Investigation of size effects in ferroic materials using phase field simulations

该项目通过相场模拟研究了铁材料的尺寸效应。在第一个资助期，研究重点是铁电材料。用数值方法研究了薄膜和裂纹尖端的尺寸效应。在薄膜中，显示了薄膜厚度对极化行为的影响。在薄膜中，电极材料的晶格失配导致活性材料中的机械负荷。证明了电极材料的这种影响。此外，建立了基于不变公式的三维模型，并在有限元法中实现。对铁电材料薄膜的模拟将继续进行。重点研究了电极与活性材料界面位错的影响。此外，这些方法将在下一个资助期扩展到铁磁性材料。研究的重点是通过材料界面的机械变形来耦合铁电相和铁磁相。为此目的，必须发展一种适当的有限元公式，在一个共同的模拟中考虑两个铁相。预计在铁电相和铁磁相中会出现复杂的相互作用域结构。这种相互作用将根据尺寸效应进行数值研究。

The project investigates size effects in ferroic materials by phase filed simulations. In the first funding period the research focus was onferroelectric materials. The size effects in thin films and at crack tips were investigated numerically. In thin films the effect of the film thickness on the poling behaviour was shown. In thin films the lattice mismatch of the electrode material leads to mechanical load in the active material. This influence of the electrode material was demonstrated. In addition, a three dimensional model, which is basedon an invariant formulation, was developed an implemented within the finite element method. The simulations of thin films of ferroelectric materials will be continued. Especially the effect of dislocations at the interface of the electrode and active material will be studied. Furthermore, the methods will be extended to ferromagnetic materials in the next funding period. The investigations focus on the coupling of the ferroelectric and ferromagnetic phase via mechanical deformations at the material interface. To this end a suitable finite element formulation has to be developed that accounts for both ferroic phases in a common simulation. It is anticipated that complex interacting domain structures appear in the ferroelectric as well as in the ferromagnetic phase. The interaction will be studied numerically with regard to size effects.