PhysicalReview,78:275-289.
ROLLET A D.1997. Overview of modeling and simulation of recrystallization[J]. Progress inMaterials Science,42:79-99.
ROBERTS W, AHLBLOM B. A nucleation criterion for dynamic recrystallization during hotworking[J].1978. Acta Metallurgica,26:801-813.
ROBERTS W, BODEN H, AHLBLOM B. Dynamic recrystallization kinetics[J].1979.Metal Science,13(3-4):195-205.
ROTERS F, RAABE D, GOTTSTEIN G.2000. Work hardening in heterogeneous alloys-Amicrostructural approach based on three internal state variables[J]. Acta Materialia,48:4181-4189.
SAADIA A, MARIE C E J.2002. Vegetation dynamics modelling: a method for coupling local andspace dynamics[J]. Ecological Modelling,154(3):237-249.
SAKAI T, AKBEN M G, JONAS J J.1983. Dynamic recrystallization during the transientdeformation of a vanadium microalloyed steel. Acta Metallurgica,31:631-641.
SAKAI T, JONAS J J.1984. Overview no.35Dynamic recrystallization:Mechanical andmicrostructural considerations. Acta Metallallurgica,32(2):189-209.
单德彬,吕炎,王真.1997.金属体积成形过程三维刚塑性有限元模拟技术的研究[J].塑性工程学报,4(3):98-102.
SATIO Y.1997. Modeling of microstructural evolution in thermomechanical processing ofstructurals steels[J]. Materials Science and Technology,233:134-145.
SELLARS C M, WHITEMAN J A.1979. Recrystallization and grain growth in hot rolling[J]. MetalScience,13(3-4):187-194.
SELLARS C M.1990. Modelling microstructural development during hot rolling[J]. MaterialsScience and Technology,6:1072-1081.
SELLARS C M, ZHU Q.2000. Microstructural modeling of aluminium alloys duringthermomechanical processing[J]. Materials Science and Engineering A,280:1-7.
SENUMA T, YADA H.1986. Microstructural evolution of planin carbon steels in multiple hotworking proceedings of the riso international symposium on metallurgy and materials science7th:547-552.
沈健, GOTTSTEIN G.2001.铝合金热变形组织演化的模拟[J].材料科学与工艺,9(3):329-333.
申孝民，关小军，张继祥，刘运腾，麻晓飞，赵宪明.2007.有限元与Monte Carlo方法耦合的冷轧纯铝板再结晶模拟[J].中国有色金属学报,17(1):124-130.
申孝民.2008.有限元与蒙特卡罗法耦合的退火过程模拟模型及关键技术研究[D].济南:山东大学博士学位论文.
SINGH S B, BHADESHIA H K D H.1998. Estimation of bainite plate-thickness in low-alloy steels.Material Science and Enginnering A,245:72-79.
宋晓艳,刘国权,何宜柱.1998.一种改进的晶粒长大Monte Carlo模拟方法[J].自然科学进展,8(3):337-341.
宋晓艳,刘国权,谷南驹.1999.一种简便高效的材料三维组织及其演变的Monte Carlo仿真[J].科学通报,44(5):491-495.
宋晓艳.1998.基于计算机模拟的正常晶粒长大的三维特征和二维截面表征[J].材料研究学报,12(3):232-235.
SONG X Y, RETTENMAYR M, MüLLER C, EXNER H E.2001. Modeling of recrystallization afterinhomogeneous deformation[J]. Metallurgical and Materials Transaction A,32:2219-2206.
SOLAS D E, TOME C N, ENGLER O, WENK H R.2001. Deformation and recrystallization ofhexagonal metals: modeling and experimental results for zinc[J]. Acta Materialia,49:3791-3801.
SROLOVITZ D J, GREST G S, ANDERSON M P.1986. Computer simulation of recrystallization-.Homogeneous nucleation and growth[J]. Acta Metallurgica,34(9):1833-1845.
TAKUDA H, MORISHITA T, KINOSHITA T, SHIRAKAWA N.2005. Modelling of formula for flowstress of a magnesium alloy AZ31sheet at elevated temperatures. Journal of Materials ProcessingTechnology,164:1258-1262.
佟铭明,莫春立,李殿中.2002a.用Monte Carlo法模拟纯铜的静态再结晶[J].材料研究学报,16(5):485-489.
佟铭明,莫春立,李殿中.2002b.纯铜动态再结晶Monte Carlo模拟[J].金属学报,38(7):745-749.
TóTH L S, MOLINARI A, ESTRIN Y.2002. Strain hardening at large strains as predicted bydislocation based polycrystal plasticity model[J]. Journal of Engineering Materials and Technology,124:71-77.
VATNE H E, SHAHANI R, NES E.1996. Deformation of cube-oriented grains and formation ofrecrystallized cube grains in a hot deformed commercial ALMgMn aluminium alloy[J]. ActaMaterialia,44:4447-4462.
WANG L S, CAO Q X, LIU Z.1996. Numerical simulation and experimental verification ofmicrostructure evolution in a3-dimensional hot-upsetting process[J]. Journal Materials ProcessingTechnology,58:331-336.
WANG W, LEE P D, MCLEAN M.2003. A model of solidification microstructures in nickel-basedsuperalloys: predicting primary dendrite spaceing selection[J]. Acta Materialia,51:2971-2987.
WAHABI M E, CABRERA J M, PRADO J M.2003. Hot working of two AISI304steels: acomparative study[J]. Materials Science and Engineering A,343(1-2):116-125.
