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

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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.