Mesoscale simulation of discontinuous dynamic recrystallization using the cellular automaton method

A dynamic recrystallization (DRX) cellular automaton (CA) model that can mark the microstructure with DRX circle was developed. The effects of initial grain size on the stress-strain curve, mean grain size and DRX fraction were mainly investigated, and the simulated results were compared with those obtained from previous researches. The results show that the shape of the stress-strain curve is sensitive, while the stress and mean grain size at the steady state are insensitive to the initial grain size. The transition from a multiple-peak stress-strain curve to a single-peak one can be explained by variations in DRX circle fraction, and the initial grain size to make this transition is between 70 and 80 μm.     

动态再结晶过程的三维元胞自动机模拟

建立了一类模拟金属材料动态再结晶的三维元胞自动机模型,该模型把宏观尺度的热加工参数和介观尺度的位错密度变化耦合在一起,考虑了动态回复、形核率、应变和初始晶粒尺寸的影响.利用这个模型可以追踪动态再结晶过程微观组织的变化,并且可以得到再结晶晶粒形态及晶粒的取向和大小.模拟结果与动态再结晶生长动力学理论符合较好.模型预测的再结晶微观组织及晶相形状和试验微结构吻合较好.     

采用元胞自动机结合Laasraoui-Jonas位错密度模型模拟AZ31镁合金的动态再结晶行为

采用元胞自动机结合Laasraoui?Jonas 位错密度模型(LJ模型)模拟AZ31镁合金在动态再结晶过程中的位错密度和微观组织演化。LJ模型中的硬化参数、回复参数和应变速率灵敏系数决定模拟的准确性。在目前的研究中,基于 LJ 模型和 Kocks?Mecking 模型(KM 模型)求解硬化参数;采用动态再结晶中的稳态应力公式求解回复参数和应变速率灵敏系数。结果表明：模拟结果与实验结果一致。     

采用元胞自动机法模拟变温条件下低碳钢静态再结晶过程

基于亚晶异常长大形核机制,采用元胞自动机方法,建立了低碳钢静态再结晶仿真模型,模拟了退火均热温度对再结晶过程的影响。模拟结果表明,再结晶初期存在明显的孕育期,没有再结晶晶核产生;随着温度的升高,再结晶晶核优先在晶界和晶粒内储存能较大处产生;再结晶完成时的晶粒尺寸基本不受退火均热温度的影响;提高退火均热温度可以显著加快再结晶速度。     

纯镍动态再结晶过程的元胞自动机模型

将冶金学基本原理与元胞自动机方法相结合,建立了动态再结晶过程微观组织演变的实时计算模型。模型考虑到时间因素的影响,时间步长Δt定义为元胞尺寸与最大晶界移动速率的比值,每一时间步内每个元胞的位错密度随应变按一定规律增长。结果表明,利用此模型可以很好地模拟大应变速率下的动态再结晶过程微观组织变化,并能预测再结晶晶粒大小和热加工过程应力随应变的变化。     

Identification of nucleation parameter for cellular automaton model of dynamic recrystallization

The accuracy of nucleation parameter is a critical factor in the simulation of microstructural evolution during dynamic recrystallization(DRX).Based on the flow stress curve under hot deformation conditions,a new approach is proposed to identify the nucleation parameter during DRX.In this approach,a cellular automaton(CA) model is applied to quantitatively simulate the microstructural evolution and flow stress during hot deformation;and adaptive response surface method(ARSM) is applied as optimization model...     

纯铜动态再结晶的三维元胞自动机模拟

用三维元胞自动机法(CA法)模拟纯铜在400℃以0.0005s~(-1)的应变率发生动态再结晶(DRX)的过程.给出了母相和再结晶晶粒的平均位错密度随着应变量的变化规律;根据平均位错密度的变化研究了纯铜动态再结晶中形核、长大、动态回复和加工硬化等过程.模拟了纯铜动态再结晶过程中的应力.应变曲线及平均晶粒尺寸的变化规律,模拟结果与文献中的试验结果吻合较好.     