王广春.2010.金属体积成形工艺及数值模拟技术[M].北京:机械工业出版社.
王进.2007.非调制刚三维复杂热锻造过程多物理场数值模拟研究[D].上海:上海交通大学博士论文.
WOLFRAM S.1984a. Cellular automata as models of complexity[J]. Nature,311(4):419-424.
WOLFRAM S.1984b. University and complexity in cellular automata[J]. Physica D,10(1):1-35.
WOLFRAM S.1986. Theory and applications of cellular automata[J]. Advanced Series on ComplexSystems, slected papers1983-1986, Volume1, World Scientific Publishing Co. Pte. Ltd. Singapore.
XIAO H, XIE H B, YAN Y H, JUN YANAGIMOTO.2004. Simulation of dynamic recrystallizationusing cellular automaton method[J]. Iron and Steel Research,11(2):42-45.
肖宏,柳本润.2005a.采用Cellular automaton法模拟动态再结晶过程的研究[J].机械工程学报,41(2):148-152.
肖宏,徐玉辰,闫艳红.2005b.考虑晶粒变形动态再结晶过程模拟的元胞自动机法[J].中国机械工程,16(24):2245-2248.
XIAO N M, ZHENG C W, LI D Z, LI Y Y.2008. A simulation of dynamic recrystallization bycoupling a cellular automaton method with a topology deformation technique[J]. ComputionalMaterials Science,41:366-374.
徐钟济.1985.蒙特卡罗方法[M].上海:上海科学技术出版社.
薛利平,鹿守理,窦晓峰.2000.金属热变形时组织演化的有限元模拟及性能预报[J].北京科技大学学报,22(1):34-37.
杨旗,罗子健,刘东.1999.应用模糊数学预测变形高温合金锻件晶粒度[J].中国机械工程,10(7):832-834.
YANG Z, SISTA S.2000. Three dimensional Monte Carlo simulation of grain growth during GTAwelding of titanium[J]. Acta Materialia,48(8):4813-4825.
YAZDIPOUR N, DAVIES C H J, HODGSON P D.2008. Microstructural modeling of dynamicrecrystallization using irregular cellular automata[J]. Computational Materials Science,44:566-576.
YDAA H, SENUMA T.1986. Resistance to hot deformation of steel[J]. Journal of the Japan Societyfor Technology of Plasticity,27:33-44.
YEOM J T, LEE C S, KIM J H, PARK N-K.2006. Finite-element analysis of microstructureevolution in the cogging of an Alloy718ingot[J]. Materials Science and Engineering A,449-451:722-726.
YOSHINO M, SHIRAKASHI T.1995. New flow-stress equation of Ti-6AL-4V alloy[J]. Journal ofMaterials Processing Technology,48:179-186.
余永宁,刘国权.1998.体视学:组织定量分析的原理和应用[M].北京:冶金工业出版社.
YU Q, ESCHE S K.2003. A Monte Carlo algorithm for single phase normal grain growth withimproved accuracy and efficiency[J]. Computational Materials Science,27:259-270.
YU Q, ESCHE S K.2005. A multi-scale approach for microstructure prediction in thermo-mechaincal processing of metals[J]. Journal of Materials Processing Technology,169:493-502.
赵道亮.2007.紧急条件下人员疏散特殊行为的元胞自动机模拟[D].合肥:中国科学技术大学博士论文.
张跃,谷景华,尚家香.编著.2007.计算材料科学基础[M].北京:北京航空航天大学出版社.
张继祥,关小军,孙胜.2004.一种改进的晶粒长大Monte Carlo模拟方法[J].金属学报,40(5):457-461.
张立文,卢瑜,邓小虎,裴继斌,张国梁.2008.不同形核机制下对动态再结晶过程模拟研究[J].大连理工大学学报,48(3):351-355.
詹梅,杨合,刘郁丽.2005.金属塑性成形三维有限元模拟软件3D-PFS的开发[J].材料科学与工艺,13(4):402-406.
ZHANG L, ZHANG C B, WANG Y M, WANG S Q, YE H Q.2003. A cellular automatoninvestigation of the transformation from austenite to ferrite during continous cooling[J]. ActaMaterialia,51:5519-5527.
曾志朋,2002. DEFORM软件的二次开发与大型锻件锻造工艺优化[D].北京:北京机电研究所硕士学位论文.
郑成武,兰勇军,肖纳敏,李殿中,李依依.2006.热变形低碳钢中奥氏体静态再结晶介观尺度模拟[J].金属学报,42(05):474-480.
ZHENG C W, XIAO N M, LI D Z, LI Y Y.2008. Microstructure prediction of the austeniterecrystallization during multi-pass steel strip hot rolling: A cellular automaton modeling[J].Computational Materials Science,44:507-514.
郑成武.2009.低碳钢热变形中微观组织演变的元胞自动机模拟[D].沈阳:中国科学院金属研究所博士学位论文.
ZHU P, SMITH R W.1992. Dynamic simulation of crystal growth by Monte Carlo method-. Modeldescription and kinetics[J].40(4):683-692.
(参考文献共194条)
AUSTIN R A, MCDOWELL D L.2011. A dislocation-based constitutive model for viscoplasticdeformation of fcc metals at very high strain rates[J]. International Journal of Plasticity,27:1-24.
BARIANI P, BRUSCHI S, DAL NEGRO T.2000. A new constitutive model for hot forging of steeltaking into account the thermal and mechanical history[J]. Annals of CIRP,49:195-198.
