Structure of the stack actuators that were characterized. Alternate electrodes were connected to make the plates act in parallel to each other, allowing electric field E3 to induce axial strain ε33. The arrows indicate the volume average polarization of each plate.
Experimental arrangement that enables the application of stress and electric field while monitoring strain and electric displacement.
Electric displacement versus electric field for each preload stress showing the effect of electric field amplitude and stress amplitude on the minor hysteresis loop. E3 was cycled from (a) 0 to 0.5 MV/m, (b) 0 to 0.75 MV/m, (c) 0 to 1.0 MV/m, and (d) 0 to 1.5 MV/m. For all plots, the remnant polarization decreases as preload stress is increased.
Loss per cycle (Le) is plotted as a function of stress preload for each electric field amplitude. The error in the calculated loss was less than 2%.
The phase lag model expresses the measured dielectric loss in terms of the equivalent area within the ellipse shown.
Effective loss tangent as a function of stress preload for each electric field cycle amplitude. The error in the computed dielectric loss was based on the resolution of the instrumentation and found to be less than 2% for all values.
Domain states and field driven phase transformations in PMN-32% PT single crystals under  stress and electric field loading. (a) Crystal is in the rhombohedral (R) phase with  remnant polarization. (b) Increasing compressive stress induces a rhombohedral to orthorhombic (R-O) phase transformation while a subsequent increase in electric field (c) drives a reverse (O-R) transformation back to rhombohedral. Stress and electric field work against each other when driving phase transformations.
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