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
|
摘要
随着材料科学和计算机技术的发展,材料的制备正从传统的正向研究向逆向研究过渡:从材料组分、微观结构或性能出发,借助计算机模拟来设计工艺和预测材料性质或组分、微观结构,以生成满足使用要求的材料。
材料中存在的二相粒子主要是加入合金以改善性能的产物。其中,合金化和控轧控冷技术已被普遍用于低碳钢生产中以细化晶粒组织。合金化的作用是在材料中形成足够数量、细小的二相粒子,以影响到热变形材料和冷变形材料的动态再结晶、静态再结晶行为及其相应的组织变化,特别是对于冷变形材料退火期间再结晶和晶粒长大过程的影响直接决定了其最终组织结构和性能。
Cellular Automata(CA)模型是近10多年来发展起来的一种材料组织模拟模型,在材料晶粒长大和再结晶模拟中得到广泛应用。但是,对于含有二相粒子变形材料的退火过程计算机模拟应用还未及时开展,这与该模型非常适合于模拟二相粒子与基体之间局部交互作用所引起的组织演变过程的特点是不相称的。事实上,构建含有二相粒子的变形材料CA模型以模拟其再结晶和晶粒长大组织演变过程,不仅可实现二相粒子的体积分数、尺寸及其分布等参数对退火组织影响的模拟研究,实现退火过程微观组织设计、工艺控制及其性能预报,为退火工艺优化和高性能材料设计与开发打下了坚实基础,而且进一步挖掘了CA模型的潜力,拓展了其应用范围。因此,及时开展含有二相粒子的变形材料再结晶退火CA模型及其模拟研究具有重要的理论和实际意义。
本文基于CA方法、金属学和材料再结晶等相关理论,提出并建立了具有较强物理基础的单相材料变温回复-再结晶和晶粒长大的CA模型;在这些模型的基础上,创建了二相粒子材料变温回复-再结晶和晶粒长大CA模型,进而得到了二相粒子材料退火组织CA模型;自主开发了相关再结晶模拟的关键技术;采用C++编程语言,编写了上述模型的应用程序,并开展了相关的模拟研究和实验研究,对模型的合理性及其应用效果进行了检验。
首先,分析了现有的晶粒长大CA模型的不足,基于曲率和能量机制,提出了元胞取向状态转变的二次判断方式和相应规则,建立了具有更好物理基础的晶粒长大CA模型。该模型将晶界能作为晶粒长大的驱动力,考虑了晶界曲率对晶界移动方向的影响,解决了晶界朝曲率中心运动方向与及能量降低方向不一致的问题,晶粒尺寸分布更为理想。
其次,以单相材料正常晶粒长大的CA模型为基础,引入二相粒子影响及其对应的改进转变规则,建立了一个新的二相粒子材料晶粒长大过程CA模型。该模型的模拟结果很好地反映了二相粒子体积分数、尺寸及其分布对晶粒长大的影响规律,并与相关实验结果相符。
然后,分析了现有再结晶CA模型存在的储存能均匀分布、形核机制不完善、温度恒定、忽略回复影响等不足,基于相关实验研究,建立了一个新的具有明确物理基础的单相材料变温回复-再结晶CA模型。该模型特点在于:①采用非均匀储能场,初步解决了冷变形材料储存能分布不均匀问题;②基于亚晶异常长大形核机制,并考虑了回复对形核过程的影响;③考虑了温度变化对再结晶过程的影响。与原有模型相比,该模型的模拟结果更正确地反映了退火温度和变形程度对再结晶过程的影响规律,并与相关实验结果更加接近。
随后,根据细小及大尺寸二相粒子对再结晶过程影响的相关实验研究,在单相材料变温回复-再结晶CA模型基础上,创建了二相粒子材料变温回复-再结晶CA模型。该模型综合考虑了与二相粒子尺度有关的位错运动及其分布状态,改进了储存能模型和晶核长大模型,较好地模拟了二相粒子对再结晶影响的实验规律。
最后,基于二相粒子材料变温回复-再结晶模型和晶粒长大CA模型,得到了一个二相粒子材料退火组织CA模型。为了验证该模型的合理性及其应用效果,分别以两组冷轧钢板为研究对象,实验研究了含有二相粒子和二相粒子含量不同条件下再结晶退火组织变化过程,并与其模拟结果进行了对比。结果表明:本文所建模型能较准确地模拟二相粒子材料的冷轧组织、再结晶形核位置、再结晶完成组织及随后的晶粒长大组织;模拟的二相粒子对再结晶过程的影响规律与退火实验预测结果及相关再结晶理论一致:二相粒子的存在阻碍了再结晶进行,使再结晶形核及晶核长大过程滞后,且粒子含量越多,影响效果越明显。模拟的退火速度与实际值相比存在一定的误差,这与模型假设、实验误差等有关,进一步完善该模型有助于其模拟精度的提高和实际应用的拓展。
With the development of material science and computer technology, the science of material preparation is changing from traditional design manner to its reverse one. By the aid of computer simulation, material properties can be predicted based on its components microstructure, vice versa, and the optimum manufacturing techniques can be selected to derive some functional materials which can meet the actual needs.
The sceond phase particle in material is mainly the product caused by adding alloy elements to improve the performance of material. Alloying and controlled rolling and cooling technology have been widely used in the process of low-canbon steel manifacture to control the grain growth. The aim of alloying is to generate sufficient amount and fine second phase particles in the material, which affect the behaviors of dynamic recrystallization and static recrystallization and corresponding microstructure changes in the process of thermal deformation and cold one. Especially, the effects of the second phase particle on recrystallization and grain growth during the annealing directly determine the ultimate microstructure and performance of the cold deformed material.
Cellular Automata (shortly called CA) model which developed in recent more than ten years has been widely used in the simulation of grain growth and recrystallization, but it has not been applied in the simulation of the deformed material with second phase particle yet. This status is inappropriate to compare with the character of the model which suits to simulate the local interaction between the second phase particle and body organization. Actually, constructing CA model for the deformed material with second phase particle to simulate the grain growth and recrystallization process not only studies the effects of the second phase particle's size, volume fraction and distribution on annealing microstructure, and achieves the microstructure organizational design and process control of and performance prediction to establish the foundation for the annealing technology optimization and development of better performance material, but also further explores the potential of extending its application. So it has an important significance of theory and practice to study the modeling and simulation of the annealing microstructure evolving for the deformed material with second phase particle by CA method in time .
In present thesis, based on the CA method, metallography and recrystallization theory and so on, two CA models for the recrystallization and grain growth for single phase material were proposed with better physical basis, respectively. Based on the models, two CA models for the recovery - recrystallization and grain growth for the material with second phase particle under the change of annealing temperature were constructed, respectively, which formed a CA model for annealing microstructure evolution of the material with second phase particle. According to the new models and the corresponding key technologies for simulation, a computer program was compiled to simulate the annealing microstructure evolving of the material with second phase particle under the change of annealing temperature, and some experiments were finished to verify the rationality of the models.
Firstly, the limitations of previous CA models for grain growth were well analyzed, and a new criterion with the judgement of two times was proposed for the attempted transition of cell state and a new CA model was constructed with a better physical basis, based on the mechanisms of grain boundary curvature driving and the thermodynamic one. In the new CA model, the main driving force of grain growth is grain boundary energy and the influence of grain boundary curvature on the direction of grain boundary movement is also considered so that the problem that the direction of grain boundary moving to its curvature center differs to the direction of its energy decrease is solved and the distribution of grain size is more ideal.
Secondly, based on the grain growth CA model for single phase material, a new model with a modified transition rule of cell state was constructed to simulate the effects of the second phase particle on grain growth. The results gained by the model correctly reflect the effects of the second phase particle's volume fraction, size and its distribution on grain growth, which is consistent with the experimental results.
Thirdly, the limitations of stored energy distribution, nucleation, temperature change and recovery effect of previous recrystallization CA models were well analyzed, and based on corresponding experimental research and MC models, a recovery-recrystallization CA model for single phase material which has strong physical basis was constructed. The new model has the following advantages: 1) A new stored energy distribution model is constructed by using inhomogeneous distribution of stored energy. 2) A recovery model is built on the basis of subgrain abnormal growth nucleation model and considered the effect of recovery on nucleation. 3) The influences of annealing temperature change on recrystallization process are considered in the new model. In comparison with the results of previous models, the results simulated by the new model more really reflect the influence laws of annealing temperature and deformation degree on recrystallization, which is in good agreement with the experiment results.
Then, based on the experimental research on the effects of the small and large second phase particles on recrystallization and the recovery- recrystallization model for single phase material, a new recovery- recrystallization model for the material with second phase particle was proposed by CA method. In the new model, the dislocation movement and its distribution related to the second particle's size are generally considered, and the modified storage energy model and nucleation one are applied. The results simulated by the new model coincide with the experimental laws which show the effects of the second phase particle on recrystallization.
Finally, based on the recovery-recrystallization and grain growth CA models, a new annealing microstructure CA model for the material with second phase particle was obtained. To verify the rationality and application effect of the model constructed in present thesis, the annealing processes of cold-rolled steel plates which contain the second phase particle with different content are investigated in detail. The comparison of experimental results and simulated ones indicate that: 1) The initial microstructure, the nucleation sites, recrystallized microstructure and the subsequent grain growth microstructure can be better simulated by the model constructed in present thesis. 2) The simulation results are consistent with the experimental results and related recrystallization theories. 3) The second phase particle delays the process of nucleation and nucleus growth, and then hinders the whole recrystallization process. There exists definite error between simulated annealing speed and experiment one because of model hypothesis and experimental error, so that it is helpful to perfect this model further for improving its simulation accuracy and practical application.
