正常晶粒生长形貌演化的计算机模拟研究

有关多晶材料晶体生长机理及计算机模拟方法，我们已作了详细的论述。本文以蒙特卡罗（Ｍｏｎｔｅ Ｃａｒｌｏ）方法为基础，通过对Ｑ－ｓｔｅｔｅ ｐｏｔｔｓ算法进行改进，建立快速的Ｑ－ｓｔａｔｅ ｐｏｔｔｓ算法，用Ｄｅｌｐｈｌ３．０提供的Ｏｂｊｃｅｔ Ｐａｓｃａｌ语言编写软件，在ＰＣ５８６上实现了多晶材料晶粒生长结构演化的计算机模拟及统计分析。正常晶粒演化形貌图与生产动力力学相符合，逼真度较好。生长指数的     

用改进的Monte Carlo算法模拟晶粒生长

材料微观组织结构决定材料的宏观力学性能.Potts模型是实现晶粒生长过程仿真的一种重要方法.在Radhakrishnan和Zacharia提出的Monte Carlo算法的基础上提出了一种改进的Monte Carlo算法,利用该算法对晶粒生长过程进行了模拟,模拟的微观组织多为等轴晶,晶粒生长指数为0.512.模拟结果表明,该算法能够准确模拟晶粒生长过程.     

多晶材料晶粒生长的Monte Carlo计算机模拟方法：I模拟正常晶粒生长

多晶固体材料的显微结构的演化与诸多因素密切相关,是一复杂的过程,运用适当的计算机方法进行模拟完成对晶粒生长的完全预测,具有重要意义,且可为材料研究提供新的重要的依据,近年来,一些材料科学研究者运用蒙特卡罗（ＭｏｎｔｅＣａｒｌｏ）方法模拟二维晶粒生长,以取得了较大进展,本文对他们在模拟正常晶粒生长方面采用的基本方法进行综述。关于模拟异常晶粒生长的情况将在一篇文章中介绍。     

多晶材料晶粒生长的Monte Carlo计算机模拟方法 Ⅰ 模拟正常晶粒生长

多晶固体材料的显微结构的演化与诸多因素密切相关,是一复杂的过程。运用适当的计算机方法进行模拟,完成对晶粒生长的完全预测,具有重要意义,且可为材料研究提供新的重要的依据。近年来,一些材料科学研究者运用蒙特卡罗（ＭｏｎｔｅＣａｒｌｏ）方法模拟二维晶粒生长,已取得了较大进展。本文对他们在模拟正常晶粒生长方面采用的基本方法进行综述。关于模拟异常晶粒生长的情况将在下一篇文章中介绍。     

二维晶粒演变过程的模拟及分形研究

以蒙特卡罗随机模拟方法为基础，通过对原有算法进行改进，对二维晶粒的演变过程进行了计算机模拟和分形研究，获得了统计等效组织模型．分析表明，模拟的晶粒在演变过程中具有分形特性，即晶粒形态具有与时间无关的相似性，与晶粒形核和生长的物理机制相一致，证明了模拟过程的合理性．从而为后续热变形显微组织演变的模拟中晶核的空间分布和生长提供较为精确的显微组织基础．     

纳米Y-TZP材料烧结过程晶粒生长的分析

分析了无压烧结、热压烧结及SPS烧结过程中晶粒生长的行为及表现活化能．结果表明：在1100～1300℃之间,纳米Y-TZP材料在以上几种烧结条件下的晶粒生长行为不同．无压烧结时晶粒生长较慢,而热压烧结和SPS烧结时晶粒生长较快．对晶粒生长的活化能分析可在一定程度上解释以上现象．分析结果显示：无压烧结的表观活化能为281kJ／mol与纳米Y－TZP材料的晶界扩散活化能相近;热压烧结过程中,由于外压对扩散的促进作用,活化能比无压烧结时略有降低;在SPS烧结过程中,由于外加的脉冲电流能使晶粒表面大大活化,所以活化能与无压烧结相比大幅度下降．     

多晶材料晶粒生长的Monte Carlo计算机模拟方法 Ⅱ 模拟异常晶粒生长

晶粒生长的显微结构的演化是一种受诸多因素影响的复杂过程。前文已简述模拟二维正常晶粒生长所采用的基本蒙特卡罗（ＭｏｎｔｅＣａｒｌｏ）方法。异常晶粒生长的最直接原因是总体系能的改变。而导致体系能变化的因素很多。本文在重点分析由于晶界能和迁移率的各向异性引起体系能量变化的基础上,介绍模拟异常晶粒生长的基本方法,为解决如何将实际生长环境复杂性引入生长模型中及如何进一步模拟生长的问题提供重要思路。     

蒙特卡罗方法模拟陶瓷晶粒生长研究进展

概述了蒙特卡罗模拟方法的基本原理和思想,介绍了陶瓷烧结过程中,蒙特卡罗分别模拟单相系统和二相系统中晶粒生长的模型,综述了国内外蒙特卡罗方法模拟陶瓷烧结过程中晶粒生长的研究进展,指出了当前该研究领域中存在的问题,提出了今后发展的主要方向:将模型与具体材料和实际工艺联系起来,模拟定量化,并向三维模拟发展,以解决实际问题.     