BARKóCZY P, ROóSZ A, GEIGER J.2003. Simulation of recrystallization by cellular automatonmethod [J]. Mater Sci Forum,414-415:359-364.
BATE P S, HUTCHINSON W B.2005. Grain boundary area and deformation[J]. Scripta Material,52(3):199-203.
BAUDIN T, JULLIARD F, PAILLARD P, PENELLE R.2000. Simulation of primaryrecrystallization from TEM orientation data[J]. Scripta Materialia,43(1):63-68.
BAUDIN T, SOLAS D, ETTER A L, CECCALDI D, PENELLE R.2004. Simulation of primaryrecrystallization from TEM observations and neutron diffraction measurements[J]. ScriptaMaterialia,51:427-430.
BLAZ L, SAKAI T, JONAS J J.1983. Effect of initial grain size on dynamic recrystallization ofcopper[J]. Metal Science,17(12):609-616.
BUSSO E P.1998. A continuum theory for dynamic recrystallization with microstructure-relatedlength scales. Internation Journal of Plasticity,14(4-5):319-353.
COLAS R.1996. A model for the hot deformation of low-carbon steel[J]. Journal of MaterialsProcessing Technology,62(1-3):180-184.
CHUA L O, YANG L.1988. Cellular neural networks: Applications[J]. IEEE Transaction CircularSystem,35:1273-1290.
CHUNG J S, HWANG S M.1998. Application of a genetic algorithm to process optimal design innon-isothermal metal forming[J]. Jounal of Materials Processing Technology,80-81:136-143.
陈文.2011.增量体积成形数值模拟技术及其在多道次拔长工艺设计中的应用[D].上海:上海交通大学博士学位论文.
崔忠圻.1989.金属学及热处理[M].北京:机械工业出版社.
崔振山,陈文,陈飞,张效迅.2010.大锻件控性锻造过程的计算机模拟技术[J].机械工程学报,46(11):2-8.
崔振铎,刘华山.2010.金属学及热处理[M].长沙:中南大学出版社.
DAVIES C H J.1995. The effect of neighbourhood on the kinetics of a cellular automatonrecrystallization model[J]. Scripta Metallurgical et Materialia,33(7):1139-1143.
DAVIES C H J.1997. Growth of nuclei in a cellular automaton simulation of recrystallization[J].Scripta Materialia,36(1):35-40.
DAVIES C H J.1999. The cellular automaton simulation of static recrystallization in cold-rolledAA1050[J]. Scripta Materialia,40(10):1145-1150.
邓小虎.2009.金属热变形及焊缝凝固过程的元胞自动机模拟[D].大连:大连理工大学博士学位论文.
DEHGHAN-MANSHADI A, BARNETT M R, HODGSON P D.2008a. Hot deformation andrecrystallization of austenitic stainless steel: Part. Dynamic recrystallization[J]. Metallurgicaland Materials Transactions A,39:1359-1370.
DEHGHAN-MANSHADI A, BARNETT M R, HODGSON P D.2008b. Hot deformation andrecrystallization of austenitic stainless steel: Part П. Post-deformation recrystallization[J].Metallurgical and Materials Transactions A,39:1371-1381.
丁汉林.2007. AZ91镁合金高温变形行为的实验研究与数值模拟[D].上海:上海交通大学博士学位论文.
丁恒敏.2005.铸造合金的微观组织模拟—几种方法关键技术的研究[D].武汉:华中科技大学博士学位论文.
DING R, GUO Z X.2001. Coupled quantitative simulation of microstructural evolution and plasticflow during dynamic recrystallization[J]. Acta Materialia,49:3163-3175.
DING R, GUO Z X.2002. Microstructural modeling of dynamic recrystallization using an extendedcellular automaton approach[J]. Computational Materials Science,23:209-218.
DOHERTY R D, HUGHES D A, HUMPHREYS F J, JONAS J J, JUUL JENSEN D, KASSNER M E,KING W E, MCNELLEY T R, MCQUEEN H J, ROLLETT A D.1997. Current issues inrecrystallization: a review[J]. Materials Science and Engineering A,238:219-274.
DERBY B, ASHBY M F.1987. On dynamic recrystallization[J]. Scripta Metallurgica,21:879-884.
EBRAHIMI R, ZAHIRI S H, NAJAFIZADEH A.2006. Mathematical modeling of the stress-straincurves of Ti-IF steel at high temperature[J]. Journal of Materials Processing Technology,171:301-305.
ELWAZRI A M, ESSADIQI E, YUE S.2004a. Kinetics of static recrystallization in microalloyedhypereutectoid steels[J]. ISIJ International,44(1):162-170.
ELWAZRI A M, ESSADIQI E, YUE S.2004b. Kinetics of metadynamic recrystallization inmicroalloyed hypereutectoid steels[J]. ISIJ International,44(4):744-752.
FAN D, GENG C W, CHEN L-Q.1997a. Computer simulation of topological evolution in2-D graingrowth using a continuum diffuse-interface field model[J]. Acta Materialia,45(3):1115-1126.
FAN D, CHEN L–Q.1997b. Computer simulation of grain growth using a continuum field model[J].Acta Materialia,45:611-622.
FAN X G, YANG H.2011. Internal-state-variable based self-consistent constitutive modeling for hotworking of two-phase titanium alloys coupling microstructure evolution[J]. International Journalof Plasticity,27:1833-1852.
