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
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摘要
随着材料科学和计算机技术的发展,材料的制备科学正从传统的正向研究向逆向研究过渡:从材料组分、微观结构出发,借助计算机模拟预测材料性质,以便生成满足使用要求的功能材料。金属材料的微观组织是在冶炼、铸造、成形加工、热处理工艺过程中形成的,而成形加工及热处理对其最终微观组织结构及其性能起着至关重要的作用。实际生产中,金属材料的塑性变形在宏观及介观尺度上都是不均匀的,这种不均匀性引起材料内部变形储能的不均匀分布,从而导致了退火过程中变形材料内部再结晶动力学的不一致,使退火后材料各部位的组织及性能有较大差异。
对金属材料的塑性变形过程进行有限元(Finite Element Method,FEM)分析,可以获得变形过程中金属流动及应力应变等详细信息;利用Monte Carlo(MC)方法对变形金属材料的退火过程进行计算机模拟研究,可以定量、连续、动态地观察、检测在实验室中所观察不到或检测不到的现象,更好地认识退火过程中组织演变规律及其内在机理,获得退火组织的特征参数,实现退火过程介观组织设计及其性能预报,为退火工艺优化和高性能材料设计与开发打下坚实的基础。因此,通过FEM与MC方法的耦合,既可以全面了解外界变形条件引起的材料宏观尺度上储能的非均匀分布及其相应的再结晶动力学与平均晶粒尺寸变化,又可以深入研究内部组织结构差异导致的材料介观尺度上储能的非均匀分布及其相应的再结晶动力学与拓扑组织演变过程,具有重要的理论意义和实用价值。
MC方法是以概率和统计学理论为基础的一种数值计算方法。它将所求解问题转换成事件概率模型,用计算机抽样得到这个事件出现的概率,并用它作为问题的解。Monte Carlo Potts模型(简称MC Potts模型)具有可分析复杂组织与可视化仿真的能力,本文以MC Potts模型为模拟工具,基于现有实验及理论基础依次建立了FEM与MC方法的耦合模型、介观储能密度分布模型及回复模型,完成了对退火过程模拟模型的改进;结合相关退火模拟关键技术,编写了冷变形材料等温退火过程组织模拟程序;通过超低碳高强度烘烤硬化钢板与工业纯铝板的实验研究对模型及其程序进行了验证。
首先,本论文分析了现有变形材料退火模型中的储能分布模型,特别是RSRP储能分布模型的不足,从多晶体塑性变形过程中应力、位错密度及储能密度之间的关系出发,解决了以下几个关键问题:①状态变量的转换:有限元模型中流变应力转换为储能密度,②数据的移植:转换得到的储能密度移植为MC模拟区域内的平均储能密度,③介观初始储能场及相应模拟能量场的构建,④形核模型的建立,并据此建立了FEM与MC方法的耦合模型,实现了由宏观应力场向介观储能场的转换,初步解决了冷变形材料宏观及介观尺度上储能的非均匀分布问题。基于FEM与MC的耦合模型,编制了冷变形金属材料等温退火过程模拟程序。
以冷轧纯铝板为研究对象,模拟了轧件中靠近表层的储能极大区与靠近心部的储能极小区的再结晶过程,并将模拟结果与实验结果进行了对比。研究发现:①新建的耦合模型能够较好地模拟轧件各部位储能的不同引起的再结晶动力学及再结晶完成时微观组织的差异:储能较高的区域再结晶速度较快、再结晶完成时平均晶粒尺寸较小,储能较低的区域再结晶速度较慢、再结晶完成时平均晶粒尺寸较大,反映的规律与实验观察结果及现有再结晶理论相一致,即退火后轧件表层的晶粒尺寸比心部的更加细小;变形程度越大,再结晶速度越快。②再结晶动力学模拟统计结果与其微观组织直观模拟结果反映的规律相同,且这些结果与现有再结晶理论及实验结果基本一致,不仅表明了再结晶微观组织模拟结果的必然性,而且验证了本文所采用的有限元-再结晶耦合模型的合理性。
然后,本论文深入研究了多晶体塑性变形时各种介观及微观结构对位错运动及分布,进而对储能密度分布的影响,并根据其影响机制提出了合理假设并建立了相关的模型。①从Kocks复合模型出发,建立了冷变形材料中储能在不同尺寸晶粒间的分布模型,初步解决了不同晶粒间储能的分布问题;②从晶界对位错运动的作用机制出发,基于Mughrabi的剪切应力分布模型,结合应力、位错密度及储能的关系建立了晶界附近储能的分布模型;③综合考虑了高层错能及低层错能金属材料中胞状组织、孪晶乃至微带、变形带等各种局部缺陷对位错密度分布的影响,提出了局部缺陷引起储能升高的储能分布假设。基于以上模型与合理假设,建立了一个新的介观尺度储能密度分布模型。
