基于部分秩一均匀化格式的弹性非均匀两相固体的高效定量相场模型
An efficient and quantitative phase-field model for elastically heterogeneous two-phase solids based on a partial rank-one homogenization scheme
摘要：
本文提出了一个有效的和定量的相场模型的弹性非均匀合金，确保两个力学相容性$\unicode{x2014}$静态和动态，结合界面区域内的化学平衡。我们的模型与现有的相场模型，要么违反静态相容性或界面化学平衡或计算成本高。为了提高计算效率，部分秩一均匀化（PRH）计划，以执行静态和运动学的界面相容性。此外，界面化学平衡是通过取代组成场与扩散势场作为模型的独立变量。通过模拟Ni-Al $γ^{\prime}/γ$和UO $_2$ /void两种二元双相合金的四种单粒子和一种多粒子情况，验证了该方法的性能。其准确性，然后调查对分析解决方案。对于单粒子$γ^{\prime}/γ$合金，我们发现，相场结果的准确性保持不受影响的平面和非平面的几何形状时，PRH计划。幸运的是，在UO $_2$ /void模拟中，尽管有很强的弹性异质性$\unicode{x2014}$，但空位相的杨氏模量与UO $_2$相的杨氏模量之比为$10^{-4}\unicode{x2014}$，我们发现PRH方案对于平面和非平面几何形状都比Voigt-Taylor方案（VTS）显示出更好的收敛性。然而，对于与$γ^{'}/γ$情况相同的界面宽度范围，这些模拟中的界面迁移显示出对界面宽度的依赖性。相反的$γ^{\prime}/γ$模拟，我们还发现，模拟的弹性场显示偏离的非平面UO $_2$ /空隙的情况下，使用PRH方案的解析解。
英文摘要：
This paper presents an efficient and quantitative phase-field model for elastically heterogeneous alloys that ensures the two mechanical compatibilities$\unicode{x2014}$static and kinematic, in conjunction with chemical equilibrium within the interfacial region. Our model contrasts with existing phase-field models that either violate static compatibility or interfacial chemical equilibrium or are computationally costly. For computational efficiency, the partial rank-one homogenization (PRH) scheme is employed to enforce both static and kinematic compatibilities at the interface. Moreover, interfacial chemical equilibrium is ensured by replacing the composition field with the diffusion potential field as the independent variable of the model. Its performance is demonstrated by simulating four single-particle and one multi-particle cases for two binary two-phase alloys: Ni-Al $γ^{\prime}/γ$ and UO$_2$/void. Its accuracy is then investigated against analytical solutions. For the single-particle $γ^{\prime}/γ$ alloy, we find that the accuracy of the phase-field results remains unaffected for both planar and non-planar geometries when the PRH scheme is employed. Fortuitously, in the UO$_2$/void simulations, despite a strong elastic heterogeneity$\unicode{x2014}$the ratio of Young's modulus of the void phase to that of the UO$_2$ phase is $10^{-4}\unicode{x2014}$we find that the PRH scheme shows significantly better convergence compared to the Voigt-Taylor scheme (VTS) for both planar and non-planar geometries. Nevertheless, for the same interface width range as in the $γ^{'}/γ$ case, the interface migration in these simulations shows dependence on interface width. Contrary to the $γ^{\prime}/γ$ simulations, we also find that the simulated elastic fields show deviations from the analytical solution in the non-planar UO$_2$/void case using the PRH scheme.
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