冯海林.2007.生物病毒复杂系统定性仿真研究[D].合肥:中国科学技术大学博士学位论文.
FRISCH U, HASSLACER B, POMEAU Y.1986. Lattice gas automata for the Navier-Stokesequation[J]. Physical Review Letter,56:1505-1508.
GAO J, THOMPSON R G.1996. Real time-temperature models for Monte Carlo simulations ofnormal grain growth[J]. Acta Materialia,44(11):4565-4570.
GARDNER M.1970. Mathematical Games: The fantastic combinations of John Conway’s newsolitaire game “life”[J]. Scientific American:120-123.
GEIGER J, ROóSZ A, BARKóCZY P.2001. Simulation of grain coarsening in two dimensionas bycellular-automaton[J]. Acta Materialia,49:623-629.
GOETZ R L, SEETHARAMAN V.1998a. Static recrystallization kinetics with homogeneous andheterogeneous nucleation using a cellular automata model[J]. Metallurgical and MaterialsTransactions A,29:2307-2321.
GOETZ R L, SEETHARAMAN V.1998b. Modeling dynamic recrystallization using cellularautomata[J]. Scripta Materialia,38:405-413.
GOTTSTEIN G, MARX V, SEBALD R.2000. Integration of physically based models into FEM andapplication in simulation of metal forming processes[J]. Modelling and Simulation in MaterialsScience and Engineering,8(6):881-891.
关小军,焦宪友,周家娟,张继祥,刘运腾,申孝民,麻晓飞.2007.单一晶粒长大过程的元胞自动机模拟[J].中国有色金属学报,17(5):699-703.
管靖.2008.锻造成形过程微观组织优化设计方法研究[D].济南:山东大学博士学位论文.
郭娟,王艳敏,李卫,吴迪,赵宪明.2009.静态再结晶过程的元胞自动机模拟(Ⅰ)-微观组织演化和动力学研究[J].大型铸锻件,1:20-24.
郭娟,贺艺,许艺萍,吴迪,赵宪明.2009.静态再结晶过程的元胞自动机模拟(Ⅱ)-晶粒尺寸和边数的变化[J].大型铸锻件,2:4-7.
HEDLUND G A.1969. Endomorphisms and automorphisms of the shift dynamical system[J].Theory of Computing systems,3(4):320-375.
HE Y Z, DING H L, LIU L F, SHIN K.2006. Computer simulation of2D grain growth using acellular automata model based on the lowest energy principle[J]. Materials Science andEngineering A,429:236-246.
HESSELBARTH H, GOBEL I.1991. Simulation of recrystallization by cellular automata[J]. ActaMetallurgica et Materialia,39(9):2135-2143.
HESSELBARTH H, KAPS L, HAESSNER F.1993. Two dimensional simulation of therecyrstallization kinetics in the case of inhomogeneously stored energy[J]. Materials ScienceForum,317:113-115.
花福安,杨院生,郭大勇,董文辉,胡壮麒.2004.基于曲率驱动机制的晶粒生长元胞自动机模型[J].金属学报,40(11):1210-1214.
HUANG S Q, YI Y P, LIU C.2009. Investigation of dynamic recrystallization for aluminium alloy7050forging using cellular automaton [J]. Journal of Central South University of Technology(English Edition),16(1):18-24.
黄光晓.2009.外汇市场复杂性及人工外汇市场研究[D].厦门:厦门大学博士学位论文.
HUMPHREYS F J, HATHERLY M.1995. Recrystallization and related annealing phenomena[M].Elsevier Science, Oxford, UK.
IVASISHIN O M, SHEVCHENKO S V, VASILIEV N L, SEMIATIN S L.2006. A3-D Monte-Carlo(Potts) model for recrystallization and grain growth in polycrystalline materials[J]. MaterialScience and Engineering A,433:216-232.
JANG Y-S, KO D-C, KIM B-M.2000. Application of the finite element method to predictmicrostructure evolution in the hot forging of steel[J]. Journal of Processing Technology,101:85-94.
JANSSENS K G F, RAABE D, KOZESCHNIK E, MIODOWNIK M A, NESTLER B.2007.Computational materials engineering: an introduction to microstructure evolution[M]. ElsevierAcademic Press, ISBN:978-0-12-369468-3.
JANSSENS K G F.2010. An introductory review of cellular automata modeling of moving grainboundaries in polycrystalline materials[J]. Mathematics and Computers in Simulation,80(7):1361-1381.
焦宪友,关小军,刘运腾,关宇昕,张继祥，申孝民,麻晓飞.2005.基于元胞自动机法的晶粒长大模拟[J].山东大学学报(工学版),35(6):24-28.
姜锐.2003.交通流复杂动态特性的微观和宏观模式研究[D].合肥:中国科学技术大学博士论文.
江志松.2001.元胞自动机的语法复杂性[D].苏州:苏州大学博士学位论文.
金宁.1990.大锻件孔隙性缺陷的压合与焊合规律的研究及高温栅的研究[D].北京:清华大学博士学位论文.
金泉林.1994.一个新的动态再结晶过程的分析模型[J].塑性工程学报，1(1):3-14.
JING Z Y, CUI Z S.2010. Investigation on strain dependence of dynamic recrystallization behaviorusing an inverse analysis method[J]. Materials Science and Engineering A,527:3111-3119.
金朝阳.2010.基于反分析方法的低碳钢动态再结晶行为数值模拟[D].上海:上海交通大学博士学位论文.