多晶材料晶粒生长的MonteCarlo计算机模拟方法：II.模拟异常晶粒生长

晶粒生长的显微结构的演化是一种受诸多因素影响的复杂过程，前文已简述模拟二维正常晶粒生长所采用的基本蒙特卡罗（ＭｏｎｔｅＣａｒｌｏ）方法，异常晶粒生长的最直接原因是总体系能的改变。而导致体系能变化的因素很多，本文在重点分析由于晶界能和迁称率的各向异性引起体系能量变化的基础上，介绍模拟异常晶粒生长的基本方法，为解决如何实际一长环境复杂性引入生长模型中及如何进一步模拟生长的问题提供重要思路。     

各向异性条件下晶粒长大过程的相场法模拟

引入与时间有关的取向错配场变量,模拟了晶界能各向异性条件下晶粒长大的演化行为.模拟结果表明,与晶界能各向同性系统相比,随演化时间的延长,晶界能各向异性延迟晶粒的生长,使得晶粒的平均面积呈非线性变化;在相同的演化时间下,各向异性系统的晶粒尺寸分布比各向同性系统宽;晶界边数少的晶粒所占的比例明显增加;进入准稳态后,各向异性和各向同性系统中的晶粒相对尺寸分布随时间皆无明显变化.     

von Neumann–Mullins equation in the Potts model of two-dimensional grain growth

In this study, the validity of von Neumann–Mullins equation was examined for the Potts model of two-dimensional grain growth. Simple geometric consideration of the lattice in the model confirmed that the Potts model used in this study naturally satisfies von Neumann–Mullins equation, and provided the exact value of the grain boundary mobility. Monte Carlo simulation of a single grain growth demonstrated that the grain area growth rate is statistically constant for a given vertex number. The simulated grain boundary mobility agreed with its analytical prediction. The kinetics of individual grains in a polycrystalline structure was also investigated. The area change rate of the individual grains was not uniform over a short time interval, and then yielded large errors of the grain boundary mobility. Some of estimation techniques were tried to reduce the errors. Regardless of the methods we exploited, the average value of the simulated mobilities was a good approximation of the results from analytical prediction or single grain growth simulations.     

材料微观组织演变的蒙特卡洛仿真原理及应用

材料宏观力学性能由材料微观组织决定.蒙特卡洛波茨模型是实现材料微观组织演变过程仿真的一种重要方法.对蒙特卡洛波茨模型的原理、算法和应用进行了综述.     

Spinodal decomposition of fine-grained binary alloys: A Monte-Carlo simulation

The kinetics of spinodal decomposition of binary alloys in case of finite grain size and slow grain growth is studied by applying the Monte-Carlo method where a coupled algorithm of the spin-exchange Ising model and Q-state Potts model operates. The anisotropic energy of grain boundaries is incorporated by imposing a Potts spin lattice on the Ising crystal. We simulate the phase separation where the grain size is comparable with the spinodal length on the order of magnitude. It is revealed that the grain boundaries of low excess energy as rapid channel enhance the solute diffusion, whereas those boundaries of high excess energy hinder the solute diffusion. Depending on the system supersaturation, phase aggregation preferred at the grain boundaries is demonstrated. The spinodal kinetics is modulated by the grain growth so that the Lifshitz-Slyozov-Wagner law may no longer be applicable in spite of the scaling law roughly holds in present system.     

Bounding box framework for efficient phase field simulation of grain growth in anisotropic systems

A sparse bounding box algorithm is extended to perform efficient phase field simulations of grain growth in anisotropic systems. The extended bounding box framework allows to attribute different properties to different grain boundary types of a polycrystalline microstructure and can be combined with explicit, implicit or semi-implicit time stepping strategies. To illustrate the applicability of the software, the simulation results of a case study are analysed. They indicate the impact of a misorientation dependent boundary energy formulation on the evolution of the misorientation distribution of the grain boundary types and on the individual growth rates of the grains as a function of the number of grain faces.     

