A mathematical model to calculate the formation and growth of microporosity of aluminum alloys was developed by coupling with a probabilistic microstructure evolution model. The model incorporated various solidification phenomena such as grain structure evolution, solidification shrinkage, interdendritic fluid flow and formation and growth of pores during solidification processes. For microstructure evolution, the nucleation and growth of grains were modeled with a stochastic method that utilizes the results from a macro scale heat transfer model to determine the transition rules of grain evolution. Experiments were made to validate the proposed models. In fatigue life prediction, aluminum alloy castings with microporosity were treated as a kind of porous materials. Based the results of casting process simulation and stress-strain analysis, the fatigue life prediction of a sample casting with microporositis was presented.

To study the as-cast microstructure of ZG0Cr13Ni4Mo stainless steel that has been applied to turbine blade for the Three Gorges Project of Yangzi River, the physical and mathematical models of phase transformation of ZG0Cr13Ni4Mo were established based on multi-component alloy phase diagrams. Different nucleation, growth and diffusion models were used for the three stages of phase transformation. 2D and 3D microstructure of ZG0Cr13Ni4Mo stainless steel casting can be simulated. Two kinds of large sample castings were cast for experimental verification of simulation results. Then microstructure morphologies were observed by using optical microscope and SEM. The grain size of austenite, the number of martensite in austenite grains and the spacing of the lath martensite were measured. The simulation results were compared with experiments and they were in agreement.

Numerical simulation of solidification microstructure of aluminum alloy casting is studied by using a macro-micro coupled method. Different mesh sizes and time steps are used to calculate the macro temperature field and the crystal growth. The microstructure simulation is conducted by selecting a macro cell in the central region of the aluminum casting, and then the initial distribution of the temperature in the micro domain is obtained by interpolating the temperature of the macro cells near the selected cell. The crystal growth is controlled by the phase field equation, and the mathematical model also includes mix solution conservation equation and energy conservation equation to compute the distribution of the solution and the temperature. Noise is introduced to simulate the side branches. To describe the heterogeneous nucleation the Gaussian distribution is applied. The interface undercooling is considered to be the sum of thermal, solute and curvature effects. The 2-D dendritic growth morphology, the 3-D dendritic growth morphology and the crystal sizes in the region are simulated. The simulation results are compared with those obtained by experiments.

提出一种新的模拟铝合金枝晶生长的随机性方法，建立了简化的枝晶形状的物理与数学模型，并提出了一种形状函数来描述晶粒的外部轮廓。基于简化的晶粒形状，采用坐标变换技术来描述过冷液相中晶粒的生长过程及其对周围节点的捕获过程。根据上述思想，开发了等轴晶生长的模拟程序，并进行了二维计算。为了验证模拟结果，浇注了金属型和砂型试样。模拟结果表明，金属型铸造晶粒尺寸较小，砂型铸造的较大。模拟结果与金相观察结果相符。

建立了球铁稳定系和介稳定系共晶转变的数学模型，同时考虑了元素微观偏析和不同组织所产生潜热的影响。对球铁试样进行了定量金相实验分析，并与模拟结果进行了比较。结果表明，石墨球数量和尺寸以及碳化物体积分数的模拟结果与实验结果吻合。对白口共晶生长、碳化物形貌与凝固方式的关系进行了分析和讨论，表明凝固分析和模拟可以在一定程度上预测球铁中白口共晶的生长及最终碳化物的形貌。