KARHAUSEN K, KOPP R.1992. Model for ingegrated process and microstructure simulation in hotforming[J]. Steel Research,63:247-256.
KAZEMINEZHAD M, TAHERI A K, TIEU A K.2006. Utilization of the finite element and MonteCarlo model for simulating the recrystallization of inhomogeneous deformation of copper[J].Computational Materials Science,38(4):765-773.
KIM S-I, YOO Y C.2001. Dynamic recrystallization behavior of AISI304stainless steel[J].Materials Science and Engineering A,311:108-113.
KIM S-I, LEE Y, LEE D L, YOO Y C.2003. Modeling of AGS and recrystallized fraction ofmicroalloyed medium carbon steel during hot deformation[J]. Materials Science and EngineeringA,355:384-393.
KONG L X, HODGSON P D, WANG B.1999. Development of constitutive models for metalforming with cyclic strain softening[J]. Journal of Materials Processing Technology,89-90:44-45.
KOPP R, CHO M L, SOUZA M D.1987. Multi-level simulation of metal-forming processes[J].Advanced Technology of Plasticity,24-28:1229-1234.
KREMEYER K.1998. Cellular automata investigations of binary solidification[J]. Journal ofComputational Physics,142(1):243-262.
KUGLER G, TURK R.2004. Modeling the dynamic recrystallization under multi-stage hotdeformation[J]. Acta Materialia,52:4659-4668.
KUMAR M, SASIKUMAR R, KESAVAN NAIR P.1998. Competition between nucleation and earlygrowth of ferrite from austenite-studies using cellular automaton simulations[J]. Acta Materialia,46:6291-6303.
LAASRAOUI A, JONAS J J.1991a. Recrystallization of austenite alter deformation at hightemperature and strain rates-analysis and modeling[J]. Metallurgical Transaction A,22(7):151-160.
LAASRAOUI A, JONAS J J.1991b. Prediction of steel flow stresses at high temperature and strainrates[J]. Metallurgical and Materials Transactions A,22(7):1545-1558.
LANGTON C.1986. Studying artificial life with cellular automata[J]. Phisica D: NonlinearPhenamena,22(1-3):120-149.
兰勇军.2005.低碳钢奥氏体-铁素体相变介观模拟计算[D].沈阳:中国科学院金属研究所博士学位论文.
LEE B H, REDDY N S, YEOM J T, LEE C S.2007. Flow softening behavior during hightemperature deformation of AZ31Mg alloy[J]. Journal of Materials Processing Technology,187-188:766-769.
LEE M G, LIM H, ADAMS B L, HIRTH J P, WAGONER R H.2010. A dislocation density-basedsingle crystal constitutive equation[J]. International Journal of Plasticity,26(7):925-938.
李殿中,杜强,胡志勇.1999.金属成形过程组织演变的Cellular Automaton模拟技术[J].金属学报,35:1201-1205.
李恒德.编著.2002.材料科学与工程国际前沿[M].山东:山东科学技术出版社.
LI D Z, XIAO N M, LAN Y J, ZHENG C W, LI Y Y.2007. Growth modes of individual ferrite grainsin the austenite to ferrite transformation of low carbon steels[J]. Acta Materilia,55:6234-6249.
LI M Q, CHEN D J, XIAOG A M.2002. An adaptive prediction model of grain size for the formingof Ti-6Al-4V alloy based on fuzzy neural networks[J]. Journal of Materials Technology,123:377-381.
LI M Y, KANNATEY E.2002. Monte Carlo simulation of Heat-Affected zone microstructure inLaser-Beam-Welded Nickel sheet[J]. Welding Journal,3:37-44.
李强.2004.凝固过程枝晶演变的数值模拟研究[D].沈阳:中国科学院金属研究所博士学位论文.
李晓丽.2005.钛合金高温变形时跨层次模型及数值模拟[D].西安:西北工业大学博士学位论文.
刘国权,王浩,岳景朝.2008.晶粒、细胞或皂泡的三维多面体模型评述[J].第十二届中国体视学与图像分析学术会议,34-37.
刘志勇,许庆彦,柳百成.2007.枝晶生长的介观尺度三维数值模拟[J].清华大学学报(自然科学版),47(8):1253-1258.
李才伟.1997.元胞自动机及复杂系统的时空演化模拟[D].武汉:华中科技大学博士学位论文.
刘建生,郭会光,孙捷先.1997.刚粘塑性有限元软件TRORM2及应用[J].太原重型机械学院学报,18(3):255-259,268.
LIU Y, BAUDIN T, PENELLE R.1996. Simulation of normal grain growth by cellular automata[J].Scripta Materialia,34(11):1679-1683.
LIU J, CUI Z S, LI C X.2008a. Modelling of flow stress characterizing dynamic recrystallization formagnestium alloy AZ31B[J]. Computational Materials Science,41:375-382.
刘娟.2008b.镁合金锻造成形性研究及数值模拟[D].上海:上海交通大学博士学位论文.
LIU Y, BAUDIN T, PENELLE R.1996. Simulation of normal grain growth by cellular automata[J].Scripta Materialia,34(11):1679-1683.
LIN Y C, CHEN M S, ZHONG J.2008. Effect of temperature and strain rate on the compressivedeformation behavior of42CrMo steel[J]. Journal of Materials Processing Technology,205:308-315.
LIN Y C, CHEN M S.2009. Numerical simulation and experimental verification of microstructureevolution in a three-dimensional hot upsetting process[J]. Journal of Materials ProcessingTechnology,209:4578-4583.
