Electroelastic Coupled-Wave Scattering and Dynamic Stress Concentration of Triangular Defect Piezoceramics

Abstract

In this paper, a method to calculate the dynamic stress concentration around the triangular defect of piezoelectric material under electroelastic coupling is studied and applied to the promising barium calcium zirconate titanate. Firstly, the electroelastic governing equation is decomposed by decoupling technique, and the analytical solutions of elastic wave field and electric field are obtained by wave function expansion method. Then, the conformal transformation is used to simplify the triangle boundary into a circular boundary, and the corresponding modal coefficients are determined according to the simplified boundary conditions. Finally, the analytical solution of the dynamic stress concentration factor can be obtained according to the constitutive equation. Substitute the relevant material parameters of (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 and set different temperatures, Ce doping amount, and incident wave number for numerical simulation. The numerical results show that the incident wave number, piezoelectric properties, and the shape parameters and deflection angle of the triangular defect have a great influence on the dynamic stress around the defect, and some meaningful laws are summarized through analysis.

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

“…The anti-plane shear wave propagates in the direction of degrees to the x-axis in the infinite BNT-xFN material. In this case, the anti-plane dynamics equation and simplified Maxwell equation in BNT-xFN materials in a polar coordinate system are [23].…”

“…Meanwhile, the specific mechanical properties are characterized by the dynamic stress concentration factor (DSCF). [23] Firstly, the Maxwell equation and dynamic equation are used to establish the overall model, and then the elastic wave field and potential are described by the wave function expansion method. Among them, the specific coefficients of the diffraction field expansion of BNT-xFN can be determined by combining the boundary conditions.…”

“…The anti-plane shear wave propagates in the direction of degrees to the x-axis in the infinite BNT-xFN material. In this case, the anti-plane dynamics equation and simplified Maxwell equation in BNT-xFN materials in a polar coordinate system are [23]. (2) where c 44 is the elastic stiffness constant of BNT-xFN materials, e 15 is the piezoelectric stress constant, ε 11 is the dielectric constant and ϕ is the potential in materials.…”

“…In this paper, the electroelastic coupling wave is used to simulate the vibration of the BNT-xFN material in different working environments, and the typical triangular defect structure observed under the microscope is used to characterize the defect shape. Meanwhile, the specific mechanical properties are characterized by the dynamic stress concentration factor (DSCF) [23]. Firstly, the Maxwell equation and dynamic equation are used to establish the overall model, and then the elastic wave field and potential are described by the wave function expansion method.…”