The Effect of the Doping Amount on Electroelastic Coupled-Wave Scattering and Dynamic Stress Concentration around Defects in BNT Doped FN Materials

Sodium bismuth titanate (Bi0.5Na0.5TiO3, BNT) has attracted much attention because of its excellent dielectric, piezoelectric and electromechanical properties. The microstructure of sodium bismuth titanate-doped ferrum niobium material (Bi0.5Na0.5TiO3 doped (Fe0.5Nb0.5)(4+), BNT-xFN) shows a triangle as its typical defect shape. Since piezoelectric devices usually operate under dynamic loads, they fail easily owing to dynamic stress concentration or dynamic fracture. Elastic waves can simulate many types of dynamic loads, and the dynamic stress concentration caused by an anti-plane shear wave is the basis for the calculation of the stress field strength factor of type III-dynamic fractures. In this study, the electroelastic coupled-wave diffraction and dynamic stress concentration of BNT-xFN materials with triangular defects under the incidence of anti-plane shear waves were studied. Maxwell equations are decoupled by auxiliary functions, and the analytical solutions of the elastic wave field and electric field are obtained. Based on the conformal mapping method, the triangle defect was mapped to the unit circle defect, and the dynamic stress concentration coefficient around the triangle defect was obtained by calculating the undetermined mode coefficients in the expression through boundary conditions. The numerical calculation shows that the size of the triangular hole, the frequency of the applied mechanical load, the incidence angle of mechanical load and the amount of FN doping have a great influence on the stress concentration of BNT-xFN materials.