Phase Field Simulation of Dielectric Breakdown in Ferroelectric Composites
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摘要: 以铁电聚合物为基体和铁电陶瓷为填充物的铁电复合材料，克服了单相铁电材料大极化强度与高击穿强度二者不可兼得的关系，表现出优异的压电、储能等多场耦合性能，受到人们越来越多的关注. 然而铁电复合材料界面的应力和电场集中会引发材料的力电耦合失效，其中介电击穿是铁电复合材料的主要失效方式之一. 因此，理解陶瓷填充物对铁电复合材料介电击穿性能的影响，对其在高性能能量转换与存储器件中的应用至关重要. 该文针对铁电复合材料的多场耦合失效问题，构建包含极化、应变和击穿序参量的相场模型，研究了铁电复合材料在电载荷作用下的介电击穿行为. 相场模拟结果表明，随着陶瓷填充物颗粒尺寸的增大，电击穿路径会避开陶瓷颗粒，同时材料内部的最大电场会逐渐增大，从而导致复合材料的击穿强度会越来越低. 此外，模拟结果还发现介电击穿强度与填充物颗粒尺寸之间呈现出非线性关系. 该文研究结果为铁电复合材料介电击穿强度的设计提供了一定的理论基础.Abstract: The ferroelectric composite material with ferroelectric polymer as the matrix and ferroelectric ceramic as the filler overcomes the inverted relationship between high polarization strength and high breakdown strength of single-phase ferroelectric materials, exhibits excellent multi-field coupling properties such as piezoelectricity and energy storage. Recently, it draws increasing attention. However, the stress and electric field concentration at the interface of ferroelectric composite materials can cause the electromechanical coupling failure of the materials, and the dielectric breakdown is one of the main failure modes of ferroelectric composite materials. Therefore, understanding the effects of ceramic fillers on the dielectric breakdown performances of ferroelectric composite materials is crucial for their application in high-performance energy conversion and storage devices. Aimed at the multi-field coupling failure of ferroelectric composite materials, a phase field model involving polarization, strain, and breakdown order parameters was established to study the dielectric breakdown behavior of ferroelectric composite materials under electrical loads. The phase field simulation results indicate that, as the particle size of the ceramic filler increases, the electrical breakdown path will avoid the ceramic particles, and the maximum electric field inside the material will gradually increase, resulting in a lower breakdown strength of the composite material. In addition, a nonlinear relationship exists between the dielectric breakdown strength and the particle size of the filler. The work provides a certain theoretical basis for the design of dielectric breakdown strength of ferroelectric composite materials.
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图 2 包含初始击穿相的铁电复合材料PVDF-BTO示意图，沿x正方向施加电场
Figure 2. Schematic diagram of ferroelectric composite PVDF-BTO containing an initial breakdown phase with an electric field applied along the x-positive direction
图 3 在外加电场作用下、t*=0时刻的电场分布
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 3. Electric field distributions at moment t*=0 under the applied electric field
图 4 在外加电场作用下，t*=0时，复合材料相关特性
Figure 4. Under an applied electric field, the related characteristics of the composite at t*=0
图 5 在x方向240 kV/mm外加电场作用下的击穿路径随时间演化的瞬时状态
Figure 5. Transient states of the breakdown paths evolving with time under an applied electric field of 240 kV/mm in the x-direction
图 6 在外加电场作用下电场Ex随时间演化的瞬时状态
Figure 6. Transient states of electric field Ex evolving with time under an applied electric field
图 7 在外加电场作用下电场Ey随时间演化的瞬时状态
Figure 7. Transient states of electric field Ey evolving with time under an applied electric field
图 8 陶瓷颗粒尺寸对铁电复合材料击穿强度的影响
Figure 8. Effects of ceramic particle sizes on breakdown strengths of ferroelectric composites
A1 PVDF的材料参数
A1. The material parameters of the PVDF
Landau coefficient gradient energy coefficient of polarization α1/(J·m/C2) -1.412(T-108)×107 G11/(J·m3/C2) 5×10-7 α11/(J·m5/C4) 1.842×1011 G12/(J·m3/C2) 0 α12/(J·m5/C4) 3.684×1011 G44/(J·m3/C2) 2.5×10-7 α111/(J·m9/C6) 2.585×1013 G′44/(J·m3/C2) 2.5×10-7 α112/(J·m9/C6) 7.775×1013 electrostrictive coefficient elastic constant q11/(J·m/C2) -8.52×109 C11/(J/m3) 3.41×109 q12/(J·m/C2) -4.20×109 C12/(J/m3) 1.68×109 q44/(J·m/C2) 0 C44/(J/m3) 8.65×109 breakdown strength gradient energy coefficient of breakdown Eb/(kV/mm) 370 Γ/(J/m) 1×10-10 gradient energy coefficient of breakdown kw 20 kc 0.1 kf 0.1 
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A2 BaTiO3的材料参数
A2. The material parameters of the BaTiO3
Landau coefficient gradient energy coefficient of polarization α1/(m2·N/C2) 4.124/(T-115)×105 G11/(m4·N/C2) 2.2×10-11 α11/(m6·N/C4) -2.097×108 G12/(m4·N/C2) 0 α12/(m6·N/C4) 7.974×108 G44/(m4·N/C2) 1.1×10-11 α111/(m10·N/C6) 1.294×109 G′44/(m4·N/C2) 1.1×10-11 α112/(m10·N/C6) -1.950×109 α1111/(m14·N/C8) 3.863×1010 α1112/(m14·N/C8) 2.539×1010 α1122/(m14·N/C8) 1.637×1010 electrostrictive coefficient elastic constant q11/(m4/C2) 1.13×1010 C11/(N/m2) 1.78×1011 q12/(m4/C2) 2.86×108 C12/(N/m2) 9.60×1010 q44/(m4/C2) 7.08×109 C44/(N/m2) 1.22×1011 breakdown strength gradient energy coefficient of breakdown Eb/(kV/mm) 50 Γ/(J/m) 1×10-10 gradient energy coefficient of breakdown kc 0.1 kf 0.1
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