Optimization of deformation parameters of dynamic recrystallization for 7055 aluminum alloy by cellular automaton

In order to simulate the microstructure evolution during hot compressive deformation, models of dynamic recrystallization (DRX) by cellular automaton (CA) method for 7055 aluminum alloy were established. The hot compression tests were conducted to obtain material constants, and models of dislocation density, nucleation rate and recrystallized grain growth were fitted by least square method. The effects of strain, strain rate, deformation temperature and initial grain size on microstructure variation were studied. The results show that the DRX plays a vital role in grain refinement in hot deformation. Large strain, high temperature and small strain rate are beneficial to grain refinement. The stable size of recrystallized grain is not concerned with initial grain size, but depends on strain rate and temperature. Kinetic characteristic of DRX process was analyzed. By comparison of simulated and experimental flow stress–strain curves and metallographs, it is found that the established CA models can accurately predict the microstructure evolution of 7055 aluminum alloy during hot compressive deformation.     

A three-dimensional cellular automaton model for dendritic growth in multi-component alloys

A three-dimensional (3-D) cellular automaton model for dendritic growth in multi-component alloys is developed. The velocity of advance of the solid/liquid (S/L) interface is calculated using the solute conservation relationship at the S/L interface. The effect of interactions between the alloying elements on the diffusion coefficient of solutes in the solid and liquid phases are considered. The model is first validated by comparing with the theoretical predictions for binary and ternary alloys, and then applied to simulate the solidification process of Al-Cu-Mg alloys by a coupling of thermodynamic and kinetic calculations. The numerical results obtained show both the free dendrite growth process as well as the directional solidification process. The calculated secondary dendrite arm spacing in the directionally solidified Al-Cu-Mg alloy is in good agreement with the experimental results. The effect of interactions between the various alloying elements on dendritic growth is discussed.     

应用元胞自动机模型模拟析出相对材料晶粒长大的影响

为了探讨元胞自动机(CA)方法模拟析出相粒子对材料晶粒长大过程影响的应用,在现有晶粒长大CA模型的基础上,综合应用曲率驱动机制和能量驱动机制,建立了适合于含有析出相粒子材料和具有新转变规则的晶粒长大模型,应用该模型对含有不同体积分数析出相粒子的材料晶粒长大过程进行了仿真模拟和定量分析。结果表明:所建模型能够较准确地反映析出相粒子对晶粒长大过程影响的基本规律,且更加敏感地反映了析出相粒子体积分数对晶粒长大过程的影响;随着析出相粒子体积分数的逐渐增加,晶界脱钉现象不易发生且晶粒长大指数不断减小。     

Numerical simulation of solidification morphologies of Cu-0.6Cr casting alloy using modified cellular automaton model

The purpose of this study is to predict the morphologies in the solidification process for Cu-0.6Cr (mass fraction, %) alloy by vacuum continuous casting (VCC) and verify its accuracy by the observed experimental results. In numerical simulation aspect, finite difference (FD) method and modified cellular automaton (MCA) model were used to simulate the macro-temperature field, micro-concentration field, nucleation and grain growth of Cu-0.6Cr alloy using real data from actual casting operations. From the observed casting experiment, the preliminary grain morphologies are the directional columnar grains by the VCC process. The solidification morphologies by MCAFD model are in agreement with the result of actual casting experiment well.     

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.     

基于CA模拟焊缝凝固过程枝晶生长的分析

将元胞自动机方法用于焊缝金属凝固组织演变的模拟中,不仅为焊缝微观组织演变的数值模拟开辟了一种新的途径,同时也有助于研究焊接接头组织并依此优化工艺来提高焊件质量.文中研究了焊缝凝固过程中的溶质扩散问题,构建了基于元胞自动机的焊缝枝晶生长速度模型,在此基础上进行了焊缝中心等轴晶和熔池边缘柱状晶生长的模拟.初步计算了焊缝中心等轴晶和熔池边缘柱状晶的生长形态,计算结果明显再现了二次、三次枝晶的生长及竞争生长等微观现象.结果表明,元胞自动机方法是研究和模拟焊缝微观组织的有效手段之一.     

A three-dimensional cellular automaton model for simulation of dendritic growth of magnesium alloy

A numerical model based on the cellular automaton method for the three-dimensional simulation of dendritic growth of magnesium alloy was developed. The growth kinetics was calculated from the complete solution of the transport equations. By constructing a three-dimensional anisotropy model with the cubic CA cells, simulation of dendritic growth of magnesium alloy with six-fold symmetry in the basal plane was achieved. The model was applied to simulate the equiaxed dendritic growth and columnar dendritic growth under directional solidification, and its capability was addressed by comparing the simulated results to experimental results and those in the previously published works. Meanwhile, the three-dimensional simulated results were also compared with that of in two dimensions, offering a deep insight into the microstructure formation of magnesium alloy during solidification.     

