Phase-field lattice-Boltzmann investigation of dendritic evolution under different flow modes

ABSTRACT

Numerical modelling offers an effective method to investigate the effect of convection on dendritic growth; however, the current numerical approach to modelling convection behaviour is simplified, e.g. only simulating a shear flow by setting a constant inlet velocity and a zero-velocity-gradient outlet boundary condition. In this work, based on a phase-field lattice-Boltzmann approach, the effect of various flow modes on dendritic growth is investigated by introducing an external force term to induce flow. Numerical tests (2-D and 3-D) validate that the results according to the force-induced flow agree well with those by the velocity-imposed flow. Intricate convection effects under complex boundary conditions are discussed in detail. Furthermore, this force-induced flow mode allows additional freedom by eliminating the restriction on the initial position of the nuclei, which provides new ways to the microstructure modelling under complex convection.     

三维枝晶生长的相场法数值模拟研究

基于薄界面限制、耦合界面能各向异性的相场模型,采用动态计算区域的加速算法,对纯物质的三维枝晶生长进行了定量模拟,真实再现了枝晶的生长过程.对枝晶尖端进行了剖切分析,表明主枝截面上各向异性没有主枝方向各向异性明显;对枝晶尖端生长速度、尖端半径、Peclet数及临界稳定性参数σ^*进行模拟计算,并与同条件下报道值进行了对比分析,两者符合良好,并得到了与结晶理论相一致的枝晶生长规律,证实了相场方法模拟三维空间枝晶生长可行有效. 关键词： 相场方法 枝晶生长 微观组织 三维数值模拟     

基于相场模型的金属微波烧结演化机制分析及同步辐射断层扫描实验验证

为了探索不同种类金属材料的微波烧结机制,本文针对钛和铝两种具有不同电磁学特性的金属材料,分析了微波与金属微粒的相互作用。依据经典的麦克斯韦方程,金属表面产生电子涡流和趋肤效应。由P.Mishra和K.I.Rybakov等提出的金属在微波中的加热效率理论,推导出钛金属表面的热效应明显高于铝。因为电子涡流在磁场中产生指向颗粒内部的洛伦兹力这一微波非热效应,阻碍了内部物质向外的扩散,且铝的感应涡流大于钛,故其向心力更大。由于微波的热效应和非热效应导致物质扩散的驱动力不同,得出"钛的微波烧结速率明显大于铝"这一区别于常规烧结的结论。将获得的分析结果引入相场数值模拟,改变相场模型中控制演化过程中的表面和体扩散变量,获得不同的模拟结果,定量分析了烧结颈等微观结构参数随模拟时间的演化曲线。结合同步辐射断层扫描(SR-CT)技术获得的金属在微波烧结过程中的实验参数,与理论分析和模拟结果相吻合,从而验证了分析和模拟的正确性和可行性。上述结果可为研究金属在微波烧结过程中的演化机制提供支持。     

Some Convergence Results for a Class of Nonlinear Phase-Field Evolution Equations

Two heat diffusion problems in the framework of the parabolic phase-field model are presented. The first problem is related to a single isotropic fluid and the other describes the heat transmission between two different substances in contact. Some known existence and uniqueness results are briefly recalled. Then, an asymptotic analysis of both situations is carried out as the kinetic equation collapses to a temperature-phase relation of Stefan type, in the first case in the whole material, and in the second in only one of the substances. In both cases, a convergence result for the solutions is proved. The second problem shows some more mathematical difficulties that are due to the presence of nontrivial terms on the common boundary. In order to control the latter, some tools are used from the Γ-convergence theory for convex functionals.     

Dynamic scaling behaviour of late-stage phase separation in Ni75AlxV25-x alloys

The dynamic scaling behaviour of late-stage phase separation and coarsening mechanisms of L12 and D022 in Ni75AlxV25-x （3 ≤ x ≤ 10, at.%） alloys are studied using the microscopic phase-field dynamic model. The microelaso ticity field is incorporated into the diffusion dynamic model. The results show the morphology and coarsening dynamics being greatly changed by the elastic interactions among different precipitates, the particles aligning along the dominant directions, the average domain size （ADS） of L12 and D022 deviating from the exponent of temporal power-law, and the growth slowing down due to the increasing of elastic interactions. The dynamic scaling regime of late-stage coarsening of the precipitates is attained. Thus the scaling behaviour of structure function is also applicable for elastic interaction systems. It is also found that the variations of ADS and scaling function depend on the volume fraction of precipitates.     

基于COMSOL的脆性材料相场断裂模型

相场法通过一系列微分方程描述材料断裂过程,避免了繁琐的裂纹面追踪,在模拟裂纹的萌生、扩展和分叉等方面具有优势。介绍了基于相场法的脆性材料断裂模型,给出了脆性材料断裂问题相场法控制方程的推导过程,提出了基于分步迭代法在COMSOL中实现脆性材料相场断裂模型的方法。再现了脆性材料单元模型和单边缺口平板受拉及受剪作用下的开裂过程,模拟的裂纹扩展路径与已有文献的结果相近,验证了程序的合理性。针对脆性材料相场断裂模型包含的诸多参数,采用Morris法对影响荷载-位移关系的脆性材料断裂模型参数进行了全局敏感性分析,结果表明,杨氏模量(E)、临界能量释放率(G_c)和位移增量(Δu_x)是影响模型荷载-位移关系输出结果的主要参数。基于COMSOL实现的相场断裂模型能够有效模拟脆性材料的裂纹萌生和扩展断裂过程,模型参数E,G_c和Δu_x对材料断裂性能的提升或模型参数反演效率的提高具有重要影响。