Non-Linear Analysis of Ferroelastic/Ferroelectric Materials
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Abstract Ferroelectric/ferroelastic ceramics are used in a range of smart structure applications, such as actuators and sensors due to their electromechanical coupling properties. However, their inherent brittleness makes them susceptible to cracking and understanding their fracture is of prominent importance. A numerical study for a stationary, plane strain crack in a ferroelastic material is performed as part of this work. The stress and strain fields are analyzed using a constitutive law that accounts for the strain saturation, asymmetry in tension versus compression, Bauschinger effects, reverse switching, and remanent strain reorientation that can occur in these materials due to the non-proportional loading that arises near a crack tip. The far-field K-loading is applied using a numerical method developed for two-dimensional cracks allowing for the true infinite boundary conditions to be enforced. The J -integral is computed on various integration paths around the tip and the results are discussed in relation to energy release rate results for growing cracks and for stationary cracks in standard elastic–plastic materials. In addition to the fracture studies, we examine the far field electromechanical loading conditions that favor the formation, existence and evolution of stable needle domain array patterns, using a phase-field modeling approach. Such needle arrays are often seen in experimental imaging of ferroelectric single crystals, where periodic arrays of needle-shaped domains of a compatible polarization variant coexist with a homogeneous single domain parent variant. The infinite arrays of needles are modeled via a representative unit cell and the appropriate electrical and mechanical periodic boundary conditions. A theoretical investigation of the generalized loading conditions is carried out to determine the sets of averaged loading states that lead to stationary needle tip locations. The resulting boundary value problems are solved using a non-linear finite element method to determine the details of the needle shape as well as the field distributions around the needle tips.