Magnetically controlled microstructure evolution in non-ferromagnetic metals

The microstructure evolution during grain growth in magnetically anisotropic materials can be affected by a magnetic field due to an additional driving force for grain boundary motion which arises from a difference in magnetic free energy density between differently oriented grains. Therefore each grain of a polycrystal, exposed to a magnetic field, is inclined to grow or to shrink by a magnetic force depending on the orientation of the respective grain and its surrounding neighbors with regard to the field direction. A theoretical analysis of the grain growth kinetics in the presence of an external magnetic field reveals that magnetically affected grain growth may result in an orientation distribution that favours grains with a lower magnetic free energy density. As it is experimentally demonstrated on polycrystalline zinc, titanium and zirconium, the crystallographic texture in magnetically anisotropic non-magnetic materials can be effectively changed and controlled by means of annealing in a magnetic field. EBSD-analysis revealed that the observed asymmetrical texture after magnetic annealing is due to a large extent to a significant difference in the number of grains that make up different texture components. The results of computer simulations of magnetically affected grain growth in 2-D polycrystals are in a good agreement with theoretical predictions and experimental findings.     

A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials

In this paper, a cohesive grain boundary integral formulation is proposed, for simulating intergranular microfracture evolution in polycrystalline brittle materials. Artificially generated polycrystalline microstructures are discretized using the proposed anisotropic boundary element method, considering the random location, morphology and material orientation of each grain. Each grain is assumed as a single crystal with general elastic orthotropic mechanical behaviour. Crack initiation and propagation along the grain boundaries interfaces are modelled using a linear cohesive law, considering mixed mode failure conditions. Furthermore, a non‐linear frictional contact analysis is performed over cracked grain interfaces to encounter cases where crack surfaces come into contact, slide or separate. The effect of randomly located pre‐existing flaws on the overall behaviour and microcracking evolution of a polycrystalline material is also investigated for different Weibull moduli. The stochastic effects of each grain morphology‐orientation, internal friction and randomly distributed pre‐existing flaws, under different loading conditions, are studied probabilistically by simulating various randomly generated microstructures. Copyright © 2006 John Wiley & Sons, Ltd.     

薄规格取向硅钢二次再结晶过程中Goss织构演变的Monte Carlo模拟

通过EBSD实验获取了薄规格取向硅钢(0.18 mm厚)初次再结晶样品表面晶粒组织的取向数据,并以此构建模拟的初始组织.采用Potts模型Monte Carlo方法对薄规格取向硅钢初次再结晶样品的二次再结晶过程进行了模拟仿真,研究了表面能对Goss织构演变的影响.模拟结果表明:Goss取向晶粒与相邻晶粒的表面能差是Goss取向晶粒异常长大的重要驱动力;表面能差存在一个临界值(约12％),只有当表面能差大于此临界值时才会发生表面能驱动Goss取向晶粒的异常长大.     

Monte Carlo simulation of polycrystalline microstructures and finite element stress analysis

A two-dimensional numerical model of microstructural effects is presented, with an aim to understand the mechanical performance in polycrystalline materials. The microstructural calculations are firstly carried out on a square lattice by means of a 2-D Monte Carlo (MC) simulation for grain growth, then the conventional finite element method is applied to perform stress analysis of a plane strain problem. The mean grain size and the average stress are calculated during the MC evolution. The simulation result shows that the mean grain size increases with the simulation time, which is about 3.2 at 100 Monte Carlo step (MCS), and about 13.5 at 5000 MCS. The stress distributions are heterogeneous in materials because of the existence of grains. The mechanical property of grain boundary significantly affects the average stress. As the grains grow, the average stress without grain boundary effect slightly decreases as the simulation time, while the one with strengthening effect significantly decreases, and the one with weakening effect increases. The average stress and the grain size agree well with the Hall–Petch relationship.     

Multiphase-field modelling of concurrent grain growth and coarsening in complex multicomponent systems

Phase-field modelling of microstructural evolution in polycrystalline systems with phase-associated grains has largely been confined to continuum-field models. In this study, a multiphase-field approach,with a provision for introducing grain boundary and interphase diffusion, is extended to analyse concurrent grain growth and coarsening in multicomponent polycrystalline microstructures with chemically-distinct grains. The effect of the number of phases and components on the kinetics of evolution is investigated by considering binary and ternary systems of duplex and triplex microstructures, along with a single phase system. It is realised that the mere increase in the number of phases minimises the rate of concurrent grain growth and coarsening. However, the effect of components is substantially dependent on the respective kinetic coefficients. This work unravels that the disparity in the influence of phases and components is primarily due to the corresponding change introduced in the transformation mechanism.While the raise in number of phases convolutes the diffusion paths, the increase in number of component effects the rate of evolution through the interdiffusion, which introduces interdependency in the diffusing chemical-species. Additionally, the role of phase-fractions on the transformation rate of triplex microstructure is studied, and correspondingly, the interplay of interface-and diffusion-governed evolution is elucidated. A representative evolution of three-dimensional triplex microstructure with equal phase-fraction is comparatively analysed with the evolution of corresponding two-dimensional setup.