建立了新的模拟两相多孔材料烧结过程的相场模型, 采用Cahn-Hillard方程和Allen-Cahn方程来控制相对密度场和长程取向场的变化, 通过分析相场方程的特点, 对模型进行数学处理得到一组相场模型的唯象系数, 建立了原子扩散系数与晶界扩散、表面扩散和体积扩散的函数关系式. 模拟结果表明: 该模型能够有效地模拟两相多孔材料的烧结过程, 通过分析模拟图像可以很好地观察到两相多孔材料的微观组织演化过程.

Sintering is a process of bonding between solid particles which typically occurs under high temperature. Currently, simulation of sintering process is mainly concentrated on the single–phase polycrystalline materials. As there are a lot of materials which are biphasic porous system, it is of practical significance to simulate the microstructural evolution of biphasic porous system during sintering process. In this work, a new phase field model is established to simulate sintering process in biphasic porous system. The evolution of the component is governed by Cahn–Hilliard equation, while the orientation field by the time–dependent Allen–Cahn equation. A function is established to describe the relationship between atomic diffusion coefficient and grain boundary diffusion, surface diffusion and volume diffusion. A group of phenomenological coefficients are obtained by analyzing the characteristic of the phase–field model. The simulation results show that the new phase–field model can effectively simulate the sintering process in biphasic porous system. The formation and growth of sintering neck, the seal spheroidization and disappearance of pores as well as the mergence and growth of grains are observed during simulation. The sintering necks between the parent phase and the second phase grow very fast at the early stage of simulation, while at the late stage, because of the pinning effect, the growth rate of the sintering neck slows down obviously, pores become isolated by the grains, and its shape change from concave to convex, the relative small pores are eliminated, which leads to densification. As the sintering proceeds, the grain size of the second phase gradually decreases and the parent–phase grains are wrapped by the second–phase grains. Because of the pinning effect of the second phase, the migration rate of the grain boundary of the parent phase is restrained. The evolution course of pores depends largely on the interaction between the second phase and the pores.  The evolution rate of pores is quantitatively compared between the biphasic porous system and the single–phase system. In the case of biphasic porous system, the evolution rate of pores is slower than that in single–phase system. The simulating growth exponents of the parent phase are calculated with different volume fractions of the second phase. As the volume fractions of the second phase increase from 15% to 25%, the grain growth exponent changes from 2.9 to 3.4.