Laser remelting of Al-1.5 wt%Fe alloy surfaces: Numerical and experimental analyses

A 3D heat transfer mathematical model based on the finite element method is applied to the laser surface remelting (LSR) process with a view to simulating temperature fields and melt pool dimensions. The theoretical predictions furnished by the model are validated against LSR experimental results from tests carried out in the present study with Al-1.5 wt%Fe alloy samples. The work also encompasses an analysis of microstructural and microhardness variations throughout the resulting treated and untreated zones. A remarkable effect of the LSR treatment on the mechanical and corrosion resistance of the treated samples is shown.     

Computational and experimental study of a melt-hardened zone on a roller modified by wide-band laser treatment

A three-dimensional finite element model has been developed to simulate the wide-band laser remelting process and predict the thermal and mechanical properties in the melt-hardened zone. The simulation of the laser remelting process was performed using the nonlinear thermo-mechanical properties, based on a wide-band heat source model. The temperature fields, phase transformations, hardness and residual stress distributions in the melt-hardened zone were analyzed. In the remelting zone, the transformed volumetric percentage of martensite is beyond 80% and the excessive transformed martensitic structure greatly affects the mechanical properties in the melt-hardened zone with its volumetric expansion effect. After remelting, the hardness can be improved and the residual stress distributed within the melted zone is mainly of the compressive type, while the tensile stress in the heat-affected zone (HAZ) may cause the initiation of cracks. The computational results are in good agreement with experimental measurements.     

Heat transfer modelling and stability analysis of selective laser melting

The process of direct manufacturing by selective laser melting basically consists of laser beam scanning over a thin powder layer deposited on a dense substrate. Complete remelting of the powder in the scanned zone and its good adhesion to the substrate ensure obtaining functional parts with improved mechanical properties. Experiments with single-line scanning indicate, that an interval of scanning velocities exists where the remelted tracks are uniform. The tracks become broken if the scanning velocity is outside this interval. This is extremely undesirable and referred to as the “balling” effect. A numerical model of coupled radiation and heat transfer is proposed to analyse the observed instability. The “balling” effect at high scanning velocities (above ∼20 cm/s for the present conditions) can be explained by the Plateau-Rayleigh capillary instability of the melt pool. Two factors stabilize the process with decreasing the scanning velocity: reducing the length-to-width ratio of the melt pool and increasing the width of its contact with the substrate.     

Nonlinear Couette Flow in a Low Density Granular Gas

A model kinetic equation is solved exactly for a special stationary state describing nonlinear Couette flow in a low density system of inelastic spheres. The hydrodynamic fields, heat and momentum fluxes, and the phase space distribution function are determined explicitly. The results apply for conditions such that viscous heating dominates collisional cooling, including large gradients far from the reference homogeneous cooling state. Explicit expressions for the generalized transport coefficients (e.g., viscosity and thermal conductivity) are obtained as nonlinear functions of the coefficient of normal restitution and the shear rate. These exact results for the model kinetic equation are also shown to be good approximations to the corresponding state for the Boltzmann equation via comparison with direct Monte Carlo simulation for the latter.     

Study of the crystallization morphology of VT3-1 alloy during VAR

In this paper, we consider the crystallization morphology formation of VT3-1 titanium alloy in the process of vacuum arc remelting (VAR). Based on experimental data obtained by the method of autoradiography, we numerically determine remelting parameters such as the temperature gradient G at the solidification front and its velocity V. Since practically all kinds of morphology of the crystallization microstructure of metal systems are present in an ingot (planar front, cellular, cellular-dendritic, and dendritic structures), we consider two simple models of transition from one structure to another. The models greatly depend on the parameters G and V. In this paper, the liquidus curve slopes for the alloying elements of VT3-1 alloy are determined and a morphology map is constructed. Also, the results are compared with those obtained earlier by other authors.     

A keyhole volumetric model for weld pool analysis in Nd:YAG pulsed laser welding

This study presents a new model for analyzing the temperature distribution and weld pool shape in Nd:YAG pulsed laser welding. In the proposed approach, a surface flux heat transfer model is applied in the low laser energy intensity region of the weld, while a keyhole heat transfer model based on a volumetric heat source is applied in the high laser energy intensity region of the weld. The correlation between the intensity of the laser input energy and the geometric parameters of the volumetric heat source is derived experimentally. A series of MARC finite element simulations based on the proposed single pulse model are performed to investigate the shape and size of the weld pool given different laser energy intensities. A good agreement is observed between the simulation results and the experimental results obtained under equivalent single pulse welding conditions. Thus, the basic validity of the proposed model is confirmed.     