以冷轧纯铁素体钢板为例,研究了所建模型在退火过程中的应用。①基于不同储能密度分布模型研究了同一平均储能密度下的再结晶退火过程,分析了不同储能分布模型对再结晶微观组织演变及其动力学的影响。研究表明,新模型考虑了较大变形条件下晶粒内部储能的局部升高,所模拟的新晶核分布能更真实地反映变形金属材料再结晶形核机制;新模型模拟的再结晶速度在开始时刻较小,随着再结晶晶核的大量出现,在再结晶中段迅速升高,并在再结晶后期由于新晶粒的相互接触而减慢,更能反映出再结晶动力学的“S”型曲线关系及对数分析曲线的线性关系。②基于新建介观储能密度分布模型,模拟了变形量和再结晶温度对微观组织演变及再结晶动力学的影响。结果表明:随着变形量的增大,晶粒内部缺陷的增多,再结晶形核方式由晶界形核逐渐向晶内形核过渡,形核率急剧增加,再结晶速度显著提高,再结晶完成时晶粒得到明显细化,Avrami指数n值减小;再结晶温度可以显著提高形核率,提高再结晶速度,缩短再结晶时间,但对n值及再结晶完成时的微观组织结构影响较小。反映的规律与现有再结晶理论及实验结果相一致,证明了该模型的合理性。
随后,本论文分析了现有再结晶模型不能反映回复过程的原因,基于相关实验研究确立了新的初始亚晶平均取向差-应变关系;考虑了回复过程中的储能密度降低现象,提出了“储能密度的降低是亚晶长大过程驱动力”的新观点,并据此建立了回复过程中的实时模型;提出了“亚晶异常长大形核模型中临界形核尺寸随储能密度的降低而增大”的观点。在亚晶异常长大形核模型及以上改进的基础上,建立了一个具有明确物理基础的回复模型。
将该回复模型与再结晶的MC Potts模型相结合,建立了一个回复-再结晶模型,并据此对冷轧纯铁素体钢板的退火过程进行了模拟。结果表明:①新模型合理考虑了变形量对初始亚晶取向差的影响机制,实现了再结晶过程孕育期的模拟;考虑了退火过程中的储能降低,减缓了再结晶动力学,使模拟结果与实际更为相符。②变形量一定时,退火温度越高,孕育期越短,再结晶速度越快,温度一定时,变形量越大,孕育期越短,再结晶速度越快。上述模拟结果可由现有再结晶理论和实际退火规律得到证实。
最后,为了验证本文建立的基于FEM与MC方法耦合的回复-再结晶模型的合理性及其应用效果,实验研究了冷轧ELC-BH钢板及1060工业纯铝板的退火过程,并与本文所建模型的相应模拟结果进行了对比,结果表明:①本文所建模型能较准确地模拟两种材料的冷轧组织(特别是大变形量时的冷轧组织)、再结晶形核位置、再结晶完成时的微观组织及随后的晶粒长大组织;②模拟的再结晶分数曲线接近于S形曲线,与退火实验的预测结果及相关再结晶理论一致,③实现了退火过程中孕育期的模拟,且反映的冷轧压下率与退火温度对孕育期及再结晶动力学的影响规律与实验结果一致:压下率越大,孕育期越短且随后的再结晶过程速度也越快。以上结果验证了本文所建FEM与MC方法的耦合模型、介观储能密度分布模型与回复模型的合理性,能较好地模拟实际变形材料的退火过程。
With the development of material science and computer technology, science of material preparation is changing from traditional design to reverse manner. By the aid of computer, material properties can be predicted based on its components and microstructure, and the optimum manufacturing techniques can be selected to derive some functional materials which can meet the needs of actual production. The microstructure of metallic materials is formed during the process of smelting, casting, forming and heat treating, in which forming and heat treating are critical to materials' microstructure and properties. However, the inhomogeneous pre-deformation induces the inhomogeneous distribution of the stored energy, which, as the driving force for recrystallization, leads to different recrystallization kinetics and different properties of the annealed materials.
