宏微观耦合模拟熔池不同区域中枝晶竞争生长过程

针对熔化焊过程建立了宏微观耦合模型,模拟了熔池内不同区域凝固过程中随机取向枝晶的竞争生长过程. 通过宏观三维有限元模型计算熔池中瞬态的传热传质过程,利用双线性插值算法将凝固参数传递给微观组织模型. 采用元胞自动机法模拟随机取向的枝晶在熔池凝固条件下的竞争生长过程. 模拟结果表明,所建立的微观模型能够精确模拟任意生长取向的枝晶. 凝固条件中最大温度梯度方向对枝晶竞争过程有明显选择作用,生长方向与最大温度梯度方向相同或接近的枝晶在竞争中具有更大优势. 焊缝中的晶粒组织由枝晶簇发展形成,晶粒组织的形貌演变取决于相邻枝晶簇之间的竞争过程,具有择优取向的枝晶簇会逐渐排挤非择优取向的枝晶簇并最终将其阻挡在凝固组织内部,宏观晶粒的取向与其内部枝晶簇的生长方向并不一定相同. 熔池中心线附近区域在焊接过程中具有更小的温度梯度、更大的凝固速率以及更大的局部冷却速率,凝固后可以获得更加细小的焊缝枝晶组织. 枝晶间距的模拟结果与相应凝固条件下的试验数据符合较好. 关键词： 焊接熔池 枝晶形貌 竞争生长 元胞自动机     

Numerical simulation of transient temperature field during laser keyhole welding of 304 stainless steel sheet

A three-dimensional transient numerical model was developed to study the temperature field and molten pool shape during continuous laser keyhole welding. The volume-of-fluid (VOF) method was employed to track free surfaces. Melting and evaporation enthalpy, recoil pressure, surface tension, and energy loss due to evaporating materials were considered in this model. The enthalpy-porosity technique was employed to account for the latent heat during melting and solidification. Temperature fields and weld pool shape were calculated using FLUENT software. The calculated weld dimensions agreed reasonable well with the experimental results. The effectiveness of the developed computational procedure had been confirmed.     

Study on the solidification microstructure in AZ91D Mg alloy after laser surface melting

Laser surface melting (LSM) is known to enhance the wear and corrosion resistance of Mg alloys, but its effect on microstructural evolution of Mg alloys is not well understood. An effort has been made to study the effect of rapid solidification following LSM on the microstructural evolution of AZ91D Mg alloy. The results of X-ray diffractometry, scanning electron microscopy, transmission electron microscopy and energy-dispersive X-ray spectroscopy indicated that the solidification microstructure in the laser-melted zone was mainly cellular/dendrite structure of primarily α-Mg phase and continuous network of β-Mg₁₇Al₁₂ phase. Numerical prediction of the laser-melted zone suggested that cooling rates increased strongly from the bottom to the top surface in the irradiated regions. An attempt has been made to correlate dendrite cell sizes of the solidification microstructure with the cooling rates in the laser-treated AZ91D Mg alloy.     

热镀铜层冷凝过程的分子动力学模拟

采用常温、常压分子动力学模拟方法和FS(Finnis Sinclair)势 ,研究了在周期性边界条件下由 5 0 0个原子构成的液态Cu模型系统的凝固过程 ,考察了不同降温速率下Cu的凝固行为 ,得到了不同温度、不同冷却速率下Cu的双体分布函数 ;采用HA键型指数法统计了各种小原子团在不同温度下所占比例 ,采用键取向序分析了体系降温全过程的局域取向对称性 ,得到原子体系微观结构组态变化的重要信息 ;最后 ,利用能量分析的方法对体系微观结构的变化进行了说明 ,给出了液态Cu冷凝过程中微观结构转变的重要信息 .     

Exact Solutions of the φ6 + φ5 Model Using Truncated Method

In this letter, the φ6 φ5 model in (D 1) dimensions can be solved by a truncated series method. A series of solitary solutions of the φ6 φ5 model in (D 1) dimensions have be obtained.     

An extension to the Wheeler phase-field model to allow decoupling of the capillary and kinetic anisotropies

The formulation of the phase-field problem due to Wheeler et al. [Physica D 66, 243 (1993)] has been adopted and extended as a tool for solidification research by many groups around the World. However, an intrinsic problem of this model is that it couples two physically distinct anisotropies, those associated with the surface energy of the solid-liquid interface and attachment kinetics, into a single anisotropy parameter. In this paper we present a simple extension to the Wheeler model in which we show that introducing a complex form of the anisotropy function allows these two physical parameters to be decoupled.Received: 16 June 2004, Published online: 21 October 2004PACS: 81.10.-h Methods of crystal growth; physics of crystal growth - 81.30.Fb Solidification - 64.70.Dv Solid-liquid transitions     

