Multi-scale modeling of fracture behavior of polycrystalline ferroelectric ceramics under monotonic and cyclic electromechanical loading

目前，功能铁电陶瓷在工程中广泛应用于传感器、执行器或智能复合材料的集成组件，在这些领域中，它们暴露于耦合的电气和机械在役载荷下。由于其脆性，裂纹可以在材料缺陷和局部应力集中处形成和扩展，从而损害此类器件的强度、寿命和可靠性。本项目旨在研究铁电材料和器件在电、机械和复合载荷作用下的断裂过程。加载可能发生单调或循环，导致脆性断裂或疲劳损伤。建立了多晶铁电陶瓷材料行为的多尺度模型，包括微观尺度上的畴过程和宏观尺度上的非线性机电连续体规律。这些模型是用有限元方法实现的。循环机电黏聚区单元用于模拟损伤、裂纹形成和裂纹扩展等破坏现象。利用这些模型对裂纹处的机电应力情况进行了研究，以期找到合适的断裂力学参数和失效准则。在宏观尺度上，构型力的概念更受青睐。在微观尺度上，再现了多晶的离散微观结构来模拟断裂过程区。这种方法允许将加工区的特性与宏观可测量的断裂韧性和裂纹参数相关联。重点研究了电场对加载状态和断裂韧性的影响。作为该项目的结果，将开发一种模拟工具，使铁电陶瓷的基本破坏过程、裂纹萌生和裂纹扩展的尺度桥接定量描述成为可能。最后，通过与现有断裂实验的对比，验证了模型的正确性。它们典型地应用于选定的铁电器件，如多层堆叠致动器或宏纤维复合材料。

Nowadays, functional ferroelectric ceramics are widespread applied in engineering as sensors, actuators, or integrated component of smart composites, where they are exposed to coupled electrical and mechanical in-service loads. Because of their brittleness, cracks can be formed and propagate at material defects and local stress concentrations, which impairs the strength, life time and reliability of such devices. This project is aiming at investigating the fracture processes in ferroelectric materials and devices under electrical, mechanical and combined loading. The loading may happen monotonic or cyclic, which leads either to brittle fracture or to fatigue damage. A multi-scale approach is developed to model the material behavior of polycrystalline ferroelectric ceramics, which comprises the domain processes on the micro-scale and the non-linear electromechanical continuum laws on the macro-scale. These models are implemented in a finite element method. Cyclic electromechanical cohesive zone elements are used to simulate failure phenomena like damage, crack formation and crack growth.By means of these models, the electromechanical stress situation at cracks is investigated in order to find suitable fracture mechanical parameters and failure criteria. At the macro-scale, the configurational force concept is favored. At the micro-scale, the discrete microstructure of the polycrystal is reproduced to model the fracture process zone. This approach allows to correlate the properties of the process zone with the macroscopically measureable fracture toughness and crack parameters. The focus lies on the influence of the electric field on the loading situation and fracture toughness.As a result of the project, a simulation tool will be developed, which enables a scale-bridging quantitative description of the elementary failure processes, crack initiation and crack propagation of ferroelectric ceramics.Finally, the elaborated models are verified by comparison with available fracture experiments. They are exemplarily applied to selected ferroelectric devices such as multi-layer stack actuators or macro-fiber-composites.