刘助柏,李纬民.1994a.新FM锻造法[J].机械工程学报,30(4):79-82.
刘助柏.1994b.平砧拔长矩形截面毛坯的新理论[J].机械工程学报,30(5):47-49.
卢瑜,张立文,邓小虎,裴继斌,王赛,张国梁.2007.纯铜动态再结晶过程的元胞自动机模拟[J].金属学报,44(3):292-296.
吕炎编著.1995.锻造工艺学[M].北京:机械工业出版社.
吕炎编著.1999.锻件缺陷分析与对策[M].北京:机械工业出版社.
刘鑫,钟约先,马庆贤,袁朝龙.2010.低压转子钢30Cr2Ni4MoV动态再结晶行为研究[J].中国机械工程,21(5):603-606.
蔺永诚,陈明松,钟掘.2008.42CrMo钢的热压缩流变应力行为[J].中南大学学报(自然科学版),39(3):550-553.
麻晓飞.2008.二相粒子材料再结晶退火的元胞自动机模型及其模拟研究[D].济南:山东大学博士学位论文.
马新武.2002.体积成形过程数值模拟与优化技术及其系统开发研究[D].济南:山东大学博士学位论文.
MARX V, REHER F R, GOTTSTEIN G.1999. Simulation of primary recrystallization using amodified three-dimensional cellular automaton[J]. Acta Materilia,47(4):1219-1230.
毛卫民,赵新兵编著.1994.金属的再结晶与晶粒长大[M].北京:冶金工业出版社.
MCQUEEN H J.1988. Initiating nucleation of dynamic recrystallization, primarily in polycrystals.Materials Science and Engineering A,101:149-160.
MCQUEEN H J, RYAN N D.2002. Constitutive analysis in hot working[J]. Materials Science andEngineering A,322:43-63.
MCQUEEN H J.2004. Development of dynamic recrystallization theory[J]. Materials Science andEngineering A,387-389:203-208.
MECKING H, KOCKS U F.1981. Kinetics of flow and strain-hardening[J]. Acta Metallurgica,29(11):1865-1875.
MISHRA S, DEBROY T.2004. Measurements and Monte Carlo simulation of grain growth in theheat affected zone of Ti-6Al-4V welds[J]. Acta Materialia,52(5):1183-1192.
MUKHOPADHYAY P, LOECK M, GOTTSTEIN G.2007. A cellular operator model for thesimulation of static recrystallization[J]. Acta Materialia,55:551-564.
MULLINS W W.1956. Two-dimension motion of idealized grain boundaries[J]. Journal of AppliedPhysics27:900-904.
NAGATANI T.1993. Jamming transition in the traffic-flow model with two-level crossings. PhysicalReview E,48:3290-3294.
PALMER M, PAJAN K, GLICKSMAN M, FRADKOV V E, NORDBERG J.1995. Two-dimensionalgrain growth in rapidly solidified succinonitrile films[J]. Metallurgical Materials Transactions A,26:1061-1066.
PECZAK P, LUTON M J.1993. The effect of nucleation models on dynamic recrystallization Ι.Homogeneous stored energy distribution[J]. Philosophical Magazine B,68(1):115-144.
PECZAK P, LUTON M J.1994. The effect of nucleation models on dynamic recrystallization Ⅱ.Heterogeneous stored energy distribution[J]. Philosophical Magazine B,70(4):817-849.
PECZAK P.1995. A Monte Carlo study of influence of deformation temperature on dynamicrecrystallization[J]. Acta Metallurgica Et Materialia,43(3):1279-1291.
裴鹿成,王仲奇.1998.蒙特卡洛方法及应用[M].北京:海洋出版社.
POURSINA M, EBRAHIMI H, PARVIZIAN J.2008. Flow stress behavior of two stainless steels: Anexperimental-numerical investigation[J]. Journal of Materials Processing Technology,199:287-294.
曲杰.2004.考虑动态再结晶的粘塑性本构模型的参数识别[D].北京:清华大学博士学位论文.
RAABE D.1999. Introduction of a scalable three-dimensional cellular automaton with aprobabilistic swiching rule for the discrete mesoscale simulation of recrystallization phenomena[J].Philosophical Magazine A,79(10):2339-2358.
RAABE D, BECKER R C.2000. Coupling of a crystal plasticity finite-element model with aprobabilistic cellular automaton for simulation primary static recrystallization in aluminium[J].Modeling and Simulation in Materials Science and Engineering,8:445-462.
RAABE D, SACHTLEBER M, ZHAO Z, ROTERS F, ZAEFFERER S.2001. Micromechanical andmacromechanical effects in grain scale polycrystal plasticity experimentation and simulation[J].Acta Materialia,49:3433-3441.
RAABE D.2002. Cellular automata in materials science with particular reference to recrystallizationsimulation[J]. Annual Review of Materials Research,32:53-76.
RAABE D, ROTERS F, BARLAT F, CHEN L Q.2004. Continuum scale simulation of engineeringmaterials[M]. Wiley-VCH, Weinheim, ISBN:3-527-30760-5.
RAABE D, HANTCHERLI L.2005.2D cellular automaton simulation of the recrystallizationtexture of an IF sheet steel under consideration of Zener pinning[J]. Computational MaterialsScience,34:299-313.
RADHAKRISHNAN B, ZACHARIA T.1995. Monte Carlo simulation of grain boundary pinning inthe weld-heat-affected zone[J]. Metallurgical and Materials Transactions A,26(8):2123-2130.
