Electromechanical Behavior of a Doped Barium Titanate Piezoceramic Under Mechanical Stress: Modeling and Comparison With Experimental Measurements

Barium titanate (BaTiO₃) is being studied extensively to replace lead-based piezoelectric materials, such as the lead zirconate titanate (PZT) family, due to lead toxicity. As a result, researchers are turning to materials such as BaTiO₃ and seek to improve their properties with the use of dopants. In many applications such as Tonpilz transducers, piezoelectric materials undergo mechanical stress which is important to control and predict their electro-acoustic performance. Thus, this study deals with a fully tensorial model that allows us to simulate the behaviors of electrical displacements and elastic strains under mechanical stress. The simulated curves are compared with the experimental ones obtained for a doped BaTiO₃ composition and the hysteretic curves of strains are in good agreement both for the unpoled and poled samples. The values and global behavior of the theoretical electrical displacement are also found to be in fair agreement, though some discrepancies are observed. The optimized values of the physical parameters, such as d₃₃, are discussed and improvements both of the model and the optimization procedure are finally proposed to better predict the mechanical behavior of the doped BaTiO₃ piezoceramics.