材料中存在的二相粒子主要是加入合金以改善性能的产物。其中,合金化和控轧控冷技术已被普遍用于低碳钢生产中以细化晶粒组织。合金化的作用是在材料中形成足够数量、细小的二相粒子,以影响到热变形材料和冷变形材料的动态再结晶、静态再结晶行为及其相应的组织变化,特别是对于冷变形材料退火期间再结晶和晶粒长大过程的影响直接决定了其最终组织结构和性能。
Cellular Automata(CA)模型是近10多年来发展起来的一种材料组织模拟模型,在材料晶粒长大和再结晶模拟中得到广泛应用。但是,对于含有二相粒子变形材料的退火过程计算机模拟应用还未及时开展,这与该模型非常适合于模拟二相粒子与基体之间局部交互作用所引起的组织演变过程的特点是不相称的。事实上,构建含有二相粒子的变形材料CA模型以模拟其再结晶和晶粒长大组织演变过程,不仅可实现二相粒子的体积分数、尺寸及其分布等参数对退火组织影响的模拟研究,实现退火过程微观组织设计、工艺控制及其性能预报,为退火工艺优化和高性能材料设计与开发打下了坚实基础,而且进一步挖掘了CA模型的潜力,拓展了其应用范围。因此,及时开展含有二相粒子的变形材料再结晶退火CA模型及其模拟研究具有重要的理论和实际意义。
本文基于CA方法、金属学和材料再结晶等相关理论,提出并建立了具有较强物理基础的单相材料变温回复-再结晶和晶粒长大的CA模型;在这些模型的基础上,创建了二相粒子材料变温回复-再结晶和晶粒长大CA模型,进而得到了二相粒子材料退火组织CA模型;自主开发了相关再结晶模拟的关键技术;采用C++编程语言,编写了上述模型的应用程序,并开展了相关的模拟研究和实验研究,对模型的合理性及其应用效果进行了检验。
首先,分析了现有的晶粒长大CA模型的不足,基于曲率和能量机制,提出了元胞取向状态转变的二次判断方式和相应规则,建立了具有更好物理基础的晶粒长大CA模型。该模型将晶界能作为晶粒长大的驱动力,考虑了晶界曲率对晶界移动方向的影响,解决了晶界朝曲率中心运动方向与及能量降低方向不一致的问题,晶粒尺寸分布更为理想。
其次,以单相材料正常晶粒长大的CA模型为基础,引入二相粒子影响及其对应的改进转变规则,建立了一个新的二相粒子材料晶粒长大过程CA模型。该模型的模拟结果很好地反映了二相粒子体积分数、尺寸及其分布对晶粒长大的影响规律,并与相关实验结果相符。
然后,分析了现有再结晶CA模型存在的储存能均匀分布、形核机制不完善、温度恒定、忽略回复影响等不足,基于相关实验研究,建立了一个新的具有明确物理基础的单相材料变温回复-再结晶CA模型。该模型特点在于:①采用非均匀储能场,初步解决了冷变形材料储存能分布不均匀问题;②基于亚晶异常长大形核机制,并考虑了回复对形核过程的影响;③考虑了温度变化对再结晶过程的影响。与原有模型相比,该模型的模拟结果更正确地反映了退火温度和变形程度对再结晶过程的影响规律,并与相关实验结果更加接近。
随后,根据细小及大尺寸二相粒子对再结晶过程影响的相关实验研究,在单相材料变温回复-再结晶CA模型基础上,创建了二相粒子材料变温回复-再结晶CA模型。该模型综合考虑了与二相粒子尺度有关的位错运动及其分布状态,改进了储存能模型和晶核长大模型,较好地模拟了二相粒子对再结晶影响的实验规律。
最后,基于二相粒子材料变温回复-再结晶模型和晶粒长大CA模型,得到了一个二相粒子材料退火组织CA模型。为了验证该模型的合理性及其应用效果,分别以两组冷轧钢板为研究对象,实验研究了含有二相粒子和二相粒子含量不同条件下再结晶退火组织变化过程,并与其模拟结果进行了对比。结果表明:本文所建模型能较准确地模拟二相粒子材料的冷轧组织、再结晶形核位置、再结晶完成组织及随后的晶粒长大组织;模拟的二相粒子对再结晶过程的影响规律与退火实验预测结果及相关再结晶理论一致:二相粒子的存在阻碍了再结晶进行,使再结晶形核及晶核长大过程滞后,且粒子含量越多,影响效果越明显。模拟的退火速度与实际值相比存在一定的误差,这与模型假设、实验误差等有关,进一步完善该模型有助于其模拟精度的提高和实际应用的拓展。
With the development of material science and computer technology, the science of material preparation is changing from traditional design manner to its reverse one. By the aid of computer simulation, material properties can be predicted based on its components microstructure, vice versa, and the optimum manufacturing techniques can be selected to derive some functional materials which can meet the actual needs.
The sceond phase particle in material is mainly the product caused by adding alloy elements to improve the performance of material. Alloying and controlled rolling and cooling technology have been widely used in the process of low-canbon steel manifacture to control the grain growth. The aim of alloying is to generate sufficient amount and fine second phase particles in the material, which affect the behaviors of dynamic recrystallization and static recrystallization and corresponding microstructure changes in the process of thermal deformation and cold one. Especially, the effects of the second phase particle on recrystallization and grain growth during the annealing directly determine the ultimate microstructure and performance of the cold deformed material.
Cellular Automata (shortly called CA) model which developed in recent more than ten years has been widely used in the simulation of grain growth and recrystallization, but it has not been applied in the simulation of the deformed material with second phase particle yet. This status is inappropriate to compare with the character of the model which suits to simulate the local interaction between the second phase particle and body organization. Actually, constructing CA model for the deformed material with second phase particle to simulate the grain growth and recrystallization process not only studies the effects of the second phase particle's size, volume fraction and distribution on annealing microstructure, and achieves the microstructure organizational design and process control of and performance prediction to establish the foundation for the annealing technology optimization and development of better performance material, but also further explores the potential of extending its application. So it has an important significance of theory and practice to study the modeling and simulation of the annealing microstructure evolving for the deformed material with second phase particle by CA method in time .
In present thesis, based on the CA method, metallography and recrystallization theory and so on, two CA models for the recrystallization and grain growth for single phase material were proposed with better physical basis, respectively. Based on the models, two CA models for the recovery - recrystallization and grain growth for the material with second phase particle under the change of annealing temperature were constructed, respectively, which formed a CA model for annealing microstructure evolution of the material with second phase particle. According to the new models and the corresponding key technologies for simulation, a computer program was compiled to simulate the annealing microstructure evolving of the material with second phase particle under the change of annealing temperature, and some experiments were finished to verify the rationality of the models.
Firstly, the limitations of previous CA models for grain growth were well analyzed, and a new criterion with the judgement of two times was proposed for the attempted transition of cell state and a new CA model was constructed with a better physical basis, based on the mechanisms of grain boundary curvature driving and the thermodynamic one. In the new CA model, the main driving force of grain growth is grain boundary energy and the influence of grain boundary curvature on the direction of grain boundary movement is also considered so that the problem that the direction of grain boundary moving to its curvature center differs to the direction of its energy decrease is solved and the distribution of grain size is more ideal.
Secondly, based on the grain growth CA model for single phase material, a new model with a modified transition rule of cell state was constructed to simulate the effects of the second phase particle on grain growth. The results gained by the model correctly reflect the effects of the second phase particle's volume fraction, size and its distribution on grain growth, which is consistent with the experimental results.
Thirdly, the limitations of stored energy distribution, nucleation, temperature change and recovery effect of previous recrystallization CA models were well analyzed, and based on corresponding experimental research and MC models, a recovery-recrystallization CA model for single phase material which has strong physical basis was constructed. The new model has the following advantages: 1) A new stored energy distribution model is constructed by using inhomogeneous distribution of stored energy. 2) A recovery model is built on the basis of subgrain abnormal growth nucleation model and considered the effect of recovery on nucleation. 3) The influences of annealing temperature change on recrystallization process are considered in the new model. In comparison with the results of previous models, the results simulated by the new model more really reflect the influence laws of annealing temperature and deformation degree on recrystallization, which is in good agreement with the experiment results.
Then, based on the experimental research on the effects of the small and large second phase particles on recrystallization and the recovery- recrystallization model for single phase material, a new recovery- recrystallization model for the material with second phase particle was proposed by CA method. In the new model, the dislocation movement and its distribution related to the second particle's size are generally considered, and the modified storage energy model and nucleation one are applied. The results simulated by the new model coincide with the experimental laws which show the effects of the second phase particle on recrystallization.
Finally, based on the recovery-recrystallization and grain growth CA models, a new annealing microstructure CA model for the material with second phase particle was obtained. To verify the rationality and application effect of the model constructed in present thesis, the annealing processes of cold-rolled steel plates which contain the second phase particle with different content are investigated in detail. The comparison of experimental results and simulated ones indicate that: 1) The initial microstructure, the nucleation sites, recrystallized microstructure and the subsequent grain growth microstructure can be better simulated by the model constructed in present thesis. 2) The simulation results are consistent with the experimental results and related recrystallization theories. 3) The second phase particle delays the process of nucleation and nucleus growth, and then hinders the whole recrystallization process. There exists definite error between simulated annealing speed and experiment one because of model hypothesis and experimental error, so that it is helpful to perfect this model further for improving its simulation accuracy and practical application.
