Strain hysteresis evolution of a (001)-oriented 5 × 5 × 2 mm3 cuboidal barium titanate (BaTiO3) single crystal during a combined electromechanical loading sequence in the non-variant  direction is investigated. The goal is to compare the strain behaviors of the BaTiO3 single crystal subjected to loading in the variant  and non-variant  directions. The simultaneous application of compressive stress and electric field in the  direction was achieved by machining the square cuboid crystal into a hexagonal prism and applying the loads parallel to the hexagonal side faces of the prism (i.e., perpendicular to the  and 45° to the  and  directions). The room temperature strain hystereses show that the maximum total electro strains produced from loading and measuring in the  and  directions (denoted as ε,max,RT and ε,max,RT, respectively, where the last term of the subscript describes the testing temperature) are 0.20% at 3.0 MPa and 0.45% at 2.7 MPa, respectively. The ratio between ε,max,RT and ε,max,RT is 0.44, which is in good agreement with the ratio, predicated by the analytical calculations. Factors which may influence the strain behavior, such as the bias stress level, depolarization field and switching coercivities, are examined by repeating the loading experiment at 55 °C. The strain hystereses measured at 55 °C show that ε,max,55 is 0.19% at 11.9 MPa — this maximum  strain is similar to the one obtained at room temperature, but is only achieved with a much larger bias stress. When the out-of-plane depolarization field and the in-plane switching coercivities are reduced at 55 °C, more domains are randomized in the in-plane variant directions during electric field unloading by the depolarization fields. Therefore, a much larger bias stress is required at 55 °C to switch a sufficient number of domains to the out-of-plane variant directions at small electric fields, which can then be switched back to the in-plane variant directions at high electric fields, producing strain in the  direction. The strain hysteresis study has revealed that the combined effect of the depolarization field and switching coercivity is a critical factor governing the strain behavior of the BaTiO3 single crystal.
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Strain Actuation Behavior of Barium Titanate Single Crystal Loaded Electromechanically in Non-Variant  Direction
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Shieh, J, Lin, Y, & Shu, Y. "Strain Actuation Behavior of Barium Titanate Single Crystal Loaded Electromechanically in Non-Variant  Direction." Proceedings of the ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Volume 2: Mechanics and Behavior of Active Materials; Integrated System Design and Implementation; Bio-Inspired Materials and Systems; Energy Harvesting. Stone Mountain, Georgia, USA. September 19–21, 2012. pp. 149-153. ASME. https://doi.org/10.1115/SMASIS2012-8034
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