Isothermal solidification stage during transient liquid-phase bonding single-crystal superalloys

In this work, the isothermal solidification stage during transient liquid-phase bonding (TLP) single-crystal superalloys has been investigated. Experiments were performed to ascertain the bonding microstructures and the kinetics during the isothermal solidification. The results have shown that the isothermal solidification stage deviates from the standard parabolic TLP models. Lots of the borides with fine, short bar and acicular morphologies formed in the diffusion affected zone (DAZ) in the thick wall and thin wall substrate specimens at the isothermal solidification stage. Electron probe microanalysis results have shown that there exists B composition peak in the DAZ. Examination of the bonding kinetics presented that there are three stages in the isothermal solidification stage: initial stage, transient stage and final stage with different growth velocity of the isothermal solidification zone (ISZ). And the relationship of the width of the ISZ with the square root of the bonding time didn’t satisfy the parabolic relationship. Based on the microstructures and kinetics observed, a film ISZ mechanism is proposed, and a model is constructed to illustrate the isothermal solidification stage during bonding single-crystal superalloys.     

Anisotropic growth of multigrain in equiaxial solidification simulated with the phase field method

The phase field method has been mainly used to simulate the growth of a single crystal in the past. But polycrystalline materials predominate in engineering. In this work, a phase field model for multigrain solidification is developed, which takes into account the random crystallographic orientations of crystallites and preserves the rotational invariance of the free energy. The morphological evolution of equiaxial multigrain solidification is predicted and the effect of composition on transformation kinetics is studied. The numerical results indicate that due to the soft impingement of grains the Avrami exponent varies with the initial melt composition and the solidification fraction.     

Critical exponents of the random-field O(N) model

The critical behavior of the random-field Ising model has long been a puzzle. Different methods predict that its critical exponents in D dimensions are the same as in the pure (D-2)-dimensional ferromagnet with the same number of the magnetization components contrary to the experiments and simulations. We calculate the exponents of the random-field O(N) model with the (4+epsilon)-expansion and obtain values different from the exponents of the pure ferromagnet in 2+epsilon dimensions. An infinite set of relevant operators missed in previous studies leads to a breakdown of the (6-epsilon)-expansion.     

Exact Solutions of the φ^6 ＋ φ^5 Model Using Truncated Method

In this letter, the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions can be solved by a truncated series method. A series of solitary solutions of the φ^6 ＋ φ^5 model in （D ＋ 1） dimensions have be obtained.     

Al-Ti-B细化工业纯铝凝固组织演变过程数值模拟

采用耦合群体动力学方法与元胞自动机方法建立了细化处理条件下铝合金凝固微观组织演变的数值模型.该模型考虑了a-Al的非均匀形核过程、晶粒的初始球形长大以及之后的枝晶生长过程.利用建立的模型模拟了Al-5Ti-1B中间合金细化工业纯铝凝固组织演变过程.结果表明:形核初始阶段,熔体中存在充足数量的有效形核粒子, a-Al形核率随着熔体过冷度的增大逐渐增高;形核开始不久后, a-Al的异质形核过程由熔体中有效形核粒子数量控制,直到再辉发生,形核停止.模拟分析了中间合金添加量以及熔体冷却速度对工业纯铝凝固组织演变过程的影响,模拟结果与实验结果相符,验证了模型的准确性.     

Diffusion-influenced fluorescence quenching dynamics in one to three dimensions

The fluorescence decay curves obtained from diffusion-influenced quenching in various spatial dimensions are discussed. The two-dimensional quenching has, because of intractable fitting functions, previously been dealt with only in the completely diffusion-controlled case (corresponding to the Smoluchowski boundary condition). In this paper, an approximation for the two-dimensional (2D)-quenching behavior with the Collins-Kimball boundary condition is presented. The nonlinear least-squares method has been used to analyze simulated decay data. The consequences the choice of an incorrect model has on the final results as well as the possibility to discriminate between different dimensionalities are investigated. Also, some inherent properties of the fitting functions are studied.     

2D spectral and turbulence length scale estimation with PIV

A new method to apply spatial two-dimensional power spectral density (2D PSD) analysis to the data measured with Particle Image Velocimetry (PIV) has been introduced. Applying the method to a set of the velocity vector fields characteristic turbulence length scales can be estimated. In this method the computation of 2D PSD has been performed to two kinds of pre-processed data. In the first set, the local average has been spatially subtracted (Spatial decomposition) and in the second set the time-average has been subtracted (Reynolds decomposition). In the computation of 2D PSD the 2D FFT with the variance scaling has been used. Besides 2D spectral analysis this paper uses the distribution analysis of the various turbulence quantities and a structure analysis method to estimate the dimensions of coherent structures in the flow. Another method to analyse turbulence length scales is the estimation of the spatial 2D Auto Correlation Coefficient Function (2D ACCF). All these methods applied side by side to the PIV data increase the understanding of the turbulence, its scales and the nature of the coherent structures.     