引文
[1]熊家迥.材料设计[M].天津:天津大学出版社,2000:1-2
[2]俞汉清.金属塑性成形原理[M].北京:机械工业出版社,2003:18,139
[3]毛卫民,赵新兵.金属的再结晶和晶粒长大[M].北京:冶金工业出版社,1994:36,16,64,45,71
[4]R.W.Calm.New theory of recrystallization nuclei[J].Physical Society-Proceedings,1950,63(364A):323-336
[5]W.G.Burgers.Prozesse der Keimbildung bei der Rekristallisation(Process of nucleation in recrystallization)[J].Zeitschrift fuer Metallkunde,1961,52(1):19-26
[6]Y.D.Huang,L.Froyen.Recovery,recrystallization and grain growth in Fe_3Al-based alloys[J].Intermetallics,2002,10(5):473-484
[7]S.P.Bellier,R.D.Doherty.Structure of deformed aluminum and its recrystallization em dash investigations with transmission kossel diffraction[J].Acta Metallurgica,1977,25(5):521-538
[8]M.Muraki,T.Toge,K.Sakata,T.Obara,E.Furubayashi.Formation mechanism of {111}recrystallization texture in ferritic steels[J],Tetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan,1999,85(10):751-757
[9]T.Urabe,J.J.Jonas.Modeling texture change during recrystallization of an IF steel[J],ISIJ International,1994,34(5):435-442
[10]S.S.葛列里克著,仝健民译.金属和合金的再结晶[M].北京:机械工业出版社,1985:44,72,56,40
[11]W.A.Johnson,R.F.Mehl.Reaction kinetics in processes of nucleation and growth[A],American Institute of Mining and Metallurgical Engineers-Transactions,1939,135:416-442
[12]M.Avrami.Kinetics of phase change Ⅰ:general theory[J].Journal of Chemical Physics,1939,7(12):1103-1112
[13]W.A.Anderson,R.E Mehl.Recrystallization of aluminum in terms of rate of nucleation and rate of growth[J].Metallugia,1945,33(193):45-46
[14]B.F.Decker,D.Harker.Activation energy for recrystallization in rolled copper[A].American Institute of Mining and Metallurgical Engineers-Journal of Metals,1950,188(6):887-890
[15]J.W.Cahn.Kinetics of grain boundary nucleated reactions[J].Acta Metallurgica,1956,4(5):449-459
[16]R.A.Vandermeer,E Grodon.Edge-nucleated,growth controlled recrystallization in aluminum[J].Metallurgical Society of AIME,1959,215(4):577-588
[17]N.H.Lin,C.P.Chang,E W.Kao.Effect of annealing temperature on the recrystallization kinetics of commercially pure aluminum[J].Metallurgical and Materials Transactions A,1995,26A(8):2185-2187
[18]S.H.Choi,Y.C.Yoo.Static recrystallization kinetics of 304 stainless steels[J].Journal of Materials Science,2001,36(17):4273-4278
[19]D.Weygand,Y.Brechet,J.Lepinoux.Mechanisms and kinetics of recrystallization:A two dimensional vertex dynamics simulaton[J].Iterface Science,2001,9(3):311-317
[20]S.Sangal,S.S.Sahay,A.K.Jena.Nucleation and recrystallization kinetics in boron doped Ni76A124 deformed to small strains[J].Materials Science & Engineering,1997,239:293-296
[21]R.A.Vandermeer,D.Jenson.Microstructure path and temperature dependence of recrystallization in commercial aluminum[J].Acta Materialia,200 l,49(11):2083-2064
[22]W.P.Ye,R L Gall,G Saindrenan.A study of recrystallization of an IF steel bu kinetics models[J].Materials Scinece & Engineering A,2002,332(1-2):41-46
[23]C.Garcia-Mateo,B.Lopez,J.M.Rodriguez-lbabe.static recrystallization kinetics in warm worked vanadium microalloyed steels[J].Materials Scinece & Engineering A,2001,303(1):216-225
[24]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.Effect of inhomogeneous deformation on the recrystallization kinetics of deformed metals[J].ISIJ international,2004,44(11):1931-1936
[25]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.A metallurgical interpretation of the static recrystallization kinetics of an intercritically deformed C-Mn steel[J].Metallurgical and Materials Transections A,2004,35(6):1889-1898
[26]C.Zener.Private communication to Smith[J].Trans Amer Inst Metall Engrs,1949,175:15-17
[27]王国承,王铁明,尚德礼,方克明.超细第二相粒子强化钢铁材料的研究进展[J].钢铁研究学报,2007,19(6):5-8
[28]东涛,付俊岩.试论我国钢的微合金化发展方向[J].中国冶金,2005,5:16-19
[29]董成瑞,任海鹏,金同哲.微合金非调质钢[M].北京:冶金工业出版社,2000
[30]马衍伟,王先进.超深部IF钢研究的最新进展[J].钢铁,1998,33(4):65-69
[31]景财年,王作成,韩福涛.IF钢中的析出物[J].材料导报,2005,19(5):50-64
[32]D.Strzeciwilk,Z.wokulski,P.Tkacz.Microstructure of TiC crystals obtained from high temperature nickel solution[J].Journal of Alloys and Compounds,2003,350(1):256-263
[33]R.Mendoza,J.Huante,M.Alanis,C.Gonzalez-Rivera,J.A.Juarez-Islas.Processing of ultra low carbon steels with mechanical properties adequate for automotive applications in the as-annealed condition[J].Materials Science and Engineering A,2000,276(1):203-209
[34]商建辉,王先进.Ti-IF钢热轧时第二相粒子析出行为研究的最新进展[J].钢铁研究学报,2000,12(6):55-60
[35]王作成,石京.不同退火工艺下Ti-IF钢二相料演变的比较[J].材料科学与工艺,1999,7(3):41-45
[36]N.Mizui.Precipitation control and related mechanical properties in ultra low carbon sheet steels[A].Modern Lc and ULC Sheet steels for Cold Forming:Processing and Properties[C].Japan,1998:187-198
[37]M.Joonoh,L.Jongbong,L.changhee.Prediction for the austenite grain size in the presence of growing particles in the weld HAZ of Ti-microalloyed steel[J].Materials Science and Engineering,2007,459(1):40-46
[38]曾周亮,宁康琪,彭北山.高强铝合金第二相强化及其机理[J].冶金丛刊,2008,4:5-7
[39]王锦,卜春阳.第二相粒子尺度对钼镧合金加工硬化影响[J].中国钼业,2006,30(3):43-46
[40]K.W.Mahin,K.Hanson,J.W.J.Morris.Computer simulation of homogeneous nucleation and growth processes[J].Nuclear Metallurgy,Metallurgical Society of AIME,1976,20(1):39-50
[41]H.J.Frost,C.V.Thompson,C.L.Howe,J.Whang.Two dimensional computer simulation of capillarity-driven grain growth:preliminary results[J].Scripta Metallurgica,1988,22(1):65-70
[42]H.J.Frost,C.V.Thompson.The effect of nucleation conditions on the topology and geometry of two-dimensional grain structures[J].Acta Metallurgica,1987,35(2):529-540
[43]C.V.Thompson,H.J.Frost.The relative rates of secondary and normal grain growth[J].Acta Metallurgica,1987,35(4):887-890
[44]D.J.Jensen.Simulation of recrystallization microstructure and texture:effects of preferential growth[J].Metallurgical and Materials Transaction A:Physical Metallurgy and Materials Science,1997,28A(1):15-25
[45]D.L.Jensen.Modeling of microstructure development during recrystallization[J].Scripta Metallurgica et Materialia,1992,27(11):1551-1556
[46]H.E.Vatne,T.Furu,R.φrsund,E.Nes.Modelling recrystallization after hot deformation of aluminum[J].Acta Materialia,1996,44(11):4463-4473
[47]V.Y.Novikov,I.S.Gavrikov.Influence of heterogeneous nucleation on microstructure and kinetics of primary recrystallization[J].Acta Metallurgica et Materialia,1995,43(3):973-976
[48]I.S.Gavrikov,V.Y.Novikov.The effect of the initial grain size on the kinetics and microstructure of primary recrystallization:computer simulation[J].Physics of Metals and Metallography,1994,77(4):348-352
[49]S.Gavrikov,V.Y.Novikov.Influence of initial grain size on kinetics of primary recrystallization[J].Fizika Metallov i Metallovedenie,1994,77(4):29-35
[50]T.O.Saetre,O.Hunderi,E.Nes.Computer simulation of primary recrystallization microstructure:the effects of nucleation and growth kietics[J].Acta Metallurgica,1986,34(6):981-987
[51]T.Furu,R.φrsund,E.Nes.Subgrain growth in heavily deformed aluminium - experimental investigation and modeling treatment[J].Acta Metallurgica et Materialia,1995,43(6):2209-2232
[52]Price C W.Use of Kolmogorov-Johnson-Mehl-Avrami kinetics in recrystallization of metals and crystallization of metallic glasses[J].Acta Metallurgica,1990,38(5):727-738
[53]C.W.Price.Simulations of grain impingement and recrystallization kinetics[J].Acta Metallurgica,1987,35(6):1377-1390
[54]C.W.Price.Analysis of models for grain-impingement compensation and their effect on recrystallization kinetics[J].Acta Metallurgica,1991,39(8):1807-1816
[55]K.Kawasaki,T.Nagai,K.Nakashima.Vertex models for two-dimensional grain growth[J].philosophical Magazine B:Physics of Condensed Matter,Electronic,Optical and Magnetic Properties,1989,60(3):339-421
[56]F.J.Humphreys.Network model for recovery and recrystallization[J].Scripta Metallurgica et Materialia,1992,27(11):1557-1562
[57]D.Weygand,Y.Brechet,J.Lepinoux.A vertex simulation of grain growth in 2D and 3D.Advanced Engineering Materials.2001,3(1):67-71
[58]D.Weygand,Y.Brechet,J.Lepinoux.Zener pinning and grain growth:a two-dimensional vertex computer simulation.Acta Materialia.1999,47(3):961-970
[59]D.J.Srolovitz,G.S.Grest,M.P.Anderson.Computer simulation of recrystallization- Ⅰ.homogeneous nucleation and growth[J].Acta Metallurgica,1986,34(9):1833-1845
[60]D.J.Srolovitz,G.S.Grest,M.P.Anderson,A.D.Rollett.Computer simulation of recrystallization - Ⅱ.Heterogeneous nucleation and growth[J].Acta Metallurgica,1988, 36(8): 2115-2128