RADHAKRISHNAN B, SARMA G, ZACHARIA T.1998. Coupled finite element-Monte Carlosimulation of microstructure and texture evolution during thermomechanical processing[J].Proceedings of the TMS Fall Meeting, November,267-278.
READ W T, SHOCKLEY W.1950. Dislocation models of crystal grain boundaries[J]. PhysicalReview,78:275-289.
ROLLET A D.1997. Overview of modeling and simulation of recrystallization[J]. Progress inMaterials Science,42:79-99.
ROBERTS W, AHLBLOM B. A nucleation criterion for dynamic recrystallization during hotworking[J].1978. Acta Metallurgica,26:801-813.
ROBERTS W, BODEN H, AHLBLOM B. Dynamic recrystallization kinetics[J].1979.Metal Science,13(3-4):195-205.
ROTERS F, RAABE D, GOTTSTEIN G.2000. Work hardening in heterogeneous alloys-Amicrostructural approach based on three internal state variables[J]. Acta Materialia,48:4181-4189.
SAADIA A, MARIE C E J.2002. Vegetation dynamics modelling: a method for coupling local andspace dynamics[J]. Ecological Modelling,154(3):237-249.
SAKAI T, AKBEN M G, JONAS J J.1983. Dynamic recrystallization during the transientdeformation of a vanadium microalloyed steel. Acta Metallurgica,31:631-641.
SAKAI T, JONAS J J.1984. Overview no.35Dynamic recrystallization:Mechanical andmicrostructural considerations. Acta Metallallurgica,32(2):189-209.
单德彬,吕炎,王真.1997.金属体积成形过程三维刚塑性有限元模拟技术的研究[J].塑性工程学报,4(3):98-102.
SATIO Y.1997. Modeling of microstructural evolution in thermomechanical processing ofstructurals steels[J]. Materials Science and Technology,233:134-145.
SELLARS C M, WHITEMAN J A.1979. Recrystallization and grain growth in hot rolling[J]. MetalScience,13(3-4):187-194.
SELLARS C M.1990. Modelling microstructural development during hot rolling[J]. MaterialsScience and Technology,6:1072-1081.
SELLARS C M, ZHU Q.2000. Microstructural modeling of aluminium alloys duringthermomechanical processing[J]. Materials Science and Engineering A,280:1-7.
SENUMA T, YADA H.1986. Microstructural evolution of planin carbon steels in multiple hotworking proceedings of the riso international symposium on metallurgy and materials science7th:547-552.
沈健, GOTTSTEIN G.2001.铝合金热变形组织演化的模拟[J].材料科学与工艺,9(3):329-333.
申孝民，关小军，张继祥，刘运腾，麻晓飞，赵宪明.2007.有限元与Monte Carlo方法耦合的冷轧纯铝板再结晶模拟[J].中国有色金属学报,17(1):124-130.
申孝民.2008.有限元与蒙特卡罗法耦合的退火过程模拟模型及关键技术研究[D].济南:山东大学博士学位论文.
SINGH S B, BHADESHIA H K D H.1998. Estimation of bainite plate-thickness in low-alloy steels.Material Science and Enginnering A,245:72-79.
宋晓艳,刘国权,何宜柱.1998.一种改进的晶粒长大Monte Carlo模拟方法[J].自然科学进展,8(3):337-341.
宋晓艳,刘国权,谷南驹.1999.一种简便高效的材料三维组织及其演变的Monte Carlo仿真[J].科学通报,44(5):491-495.
宋晓艳.1998.基于计算机模拟的正常晶粒长大的三维特征和二维截面表征[J].材料研究学报,12(3):232-235.
SONG X Y, RETTENMAYR M, MüLLER C, EXNER H E.2001. Modeling of recrystallization afterinhomogeneous deformation[J]. Metallurgical and Materials Transaction A,32:2219-2206.
SOLAS D E, TOME C N, ENGLER O, WENK H R.2001. Deformation and recrystallization ofhexagonal metals: modeling and experimental results for zinc[J]. Acta Materialia,49:3791-3801.
SROLOVITZ D J, GREST G S, ANDERSON M P.1986. Computer simulation of recrystallization-.Homogeneous nucleation and growth[J]. Acta Metallurgica,34(9):1833-1845.
TAKUDA H, MORISHITA T, KINOSHITA T, SHIRAKAWA N.2005. Modelling of formula for flowstress of a magnesium alloy AZ31sheet at elevated temperatures. Journal of Materials ProcessingTechnology,164:1258-1262.
佟铭明,莫春立,李殿中.2002a.用Monte Carlo法模拟纯铜的静态再结晶[J].材料研究学报,16(5):485-489.
佟铭明,莫春立,李殿中.2002b.纯铜动态再结晶Monte Carlo模拟[J].金属学报,38(7):745-749.
TóTH L S, MOLINARI A, ESTRIN Y.2002. Strain hardening at large strains as predicted bydislocation based polycrystal plasticity model[J]. Journal of Engineering Materials and Technology,124:71-77.
VATNE H E, SHAHANI R, NES E.1996. Deformation of cube-oriented grains and formation ofrecrystallized cube grains in a hot deformed commercial ALMgMn aluminium alloy[J]. ActaMaterialia,44:4447-4462.
WANG L S, CAO Q X, LIU Z.1996. Numerical simulation and experimental verification ofmicrostructure evolution in a3-dimensional hot-upsetting process[J]. Journal Materials ProcessingTechnology,58:331-336.