With the aid of finite element model (FEM), the process of plastic deformation of metallic materials can be simulated effectively, and the detailed information (such as the distribution of stress and strain) can be obtained. Meanwhile, by the simulation of annealing process of deformed materials, the information which is not easily observed in experiments can be reproduced quantitatively, continuously and dynamically. This method is helpful for better understanding of microstructure evolution and its inner mechanism, controlling the characteristic parameters of annealed microstructure and forecasting the properties of materials. In this way a solid foundation can be laid for optimizing annealing process and developing high performance materials. Therefore, the macroscopic and mesoscopic inhomogeneous distribution of stored energy, microstructure evolution and the corresponding recrystallization kinetics can be studied comprehensively and thoroughly with the coupling model of FEM and MC method, which is of great theoretical and practical value.
MC method is a numerical calculation technique based on probability and statistics theories. Firstly, a probability model of special events associating to the investigated subject is established; secondly, a computer sampling plan is determined; finally, by means of the sampling plan, the occurrence frequencies of the events are derived as solutions of the subject investigated. In present thesis, Monte Carlo Potts model is used as the simulating tool to analyze complicated microstructure and to visualize the process of the emulation. A new coupling model of FEM with MC method, a new mesoscopic stored energy density distribution model and a new recovery model are constructed based on the experimental and theoretical researches. According to the new models and the corresponding key technologies, a computer program is compiled to simulate the isothermal annealing process of cold worked materials. Finally, the experimental results of extra-low carbon and high strength bake-hardening steel plate (ELC-BH steel plate) and industrial pure aluminum plate are used to certificate the rationality of the models.
Firstly, the limitations of previous stored energy distribution models, especially the RSRP model, are well analyzed. According to the relationship among stress, dislocation density and stored energy density in poly-crystal undergoing plastic deformation, the coupling model of FEM with Monte Carlo method is built through the translating of the state variables between forming simulation and annealing simulation, the mapping of the data from FEM to MC nodes, the establishing of inhomogeneous stored energy distribution in mesoscale and the constructing of a appropriate nucleation model. Then the macroscopic and mesoscopic inhomogeneous stored energy distributions in cold working materials are derived. A simulated program of isothermal annealing process of cold working metallic materials is compiled based on the coupling model.
Taken the cold rolled industrial pure aluminum plate as an example, the recrystallization process of both the maximum and the minimum stored energy regions of the blank are simulated with the simulated program, and the rational simulated results are derived: 1) The variation in recrystallization kinetics and microstructures in vary parts of the blank resulted from the difference in stored energy is simulated effectively. The region with higher stored energy, which is close to the surface of the blank, possesses faster recrystallization kinetics and smaller average recrystallized grain size. 2) The statistical results of recrystallization kinetics accord with the intuitive results of microstructure evolution in the simulation; meanwhile, the simulated results are consistent with the experimental and theoretical ones, which certificate the rationality of the new structured coupling model.
Secondly, the mechanism of various mesoscopic structures' effect on the distribution of dislocations and stored energy density is deeply studied, and several models and hypotheses are constructed based on the experimental and theoretical researches. 1) Based on Kocks composite model, the problem of stored energy distribution among grains is then preliminarily solved by the foundation of a new model about grain size dependent stored energy distribution. 2) Starting from the action mechanism of grain boundaries on the dislocations, the changing rule of stored energy along with the distance to grain boundary is established based on Mughrabi's shearing stress distribution model. 3) A hypothesis is established considering the effect of various kinds of local defects (e.g. cell structure, twins, microbands or shearbands et al) on the dislocation distribution in different materials. Based on the models and the hypothesis above, a new mesoscopic stored energy distribution model is constructed.
Taken the cold rolled pure ferrite steel plate as an example, the application of the mesoscopic stored energy distribution model in annealing simulation is deeply studied. 1) The recrystallization process is simulated under different stored energy distribution models. It can be seen from the simulated results, on the one hand, the new model can simulate the recrystallization process, especially the nucleation process, more efficiently because of the consideration of local defects inside grains on the condition of large deformation; on the other hand, the sigmoid relation of recrystallization volume fraction curve and the linear relation of its logarithm analysis curve are derived as expected. 2) With the new model, the effect of rolling reduction and annealing temperature on the microstructure evolution and the recrystallization kinetics are discussed. And the results are reasonable: with the increase of rolling reduction, the defects inside grains multiply rapidly, which leads to the transition from boundary nucleation to core nucleation and then the refinement of recrystallized grains; the annealing temperature can speed up recrystallization kinetics but has little effect on Avrami index and the size of recrystallized grains.
Thirdly, the limitations of the previous nucleation model, which can not reflect the recovery process, are further studied. A new relationship between initial subgrain mean misorientation and strain is constructed based on experimental results. The reducing of stored energy during recovery is well considered, and a new viewpoint is proposed that the reduction of stored energy during recovery is the main driving force of the subgrain growth; based on the new viewpoint, a converse model from Monte Carlo step to real time during recovery is constructed. A new viewpoint is proposed that the critical size of recrystallization nucleus increases with the inducing of stored energy during recovery in subgrain abnormal growth nucleation model. Then, a recovery model is built on the basis of subgrain abnormal growth nucleation model and the modification mentioned above.
Based on the recovery model and the recrystallization MC Potts model, a recovery-recrystallization model is constructed, with which, the annealing process of cold rolled pure ferrite steel plate is simulated efficiently, and the expectable simulated results are attained. 1) Recovery process is simulated successfully with the new model, which reflects the appropriate relationship between strain and initial subgrain mean misorientation; the reducing of stored energy slows down the recrystallization kinetics, which assures the simulated results accord with the experimental ones better. 2) The rise of the temperature results in the shortening of the incubation time; similarly, under a certain temperature, the increase of the rolling reduction leads to the shortening of the incubation time. The simulated results can be verified by the existing theoretical and experimental results.
To certificate the rationality and the application effect of the model constructed in present thesis, annealing processes of ELC-BH steel plate and industrial pure aluminum (1060) plate are investigated in detailed. The comparison of experimental and simulated results indicates that: 1) the initial microstructure (especially with a large deformation), the nucleation sites, recrystallized microstructure and the subsequent grain growth microstructure can be simulated with the model constructed in present thesis; 2) the sigmoid relation of recrystallization volume fraction curve is derived, which is consistent with the experimental results; 3) the recovery process is simulated successfully, and the simulated influential rules of rolling reduction and annealing temperature on incubation time and recrystallization kinetics are consistent with the experimental ones: the increase of rolling reduction shortens incubation time and speeds up recrystallization velocity. The results mentioned above certificate the rationality of the coupling model of FEM and MC method, the mesoscopic stored energy density distribution model and the recovery model constructed in present thesis.
对金属材料的塑性变形过程进行有限元(Finite Element Method,FEM)分析,可以获得变形过程中金属流动及应力应变等详细信息;利用Monte Carlo(MC)方法对变形金属材料的退火过程进行计算机模拟研究,可以定量、连续、动态地观察、检测在实验室中所观察不到或检测不到的现象,更好地认识退火过程中组织演变规律及其内在机理,获得退火组织的特征参数,实现退火过程介观组织设计及其性能预报,为退火工艺优化和高性能材料设计与开发打下坚实的基础。因此,通过FEM与MC方法的耦合,既可以全面了解外界变形条件引起的材料宏观尺度上储能的非均匀分布及其相应的再结晶动力学与平均晶粒尺寸变化,又可以深入研究内部组织结构差异导致的材料介观尺度上储能的非均匀分布及其相应的再结晶动力学与拓扑组织演变过程,具有重要的理论意义和实用价值。
MC方法是以概率和统计学理论为基础的一种数值计算方法。它将所求解问题转换成事件概率模型,用计算机抽样得到这个事件出现的概率,并用它作为问题的解。Monte Carlo Potts模型(简称MC Potts模型)具有可分析复杂组织与可视化仿真的能力,本文以MC Potts模型为模拟工具,基于现有实验及理论基础依次建立了FEM与MC方法的耦合模型、介观储能密度分布模型及回复模型,完成了对退火过程模拟模型的改进;结合相关退火模拟关键技术,编写了冷变形材料等温退火过程组织模拟程序;通过超低碳高强度烘烤硬化钢板与工业纯铝板的实验研究对模型及其程序进行了验证。
首先,本论文分析了现有变形材料退火模型中的储能分布模型,特别是RSRP储能分布模型的不足,从多晶体塑性变形过程中应力、位错密度及储能密度之间的关系出发,解决了以下几个关键问题:①状态变量的转换:有限元模型中流变应力转换为储能密度,②数据的移植:转换得到的储能密度移植为MC模拟区域内的平均储能密度,③介观初始储能场及相应模拟能量场的构建,④形核模型的建立,并据此建立了FEM与MC方法的耦合模型,实现了由宏观应力场向介观储能场的转换,初步解决了冷变形材料宏观及介观尺度上储能的非均匀分布问题。基于FEM与MC的耦合模型,编制了冷变形金属材料等温退火过程模拟程序。
以冷轧纯铝板为研究对象,模拟了轧件中靠近表层的储能极大区与靠近心部的储能极小区的再结晶过程,并将模拟结果与实验结果进行了对比。研究发现:①新建的耦合模型能够较好地模拟轧件各部位储能的不同引起的再结晶动力学及再结晶完成时微观组织的差异:储能较高的区域再结晶速度较快、再结晶完成时平均晶粒尺寸较小,储能较低的区域再结晶速度较慢、再结晶完成时平均晶粒尺寸较大,反映的规律与实验观察结果及现有再结晶理论相一致,即退火后轧件表层的晶粒尺寸比心部的更加细小;变形程度越大,再结晶速度越快。②再结晶动力学模拟统计结果与其微观组织直观模拟结果反映的规律相同,且这些结果与现有再结晶理论及实验结果基本一致,不仅表明了再结晶微观组织模拟结果的必然性,而且验证了本文所采用的有限元-再结晶耦合模型的合理性。
然后,本论文深入研究了多晶体塑性变形时各种介观及微观结构对位错运动及分布,进而对储能密度分布的影响,并根据其影响机制提出了合理假设并建立了相关的模型。①从Kocks复合模型出发,建立了冷变形材料中储能在不同尺寸晶粒间的分布模型,初步解决了不同晶粒间储能的分布问题;②从晶界对位错运动的作用机制出发,基于Mughrabi的剪切应力分布模型,结合应力、位错密度及储能的关系建立了晶界附近储能的分布模型;③综合考虑了高层错能及低层错能金属材料中胞状组织、孪晶乃至微带、变形带等各种局部缺陷对位错密度分布的影响,提出了局部缺陷引起储能升高的储能分布假设。基于以上模型与合理假设,建立了一个新的介观尺度储能密度分布模型。
以冷轧纯铁素体钢板为例,研究了所建模型在退火过程中的应用。①基于不同储能密度分布模型研究了同一平均储能密度下的再结晶退火过程,分析了不同储能分布模型对再结晶微观组织演变及其动力学的影响。研究表明,新模型考虑了较大变形条件下晶粒内部储能的局部升高,所模拟的新晶核分布能更真实地反映变形金属材料再结晶形核机制;新模型模拟的再结晶速度在开始时刻较小,随着再结晶晶核的大量出现,在再结晶中段迅速升高,并在再结晶后期由于新晶粒的相互接触而减慢,更能反映出再结晶动力学的“S”型曲线关系及对数分析曲线的线性关系。②基于新建介观储能密度分布模型,模拟了变形量和再结晶温度对微观组织演变及再结晶动力学的影响。结果表明:随着变形量的增大,晶粒内部缺陷的增多,再结晶形核方式由晶界形核逐渐向晶内形核过渡,形核率急剧增加,再结晶速度显著提高,再结晶完成时晶粒得到明显细化,Avrami指数n值减小;再结晶温度可以显著提高形核率,提高再结晶速度,缩短再结晶时间,但对n值及再结晶完成时的微观组织结构影响较小。反映的规律与现有再结晶理论及实验结果相一致,证明了该模型的合理性。
随后,本论文分析了现有再结晶模型不能反映回复过程的原因,基于相关实验研究确立了新的初始亚晶平均取向差-应变关系;考虑了回复过程中的储能密度降低现象,提出了“储能密度的降低是亚晶长大过程驱动力”的新观点,并据此建立了回复过程中的实时模型;提出了“亚晶异常长大形核模型中临界形核尺寸随储能密度的降低而增大”的观点。在亚晶异常长大形核模型及以上改进的基础上,建立了一个具有明确物理基础的回复模型。
将该回复模型与再结晶的MC Potts模型相结合,建立了一个回复-再结晶模型,并据此对冷轧纯铁素体钢板的退火过程进行了模拟。结果表明:①新模型合理考虑了变形量对初始亚晶取向差的影响机制,实现了再结晶过程孕育期的模拟;考虑了退火过程中的储能降低,减缓了再结晶动力学,使模拟结果与实际更为相符。②变形量一定时,退火温度越高,孕育期越短,再结晶速度越快,温度一定时,变形量越大,孕育期越短,再结晶速度越快。上述模拟结果可由现有再结晶理论和实际退火规律得到证实。
最后,为了验证本文建立的基于FEM与MC方法耦合的回复-再结晶模型的合理性及其应用效果,实验研究了冷轧ELC-BH钢板及1060工业纯铝板的退火过程,并与本文所建模型的相应模拟结果进行了对比,结果表明:①本文所建模型能较准确地模拟两种材料的冷轧组织(特别是大变形量时的冷轧组织)、再结晶形核位置、再结晶完成时的微观组织及随后的晶粒长大组织;②模拟的再结晶分数曲线接近于S形曲线,与退火实验的预测结果及相关再结晶理论一致,③实现了退火过程中孕育期的模拟,且反映的冷轧压下率与退火温度对孕育期及再结晶动力学的影响规律与实验结果一致:压下率越大,孕育期越短且随后的再结晶过程速度也越快。以上结果验证了本文所建FEM与MC方法的耦合模型、介观储能密度分布模型与回复模型的合理性,能较好地模拟实际变形材料的退火过程。
With the development of material science and computer technology, science of material preparation is changing from traditional design to reverse manner. By the aid of computer, material properties can be predicted based on its components and microstructure, and the optimum manufacturing techniques can be selected to derive some functional materials which can meet the needs of actual production. The microstructure of metallic materials is formed during the process of smelting, casting, forming and heat treating, in which forming and heat treating are critical to materials' microstructure and properties. However, the inhomogeneous pre-deformation induces the inhomogeneous distribution of the stored energy, which, as the driving force for recrystallization, leads to different recrystallization kinetics and different properties of the annealed materials.