Transient lumped heat pipe analyses

A transient lumped heat pipe formulation for conventional heat pipes is presented and the lumped analytical solutions for different boundary conditions at the evaporator and condenser are given. For high temperature heat pipes with a radiative boundary condition at the condenser, a nonlinear ordinary differential equation is solved. In an attempt to reduce computer demands, a transient lumped conductive model has been developed for noncondensible gas-loaded heat pipes. The lumped flat-front transient model was extended by accounting for axial heat conduction across the sharp vapor-gas interface. The analytical solutions for conventional and gas-loaded heat pipes were compared with the corresponding numerical results of the full two-dimensional conservation equations and experimental data, with good agreement.     

The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model

A one-dimensional （1D） Frenkel-Kontorova （FK） model is studied numerically in this paper, and two new analytical solutions （a supersonic kink and a nonlinear periodic wave） of the Sine-Gordon （SG） equation （continuum limit approximation of the FK model） are obtained by using the Jacobi elliptic function expansion method. Taking these new solutions as initial conditions for the FK model, we numerically find there exist the supersonic kink and the nonlinear periodic wave in these systems and obtain a lot of interesting and significant results. Moreover, we also investigate the subsonic kink and the breather in these systems and obtain some new feature.     

Nonlinear waves in porous media saturated with live oil

A nonlinear equation is obtained for waves propagating in porous media of arbitrary consolidation (relative rigidity) saturated with live (i.e., air-bearing) oil. The equation describes the evolution of fast and slow Biot-Frenkel longitudinal acoustic waves propagating in both directions and allows one to analyze the reflected waves and their interaction. For a wave of the second kind, the diffusion coefficient is determined. The dependences of the dispersion and dissipation parameters on the rigidity of the oil pool structure and on the depth of the oil pool occurrence are analyzed.     

The quantum-fluctuations of the optical parametric oscillator. II

We set up an effective Hamiltonian for an optical parametric oscillator. It contains the Bose operators of the three modes, signal, idler, and pump and their coupling to heat baths. This Hamiltonian is shown to be equivalent to a set of equations of motion, derived in a previous paper (I) from a microscopically exact Hamiltonian, provided that the heat baths are chosen in an adequate way. The comparison with the laser Hamiltonian makes clear the close analogy of the underlying elementary processes of spontaneous emission from atoms and spontaneous parametric emission from light modes in nonlinear media. The Hamiltonian is used to derive a master equation for the statistical operator of the three-mode system. In the coherent state representation this master equation transforms into an equivalentc-number Fokker-Planck equation without any approximation. The solution is obtained below threshold by linearization and above threshold by quasilinearization of the nonlinear dissipation coefficients. The results agree with those which were obtained by quantum mechanical Langevin methods in a previous paper (I).     

Algebro-Geometric Solutions with Characteristics of a Nonlinear Partial Differential Equation with Three-Potential Functions

With the help of a simple Lie algebra, an isospectral Lax pair, whose feature presents decomposition of element (1, 2) into a linear combination in the temporal Lax matrix, is introduced for which a new integrable hierarchy of evolution equations is obtained, whose Hamiltonian structure is also derived from the trace identity in which contains a constant γ to be determined. In the paper, we obtain a general formula for computing the constant γ. The reduced equations of the obtained hierarchy are the generalized nonlinear heat equation containing three-potential functions, the mKdV equation and a generalized linear KdV equation. The algebro-geometric solutions (also called finite band solutions) of the generalized nonlinear heat equation are obtained by the use of theory on algebraic curves. Finally, two kinds of gauge transformations of the spatial isospectral problem are produced.     

温度梯度区域熔化作用下熔池迁移的元胞自动机模拟

本文采用耦合凝固和熔化效应的二维元胞自动机(cellular automaton, CA)模型,对温度梯度区域熔化(temperature gradient zone melting, TGZM)效应引起的熔池在固液两相区中的迁移现象进行模拟研究.模拟分析了抽拉速度、熔池初始位置、温度梯度和合金成分等因素对TGZM动力学的影响,并将模拟结果与解析模型的预测结果进行比较验证.通过模拟发现,在温度梯度作用下,熔池总是向着高温方向迁移;当抽拉速度低于或高于临界抽拉速度时,熔池朝向移动的液相线或固相线迁移;对于给定的抽拉速度,位于糊状区内临界位置以上的熔池会迁移进入液相,而位于临界位置以下的熔池会逐步靠近固相线.此外,温度梯度越高,合金成分越低,熔池的迁移速度越快.     

Application of variational iteration method and homotopy–perturbation method for nonlinear heat diffusion and heat transfer equations

Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this Letter; one is He's variational iteration method (VIM) and the other is the homotopy–perturbation method (HPM). Nonlinear convective–radiative cooling equations are used as examples to illustrate the simple solution procedures. These methods are useful and practical for solving the nonlinear heat diffusion equation, which is associated with variable thermal conductivity condition. Comparison of the results obtained by both methods with exact solutions reveals that both methods are tremendously effective.     