WANG W, LEE P D, MCLEAN M.2003. A model of solidification microstructures in nickel-basedsuperalloys: predicting primary dendrite spaceing selection[J]. Acta Materialia,51:2971-2987.
WAHABI M E, CABRERA J M, PRADO J M.2003. Hot working of two AISI304steels: acomparative study[J]. Materials Science and Engineering A,343(1-2):116-125.
王广春.2010.金属体积成形工艺及数值模拟技术[M].北京:机械工业出版社.
王进.2007.非调制刚三维复杂热锻造过程多物理场数值模拟研究[D].上海:上海交通大学博士论文.
WOLFRAM S.1984a. Cellular automata as models of complexity[J]. Nature,311(4):419-424.
WOLFRAM S.1984b. University and complexity in cellular automata[J]. Physica D,10(1):1-35.
WOLFRAM S.1986. Theory and applications of cellular automata[J]. Advanced Series on ComplexSystems, slected papers1983-1986, Volume1, World Scientific Publishing Co. Pte. Ltd. Singapore.
XIAO H, XIE H B, YAN Y H, JUN YANAGIMOTO.2004. Simulation of dynamic recrystallizationusing cellular automaton method[J]. Iron and Steel Research,11(2):42-45.
肖宏,柳本润.2005a.采用Cellular automaton法模拟动态再结晶过程的研究[J].机械工程学报,41(2):148-152.
肖宏,徐玉辰,闫艳红.2005b.考虑晶粒变形动态再结晶过程模拟的元胞自动机法[J].中国机械工程,16(24):2245-2248.
XIAO N M, ZHENG C W, LI D Z, LI Y Y.2008. A simulation of dynamic recrystallization bycoupling a cellular automaton method with a topology deformation technique[J]. ComputionalMaterials Science,41:366-374.
徐钟济.1985.蒙特卡罗方法[M].上海:上海科学技术出版社.
薛利平,鹿守理,窦晓峰.2000.金属热变形时组织演化的有限元模拟及性能预报[J].北京科技大学学报,22(1):34-37.
杨旗,罗子健,刘东.1999.应用模糊数学预测变形高温合金锻件晶粒度[J].中国机械工程,10(7):832-834.
YANG Z, SISTA S.2000. Three dimensional Monte Carlo simulation of grain growth during GTAwelding of titanium[J]. Acta Materialia,48(8):4813-4825.
YAZDIPOUR N, DAVIES C H J, HODGSON P D.2008. Microstructural modeling of dynamicrecrystallization using irregular cellular automata[J]. Computational Materials Science,44:566-576.
YDAA H, SENUMA T.1986. Resistance to hot deformation of steel[J]. Journal of the Japan Societyfor Technology of Plasticity,27:33-44.
YEOM J T, LEE C S, KIM J H, PARK N-K.2006. Finite-element analysis of microstructureevolution in the cogging of an Alloy718ingot[J]. Materials Science and Engineering A,449-451:722-726.
YOSHINO M, SHIRAKASHI T.1995. New flow-stress equation of Ti-6AL-4V alloy[J]. Journal ofMaterials Processing Technology,48:179-186.
余永宁,刘国权.1998.体视学:组织定量分析的原理和应用[M].北京:冶金工业出版社.
YU Q, ESCHE S K.2003. A Monte Carlo algorithm for single phase normal grain growth withimproved accuracy and efficiency[J]. Computational Materials Science,27:259-270.
YU Q, ESCHE S K.2005. A multi-scale approach for microstructure prediction in thermo-mechaincal processing of metals[J]. Journal of Materials Processing Technology,169:493-502.
赵道亮.2007.紧急条件下人员疏散特殊行为的元胞自动机模拟[D].合肥:中国科学技术大学博士论文.
张跃,谷景华,尚家香.编著.2007.计算材料科学基础[M].北京:北京航空航天大学出版社.
张继祥,关小军,孙胜.2004.一种改进的晶粒长大Monte Carlo模拟方法[J].金属学报,40(5):457-461.
张立文,卢瑜,邓小虎,裴继斌,张国梁.2008.不同形核机制下对动态再结晶过程模拟研究[J].大连理工大学学报,48(3):351-355.
詹梅,杨合,刘郁丽.2005.金属塑性成形三维有限元模拟软件3D-PFS的开发[J].材料科学与工艺,13(4):402-406.
ZHANG L, ZHANG C B, WANG Y M, WANG S Q, YE H Q.2003. A cellular automatoninvestigation of the transformation from austenite to ferrite during continous cooling[J]. ActaMaterialia,51:5519-5527.
曾志朋,2002. DEFORM软件的二次开发与大型锻件锻造工艺优化[D].北京:北京机电研究所硕士学位论文.
郑成武,兰勇军,肖纳敏,李殿中,李依依.2006.热变形低碳钢中奥氏体静态再结晶介观尺度模拟[J].金属学报,42(05):474-480.
ZHENG C W, XIAO N M, LI D Z, LI Y Y.2008. Microstructure prediction of the austeniterecrystallization during multi-pass steel strip hot rolling: A cellular automaton modeling[J].Computational Materials Science,44:507-514.
郑成武.2009.低碳钢热变形中微观组织演变的元胞自动机模拟[D].沈阳:中国科学院金属研究所博士学位论文.
ZHU P, SMITH R W.1992. Dynamic simulation of crystal growth by Monte Carlo method-. Modeldescription and kinetics[J].40(4):683-692.
(参考文献共194条)
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |