Cellular Automaton法模拟金属凝固显微组织研究进展

介绍了金属凝固过程中显微组织模拟的数学模型和计算模型以及元胞自动机（Cellular automation）法的原理及发展历程。概述了晶粒形核和生长的几个物理模型，并对元胞自动机在凝固过程中微观组织形成过程的计算机模拟的应用作了较详细的介绍。元胞自动机考虑了形核和生长动力学问题，通过宏微观耦合模型可计算固相分数和潜热释放的变化。介绍了两种元胞自动机和有限元方法的耦合方式，并对元胞自动机法的未来发展方向进行了展望。     

元胞自动机法模拟铝合金三维枝晶生长

以元胞自动机模型为基础,基于晶粒形核和生长的物理过程及热质传输过程,建立了铝合金凝固过程微观组织形成及枝晶形貌演化的三维元胞自动机模型.与传统的元胞自动机不同,该模型不仅考虑了温度场扩散而且考虑了固液相中的溶质扩散、曲率过冷等重要因素.枝晶尖端生长速度与局部过冷度的关系采用KGT(Kurz-Giovanola-Trivedi)模型,温度场和浓度场计算采用有限差分法.使用该模型模拟了单晶生长和多晶生长.模拟结果表明,所建立的模型能够合理反映质点形核、单晶粒生长和多晶粒生长,微观组织形貌的模拟计算结果合理.     

铝带铸轧凝固过程中的枝晶生长模拟

采用元胞自动机方法(Cellular Automation Method) 模拟铝带铸轧过程中晶粒的生长,模拟过程中用简化的二元合金模拟了过冷熔体中枝晶的生长,且过冷熔体中枝晶的生长模型采用LGK模型.在枝晶生长的基础上模拟了铝带在铸轧过程中冷却及铸轧速度引发的过冷度对晶粒生长的影响.结果表明,在形核率一定的情况下,过冷度越大,晶粒越大.     

低碳微量铌钢形变过程中动态相变的特点

用热模拟变形实验研究了低碳微量铌钢形变中的动态相变以及形变后冷却中的相变行为,透射电镜观察了Nb（CN）的析出及对铁素体晶粒截径和体积转变量的影响。结果表明：含Nb钢动态相变中铁素体形核位置依次为原奥氏体晶界、铁素体,奥氏体的相界前沿直至奥氏体晶内,随着细小的应变诱导Nb（CN）析出在基体上弥散分布,铁素体的转变量大幅增加并且其相变长大趋势得到有效抑制,使得铁素体的长大在时间和空间上均受到限制,是一个以形核为主的过程,相变完成后铁素体晶粒截径约为2舯;而形变后冷却相变工艺中铁素体的形核位置主要为奥氏体晶界以及形变带,而大量弥散分布的Nb（CN）析出对细化铁素体晶粒的作用并不明显,是一个形核长大的过程,最终得到的铁素体晶粒截径约为7μm。     

Ti-6Al-2Zr-1Mo-1V合金在β单相区等温变形过程中不连续动态再结晶的模拟与实验研究

西北工业大学武川等人研究了元胞自动机法模拟Ti-6A1-2Zr-1Mo-1V合金在β单相区等温压缩过程中的不连续动态再结晶现象。首先建立了元胞自动机模型，动态模拟了再结晶的形核和后续长大过程。研究发现，再结晶晶粒长大的驱动力由晶界处位错密度的演化提供。为了验证建立的元胞自动机模型的正确性，将通过该模型预测所得的应力-应变曲线与实验值进行对比。     

一种改进的三维元胞自动机模拟铝合金凝固

以元胞自动机模型为基础,基于晶粒形核和生长的物理过程,建立了铝合金凝固过程演化的三维元胞自动机模型.枝晶尖端生长速度与局部过冷度的关系采用KGT模型,温度场和浓度场的计算采用有限差分法.模型中采用大小两套网格分别进行宏观温度场和微观组织演变的计算,提高了计算效率,使用该模型模拟了铝合金单晶生长以及铝合金在金属模具中的凝固情况,得到了在不同浇注温度下典型的柱状晶向等轴晶转变的三维图形.     

焊缝金属凝固组织元胞自动机模拟

应用元胞自动机方法进行了焊缝金属凝固组织的模拟.所建立的焊缝凝固组织二维元胞自动机模型考虑了晶粒的概率性成核、曲率过冷、温度过冷、成分过冷、潜热的释放、溶质浓度的再分布以及焊接熔池晶粒的联生长大等影响因素.模型在统一网格下分别采用差分法计算温度和溶质的扩散,应用元胞自动机方法模拟晶粒形核及生长.模拟结果能够定性地再现焊缝金属晶粒择优取向与竞争长大机制.结果表明,元胞自动机方法较好地反映了焊缝金属凝固的特点,是焊缝凝固组织模拟的新途径.     

元胞自动机在研究模锻叶片动态再结晶中的应用

利用元胞自动机模型研究金属热成形过程中动态回复与再结晶现象,是目前业界关注的热点之一。文章介绍了元胞自动机模型的理论基础和工作原理,并根据叶片模锻成形的特点,综合考虑应变速率、变形温度对再结晶形核率与平均晶粒尺寸,以及终锻冷却对叶片锻件最终组织的影响,在DEFORM-3D平台上,成功地仿真了叶片模锻过程中的微观组织演变,得到了同经典理论分析和物理实验结果吻合较好的动态再结晶动力学特征。     

采用CA-FE法模拟双辊连铸纯铝凝固微观组织

使用有限元软件Procast中的元胞自动机-有限元模型,建立了一个模拟双辊连续铸轧纯铝凝固微观组织形成的随机性模型.综合考虑了溶质再分配、界面曲率、晶粒择优生长的作用,基于有限元建立了宏观温度场计算和一个改进的元胞自动机模型.采用基于高斯分布的连续性形核模型,辊面和熔体内部的形核分别采用两种形核分布函数;枝晶尖端生长速度采用与局部过冷度有关的修正KGT模型.利用软件计算结果模拟了不同浇注温度和熔液内部平均形核过冷度对凝固微观组织形成的影响.     

15SiMn钢奥氏体等温相变的元胞自动机模拟

建立了15SiMn钢奥氏体一铁素体相变的二维元胞自动机介观模型.模拟结果显示,对于某一给定温度,铁索体的长大速度在相变过程中逐渐降低.当生长速度接近0时,奥氏体相中相界面处平衡碳的质量分数为0.523 95%.此外,模拟结果还显示,由于奥氏体晶界上的碳原子扩散和奥氏体-铁素体相界面移动都较奥氏体晶内更快,所以奥氏体晶界上铁素体晶粒形貌为椭圆形.     

A cellular automaton investigation of the transformation from austenite to ferrite during continuous cooling

A cellular automaton model has been employed to investigate the transformation from austenite to ferrite in low carbon steels during continuous cooling. An important aspect of this approach is the implementation of incorporating local concentration changes into a nucleation or growth function, which is utilized by the automaton in a probabilistic fashion. The modeling gives a visual insight into the effect of cooling conditions on this transformation. The final nucleation number, the number of ferrite grains per austenite grain, ferrite grain size and the kinetics of ferrite formation are obtained as a function of the cooling rate or the undercooling temperature.     

Modeling austenite decomposition into ferrite at different cooling rate in low-carbon steel with cellular automaton method

The austenite decomposition into ferrite during continuous cooling in low-carbon steel has been investigated with a two-dimensional cellular automaton (CA) approach. In this model, the growth of ferrite grain is controlled by both carbon diffusion and γ–α interface dynamics. In order to predict the growth kinetics of ferrite grain, the coupled carbon diffusion behavior in untransformed austenite and γ–α interface dynamics are numerically resolved. The simulation provides an insight into the carbon diffusion process in retained austenite and microstructure evolution during the transformation. The predicted ferrite growth kinetics and average grain size at different cooling rates are compared with experimental results in the literature and the simulated results show that the final grain size and newly formed ferrite fraction vary with cooling rate. The γ–α interface is stable in the studied cooling rate range (up to 58 °C s⁻¹) in this work, so the simulated morphology of ferrite grain is almost equiaxed, which is not influenced by the anisotropy of the hexagonal mesh in this CA model.     

Growth modes of individual ferrite grains in the austenite to ferrite transformation of low carbon steels

The mesoscale deterministic cellular automaton (CA) method and probabilistic Q-state Potts-based Monte Carlo (MC) model have been adopted to investigate independently the individual growth behavior of ferrite grain during the austenite (γ)–ferrite (α) transformation. In these models, the γ–α phase transformation and ferrite grain coarsening induced by α/α grain boundary migration could be simulated simultaneously. The simulations demonstrated that both the hard impingement (ferrite grain coarsening) and the soft impingement (overlapping carbon concentration field) have a great influence on the individual ferrite growth behavior. Generally, ferrite grains displayed six modes of growth behavior: parabolic growth, delayed nucleation and growth, temporary shrinkage, partial shrinkage, complete shrinkage and accelerated growth in the transformation. Some modes have been observed before by the synchrotron X-ray diffraction experiment. The mesoscopic simulation provides an alternative tool for investigating both the individual grain growth behavior and the overall transformation behavior simultaneously during transformation.     

Two-dimensional cellular automaton model for simulating structural evolution of binary alloys during solidification

1Introduction During solidification of cast metallic materials,simulations of microstructural evolution,which track kinetics in a local fashion,are of interest for two reasons.First,from a fundamental point of view,it is desirable to better understand the…     

Numerical simulation of dynamic strain-induced austenite–ferrite transformation in a low carbon steel

A modified cellular automaton modeling has been performed to investigate the dynamic strain-induced transformation (DSIT) from austenite (γ) to ferrite (α) in a low carbon steel. In this modeling, the γ–α transformation, ferrite dynamic recrystallization and the hot deformation were simulated simultaneously. The simulation provides an insight into the mechanism of the ferrite refinement during the DSIT. It is found that the refinement of ferrite grains derived from DSIT was the result of the increasing ferrite nuclei density by the “unsaturated” nucleation, the limited ferrite growth and the ferrite dynamic recrystallization. The effects of prior austenite grain size and strain rate on the microstructural evolution of the DSIT ferrite and the characteristics of the resultant microstructure are also discussed.     

Mesoscale simulation of spherulite growth during polymer crystallization by use of a cellular automaton

The paper introduces a 3D cellular automaton model for the spatial and crystallographic prediction of spherulite growth phenomena in polymers at the mesoscopic scale. The automaton is discrete in time, real space, and orientation space. The kinetics is formulated according to the Hoffman–Lauritzen secondary surface nucleation and growth theory for spherulite expansion. It is used to calculate the switching probability of each grid point as a function of its previous state and the state of the neighboring grid points. The actual switching decision is made by evaluating the local switching probability using a Monte Carlo step. The growth rule is scaled by the ratio of the local and the maximum interface energies, the local and maximum occurring Gibbs free energy of transformation, the local and maximum occurring temperature, and by the spacing of the grid points. The use of experimental input data provides a real time and space scale.     

Fe-9Cr合金在连续冷却过程中的奥氏体→铁素体相变动力学

通过分析由高精度差分膨胀仪所记录的Fe-9Cr合金试样在连续冷却过程中的膨胀曲线,获得了试样在奥氏体(γ)→铁素体(α)转变过程中的相关动力学信息;并进一步利用等时转变动力学模型拟合了Fe-9Cr试样中铁素体转变体积分数随温度变化的试验曲线。根据动力学参数的拟合结果得出:晶核的形成主要是依靠母相中单个原子的热激活跃迁,而晶核的长大则是以原子的集体热激活跃迁为主。     

TA15钛合金焊接热影响区组织演变的数值模拟

基于相变热力学和动力学经典理论,构建了TA15焊接热影响区β-α相变组织演变元胞自动机模型,并将其应用于不同焊接热影响区位置不同冷却速度的TA15组织演变模拟.该模型考虑了冷却速度对相变过冷度和固溶体溶解度、相变形核率以及相界面迁移率的影响,充分体现了焊接快速冷却过程的相变组织演变规律,计算结果表明,在临界冷却速度范围内,冷却速度越快,扩散型相变组织产物越细小,新相长大速度越快,但最终相变分数降低.综合考虑工艺、组织与力学性能的关系,通过模拟获得最佳焊接工艺应为中等热输入.     

低碳微合金钢中针状铁素体的形成与控制

低碳微合金钢连续冷却时都会产生多种类型的中温转变组织,低冷速下主要得到粒状贝氏体组织,高冷速下主要得到板条贝氏体组织．连续冷却时,在较高中温转变温度范围可形成针状铁素体,其转变受冷却速度和过冷温度影响．通过控冷可以在低碳微合金钢中得到贝氏体和针状铁素体多相组织,利用针状铁素体能改善高强度低碳微合金钢的综合力学性能．     

Modeling of structure of double-phase low-carbon chromium steels

A physical model for determining the relative amount of phase components and the size of ferrite grains after decomposition of austenite in the process of cooling of double-phase steels is suggested. The main products of austenite transformation, i.e., polygonal ferrite, pearlite, bainite, and martensite, are considered. The driving forces of the transformation and the concentration of carbon on the phase surface are determined with the use of methods of computational thermodynamics. The model is based on equations of the classical theory of nucleation and growth. It allows for the structural features of the occurrence of γ → α transformation and contain some empirical parameters. The latter are determined using data of dilatometric measurements of the kinetics of austenite transformation and metallographic measurements of the size of ferrite grains. The model is used for predicting the kinetics of the transformation under the complex cooling conditions implemented by the VOEST-ALPINE STAHL LINZ GmbH rolling mill within the computer system for control of mechanical properties of hot-rolled strip.