With the aid of finite element model (FEM), the process of plastic deformation of metallic materials can be simulated effectively, and the detailed information (such as the distribution of stress and strain) can be obtained. Meanwhile, by the simulation of annealing process of deformed materials, the information which is not easily observed in experiments can be reproduced quantitatively, continuously and dynamically. This method is helpful for better understanding of microstructure evolution and its inner mechanism, controlling the characteristic parameters of annealed microstructure and forecasting the properties of materials. In this way a solid foundation can be laid for optimizing annealing process and developing high performance materials. Therefore, the macroscopic and mesoscopic inhomogeneous distribution of stored energy, microstructure evolution and the corresponding recrystallization kinetics can be studied comprehensively and thoroughly with the coupling model of FEM and MC method, which is of great theoretical and practical value.
MC method is a numerical calculation technique based on probability and statistics theories. Firstly, a probability model of special events associating to the investigated subject is established; secondly, a computer sampling plan is determined; finally, by means of the sampling plan, the occurrence frequencies of the events are derived as solutions of the subject investigated. In present thesis, Monte Carlo Potts model is used as the simulating tool to analyze complicated microstructure and to visualize the process of the emulation. A new coupling model of FEM with MC method, a new mesoscopic stored energy density distribution model and a new recovery model are constructed based on the experimental and theoretical researches. According to the new models and the corresponding key technologies, a computer program is compiled to simulate the isothermal annealing process of cold worked materials. Finally, the experimental results of extra-low carbon and high strength bake-hardening steel plate (ELC-BH steel plate) and industrial pure aluminum plate are used to certificate the rationality of the models.
Firstly, the limitations of previous stored energy distribution models, especially the RSRP model, are well analyzed. According to the relationship among stress, dislocation density and stored energy density in poly-crystal undergoing plastic deformation, the coupling model of FEM with Monte Carlo method is built through the translating of the state variables between forming simulation and annealing simulation, the mapping of the data from FEM to MC nodes, the establishing of inhomogeneous stored energy distribution in mesoscale and the constructing of a appropriate nucleation model. Then the macroscopic and mesoscopic inhomogeneous stored energy distributions in cold working materials are derived. A simulated program of isothermal annealing process of cold working metallic materials is compiled based on the coupling model.