[61] A. D. Rollett, D. J. Srolovitz, M. P. Anderson, R. D. Doherty. Computer simulation of recrystallization. III. Influence of a dispersion of fine particles[J]. Acta Metallurgica et Materialia, 1992,40(12): 3475-3495
[62] M. P. Anderson, G S. Grest, D. J. Srolovitz. Microstructural dynamics of primary and secondary recrystallization[J]. Metallurgical Soc of AIME, 1986: 77-93
[63] R. D. Doherty, A. D. Rollett, D. J. Srolovitz. Structural Evolution During recrystallization[A]. Proceedings of the Riso International Symposium on Metallurgy and Materials Science 7th, 1986: 53-67
[64] A. D. Rollett, D. J. Srolovitz, R. D. Doherty, M. P. Anderson. Computer simulation of recrystallization in non-uniformly deformed metals[J]. Acta Metallurgica, 1989, 37(2):627-639
[65] B. Radhakrishnan, G. B. Sama, T. Zacharia. Modeling the kinetics and microstructural evolution during static recrystallization-Monte Carlo simulation of recrystallization[J]. Acta Metallurgica, 1998,46(12): 4415-4433
[66] B. Radhakrishnan, G. B. Sama, T. Zacharia. Monte Carlo simulation of deformation substructure evolution during recrystallization[J]. Scripta Materialia, 1998, 39(12):1639-1645
[67] B. Radhakrishnan, G. B. Sama, H. Weiland, P. Baggethun. Simulations of deformation and recrystallization of single crystals of aluminium containing hard particles[J]. Modelling and Simulation in Materials Science and Engineering, 2000, 8(5): 737-750
[68] B. Radhakrishnan, G. B. Sama, T. Zacharia. Coupled finite element-Monte Carlo simulation of microstructure and texture evolution during thermomechanical processing[A].Proceedings of the TMS Fall Meeting, 1998: 267-278
[69] E. A. Holm, M. A. Miodownik, A. D. Rollett. On abnormal subgrain growth and the origin of recrystallization nuclei[J]. Acta Materialia, 2003,51(9): 2701-2716
[70] M. A. Miodownik, E. A. Holm, A. W. Godfrey, D. A. Hughes, Lesar R. Multiscale modeling of recrystallization[A]. Materials Research Society Symposium- Proceeding, 1999, 538:157-162
[71] E. A. Holm, K. J. Healey, C. C. Battaile. Coupled computer simulations of recrystallization in deformed polycrystals[A]. Materials Science Forum, 2004,467-470(1): 641-646
[72] P. Gerber, J. Tarasiuk, D. Solas, S. Jakani, M. H. Mathon, T. Baudin. Monte Carlo modelling of recrystallization mechanisms in wire-drawn copper from EBSD data[A].Materials Science Forum, 2004,467-470: 635-640
[73] F. Caleyo, T. Baudin, R. Penelle. Monte Carlo simulation of recrystallization in Fe-50%Ni starting from EBSD and bulk texture measurements[J]. Scripta Materialia, 2002, 46(12):829-835
[74] J. Tarasiuk, P. Gerber, B. Bacroix, K. Pickos. Modeling of recrystallization using Monte Carlo method based on EBSD data[A]. Materials Science Forum, 2002, 408-412( I ):395-400
[75] T. Koseki, T. Araki. Modeling of steel weld microstructure using Monte Carlo and finite difference hybrid method[A]. Materials Science Forum, 2006, 539-543(4): 4002-4007
[76] M. Kazeminezhad, T. A. Karimi, T. A. Kiet. Utilization of the finite element and Monte Carlo model for simulation the recrystallization of inhomogeneous deformation of copper[J].Computational Materials Science, 2007,38(4): 765-773
[77] S. Ling, M. P. Anderson. Monte Carlo simulation of grain growth and recrystallization in polycrystalline materials[J].JOM,1992,44(9):30-36
[78]B.Radhakrishnan,T.Zacharia.On the prediction of HAZ grain size using Monte Carlo simulation[A].Modeling and Control of Joining Processes,American Welding Society international conference.Orlando,FL,1993
[79]J.H.Gao,R.G.Thompson.Real time temperature models for Monte Carlo simulations of normal grain growth[J].Acta Mater,1996,44(11):4565-4570
[80]B.K.Kad,P.M.Hazzledine.Monte carlo simulations of grain growth and zener pinning[J].Materials Science and Engineering,1997,238:70-77
[81]M.Soucail,R.Messina,A.Cosnuau,L.P.Kubin.Monte Carlo simulation of Zener pinning in two dimensions[J].Materials Science and Engineering,1999,271(1):1-7
[82]N.Maazi,N.Rouag.Consideration of Zener drag effect by introducing a limiting radius for neighbourhood in grain growth simulation[J].Journal of Crystal Growth,2002,243(2):361-369
[83]J.H.Gao,R.G.Thompson,B.R.Patterson.Computer simulation of grain growth with second phase particle pinning[J].Acta mater,1997,49(9):3653-3658
[84]窦晓锋,鹿守理,赵辉.钢静态再结晶的蒙特卡罗模拟[J].钢铁研究,1997,98(5):19-21
[85]薛利平,鹿守理,窦晓锋.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,2000,22(1):34-37
[86]宋晓艳,刘国权,谷南驹.第二相粒子尺寸对基体晶粒长大影响的仿真研究[J].金属学报,1999,35(6):565-568
[87]X.Y.Song,G.Q.Liu,N.J.Gu.Influence of the second phase particle size on grain growth based on coumputer simulation[J].Materials Science and Engineering,1999,270(2):178-182
[88]宋晓艳,刘国权,谷南驹.有第二相粒子的复相材料显微组织及其演变的仿真研究[J].自然科学进展,1999,10(2):161-166
[89]宋晓艳,谷南驹,刘国权,王宝奇.第二相粒子含量对基体晶粒长大影响的计算机仿真研究[J].金属学报,2000,36(6):592-596
[90]X.Y.Song,M.Rettenmayr.Modelling study on recrystallization,recovery and their temperature dependence in inhomogeneously deformed materials[J].Materials Science and Engineering A,2002,332(1-2):153-160
[91]X.Y.Song,M.Rettenmayr,Muller C,Exner H E.Modeling of recrystallization after inhomogeneous deformation[J].Metallurgical and Materials Transactions A:Physical Metallurgy and Materials Science,2001,32(9):2199-2206
[92]张继祥,关小军,孙胜.一种改进的晶粒长大Monte Carlo模拟方法[J].金属学报,2004,40(5):457-461
[93]张继祥,关小军.异常晶粒长大Monte Carlo模拟研究[J].中国有色金属学报,2006,16(10):1689-1697
[94]申孝民,关小军,张继祥,刘运腾,麻晓飞,赵宪明.有限元与Monte Cado方法耦合的冷轧纯铝板再结晶模拟[J].中国有色金属学报,2007,17(1):124-130
[95]关小军,张继祥,孙胜.再结品过程计算机模拟[J].特殊钢,2004,25(3):34-37
[96]邓章铭,周浪.元胞自动机模型方法及其在材料组织结构模拟中的应用[J].材料科学与工程,2000,18(3):123-129
[97]焦宪友.基于元胞自动机法的材料品粒长大和再结晶模拟[D].山东大学硕士毕业论文.2006:13-17
[98]金文忠.热加工过程静态再结晶的元胞自动机模拟[D].东北大学硕士学位论文.2006:10-20
[99]S.Wofram.Statistical Mechanics of Cellular Automata[J].Rev.Mod.Phys,1983,55(3):601-622
[100]N.Packard.Theory and Applications of Cellular Automata[M].Singapore:World Scientific,1986:305
[101]M.Rappaz,Ch.-A.Gandin.Probabilistic modelling of microstructure formation in solidification processes[J].Acta Metallurgica et Materialia,1993,41(2):345-360
[102]Ch.-A.Gandin,M.Rappaz.A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes[J].Acta Metallurgica et Materialia,1994,42(7):2233-2246
[103]J.F.McCarthy.Lattice gas cellular automata method for flow in the interdendritic region[J].Acta Metallurgica et Materialia,1994,42(5):1573-1581
[104]R.K.Shelton,D.C.Dunand.Computer modeling of particle pushing and clustering during matrix crystallization[J].Acta Materialia,1996,44(1):4571-4585
[105]K.Kevin.Cellular Automata Investigations of Binary Solidification[J].Journal of Computational Physics,1998,142(1):243-262
[106]P.Carter,D.C.Cox,C.A.Gandin,R.C.Reed.Process modelling of grain selection during the solidification of single crystal superalloy castings[J].Materials Science and Engineering,2000,280(2):233-246
[107]M.Vandyoussefi,A.L.Greer,Application of cellular automaton-finite element model to the grain refinement of directionally solidified A1-4.15 wt%Mg alloys[J].Acta Materialia,2002,50(6):1559-1569
[108]W.Wang,P.D.Lee,M.McLean.A model of solidification microstructures in nickel-based superalloys:predicting primary dendrite spacing selection[J].Acta Materialia,2003,51(10):2971-2987
[109]Y.Liu,Q.Y.Xu,B.Liu.A Modified Cellular Automaton Method for the Modeling of the Dendritic Morphology of Binary Alloys[J].Tsinghua.Science & Technology,2006,11(5):495-500
[110]L.Zhang,C.B.Zhang.Two-dimensional cellular automaton model for simulating structural evolution of binary alloys during solidification[J].Transactions of Nonferrous Metals Society of China,2006,16(6):1410-1416
[111]K.F.Wang,B.S Li,G.F.Mi,J.J.GUO,H.Z.FU.Modeling of Cell/Dendrite Transition During Directional Solidification of Ti-Al Alloy Using Cellular Automaton Method[J].Journal of Iron and Steel Research,2008,456(1):85-95
[112]H.W.Hesselbarth,I.R.Gobel.Simulation of recrystallization by cellular automata[J].Acta Metallurgica et Materialia,1991,39(9):2135-2143
[113]C.H.J.Davies.The effect of neighbourhood on the kinetics of a cellular automaton recrystallisation model[J].Scripta metallurgica et materialia,1995,33(7):1139-1143
[114]C.H.J.Davies.Growth of Nuclei in a Cellular Automaton Simulation of Recrystallisation[J].Scripta materialia,1996,36(1):35-40
[115]C.H.J.Davies,L.Hong.Cellular automaton simulation of static recrystallization in cold-rolled AA 1050[J].Scripta materialia,1998,40(10):1145-1150
