Deviation from local equilibrium at migrating phase interfaces

The effects of four causes of deviation from local equilibrium at migrating phase interfaces are illustrated with molar Gibbs energy diagrams and using the sharp interface model. The conditions during solidification and melting are compared. In particular, it is examined when the composition of a growing phase can move inside the two-phase field.     

Numerical procedure for simulation of multicomponent and multi-layered phase diffusion

A mass balance error-free numerical procedure for simulation of multicomponent and multi-layered phase diffusional reactions has been suggested, based on an explicit fixed grid finite difference method. Basically, a local equilibrium was assumed at each phase interface and one dimensional movement of interfaces was considered. Attention was paid to the treatments of newly formed thin phase layers and different molar volumes among interacting phases, together with the removal of a mass balance error. Specially derived finite difference forms were used to treat phase layers thinner than two inter-grid distances. A new flux balance equation which is independent from the molar volume differences among phases and leaves no mass balance error was developed by a transformation of space variable system and by a systematic analysis of sources of mass balance error, respectively. Through some model simulations, it could be shown that the present numerical procedure cantreat multi-layered phase diffusion including thin layered phases and can reproduce transitions of layer sequences during diffusional reactions successfully, leaving no mass balance error.     

A note on the contact conditions at migrating interfaces

In addition to mass conservation and energy balance relations, conditions at the migrating interface (“contact conditions”) are required to predict the values of the variables at a sharp interface. In this paper frequently used contact conditions are discussed with respect to their inherent presuppositions, and a thick interface with zero internal fluxes is investigated. The contact conditions are automatically related to an off-equilibrium situation in the case of a finite interface mobility and can be derived from the principle of maximum Gibbs energy dissipation. The transformation kinetics for a deviation from local equilibrium has recently been studied by utilizing schematic Gibbs energy diagrams. The numerical results obtained in the present work confirm the predictive character of these schematic diagrams.     

Synthetic approach to alloy thermodynamics and kinetics by cluster variation method and path probability method

The cluster variation method of equilibrium thermodynamics is employed to calculate the Ll₀-disorder phase diagram. The stability analysis based on the second-order derivative of the free energy functional with respect to the deviation of correlation functions from their equilibrium values yields the 100 instability locus in the phase diagram. The time evolution of cluster probabilities at the phase transition is investigated on the basis of the path probability method of non-equilibrium statistical mechanics. Thereby the synthetic study of thermodynamics and kinetics based on the cluster variation method and the path probability method is attempted. It is shown that the fluctuation is necessary to drive the ordering reaction above the instability temperature, whereas the spinodal-like ordering transition takes place below the instability temperature. The extension of the present study of a spin system to an alloy system is briefly discussed and a critical problem to be settled is pointed out.     

基于晶体微观有限元方法的多相复合涂层高温摩擦应力场模拟*

对高温摩擦磨损工况下多相复合涂层的热-力耦合应力场的模拟研究尚不充分。基于 Voronoi 多边形建立 NiCr-Cr₃C₂-CaF₂ / BaF₂多相复合涂层的晶体微观有限元模型,模拟复合涂层中各相的占比、分布形态和热-力学参数,求解得到热-力耦合工况下的 von Mises 应力和第一主应力分布。结果表明：在高温摩擦工况下,多相复合涂层的应力显著高于均匀涂层,尤其是在硬质相尖端附近易产生局部高应力区域,改善相的形态将锐角钝化能够有效缓解局部高应力现象;热-力耦合应力场与黏结相和硬质相的弹性模量密切相关,通过调节各相模量能够有效调控复合涂层的 Mises 应力和拉应力值。基于微观有限元方法的热-力耦合应力场模拟可为高温摩擦磨损工况下多相复合涂层的优化设计提供理论依据。     

On the numerical simulation of diffusion-controlled reactions under local equilibrium conditions

To estimate the interfacial velocity in a multicomponent moving boundary problem, existing procedures require an interative technique to be used if a sharp interface method is employed. The need to use an interative technique can cause convergence problems; these become more frequent as more components are added. In this paper, two new methods are suggested which allow the velocity of a phase interface to be evaluated directly from the fluxes of the components under the assumption of local equilibrium. The methods assume that the interface has a fixed width in which the incoming and outgoing components are distributed in a way that moves the interface while maintaining local equilibrium. Example simulations are presented and results are in good agreement with established front-tracking simulation software (DICTRA); moreover, the superior convergence of the new methods is demonstrated.     