Taken the cold rolled industrial pure aluminum plate as an example, the recrystallization process of both the maximum and the minimum stored energy regions of the blank are simulated with the simulated program, and the rational simulated results are derived: 1) The variation in recrystallization kinetics and microstructures in vary parts of the blank resulted from the difference in stored energy is simulated effectively. The region with higher stored energy, which is close to the surface of the blank, possesses faster recrystallization kinetics and smaller average recrystallized grain size. 2) The statistical results of recrystallization kinetics accord with the intuitive results of microstructure evolution in the simulation; meanwhile, the simulated results are consistent with the experimental and theoretical ones, which certificate the rationality of the new structured coupling model.
Secondly, the mechanism of various mesoscopic structures' effect on the distribution of dislocations and stored energy density is deeply studied, and several models and hypotheses are constructed based on the experimental and theoretical researches. 1) Based on Kocks composite model, the problem of stored energy distribution among grains is then preliminarily solved by the foundation of a new model about grain size dependent stored energy distribution. 2) Starting from the action mechanism of grain boundaries on the dislocations, the changing rule of stored energy along with the distance to grain boundary is established based on Mughrabi's shearing stress distribution model. 3) A hypothesis is established considering the effect of various kinds of local defects (e.g. cell structure, twins, microbands or shearbands et al) on the dislocation distribution in different materials. Based on the models and the hypothesis above, a new mesoscopic stored energy distribution model is constructed.
Taken the cold rolled pure ferrite steel plate as an example, the application of the mesoscopic stored energy distribution model in annealing simulation is deeply studied. 1) The recrystallization process is simulated under different stored energy distribution models. It can be seen from the simulated results, on the one hand, the new model can simulate the recrystallization process, especially the nucleation process, more efficiently because of the consideration of local defects inside grains on the condition of large deformation; on the other hand, the sigmoid relation of recrystallization volume fraction curve and the linear relation of its logarithm analysis curve are derived as expected. 2) With the new model, the effect of rolling reduction and annealing temperature on the microstructure evolution and the recrystallization kinetics are discussed. And the results are reasonable: with the increase of rolling reduction, the defects inside grains multiply rapidly, which leads to the transition from boundary nucleation to core nucleation and then the refinement of recrystallized grains; the annealing temperature can speed up recrystallization kinetics but has little effect on Avrami index and the size of recrystallized grains.
Thirdly, the limitations of the previous nucleation model, which can not reflect the recovery process, are further studied. A new relationship between initial subgrain mean misorientation and strain is constructed based on experimental results. The reducing of stored energy during recovery is well considered, and a new viewpoint is proposed that the reduction of stored energy during recovery is the main driving force of the subgrain growth; based on the new viewpoint, a converse model from Monte Carlo step to real time during recovery is constructed. A new viewpoint is proposed that the critical size of recrystallization nucleus increases with the inducing of stored energy during recovery in subgrain abnormal growth nucleation model. Then, a recovery model is built on the basis of subgrain abnormal growth nucleation model and the modification mentioned above.
Based on the recovery model and the recrystallization MC Potts model, a recovery-recrystallization model is constructed, with which, the annealing process of cold rolled pure ferrite steel plate is simulated efficiently, and the expectable simulated results are attained. 1) Recovery process is simulated successfully with the new model, which reflects the appropriate relationship between strain and initial subgrain mean misorientation; the reducing of stored energy slows down the recrystallization kinetics, which assures the simulated results accord with the experimental ones better. 2) The rise of the temperature results in the shortening of the incubation time; similarly, under a certain temperature, the increase of the rolling reduction leads to the shortening of the incubation time. The simulated results can be verified by the existing theoretical and experimental results.
To certificate the rationality and the application effect of the model constructed in present thesis, annealing processes of ELC-BH steel plate and industrial pure aluminum (1060) plate are investigated in detailed. The comparison of experimental and simulated results indicates that: 1) the initial microstructure (especially with a large deformation), the nucleation sites, recrystallized microstructure and the subsequent grain growth microstructure can be simulated with the model constructed in present thesis; 2) the sigmoid relation of recrystallization volume fraction curve is derived, which is consistent with the experimental results; 3) the recovery process is simulated successfully, and the simulated influential rules of rolling reduction and annealing temperature on incubation time and recrystallization kinetics are consistent with the experimental ones: the increase of rolling reduction shortens incubation time and speeds up recrystallization velocity. The results mentioned above certificate the rationality of the coupling model of FEM and MC method, the mesoscopic stored energy density distribution model and the recovery model constructed in present thesis.
引文
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