Scale invariance in disordered systems: the example of the random-field Ising model

We show by numerical simulations that the correlation function of the random-field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this nonperturbative phenomenon is not particular to the RFIM in 3D. It is generic for disordered systems in two dimensions and may also happen in other three-dimensional disordered systems.     

层状共晶定向凝固

本文从理论和实验两方面研究层状共晶定向凝固。理论上将层状共晶定向凝固与胞晶列定向凝固及Hele-Shaw胞中粘性指发展进行类比,给出层状共晶稳态凝固条件下溶质扩散、热传输与界面张力效应之间的耦合系,导出λ²ν=consi标度关系。实验上考察了规则Al-Al₂Cu共晶和非规则Al-Si共晶定向凝固,证实耦合关系存在。还讨论了两种共晶凝固界面特征和热传输的影响。 关键词：     

Diffusion-stress coupling in liquid phase during rapid solidification of binary mixtures

An analytical model has been developed to describe the diffusion-viscous stress coupling in the liquid phase during rapid solidification of binary mixtures. The model starts with a set of evolution equations for diffusion flux and viscous pressure tensor, based on extended irreversible thermodynamics. It has been demonstrated that the diffusion-stress coupling leads to non-Fickian diffusion effects in the liquid phase. With only diffusive dynamics, the model results in the nonlocal diffusion equations of parabolic type, which imply the transition to complete solute trapping only asymptotically at an infinite interface velocity. With the wavelike dynamics, the model leads to the nonlocal diffusion equations of hyperbolic type and describes the transition to complete solute trapping and diffusionless solidification at a finite interface velocity in accordance with experimental data and molecular dynamic simulation.     

Does a single zealot affect an infinite group of voters?

A method for studying the exact properties of a class of inhomogeneous stochastic many-body systems is developed and presented in the framework of a voter model perturbed by the presence of a "zealot," an individual allowed to favor an "opinion." We compute exactly the magnetization of this model and find that in one (1D) and two dimensions (2D) it evolves, algebraically ( approximately t(-1/2)) in 1D and much slower ( approximately 1/ln(t) in 2D, towards the unanimity state chosen by the zealot. In higher dimensions the stationary magnetization is no longer uniform: the zealot cannot influence all the individuals. The implications to other physical problems are also pointed out.     

Three-dimensional holographic fluorescence microscopy

Most commonly used methods for three-dimensional (3D) fluorescence microscopy make use of sectioning techniques that require that the object be physically scanned in a series of two-dimensional (2D) sections along the z axis. The main drawback in these approaches is the need for these sequential 2D scans. An alternative approach to fluorescence imaging in three dimensions has been developed that is based on optical scanning holography. This novel approach requires only a 2D scan to record 3D information. Holograms of 15-microm fluorescent latex beads with longitinal separation of ~2 mm have been recorded and reconstructed. To our knowledge, this is the first time holograms of fluorescent specimens have been recorded by an optical holographic technique.     

On the Fully Implicit Solution of a Phase-Field Model for Binary Alloy Solidification in Three Dimensions

A fully implicit numerical method, based upon a combination of adaptively refined hierarchical meshes and geometric multigrid, is presented for the simulation of binary alloy solidification in three space dimensions. The computational techniques are presented for a particular mathematical model, based upon the phase-field approach, however, their applicability is of greater generality than for the specific phase-field model used here. In particular, an implicit second order time discretization is combined with the use of second order spatial differences to yield a large nonlinear system of algebraic equations as each time step. It is demonstrated that these equations may be solved reliably and efficiently through the use of a nonlinear multigrid scheme for locally refined grids. In effect, this paper presents an extension of earlier research in two space dimensions (J. Comput. Phys., 225 (2007), pp. 1271-1287) to fully three-dimensional problems. This extension is validated against earlier two-dimensional results and against some of the limited results available in three dimensions, obtained using an explicit scheme. The efficiency of the implicit approach and the multigrid solver are then demonstrated and some sample computational results for the simulation of the growth of dendrite structures are presented.     

An inverse model for a free-boundary problem with a contact line: Steady case

This paper reformulates the two-phase solidification problem (i.e., the Stefan problem) as an inverse problem in which a cost functional is minimized with respect to the position of the interface and subject to PDE constraints. An advantage of this formulation is that it allows for a thermodynamically consistent treatment of the interface conditions in the presence of a contact point involving a third phase. It is argued that such an approach in fact represents a closure model for the original system and some of its key properties are investigated. We describe an efficient iterative solution method for the Stefan problem formulated in this way which uses shape differentiation and adjoint equations to determine the gradient of the cost functional. Performance of the proposed approach is illustrated with sample computations concerning 2D steady solidification phenomena.