In situ observation of austenite–ferrite interface migration in a lean Mn steel during cyclic partial phase transformations

High-temperature laser scanning confocal microscopy (HT LSCM) has been applied to investigate the austenite–ferrite interface migration during cyclic phase transformations in situ in a Fe–Mn–C alloy. It has been found that during the cyclic phase transformations the transformation proceeds via the migration of existing austenite–ferrite interfaces. The interfaces migrate in a retraceable way. For the first time, the so–Called stagnant stage has been observed directly. The new in situ observations show that the interface migration rates for interfaces in different grains are comparable with each other prior to soft impingement, while the equilibrium migration distances for different interfaces can be quite different, depending on the local grain size. The average interface velocities as measured by HT LSCM are in very good agreement with the velocities derived from dilatometric data, and those are predicted by a local equilibrium transformation model.     

Thermodynamic considerations in the analysis of phase stability: The role of interfacial equilibrium in the determination of phase diagrams by X-ray microanalytical techniques

Although the time required for full equilibration may be too long to attain experimentally, equilibrium tie lines between coexisting phases can be determined from unequilibrated alloys and multiphase diffusion couples if the compositions of the two phases coexisting at the interface can be resolved, assuming that the interface is in “local equilibrium”. The capability to examine elemental segregation on a fine spatial scale allows for more rigorous testing of the assumption of local equilibrium at phase interfaces and for the determination of phase equilibria at temperatures below those accessible with more conventional techniques.     

含铝TRIP钢的相图计算与实验研究

利用真空熔炼试制了三种不同C含量的含铝TRIP钢,采用DSC测试方法测得一系列相变点,并借助Thermo-Calc软件对试验钢进行了平衡热力学计算,得到了试验钢的平衡相图及相变点的计算值,实验值比计算值偏高。综合考虑实验值与计算值的偏差,可为Al代Si TRIP钢的成分优化及热处理工艺提供参考。     

A study of the influence of Mn and Ni on the kinetics of the proeutectoid ferrite reaction in steels

The kinetic transition between partitioned and unpartitioned growth of proeutectoid ferrite has been studied for high-purity Fe–C–Mn and Fe–C–Ni alloys, and for temperatures just above the eutectoid. These results (and certain results of previous investigations) are compared with computed paraequilibrium and equilibrium ternary phase diagrams, and it is shown that the transition occurs well within the paraequilibrium two-phase regions, but significantly outside the limit predicted by the local equilibrium analysis of the ternary precipitation reaction. These observations are interpreted in terms of solute drag theory. It is inferred that both Mn and Ni exert a drag on the moving ferrite/austenite interfaces, and that this drag force is due to substitutional solute diffusion within the moving interface. The equilibrium binding energies of each of the substitutional solutes to the boundary are expected to be of order RT.     

LOCAL EQUILIBRIUM METHOD IN STUDYING PHASE DIAGRAM OF Mn-MnO SYSTEM

A special method based on the local equilibrium principle has been introduced in the researchof the phase diagram of Mn-MnO system.With this method,the problems of volatilization ofMn and the corrosion of Mn and MnO to refractory materials were prevented efficiently.Thesolubility of oxygen in Mn and the composition of the interface between MnO and Mn weredetermined.Partial phase diagram of Mn-MnO system were constructed according to pres-ent experimental results.     

用局部平衡法研究Mn-MnO体系相图

采用一种特殊的局部平衡法测定了Mn-MnO系相图。研究该系统所遇到的一些困难,如Mn的挥发以及Mn与MnO对耐火材料的侵蚀等,在此法中得以避免,测定了氧在Mn中的溶解度和Mn/MnO界面处各相的组成,并由此确定了Mn MnO系的局部相图。     

A modified displacement adjustment method to compensate for surface deflections in the automobile exterior panels

Surface deflections are becoming more and more concerned by automotive manufacturers because these defects spoil the appearance of automobiles greatly. In this paper, a modified displacement adjustment (DA) method is proposed to compensate for surface deflections in the automobile exterior panels. The proposed modified DA method has two advantages. One is that it distinguishes the global deviation and the local deviation and is able to compensate for the local deviation (surface deflection) independently. The other feature is that the iterative scheme in the DA method is substituted with a compensation factor so that time-consuming iterations are reduced and the convergence problems caused by the small tolerance of surface deflection are avoided. In order to test the effectiveness of the proposed method, it is applied to compensate for surface deflections in a cylinder shallow shell part and a door handle part. The compensation results show that the proposed method is effective in reducing surface deflections in both parts. The work in this study provides a new method to reduce surface deflections by die design. For parts in which mechanical methods to increase the sheet tension during bending are not effective or suitable, the proposed modified displacement adjustment method is an effective alternative.     