[116]V.Marx,F.R.Reher,G.Gottstein.Simulation of primary recrystallization using a modified three-dimensional cellular automaton[J].Acta Materialia,1999,47(4):1219-1230
[117]D.Raabe.Introduction of a scaleable 3D cellular automaton with a probabilistic switching rule for the discrete mesoscale simulation of recrystallization phenomena[J].Philosophical Magazine A,1999,79:2339-2358
[118]D.Raabe,R.Becker.Coupling of a crystal plasticity finite element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminum[J].Modelling and Simulation in Materials Science and Engineering,2000,8:445-462
[119]A.D.Rollett,D.Raabe.A hybrid model for mesoscopic simulation of recrystallization[J].Computational Materials Science,2001,21(1):69-78
[120]D.Raabe.Yield surface simulation for partially recrystallized aluminum polycrystals on the basis of spatially discrete data[J].Computational Materials Science,2000,19(1):13-26
[121]D.Raabe,L.Hantchedi.2D cellular automaton simulation of the recrystallization texture of an IF sheet steel under consideration of Zener pinning[J].Computational Materials Science,2005,34(4):299-313
[122]Y.Liu,T.Baudin.Penelle R.Simulation of grain growth by cellular automata[J].Scripta Materialia,1996,34(11):1679-1683
[123]J.Geiger,A.Roosz,P.Barkoczy.Simulation of grain coarsening in two dimensions by cellular-automaton[J].Acta Mater,2001,49(4):623-629
[124]W.H.Yu,E.J.Palmiere,S.P.Banks,J.G.Han.Cellular automata modeling of austenite grain coarsening during reheating-Ⅰ.Normal grain coarsening[J].Journal of University of Science and Technology Beijing,2004,11(6):517-523
[125]W.H.Yu,E.J.Palmiere,S.P.Banks,J.G.Han.Cellular automata modeling of austenite grain coarsening during reheating-Ⅱ.Abnormal grain growth[J].Journal of University of Science and Technology Beijing,2005,12(1):26-32
[126]焦宪友,关小军,刘运腾,关宇昕,张继祥,申孝民,麻晓飞.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),2005,35(6):24-28
[127]花福安,杨院生,郭大勇,童文辉,胡壮麒.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,2004,40(11):1210-1214
[128]Y.Z.He,H.L.Ding,L.E Liu,S.Keesam.Computer simulation of 2Dgrain growth using a cellular atuomata model based on the lowest energy principle[J].Materials Scinence and Engineering,2006,429(1):236-246
[129]H.L.Ding,Y.Z.He,L.F.Liu,W.L.Ding.Cellular automata simulation of grain growth in three dimensions based on the lowest-energy principle[J].Journal of Crystal Growth,2006,293(2):489-497
[130]刘祖耀,李世畏,郑子樵.正常晶粒长大的计算机模拟Ⅰ-晶粒长大动力学跃迁概率的改进[J].中国有色金属学报,2003,13(6):1357-1360
[131]刘祖耀,郑子樵,陈大钦,李世晨.正常晶粒长大的计算机模拟Ⅱ-第二相粒子形状及取向的影响[J].中国有色金属学报,2004,14(1):122-126
[132]关小军,焦宪友,周家娟,张继祥,刘运腾,申孝民,麻晓飞.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,2007,17(5):699-704
[133]刘振亭,范新会,李炳,严文.单品铜线材晶粒演化过程的元胞自动机法模拟[J].西安工业大学学报,2008,28(2):147-152
[134]R.L.Goetz,V.Seetharaman.Modeling Dynamic Recrystallization Using Cellular Automata[J].Scripta Materialia,1998,38(1):405-413
[135]M.Qian,Z.X.Guo.Cellular automata simulation of microstructural evolution during dynamic recrystallization of an HY-100 steel[J].Materials Science and Engineering,2004,365(1):180-185
[136]R.Ding,Z.X.Guo.Coupled quantitative simulation of microstructural evolution and plastic flow during dynamic recrystallization[J].Acta Materialia,2001,49(16):3163-3175
[137]R.Ding,Z.X.Guo.Microstructural evolution of a Ti-6A1-4V alloy during β-phase processing:experimental and simulative investigations[J].Materials Science and Engineering,2004,365(1):172-179
[138]G.Kugler,R.Turk.Modeling the dynamic recrystallization under multi-stage hot deformation[J].Acta Materialia,2004,52(15):4659-4668
[139]N.M.Xiao,C.Wu Zheng,D.Z.Li,Y.Y Li.A simulation of dynamic recrystallization by coupling a cellular automaton method with a topology deformation technique[J].Computational Materials Science,2008,41(3):366-374
[140]J.W.Zhao,H.Ding,W.J.Zhao,F.R.Cao,H.L.Hou,Z.Q.Li.Modeling of dynamic reerystallization of Ti6A14V alloy using a cellular automaton approach[J].Aeta Metallurgica Sinica(English Letters),2008,21(4):260-268
[141]郭洪民,刘旭波,杨湘杰.元胞自动机方法模拟微观组织演变的建模框架[J].材料工程,2003,8:23-27
[142]张继祥.基于Monte Carlo方法的材料退火过程模拟模型及计算机仿真关键技术研究[D].山东大学博士毕业论文.2006:47-48
[143]D.Tumbull.Theory of grain boundary migration rates[J].American Institute of Mining and Metallurgical Engineers-Journal of Metals,1951,3(8):661-665
[144]申孝民.有限元与蒙特卡罗方法耦合的退火过程模拟模型及关键技术研究[D].山东大学博士毕业论文,2008:53-65,67-87
[145]D.Wolf.Read-Shockley model for high angle grain boundaries[J].Scripta Metallurgica,1989,23(10):1713-1718
[146]F.J.Humphreys.Unified theory of recovery,recrystallization and grain growth,based on the stability and growth of cellular microstructures - Ⅰ.The basic model[J].Acta Materialia,1997,45(12):4231-4240
[147]J.E.Burke,D.Turnbull.Recrystallization and grain growth progress in metal physics[M].London:Pergamon Press:1952,3:220-292
[148]Feltham P.Grain growth in metals[J].Acta Metallurgica,1957,5(2):97-105
[149]关小军,周家娟,陈晓闵.不同冷轧状态的ELC-BH钢板连续退火再结晶规律[J].金属热处理,2003,28(2):31-33
[150]D.Y.Ye,S.Matsuoka,N.Suzuki,Y.Maeda.Further investigation of Neuber's rule and the equivalent strain energy density(ESED) method[J].International Journal of Fatigue,2004,26(5):447-455
[151]N.Aravas,K.S.Kim,E A.Leckie.On the calculation of the stored energy of cold work[J].Journal of Engineering Materials and Technology,1990,112(4):465-470
[152]P.Ralph.Design plastic stress concentration factors using Ramberg-Osgood stress-strain parameters[J].AIAA Journal,1978,16(3):273-275
[153]E.A.Bonifaz,N.L.Richards.The plastic deformation of non-homogenneous polycrystals[J].International Journal of Plasticity,2008,24(2):289-301
[154]E.O.Hall.Deformation and ageing of mild steel[J].Physical Society,1951,64(381B):747-753
[155]N.J.Petch.Cleavage strength of polycrystals[J].Iron and Steel,1953,26(14):601-602
[156]T.Narutani,J.Takamura.Grain-size strengthening in terms of dislocation density measured by resistivity[J].Acta Metall,1991,39(8):2037-2049
[157]A.W.Thompson,M.I.Baskes,W.F.Flanagan.The dependence of polycrystal work hardening on grain size[J].Acta Metall,1973,227(1):1017-1028
[158]J.C.M.Li.Petch relation and grain boundary sources[J].Metallurgical Society of American Institute of Mining,Metallurgical and Petroleum Engineers - Transactions,1963,227(1):239-247
[159]关小军.成分和工艺对超低碳高强度烘烤硬化钢板组织和性能影响的研究[D].北京科技大学博士学位论文,1993:44
[160]D.A.Hughes,A.Godfrey.Dislocation structures formed during hot and cold working[A].Proceedings of the TMS Fall Meeting,1998:23-36
[161]D.A.Hughes,N.Hansen.Microstructural evolution in nickel during rolling and torsion[J].Materials Science and Technology,1991,7(6):544-553
[162]D.A.Hughes,D.C.Cb.rzan,Q.Liu,N.Hansen.Scaling of misorientation angle distributions[J]Physical Review Letters,1998,81(21):4664-4667
[163]T.Bandin,D.Solas,A.L.Etter,D.Ceccaldi,R.Penelle.Simulation of primary recrystallization from TEM observations and neutron diffraction measurements[J].Scripta Materialia,2004,51:427-430
[164]T.Huang,F.J.Humphreys.Subgrain growth and low angle boundary mobility in aluminium crystals of orientation {110} {001}[J].Acta Materialia,2000,48(8):2017-2030
[165]M.Ferry,F.J.Humphreys.Discontinuous subgrain growth in deformed and annealed {100} {001}aluminium single crystals[J].Acta Materialia,1996,44(4):1293-1308
[166]M.Oyarzábal,A.Martinez-de-guerenu,I.Gutiérrez.Effect of stored energy and recovery on the overall recrystallization kinetics of a cold rolled low carbon steel[J].Materials Science and Engineering A,2007,485(1):200-209
[167]E.Nes.Recovery revisited[J].Acta Metall.1995,43(6):2189-2207
[168]美国金属学会.金属手册[M].北京:机械工业出版社,1994
[169]R.A.Vandermeer,D.Jenson.Microstructure path-and temperature dependence of recrystallization in commercial aluminum[J].Acta Materialia,2001,49(11):2083-2064
[170]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.Effect of inhomogeneous deformation on the recrystallization kinetics of deformed metals[J].ISIJ international,2004,44(11):1931-1936
[171]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.A metallurgical interpretation of the static recrystallization kinetics of an intercritically deformed C-Mn steel[J].Metallurgical and Materials Transections A,2004,35A(6):1889-1898
[172]宋晓艳,R.Markus,张久兴.含有两尺寸组粒子分布的多相材料再结晶的研究[J].金属学报,2004,40(10):1009-1017
[173]W.Xu,M.Ferry,J.M.Cairney,F.J.Humphreys.Three-dimensional investigation of particle-stimulated nucleation in a nickel alloy[J].Acta Materialia,2007,55(15):5157-5167
