二相粒子钉扎晶界的行为研究

On the Interaction Between Grain Boundary and Immobile Second-phase Particle

基于系统能量最小原理,研究了晶界与二相粒子之间的相互作用,推导了动态条件下的晶界方程,并从功能转换的角度求解出了钉扎力的数学公式,进而建立了更为符合实际的动态的二相粒子与晶界相互作用的物理模型。结果表明,当晶界通过二相粒子的中心平面时,单一二相粒子对单一晶界施以最大的作用力2πrγ;析出物的尺寸控制在60 nm为宜。模拟结果预测了晶粒停止长大所需要的临界二相粒子个数。模型结果与已有的实验结果吻合得非常好。

On the basis of the minimum energy principle of system, this paper deals with the interaction problem between the second-phase particle and grain boundary and an expression describing the moving grain boundary has been derived. Also, a new mathematical formula, which expresses the effect of the second-phase particle on grain boundary, has been obtained as viewed from the conversion between energy and work. Hence, a new physical model of Zener pinning has been developed. The model results demonstrate that the maximum pinning force on grain boundary exerted by a single precipitate is 2πry when the grain boundary passes the central plane of the second-phase particle and the ideal precipitate size is 60 nm approximately. Also, the critical number of the second-phase particles can be obtained from the model. And, theoretical prediction of the critical number of precipitates is in good agreement with values determined by Gladman experimentally.