Development of the bifurcation theory for the microstructure changes and an application to the superalloys

近年来，人们观察到在时效过程中析出相受弹性约束时的组织演化过程中出现了一些有趣的现象。典型的微观结构变化表现为：(1)颗粒减速成若干小颗粒。这些现象在理论上得到了我们提出的“形状分岔理论”的支持。在目前的研究中，我们对这些有趣的现象进行研究，以获得更广泛的实验数据，并提供更准确的理论背景。所得结果如下：(1) Ni-Al-Ti合金的颗粒粗化速度减慢。实验得到的粗化速率开始减慢时的平均粒径与基于形状分岔理论的计算值吻合较好。(2)在Al-Zn体系GP区粗化过程中，实验观察到生长速率的减速。在Cahn-Hilliard非线性扩散方程的基础上，通过计算机模拟研究了这种随时间变化的生长速率放缓。定量计算了含GP带的斑纹微结构中波长的时间演化。将形状分岔理论与计算机模拟的动力学分析相结合，将是研究复杂微观结构变化的静、动态稳定性的有效方法。(3)采用“成分梯度法”实验研究了Fe-Si二元合金有序/无序相变线上的形态组织变化。在A2/B2转变组分附近观察到精细的B2畴结构。

Several interesting phenomena during microstructure evolution with aging have recently been observed when precipitate particles are elastically constrained. The typical exmples of the extraordinally behavior of the microstructure changes are 1) the deceleration of particle into several small particle. These phenomena have theoretically supported by "Shape Bifurcation Theory", proposed by us. In the present research, we study these interesting phenomena to get more wide range of experimental data and also to give more accurate theoretical background.The results obtained are as follows ;(1) The deceleration of particle coarsening is observed in Ni-Al-Ti alloy. The average particle size experimentally obtained when the coarsening rate started to slow down shows quite good agreement with the calculated value based on the shape bifurcation theory.(2) In the coarsening of the GP zone in Al-Zn system, the deceleration of the growth rate is observed experimentally. This time dependent slow down of the growth rate is investigated by the computer simulation on the basis of the Cahn-Hilliard non-linear diffusion equation. The time evolution of the wave length in mottled microstructure containing GP zones is calculated quantitatively. The shape bifurcation theory combined with the kinetic analysis by means of the computer simulation will extremely be a useful method to investigate the static and dynamic stability of the complex microstructure changes.(3) The morphological microstructure changes across the order/disorder phase transition line in the Fe-Si binary alloy is experimentally studied by using the "composition gradient method". The fine B2 domain structure was observed at the vicinity of the A2/B2 transition composition.