考虑极化涡旋结构大范围畴变的低维铁电材料断裂力学研究

Due to the great potential of application in data storage and micro-cooling, polarization vortices in low-dimensional ferroelectric materials have become a hot research issue in recent years. The fracture toughness of ferroelectric materials is very poor and fracture damage is a major failure mode that affects their reliable applications. The fracture process of low-dimensional ferroelectric materials is often accompanied by the occurrence of large-scale switching of polarization vortices. However, the fracture study on ferroelectric ceramics under large-scale switching has lagged obviously, the main reason of which is that: first, the accurate extraction of the crack-tip fracture parameters is extremely difficult due to the significant nonlinearity of ferroelectric ceramics; secondly, no fracture criterion is applicable to the large scale domain switching. On the basis of the assumption that the spontaneous polarization reaches a saturated state, this project aims to establish the DII-integral which can accurately extract the crack-tip field intensity factors, and adopt the crack-tip fracture parameters to develop a suitable fracture criterion for ferroelectrics under large-scale switching. Next, the “patched” finite element method which is effective in highly efficient simulation of the domain switching and crack propagations of ferroelectric materials will be developed on the basis of the phase field model. The successful implementation of this project will provide a theoretical basis and an efficient numerical analysis tool for the fracture mechanics study on ferroelectrics under large-scale domain switching. Finally, the switching of polarization vortex of low-dimensional ferroelectrics and its influences on fracture behaviors will be studied to reveal the fracture mechanism of low-dimensional ferroelectrics and to provide a design basis for the improvement of the reliability of nanoscale ferroelectric elements.

由于在数据存储、微制冷等方面的巨大应用潜力，低维铁电材料的极化涡旋结构成为近年来的研究热点。铁电材料的断裂韧性差，断裂破坏是影响其可靠应用的一个主要失效模式。低维铁电材料断裂过程常伴随极化涡旋结构大范围畴变的发生。然而，大范围畴变铁电材料断裂研究明显滞后，其主要原因在于：一是铁电材料显著非线性使得获取裂尖断裂参量极其困难；二是缺少适用于大范围畴变的断裂准则。本项目拟根据裂尖自发极化饱和假设，建立准确求解裂尖场强度因子的DII积分方法，并基于裂尖断裂参量提出适用于大范围畴变的断裂准则。然后，基于相场模型建立一套高效模拟铁电材料电畴演化及裂纹扩展的“补丁”有限元方法。本项目的成功实施将为大范围畴变铁电材料断裂力学研究提供理论基础和高效的数值分析工具。最后，研究低维铁电材料涡旋畴变及其对断裂行为的影响，揭示低维铁电材料断裂机制，为提高纳米铁电元件的可靠性提供了设计依据。

铁电材料的断裂韧性差，断裂破坏是影响其可靠应用的一个主要失效模式。低维铁电材料断裂过程常伴随大范围畴变的发生。然而，大范围畴变铁电材料断裂研究发展缓慢，其主要原因是铁电材料显著非线性使得获取裂尖断裂参量极其困难和缺少适用于大范围畴变的断裂准则。本项目首先建立了准确求解发生大范围畴变铁电材料裂尖应力和电位移强度因子的区域守恒积分（DII积分）方法，并考察了晶界、界面、裂纹面边界条件、界面残余应力等影响因素，对DII积分进行了发展与完善。接着，基于相场模型和扩展有限元方法建立了一套高效模拟铁电材料电畴演化及裂纹扩展的“补丁”有限元方法。采用“补丁”有限元方法对微纳米铁电材料电畴演化进行了仿真，给出了模型几何形状、晶粒取向、材料界面、裂纹面边界条件、载荷方式对铁电畴变行为及断裂性能的影响规律。然后，针对铁电材料表观断裂韧性的各向异性差异，提出了基于各向异性断裂韧性的断裂准则，并推导了构型力与裂纹尖端断裂参量的关系，建立了基于裂纹尖端断裂参量的各向异性断裂准则。最后，对PZT-5H铁电陶瓷试件进行了三点弯曲试验，归纳了极化方式、电场载荷、裂纹位置对铁电材料断裂行为的影响规律。

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