激光重熔对等离子喷涂ZrO_2-20%Y_2O_3热障涂层隔热性能的影响

采用大气等离子喷涂(APS)技术在铝基体表面制备氧化锆(ZrO2-20%Y2O3,质量分数)热障涂层,并用脉冲激光对其进行重熔处理,研究了激光重熔对涂层组织形貌、物相转变和隔热性能的影响。研究结果表明激光的比能量对涂层的成型及性能有重要影响,过高的比能量会使涂层表面粗糙度增加,涂层成型变差。在选用合适的低比能量激光重熔条件下,扫描电镜观察结果表明经激光重熔可消除喷涂态涂层的孔隙和层状结构。对粉末和重熔前后的涂层进行了X射线衍射分析,结果表明喷涂及重熔过程中都没有发生相变;隔热试验结果表明重熔后涂层的隔热温度有所下降。     

Absolute stability of the solidification interface in a laser resolidified Zn--2wt.%Cu hypoperitectic alloy

This paper reports on laser surface remelting experiments performed on a Zn--2wt.%}Cu hypoperitectic alloy by employing a 5kW CW CO₂ laser at scanning velocities between 6 and 1207mm/s. The growth velocities of the microstructures in the laser molten pool were accurately measured. The planar interface structure caused by the high velocity absolute stability was achieved at a growth velocity of 210~mm/s. An implicit expression of the critical solidification velocity for the cellular--planar transition was carried out by nonlinear stability analyses of the planar interface. The results showed a better agreement with the measured critical velocity than that predicted by M--S theory. Cell-free structures were observed throughout the whole molten pool at a scanning velocity of 652~mm/s and the calculated minimum temperature gradient in this molten pool was very close to the critical temperature gradient for high gradient absolute stability (HGAS) of the \eta phase. This indicates that HGAS was successfully achieved in the present experiments.     

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     

Dissipative formation of hole-like excitation in ion-acoustic plasma

A viscous plasma is analyzed by reductive perturbation theory to model dissipative soliton formation. A nonlinear Schrödinger equation with complex coefficients is derived. Such an equation can be exactly solved by the technique due to Hirota. Three types of solution can be obtained under different physical conditions: solitary waves, ion-acoustic holes, and shocks. Even in the presence of a dissipative effect like viscosity, it is possible to obtain a solitary-wave-like excitation.     

The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H ₁. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.     

采用混合模型数值模拟从深海到浅海内波的传播

在南海东沙岛附近, 从MODIS遥感图像发现内波传播是从深海经陆架坡再到浅海, 由于深海和浅海环境条件的差异以及传播模型的适用条件不同, 因此 不能采用同一模型模拟内波的传播, 需用两种模型来分别模拟内波在深海和浅海中的传播. 采用差分法, 首先用非线性薛定谔方程模拟了深海内波的传播, 然后用EKdV方程模拟了内波在浅海中的继续传播. 模拟结果与实际的MODIS遥感内波图像相符合, 并与应用单一模型模拟结果相比, 混合模型模拟该海区的内波传播更接近遥感实测, 表明了混合模型的合理性.     

On the two-dimensional instability of square-wave detonations

In order to elucidate the basic mechanisms responsible for the cells developing on detonation fronts, the two-dimensional instability of planar Chapman-Jouguet detonations is studied by the use of a square-wave model. It has been shown that there are two main instability mechanisms: the high sensitivity of the heat release rate to temperature and the hydrodynamic effect arising from the interface (reaction front) subject to the influence of the deflection of streamlines across the perturbed shock. Since for ordinary gaseous detonations the density across the shock is very large, the instability related to this pure hydrodynamic effect is very strong. An exact dispersion relation is derived and it is shown that the instability of square-wave detonations is described by a differential-difference equation of advanced type, which has a set of an infinite number of unstable solution branches with the growth rate increasing with the number of modes. The nonlinear solution shows that the discontinuity develops from smooth initial data within a finite time. Therefore the results obtained from square-wave detonations cannot be applied directly to describe the observed instability patterns. By carrying out a Taylor development of the terms with advanced time, a dispersion relation of a polynomial form is obtained and the high-frequency instability is eliminated. On the basis of the linear results with a regular reaction model, a phenomenological nonlinear equation of the fourth order for the position of the detonation surface is obtained by carrying out a Taylor series development. One-dimensional numerical solution of the phenomenological nonlinear equation shows typical nonlinear phenomena such as periodic oscillation, period doubling and dynamic quenching.