[2]俞汉清.金属塑性成形原理[M].北京:机械工业出版社,2003:18,139
[3]毛卫民,赵新兵.金属的再结晶和晶粒长大[M].北京:冶金工业出版社,1994:36,16,64,45,71
[4]R.W.Calm.New theory of recrystallization nuclei[J].Physical Society-Proceedings,1950,63(364A):323-336
[5]W.G.Burgers.Prozesse der Keimbildung bei der Rekristallisation(Process of nucleation in recrystallization)[J].Zeitschrift fuer Metallkunde,1961,52(1):19-26
[6]Y.D.Huang,L.Froyen.Recovery,recrystallization and grain growth in Fe_3Al-based alloys[J].Intermetallics,2002,10(5):473-484
[7]S.P.Bellier,R.D.Doherty.Structure of deformed aluminum and its recrystallization em dash investigations with transmission kossel diffraction[J].Acta Metallurgica,1977,25(5):521-538
[8]M.Muraki,T.Toge,K.Sakata,T.Obara,E.Furubayashi.Formation mechanism of {111}recrystallization texture in ferritic steels[J],Tetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan,1999,85(10):751-757
[9]T.Urabe,J.J.Jonas.Modeling texture change during recrystallization of an IF steel[J],ISIJ International,1994,34(5):435-442
[10]S.S.葛列里克著,仝健民译.金属和合金的再结晶[M].北京:机械工业出版社,1985:44,72,56,40
[11]W.A.Johnson,R.F.Mehl.Reaction kinetics in processes of nucleation and growth[A],American Institute of Mining and Metallurgical Engineers-Transactions,1939,135:416-442
[12]M.Avrami.Kinetics of phase change Ⅰ:general theory[J].Journal of Chemical Physics,1939,7(12):1103-1112
[13]W.A.Anderson,R.E Mehl.Recrystallization of aluminum in terms of rate of nucleation and rate of growth[J].Metallugia,1945,33(193):45-46
[14]B.F.Decker,D.Harker.Activation energy for recrystallization in rolled copper[A].American Institute of Mining and Metallurgical Engineers-Journal of Metals,1950,188(6):887-890
[15]J.W.Cahn.Kinetics of grain boundary nucleated reactions[J].Acta Metallurgica,1956,4(5):449-459
[16]R.A.Vandermeer,E Grodon.Edge-nucleated,growth controlled recrystallization in aluminum[J].Metallurgical Society of AIME,1959,215(4):577-588
[17]N.H.Lin,C.P.Chang,E W.Kao.Effect of annealing temperature on the recrystallization kinetics of commercially pure aluminum[J].Metallurgical and Materials Transactions A,1995,26A(8):2185-2187
[18]S.H.Choi,Y.C.Yoo.Static recrystallization kinetics of 304 stainless steels[J].Journal of Materials Science,2001,36(17):4273-4278
[19]D.Weygand,Y.Brechet,J.Lepinoux.Mechanisms and kinetics of recrystallization:A two dimensional vertex dynamics simulaton[J].Iterface Science,2001,9(3):311-317
[20]S.Sangal,S.S.Sahay,A.K.Jena.Nucleation and recrystallization kinetics in boron doped Ni76A124 deformed to small strains[J].Materials Science & Engineering,1997,239:293-296
[21]R.A.Vandermeer,D.Jenson.Microstructure path and temperature dependence of recrystallization in commercial aluminum[J].Acta Materialia,200 l,49(11):2083-2064
[22]W.P.Ye,R L Gall,G Saindrenan.A study of recrystallization of an IF steel bu kinetics models[J].Materials Scinece & Engineering A,2002,332(1-2):41-46
[23]C.Garcia-Mateo,B.Lopez,J.M.Rodriguez-lbabe.static recrystallization kinetics in warm worked vanadium microalloyed steels[J].Materials Scinece & Engineering A,2001,303(1):216-225
[24]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.Effect of inhomogeneous deformation on the recrystallization kinetics of deformed metals[J].ISIJ international,2004,44(11):1931-1936
[25]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.A metallurgical interpretation of the static recrystallization kinetics of an intercritically deformed C-Mn steel[J].Metallurgical and Materials Transections A,2004,35(6):1889-1898
[26]C.Zener.Private communication to Smith[J].Trans Amer Inst Metall Engrs,1949,175:15-17
[27]王国承,王铁明,尚德礼,方克明.超细第二相粒子强化钢铁材料的研究进展[J].钢铁研究学报,2007,19(6):5-8
[28]东涛,付俊岩.试论我国钢的微合金化发展方向[J].中国冶金,2005,5:16-19
[29]董成瑞,任海鹏,金同哲.微合金非调质钢[M].北京:冶金工业出版社,2000
[30]马衍伟,王先进.超深部IF钢研究的最新进展[J].钢铁,1998,33(4):65-69
[31]景财年,王作成,韩福涛.IF钢中的析出物[J].材料导报,2005,19(5):50-64
[32]D.Strzeciwilk,Z.wokulski,P.Tkacz.Microstructure of TiC crystals obtained from high temperature nickel solution[J].Journal of Alloys and Compounds,2003,350(1):256-263
[33]R.Mendoza,J.Huante,M.Alanis,C.Gonzalez-Rivera,J.A.Juarez-Islas.Processing of ultra low carbon steels with mechanical properties adequate for automotive applications in the as-annealed condition[J].Materials Science and Engineering A,2000,276(1):203-209
[34]商建辉,王先进.Ti-IF钢热轧时第二相粒子析出行为研究的最新进展[J].钢铁研究学报,2000,12(6):55-60
[35]王作成,石京.不同退火工艺下Ti-IF钢二相料演变的比较[J].材料科学与工艺,1999,7(3):41-45
[36]N.Mizui.Precipitation control and related mechanical properties in ultra low carbon sheet steels[A].Modern Lc and ULC Sheet steels for Cold Forming:Processing and Properties[C].Japan,1998:187-198
[37]M.Joonoh,L.Jongbong,L.changhee.Prediction for the austenite grain size in the presence of growing particles in the weld HAZ of Ti-microalloyed steel[J].Materials Science and Engineering,2007,459(1):40-46
[38]曾周亮,宁康琪,彭北山.高强铝合金第二相强化及其机理[J].冶金丛刊,2008,4:5-7
[39]王锦,卜春阳.第二相粒子尺度对钼镧合金加工硬化影响[J].中国钼业,2006,30(3):43-46
[40]K.W.Mahin,K.Hanson,J.W.J.Morris.Computer simulation of homogeneous nucleation and growth processes[J].Nuclear Metallurgy,Metallurgical Society of AIME,1976,20(1):39-50
[41]H.J.Frost,C.V.Thompson,C.L.Howe,J.Whang.Two dimensional computer simulation of capillarity-driven grain growth:preliminary results[J].Scripta Metallurgica,1988,22(1):65-70
[42]H.J.Frost,C.V.Thompson.The effect of nucleation conditions on the topology and geometry of two-dimensional grain structures[J].Acta Metallurgica,1987,35(2):529-540
[43]C.V.Thompson,H.J.Frost.The relative rates of secondary and normal grain growth[J].Acta Metallurgica,1987,35(4):887-890
[44]D.J.Jensen.Simulation of recrystallization microstructure and texture:effects of preferential growth[J].Metallurgical and Materials Transaction A:Physical Metallurgy and Materials Science,1997,28A(1):15-25
[45]D.L.Jensen.Modeling of microstructure development during recrystallization[J].Scripta Metallurgica et Materialia,1992,27(11):1551-1556
[46]H.E.Vatne,T.Furu,R.φrsund,E.Nes.Modelling recrystallization after hot deformation of aluminum[J].Acta Materialia,1996,44(11):4463-4473
[47]V.Y.Novikov,I.S.Gavrikov.Influence of heterogeneous nucleation on microstructure and kinetics of primary recrystallization[J].Acta Metallurgica et Materialia,1995,43(3):973-976
[48]I.S.Gavrikov,V.Y.Novikov.The effect of the initial grain size on the kinetics and microstructure of primary recrystallization:computer simulation[J].Physics of Metals and Metallography,1994,77(4):348-352
[49]S.Gavrikov,V.Y.Novikov.Influence of initial grain size on kinetics of primary recrystallization[J].Fizika Metallov i Metallovedenie,1994,77(4):29-35
[50]T.O.Saetre,O.Hunderi,E.Nes.Computer simulation of primary recrystallization microstructure:the effects of nucleation and growth kietics[J].Acta Metallurgica,1986,34(6):981-987
[51]T.Furu,R.φrsund,E.Nes.Subgrain growth in heavily deformed aluminium - experimental investigation and modeling treatment[J].Acta Metallurgica et Materialia,1995,43(6):2209-2232
[52]Price C W.Use of Kolmogorov-Johnson-Mehl-Avrami kinetics in recrystallization of metals and crystallization of metallic glasses[J].Acta Metallurgica,1990,38(5):727-738
[53]C.W.Price.Simulations of grain impingement and recrystallization kinetics[J].Acta Metallurgica,1987,35(6):1377-1390
[54]C.W.Price.Analysis of models for grain-impingement compensation and their effect on recrystallization kinetics[J].Acta Metallurgica,1991,39(8):1807-1816
[55]K.Kawasaki,T.Nagai,K.Nakashima.Vertex models for two-dimensional grain growth[J].philosophical Magazine B:Physics of Condensed Matter,Electronic,Optical and Magnetic Properties,1989,60(3):339-421
[56]F.J.Humphreys.Network model for recovery and recrystallization[J].Scripta Metallurgica et Materialia,1992,27(11):1557-1562
[57]D.Weygand,Y.Brechet,J.Lepinoux.A vertex simulation of grain growth in 2D and 3D.Advanced Engineering Materials.2001,3(1):67-71
[58]D.Weygand,Y.Brechet,J.Lepinoux.Zener pinning and grain growth:a two-dimensional vertex computer simulation.Acta Materialia.1999,47(3):961-970
[59]D.J.Srolovitz,G.S.Grest,M.P.Anderson.Computer simulation of recrystallization- Ⅰ.homogeneous nucleation and growth[J].Acta Metallurgica,1986,34(9):1833-1845
[60]D.J.Srolovitz,G.S.Grest,M.P.Anderson,A.D.Rollett.Computer simulation of recrystallization - Ⅱ.Heterogeneous nucleation and growth[J].Acta Metallurgica,1988, 36(8): 2115-2128
