相场方法模拟硬质颗粒对两相晶粒长大的影响

将多序参量的两相相场模型推广到含硬质颗粒的三相体系，建立包含第三相硬质颗粒的两相晶粒长大的热力学模型，运用扩散界面场变量动力学方程组模拟含第三相硬质颗粒的两相晶粒长大过程，研究两相晶粒长大的钉扎特点和晶粒长大的生长指数。结果显示，弥散分布的硬质第三相颗粒对基体组织的晶界具有钉扎作用，当第三相颗粒体积分数较大时，晶粒半径很快趋于稳定值。该模型能够反映第三相粒子对两相晶粒长大过程的影响，与现有的相关理论吻合。

Phase-field Method Simulation of the Grain Growth with Hard Particle

Extending a phase field model with multi-order parameters to the hard particles with three-phase system, we establish a thermodynamic model which contains the third phase hard particles of two-phase grain growth. Using the interface variables dynamics equations to simulate two-phase grain growth process with third phase particles,we study the two-phase pinning grain growth characteristics and grain growth index. The results show that the disperse distribution of the third phase hard particles has pinning effect on the matrix of grain boundaries. When the third- phase particles volume fraction is large enough, the grain radius will tend to stable quickly. The model can reflect the effect of third-phase particles on grain growth of two-phase process, which coincide with the existing theory.