中文摘要：

通过构建局域自由能函数，并考虑晶界对析出过程的影响，建立了低体积分数相析出过程的相场模型，模拟了溶质体积分数为2％的体系中第二相在晶界和晶内析出及其演变过程。结果表明，在相同相场步条件下，晶粒空间矢量平方和的幂指数项（∑ηi^2）^μ决定了第二相在晶界和晶内的析出比例；晶内析出相的比例随μ值的减小而增加；析出相尺寸的大小取决于浓度场梯度能系数κφ值的高低；μ=1或较大κφ时，析出相全部集中于晶界上。

英文摘要：

The phase field model for predicting second-phase precipitation was established based on constructing local free energy function and considering the effect of grain boundary on the second phase precipitation process. The numerical simulation of the second-phase precipitation inside the grain and on the grain boundary was carried out in the system with the solute volume fraction of 2%. The results show that the proportion of second-phase precipitates inside grain and on the grain boundary depends on the term （∑ηi^2）^μ in which ηi and μ are orientation field variable and exponent relative to the second phase profile, respectively. The proportion of the precipitates inside grain increases with decreasing μ and the size of the second phase precipitate depends on the gradient energy coefficient κφ at the same phase field step. All the precipitates appear on the grain boundary under μ=l or a larger κφ value condition.