[61] A. D. Rollett, D. J. Srolovitz, M. P. Anderson, R. D. Doherty. Computer simulation of recrystallization. III. Influence of a dispersion of fine particles[J]. Acta Metallurgica et Materialia, 1992,40(12): 3475-3495
[62] M. P. Anderson, G S. Grest, D. J. Srolovitz. Microstructural dynamics of primary and secondary recrystallization[J]. Metallurgical Soc of AIME, 1986: 77-93
[63] R. D. Doherty, A. D. Rollett, D. J. Srolovitz. Structural Evolution During recrystallization[A]. Proceedings of the Riso International Symposium on Metallurgy and Materials Science 7th, 1986: 53-67
[64] A. D. Rollett, D. J. Srolovitz, R. D. Doherty, M. P. Anderson. Computer simulation of recrystallization in non-uniformly deformed metals[J]. Acta Metallurgica, 1989, 37(2):627-639
[65] B. Radhakrishnan, G. B. Sama, T. Zacharia. Modeling the kinetics and microstructural evolution during static recrystallization-Monte Carlo simulation of recrystallization[J]. Acta Metallurgica, 1998,46(12): 4415-4433
[66] B. Radhakrishnan, G. B. Sama, T. Zacharia. Monte Carlo simulation of deformation substructure evolution during recrystallization[J]. Scripta Materialia, 1998, 39(12):1639-1645
[67] B. Radhakrishnan, G. B. Sama, H. Weiland, P. Baggethun. Simulations of deformation and recrystallization of single crystals of aluminium containing hard particles[J]. Modelling and Simulation in Materials Science and Engineering, 2000, 8(5): 737-750
[68] B. Radhakrishnan, G. B. Sama, T. Zacharia. Coupled finite element-Monte Carlo simulation of microstructure and texture evolution during thermomechanical processing[A].Proceedings of the TMS Fall Meeting, 1998: 267-278
[69] E. A. Holm, M. A. Miodownik, A. D. Rollett. On abnormal subgrain growth and the origin of recrystallization nuclei[J]. Acta Materialia, 2003,51(9): 2701-2716
[70] M. A. Miodownik, E. A. Holm, A. W. Godfrey, D. A. Hughes, Lesar R. Multiscale modeling of recrystallization[A]. Materials Research Society Symposium- Proceeding, 1999, 538:157-162
[71] E. A. Holm, K. J. Healey, C. C. Battaile. Coupled computer simulations of recrystallization in deformed polycrystals[A]. Materials Science Forum, 2004,467-470(1): 641-646
[72] P. Gerber, J. Tarasiuk, D. Solas, S. Jakani, M. H. Mathon, T. Baudin. Monte Carlo modelling of recrystallization mechanisms in wire-drawn copper from EBSD data[A].Materials Science Forum, 2004,467-470: 635-640
[73] F. Caleyo, T. Baudin, R. Penelle. Monte Carlo simulation of recrystallization in Fe-50%Ni starting from EBSD and bulk texture measurements[J]. Scripta Materialia, 2002, 46(12):829-835
[74] J. Tarasiuk, P. Gerber, B. Bacroix, K. Pickos. Modeling of recrystallization using Monte Carlo method based on EBSD data[A]. Materials Science Forum, 2002, 408-412( I ):395-400
[75] T. Koseki, T. Araki. Modeling of steel weld microstructure using Monte Carlo and finite difference hybrid method[A]. Materials Science Forum, 2006, 539-543(4): 4002-4007
[76] M. Kazeminezhad, T. A. Karimi, T. A. Kiet. Utilization of the finite element and Monte Carlo model for simulation the recrystallization of inhomogeneous deformation of copper[J].Computational Materials Science, 2007,38(4): 765-773
[77] S. Ling, M. P. Anderson. Monte Carlo simulation of grain growth and recrystallization in polycrystalline materials[J].JOM,1992,44(9):30-36
[78]B.Radhakrishnan,T.Zacharia.On the prediction of HAZ grain size using Monte Carlo simulation[A].Modeling and Control of Joining Processes,American Welding Society international conference.Orlando,FL,1993
[79]J.H.Gao,R.G.Thompson.Real time temperature models for Monte Carlo simulations of normal grain growth[J].Acta Mater,1996,44(11):4565-4570
[80]B.K.Kad,P.M.Hazzledine.Monte carlo simulations of grain growth and zener pinning[J].Materials Science and Engineering,1997,238:70-77
[81]M.Soucail,R.Messina,A.Cosnuau,L.P.Kubin.Monte Carlo simulation of Zener pinning in two dimensions[J].Materials Science and Engineering,1999,271(1):1-7
[82]N.Maazi,N.Rouag.Consideration of Zener drag effect by introducing a limiting radius for neighbourhood in grain growth simulation[J].Journal of Crystal Growth,2002,243(2):361-369
[83]J.H.Gao,R.G.Thompson,B.R.Patterson.Computer simulation of grain growth with second phase particle pinning[J].Acta mater,1997,49(9):3653-3658
[84]窦晓锋,鹿守理,赵辉.钢静态再结晶的蒙特卡罗模拟[J].钢铁研究,1997,98(5):19-21
[85]薛利平,鹿守理,窦晓锋.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,2000,22(1):34-37
[86]宋晓艳,刘国权,谷南驹.第二相粒子尺寸对基体晶粒长大影响的仿真研究[J].金属学报,1999,35(6):565-568
[87]X.Y.Song,G.Q.Liu,N.J.Gu.Influence of the second phase particle size on grain growth based on coumputer simulation[J].Materials Science and Engineering,1999,270(2):178-182
[88]宋晓艳,刘国权,谷南驹.有第二相粒子的复相材料显微组织及其演变的仿真研究[J].自然科学进展,1999,10(2):161-166
[89]宋晓艳,谷南驹,刘国权,王宝奇.第二相粒子含量对基体晶粒长大影响的计算机仿真研究[J].金属学报,2000,36(6):592-596
[90]X.Y.Song,M.Rettenmayr.Modelling study on recrystallization,recovery and their temperature dependence in inhomogeneously deformed materials[J].Materials Science and Engineering A,2002,332(1-2):153-160
[91]X.Y.Song,M.Rettenmayr,Muller C,Exner H E.Modeling of recrystallization after inhomogeneous deformation[J].Metallurgical and Materials Transactions A:Physical Metallurgy and Materials Science,2001,32(9):2199-2206
[92]张继祥,关小军,孙胜.一种改进的晶粒长大Monte Carlo模拟方法[J].金属学报,2004,40(5):457-461
[93]张继祥,关小军.异常晶粒长大Monte Carlo模拟研究[J].中国有色金属学报,2006,16(10):1689-1697
[94]申孝民,关小军,张继祥,刘运腾,麻晓飞,赵宪明.有限元与Monte Cado方法耦合的冷轧纯铝板再结晶模拟[J].中国有色金属学报,2007,17(1):124-130
[95]关小军,张继祥,孙胜.再结品过程计算机模拟[J].特殊钢,2004,25(3):34-37
[96]邓章铭,周浪.元胞自动机模型方法及其在材料组织结构模拟中的应用[J].材料科学与工程,2000,18(3):123-129
[97]焦宪友.基于元胞自动机法的材料品粒长大和再结晶模拟[D].山东大学硕士毕业论文.2006:13-17
[98]金文忠.热加工过程静态再结晶的元胞自动机模拟[D].东北大学硕士学位论文.2006:10-20
[99]S.Wofram.Statistical Mechanics of Cellular Automata[J].Rev.Mod.Phys,1983,55(3):601-622
[100]N.Packard.Theory and Applications of Cellular Automata[M].Singapore:World Scientific,1986:305
[101]M.Rappaz,Ch.-A.Gandin.Probabilistic modelling of microstructure formation in solidification processes[J].Acta Metallurgica et Materialia,1993,41(2):345-360
[102]Ch.-A.Gandin,M.Rappaz.A coupled finite element-cellular automaton model for the prediction of dendritic grain structures in solidification processes[J].Acta Metallurgica et Materialia,1994,42(7):2233-2246
[103]J.F.McCarthy.Lattice gas cellular automata method for flow in the interdendritic region[J].Acta Metallurgica et Materialia,1994,42(5):1573-1581
[104]R.K.Shelton,D.C.Dunand.Computer modeling of particle pushing and clustering during matrix crystallization[J].Acta Materialia,1996,44(1):4571-4585
[105]K.Kevin.Cellular Automata Investigations of Binary Solidification[J].Journal of Computational Physics,1998,142(1):243-262
[106]P.Carter,D.C.Cox,C.A.Gandin,R.C.Reed.Process modelling of grain selection during the solidification of single crystal superalloy castings[J].Materials Science and Engineering,2000,280(2):233-246
[107]M.Vandyoussefi,A.L.Greer,Application of cellular automaton-finite element model to the grain refinement of directionally solidified A1-4.15 wt%Mg alloys[J].Acta Materialia,2002,50(6):1559-1569
[108]W.Wang,P.D.Lee,M.McLean.A model of solidification microstructures in nickel-based superalloys:predicting primary dendrite spacing selection[J].Acta Materialia,2003,51(10):2971-2987
[109]Y.Liu,Q.Y.Xu,B.Liu.A Modified Cellular Automaton Method for the Modeling of the Dendritic Morphology of Binary Alloys[J].Tsinghua.Science & Technology,2006,11(5):495-500
[110]L.Zhang,C.B.Zhang.Two-dimensional cellular automaton model for simulating structural evolution of binary alloys during solidification[J].Transactions of Nonferrous Metals Society of China,2006,16(6):1410-1416
[111]K.F.Wang,B.S Li,G.F.Mi,J.J.GUO,H.Z.FU.Modeling of Cell/Dendrite Transition During Directional Solidification of Ti-Al Alloy Using Cellular Automaton Method[J].Journal of Iron and Steel Research,2008,456(1):85-95
[112]H.W.Hesselbarth,I.R.Gobel.Simulation of recrystallization by cellular automata[J].Acta Metallurgica et Materialia,1991,39(9):2135-2143
[113]C.H.J.Davies.The effect of neighbourhood on the kinetics of a cellular automaton recrystallisation model[J].Scripta metallurgica et materialia,1995,33(7):1139-1143
[114]C.H.J.Davies.Growth of Nuclei in a Cellular Automaton Simulation of Recrystallisation[J].Scripta materialia,1996,36(1):35-40
[115]C.H.J.Davies,L.Hong.Cellular automaton simulation of static recrystallization in cold-rolled AA 1050[J].Scripta materialia,1998,40(10):1145-1150