Simulation of dissimilar weld joints of steel P91

Abstract

Results of computer simulations of long term service exposure for weldments of the CSN 15 128/P91 and SK3STC/P91 steels are presented and compared with corresponding results of phase and composition experiments. The welded material P91 (EU designation: X10CrMoVNb 9–1) represents progressive chromium steel alloyed with molybdenum, vanadium, carbon, and nitrogen. The CSN 15 128 (13CrMoV 2–5) material is low alloy Cr–Mo–V steel. The SK3STC alloy (12CrMo 10–10) represents the consumable electrode material. The stability of the weldment microstructure is investigated at elevated temperatures (500–700° C). The simulation method is based on the Calphad approach complemented with the theory of multicomponent bulk diffusion, local conditions of phase equilibrium, and the assumption that diffusion is the process that controls the rate of phase transformation. Significant phase profiles, concentration profiles, and phase transformation processes in the diffusion affected zone are simulated, investigated, and compared with experimental results. The potentially deleterious carbon depleted region inside each weld joint is discussed. The method described can be used to predict microstructure instability in weld joints.     

热锻成形过程数值模拟与多目标设计优化技术研究

提出了一种基于有限元分析和序列二次规划的热锻成形工艺多目标优化方法,优化目标包含锻件的内部损伤值和变形均匀性两个方面。用锻件所有单元的最大损伤值作为衡量锻件变形损伤的指标,用锻件所有单元体的等效应变与整个终锻件的平均等效应变的均方差,作为锻件变形均匀性的指标,构造了多目标优化问题的评价函数。在设计过程中,优化变形工艺参数使得工件内部损伤值最小,同时工件内部变形均匀。以零件毛坯的初始高径比为设计变量,建立了热锻成形过程多目标优化设计的数学模型。应用该方法对齿轮齿圈毛坯非等温热锻成形工艺参数进行优化,取得了良好的效果。     

A diffuse-interface model of reactive wetting with intermetallic formation

A diffuse-interface model of reactive wetting with intermetallic formation is developed that incorporates fluid flow, phase change and solute diffusion. The model is based on the total molar Gibbs energy of a ternary system with four phases. Numerical simulations were performed using a mesh-adaptive finite element method, revealing the complex behavior of the reactive wetting process. The model was verified against equilibrium states derived from the classical phase diagram and from interface energy considerations. Dynamic results show that the intermetallic can either precede or follow the spreading liquid droplet, depending on the time and the choice of interface energy and kinetic coefficients. Despite this difference, the spreading rate was not affected for the cases considered.     

Elevated-temperature coarsening behavior in aluminum alloys

Coarsening kinetics of the equilibrium phase in the Al- rich end of the Al- Ti- Cu and Al- Ti- Ni systems have been studied using transmission electron microscopy as a function of annealing times at 698 K. The equilibrium phase in the Al- Ti- Ni system coarsens at a rate that is 6 times faster than that in the Al- Ti- Ni phase. This difference in the coarsening kinetics is related to the amount of mismatch of each of the equilibrium phases with respect to the Al- matrix.     

多轴机床快速有限元建模与随位动态特性预估

针对多轴机床随位动态特性难以高效求解的问题,提出一种快速有限元建模方法。该方法先根据结合部建模方案对机床进行子结构划分与前处理,再用弹簧-阻尼单元表征子结构间结合部的连接特性,最后通过局部坐标变换调节各子结构在机床中的位置与姿态,从而完成整机的参数化有限元建模。运用所提方法,建立了某型五轴动梁龙门立式车铣复合机床的参数化有限元模型。该模型仅需单次有限元前处理,即可快速预估机床工作全域内不同位姿下的结构动态特性。预估了该机床前5阶固有频率以及0~150 Hz频带内刀尖点频响函数在工作全域内的分布规律,为机床结构动力修改与加工参数优选提供了力学依据。     

基于Abaqus的SAE分体法兰密封影响因素仿真分析

针对风洞油源系统硬质管路连接法兰渗油漏油问题，在Abaqus中建立SAE分体法兰连接的油管有限元模型，分析O形密封圈预压缩率、工作油压、油管装配前的径向偏差、角度偏差对法兰连接密封性的影响规律。结果表明：O形密封圈具有自密封性，且密封性随着预压缩率的增大而增强，密封面上的接触应力随着工作油压的增大而增大；油管安装中存在的径向偏差和角度偏差造成SAE法兰焊接头端面接触应力分布不均甚至出现局部屈服现象，但是装配偏差在一定范围内对密封圈的静密封性能影响较小；当油管每100 mm径向偏差大于1.2 mm且角度偏差大于5°时，法兰密封快速失效。