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采用三维有限元方法计算了不同形状因子的γ’强化相在基体为γ相的Ni基高温合金中引起的弹性应变能密度,进而建立了以形状因子为变量的弹性应变能密度表达式。通过最小化γ’强化相引起的弹性应变能和界面能之和,得到了γ’强化相的平衡形状与其特征半径之间的函数关系。本文的分析很好地解释了文献报道的Ni基高温合金中γ’强化相形状演变的实验规律,结果表明:通过三维有限元法结合强化相粒子形状近似法计算模型,可以给出复杂情况下强化相粒子引起的弹性应变能密度的表达式,并有效地应用于材料共格相变的热力学研究。
The three-dimensional finite element method was used to calculate the elastic strain energy density induced by γ ’strengthening phases with different shape factors in the Ni-base superalloy whose γ phase was matrix phase. Then, the elastic strain energy density expression with the shape factor as the variable was established. By minimizing the sum of the elastic strain energy and the interfacial energy due to the γ ’strengthening phase, a functional relationship between the equilibrium shape of the γ’ strengthening phase and its characteristic radius is obtained. The analysis of this paper is a good explanation of the experimental rule of the shape evolution of γ ’strengthening phase in Ni-base superalloy reported in the literature. The results show that by using the three-dimensional finite element method combined with the model of the enhanced phase particle shape approximation method, The expression of elastic strain energy density caused by phase particles is enhanced and effectively applied to the thermodynamics study of coherent phase transition of materials.