一种适用于相干应力三相固体的计算有效和机械相容的多相场模型
A computationally efficient and mechanically compatible multi-phase-field model applied to coherently stressed three-phase solids
摘要：
工程合金通常表现出多相微观结构。对于模拟固态相变过程中的微观结构演变，CALPHAD引导的多相场模型与细观力学耦合已被证明是一种可靠的模拟工具。然而，它们的效率和精度仍然取决于均匀化方案用于插值的弹性性能在界面区域。在本文中，我们提出了一个相场模型的多相和多组分固体使用部分秩一均匀化计划，强制执行静态和运动学的界面区域的兼容性。为此，我们首先将秩一均匀化方案扩展到多相系统。此外，为了提高计算效率，我们解析求解了线弹性三相固体的静态相容性方程。为了定量的准确性，耦合技术是用来提取的先决条件的热力学和动力学性质的CALPHAD数据库。该模型是在一个开源的有限元框架数值求解。作为数值模拟的应用，对两种弹性应力下含金属间化合物的三相合金Ni-Al和Al-Cr-Ni的微观组织进行了模拟。模型的准确性进行了验证，对平面和同心环接口解析获得的解决方案。我们表明，模拟结果保持不变，不同的界面宽度。除了一个模拟，所有的情况下显示更好的或几乎相等的收敛性相比，使用部分秩一计划的Voigt-Taylor计划。
英文摘要：
Engineering alloys generally exhibit multi-phase microstructures. For simulating their microstructure evolution during solid-state phase transformation, CALPHAD-guided multi-phase-field models coupled with micro-mechanics have proven to be a reliable simulation tool. Nevertheless, their efficiency and accuracy still depend on the homogenization scheme used to interpolate the elastic properties in the interfacial regions. In this paper, we present a phase-field model for multi-phase and multi-component solids using a partial rank-one homogenization scheme that enforces static and kinematic compatibilities in the interfacial regions. To this end, we first extend the rank-one homogenization scheme to multi-phase systems. Moreover, for computational efficiency, we analytically solve the static compatibility equations for linear elastic three-phase solids. For quantitative accuracy, a coupling technique is used to extract the prerequisite thermodynamic and kinetic properties from CALPHAD databases. The model is solved numerically in an open source finite-element framework. As numerical applications, the microstructure of two elastically stressed intermetallic-containing three-phase alloys: Ni-Al and Al-Cr-Ni, are simulated. The accuracy of the model is verified against analytically obtained solutions for planar and concentric ring interfaces. We show that the simulation results remain unaltered with varying interface width. Except for one simulation, all cases show better or nearly equal convergence using the partial rank-one scheme compared to the Voigt-Taylor scheme.
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