Interaction between recrystallization and phase transformation during intercritical annealing in a cold-rolled dual-phase steel: A cellular automaton model

The concurrent ferrite recrystallization and austenitic transformation during intercritical annealing of cold-rolled DP steels is investigated by cellular automaton (CA) modeling. The simulations provide insight into the microstructural phenomena that result from the interaction of primary recrystallization and phase transformation. We find that the interaction between ferrite recrystallization and austenite formation affects not only the transformation kinetics but also the morphology and spatial distribution of the austenite. From this we can interpret experimental data of the observed temperature-dependent hardness and its dependence on the two metallurgical processes. The influence of the initial heating rate on subsequent isothermal transformation kinetics and the microstructure evolution is also obtained by the model.     

Simulation of microstructural evolution in directional solidification of Ti-45at.%Al alloy using cellular automaton method

The microstructural evolution of Ti-45 at.%Al alloy during directional solidification was simulated by applying a solute diffusion controlled solidification model.The obtained results have shown that under high thermal gradients the stable primary spacing can be adjusted via branching or competitive growth.For dendritic structures formed under a high thermal gradient,the secondary dendrite arms are developed not very well in many cases due to the branching mechanism under a constrained dendritic growth cond...     

Simulation of microstructure evolution in directional solidification of Ti-45at.%Al alloy using cellular automaton method

The microstructural evolution of Ti-45 at.%Al alloy during directional solidification was simulated by applying a solute diffusion controlled solidification model. The obtained results have shown that under high thermal gradients the stable primary spacing can be adjusted via branching or competitive growth. For dendritic structures formed under a high thermal gradient, the secondary dendrite arms are developed not very well in many cases due to the branching mechanism under a constrained dendritic growth condition. Furthermore, it has been observed that, with increasing pulling velocity, there exists a cell/dendrite transition region consisting of cells and dendrites,which varies with the thermal gradient in a contradicting way, i.e. increase of the thermal gradient leading to the decrease of the range of the transition region. The simulations agree reasonably well with experiment results.     

Modeling the recrystallization process using inverse cellular automata and genetic algorithms: Studies using differential evolution

An inverse modeling approach was taken up in this work to model the process of recrystallization using cellular automata (CA). Using this method after formulating a CA model of recrystallization, differential evaluation (DE), a real-coded variant of genetic algorithms, was used to search for the value of nucleation rate, providing an acceptable matching between the theoretical and experimentally observed values of fraction-recrystallized (X). Initially, the inverse modeling was attempted with a simple CA strategy, in which each of the CA cells had an equal probability of becoming nucleated. DE searched for the value of the nucleation rate yielding the best results for single-crystal iron at 550 °C. A good match could not be simultaneously achieved this way for the early stages of recrystallization as well as for the later stages. To overcome this difficulty, the CA grid was divided into two zones, having lower and higher probabilities of nucleation. This resulted in good correspondence between the predicted and experimental values of X for the entire duration of recrystallization. The introduction of a distribution in the probability of nucleation made the model even closer to the actual process, in which the probability of nucleation is often nonuniform due to nonuniformity in dislocation density as well as the presence of grain/interface boundaries.     

元胞自动机模拟形变组织的网格映射模型

文章采用正六边形网格划分法、最近邻邻居关系以及周期性边界条件的元胞自动机方法,获得等轴的母相微观组织。在此基础上建立网格映射模型,模拟得到静态再结晶前的形变组织以及动态再结晶过程中的形变组织,并与实验结果进行对比。结果表明,模型计算得到的尺寸误差较小,能够满足尺寸精度的要求。模拟得到微观组织随着应变的增加,晶粒形态沿变形方向伸长。应变越大,晶粒伸长的程度也越大。在大的应变量下,等轴的微观结构演变成纤维组织。模拟结果与实验结果符合较好,表明本模型能够用于模拟材料的形变组织。     

Morphology of corroded surfaces: Contribution of cellular automaton modelling

A simple model describes uniform and localised corrosion. We use a mesoscopic cellular automata (CA) type approach, which has proved a powerful tool in the study of rough metal–electrolyte interfaces. The model accounts for two corrosion kinetics and their relative spatial localisation. The competition between the two forms of kinetics of corrosion is shown to reproduce several types of morphology of corrosion ranging from narrow pits or larger cavities to rough surfaces. Simulation and experimental results are compared providing insight on the relation between kinetics and morphologies of the corrosion front. We emphasize the importance of stochastic simulations in relation to CA.