[116]V.Marx,F.R.Reher,G.Gottstein.Simulation of primary recrystallization using a modified three-dimensional cellular automaton[J].Acta Materialia,1999,47(4):1219-1230
[117]D.Raabe.Introduction of a scaleable 3D cellular automaton with a probabilistic switching rule for the discrete mesoscale simulation of recrystallization phenomena[J].Philosophical Magazine A,1999,79:2339-2358
[118]D.Raabe,R.Becker.Coupling of a crystal plasticity finite element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminum[J].Modelling and Simulation in Materials Science and Engineering,2000,8:445-462
[119]A.D.Rollett,D.Raabe.A hybrid model for mesoscopic simulation of recrystallization[J].Computational Materials Science,2001,21(1):69-78
[120]D.Raabe.Yield surface simulation for partially recrystallized aluminum polycrystals on the basis of spatially discrete data[J].Computational Materials Science,2000,19(1):13-26
[121]D.Raabe,L.Hantchedi.2D cellular automaton simulation of the recrystallization texture of an IF sheet steel under consideration of Zener pinning[J].Computational Materials Science,2005,34(4):299-313
[122]Y.Liu,T.Baudin.Penelle R.Simulation of grain growth by cellular automata[J].Scripta Materialia,1996,34(11):1679-1683
[123]J.Geiger,A.Roosz,P.Barkoczy.Simulation of grain coarsening in two dimensions by cellular-automaton[J].Acta Mater,2001,49(4):623-629
[124]W.H.Yu,E.J.Palmiere,S.P.Banks,J.G.Han.Cellular automata modeling of austenite grain coarsening during reheating-Ⅰ.Normal grain coarsening[J].Journal of University of Science and Technology Beijing,2004,11(6):517-523
[125]W.H.Yu,E.J.Palmiere,S.P.Banks,J.G.Han.Cellular automata modeling of austenite grain coarsening during reheating-Ⅱ.Abnormal grain growth[J].Journal of University of Science and Technology Beijing,2005,12(1):26-32
[126]焦宪友,关小军,刘运腾,关宇昕,张继祥,申孝民,麻晓飞.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),2005,35(6):24-28
[127]花福安,杨院生,郭大勇,童文辉,胡壮麒.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,2004,40(11):1210-1214
[128]Y.Z.He,H.L.Ding,L.E Liu,S.Keesam.Computer simulation of 2Dgrain growth using a cellular atuomata model based on the lowest energy principle[J].Materials Scinence and Engineering,2006,429(1):236-246
[129]H.L.Ding,Y.Z.He,L.F.Liu,W.L.Ding.Cellular automata simulation of grain growth in three dimensions based on the lowest-energy principle[J].Journal of Crystal Growth,2006,293(2):489-497
[130]刘祖耀,李世畏,郑子樵.正常晶粒长大的计算机模拟Ⅰ-晶粒长大动力学跃迁概率的改进[J].中国有色金属学报,2003,13(6):1357-1360
[131]刘祖耀,郑子樵,陈大钦,李世晨.正常晶粒长大的计算机模拟Ⅱ-第二相粒子形状及取向的影响[J].中国有色金属学报,2004,14(1):122-126
[132]关小军,焦宪友,周家娟,张继祥,刘运腾,申孝民,麻晓飞.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,2007,17(5):699-704
[133]刘振亭,范新会,李炳,严文.单品铜线材晶粒演化过程的元胞自动机法模拟[J].西安工业大学学报,2008,28(2):147-152
[134]R.L.Goetz,V.Seetharaman.Modeling Dynamic Recrystallization Using Cellular Automata[J].Scripta Materialia,1998,38(1):405-413
[135]M.Qian,Z.X.Guo.Cellular automata simulation of microstructural evolution during dynamic recrystallization of an HY-100 steel[J].Materials Science and Engineering,2004,365(1):180-185
[136]R.Ding,Z.X.Guo.Coupled quantitative simulation of microstructural evolution and plastic flow during dynamic recrystallization[J].Acta Materialia,2001,49(16):3163-3175
[137]R.Ding,Z.X.Guo.Microstructural evolution of a Ti-6A1-4V alloy during β-phase processing:experimental and simulative investigations[J].Materials Science and Engineering,2004,365(1):172-179
[138]G.Kugler,R.Turk.Modeling the dynamic recrystallization under multi-stage hot deformation[J].Acta Materialia,2004,52(15):4659-4668
[139]N.M.Xiao,C.Wu Zheng,D.Z.Li,Y.Y Li.A simulation of dynamic recrystallization by coupling a cellular automaton method with a topology deformation technique[J].Computational Materials Science,2008,41(3):366-374
[140]J.W.Zhao,H.Ding,W.J.Zhao,F.R.Cao,H.L.Hou,Z.Q.Li.Modeling of dynamic reerystallization of Ti6A14V alloy using a cellular automaton approach[J].Aeta Metallurgica Sinica(English Letters),2008,21(4):260-268
[141]郭洪民,刘旭波,杨湘杰.元胞自动机方法模拟微观组织演变的建模框架[J].材料工程,2003,8:23-27
[142]张继祥.基于Monte Carlo方法的材料退火过程模拟模型及计算机仿真关键技术研究[D].山东大学博士毕业论文.2006:47-48
[143]D.Tumbull.Theory of grain boundary migration rates[J].American Institute of Mining and Metallurgical Engineers-Journal of Metals,1951,3(8):661-665
[144]申孝民.有限元与蒙特卡罗方法耦合的退火过程模拟模型及关键技术研究[D].山东大学博士毕业论文,2008:53-65,67-87
[145]D.Wolf.Read-Shockley model for high angle grain boundaries[J].Scripta Metallurgica,1989,23(10):1713-1718
[146]F.J.Humphreys.Unified theory of recovery,recrystallization and grain growth,based on the stability and growth of cellular microstructures - Ⅰ.The basic model[J].Acta Materialia,1997,45(12):4231-4240
[147]J.E.Burke,D.Turnbull.Recrystallization and grain growth progress in metal physics[M].London:Pergamon Press:1952,3:220-292
[148]Feltham P.Grain growth in metals[J].Acta Metallurgica,1957,5(2):97-105
[149]关小军,周家娟,陈晓闵.不同冷轧状态的ELC-BH钢板连续退火再结晶规律[J].金属热处理,2003,28(2):31-33
[150]D.Y.Ye,S.Matsuoka,N.Suzuki,Y.Maeda.Further investigation of Neuber's rule and the equivalent strain energy density(ESED) method[J].International Journal of Fatigue,2004,26(5):447-455
[151]N.Aravas,K.S.Kim,E A.Leckie.On the calculation of the stored energy of cold work[J].Journal of Engineering Materials and Technology,1990,112(4):465-470
[152]P.Ralph.Design plastic stress concentration factors using Ramberg-Osgood stress-strain parameters[J].AIAA Journal,1978,16(3):273-275
[153]E.A.Bonifaz,N.L.Richards.The plastic deformation of non-homogenneous polycrystals[J].International Journal of Plasticity,2008,24(2):289-301
[154]E.O.Hall.Deformation and ageing of mild steel[J].Physical Society,1951,64(381B):747-753
[155]N.J.Petch.Cleavage strength of polycrystals[J].Iron and Steel,1953,26(14):601-602
[156]T.Narutani,J.Takamura.Grain-size strengthening in terms of dislocation density measured by resistivity[J].Acta Metall,1991,39(8):2037-2049
[157]A.W.Thompson,M.I.Baskes,W.F.Flanagan.The dependence of polycrystal work hardening on grain size[J].Acta Metall,1973,227(1):1017-1028
[158]J.C.M.Li.Petch relation and grain boundary sources[J].Metallurgical Society of American Institute of Mining,Metallurgical and Petroleum Engineers - Transactions,1963,227(1):239-247
[159]关小军.成分和工艺对超低碳高强度烘烤硬化钢板组织和性能影响的研究[D].北京科技大学博士学位论文,1993:44
[160]D.A.Hughes,A.Godfrey.Dislocation structures formed during hot and cold working[A].Proceedings of the TMS Fall Meeting,1998:23-36
[161]D.A.Hughes,N.Hansen.Microstructural evolution in nickel during rolling and torsion[J].Materials Science and Technology,1991,7(6):544-553
[162]D.A.Hughes,D.C.Cb.rzan,Q.Liu,N.Hansen.Scaling of misorientation angle distributions[J]Physical Review Letters,1998,81(21):4664-4667
[163]T.Bandin,D.Solas,A.L.Etter,D.Ceccaldi,R.Penelle.Simulation of primary recrystallization from TEM observations and neutron diffraction measurements[J].Scripta Materialia,2004,51:427-430
[164]T.Huang,F.J.Humphreys.Subgrain growth and low angle boundary mobility in aluminium crystals of orientation {110} {001}[J].Acta Materialia,2000,48(8):2017-2030
[165]M.Ferry,F.J.Humphreys.Discontinuous subgrain growth in deformed and annealed {100} {001}aluminium single crystals[J].Acta Materialia,1996,44(4):1293-1308
[166]M.Oyarzábal,A.Martinez-de-guerenu,I.Gutiérrez.Effect of stored energy and recovery on the overall recrystallization kinetics of a cold rolled low carbon steel[J].Materials Science and Engineering A,2007,485(1):200-209
[167]E.Nes.Recovery revisited[J].Acta Metall.1995,43(6):2189-2207
[168]美国金属学会.金属手册[M].北京:机械工业出版社,1994
[169]R.A.Vandermeer,D.Jenson.Microstructure path-and temperature dependence of recrystallization in commercial aluminum[J].Acta Materialia,2001,49(11):2083-2064
[170]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.Effect of inhomogeneous deformation on the recrystallization kinetics of deformed metals[J].ISIJ international,2004,44(11):1931-1936
[171]H.W.Luo,J.Sietsma,S.Xan Der Zwaag.A metallurgical interpretation of the static recrystallization kinetics of an intercritically deformed C-Mn steel[J].Metallurgical and Materials Transections A,2004,35A(6):1889-1898
[172]宋晓艳,R.Markus,张久兴.含有两尺寸组粒子分布的多相材料再结晶的研究[J].金属学报,2004,40(10):1009-1017
[173]W.Xu,M.Ferry,J.M.Cairney,F.J.Humphreys.Three-dimensional investigation of particle-stimulated nucleation in a nickel alloy[J].Acta Materialia,2007,55(15):5157-5167