Characterization of an improved 1-3 piezoelectric composite by simulation and experiment

Introduction

1-3 piezoelectric composites are composed of 1D connected piezoelectric pillars (piezoelectric phase) that are arranged in 3D connected polymers (polymer phase). Furthermore, these composites have a high electromechanical coupling factor, wide broadband, and stable mechanics and temperature characteristics. Thus, 1-3 piezoelectric composites have been widely utilized to enhance the performance of underwater and ultrasound transducers. The polymer material of 1-3 piezoelectric composites is generally epoxy resin. Given the high Young’s modulus of epoxy resin, the piezoceramic/epoxy resin 1-3 composites can only reach an electromechanical coupling factor of about 0.6. Several local and international experts have focused on improving the electromechanical coupling factor of 1-3 piezoelectric composites. For example, Li et al (1, 2) prepared 1-3 piezoelectric composites by using a single crystal as the piezoelectric phase material and the electromechanical coupling factor of the composites was 0.7. However, the high cost and unstable performance of piezoelectric single crystal inhibit its application range. Some researchers have prepared 1-3 piezoelectric composites with other flexible polymers as the polymer material and with an improved electromechanical coupling factor (about 0.68) (3, 4). However, if Young’s modulus of polymer is too low, composite easily generates bending deformation. This disadvantage seriously affects the performance of the transducer. Considering the above reasons, we prepared an improved 1-3 piezoelectric composite with epoxy resin and silicon rubber as the polymer material. This composite not only can achieve a good decoupling effect to maintain a high electromechanical coupling factor but also can prevent bending deformation.

Structure of the improved 1-3 piezoelectric composite

Figure 1 shows the structure of the improved 1-3 piezoelectric composite. It is composed of 1D connected piezoceramic pillars, 3D connected polymers (epoxy resin and silicon rubber), and electrodes. In Figure 1a, b, t, and t_s represent the piezoelectric pillar width, polymer width, composite thickness, and silicon rubber thickness, respectively. In this paper, the piezoelectric pillar arrays of the improved composite will exceed 10 columns × 10 rows. The piezoelectric phase in the improved composite percentage v_c can be expressed as a²/(a+b)², and that of the silicon rubber in the polymer phase percentage v_s is t_s/t.

Finite element simulation analysis

A finite element model composed of 1D connected piezoelectric pillars and 3D connected polymers for the improved 1-3 piezoelectric composite was established by ANSYS (Fig. 2). In this model, thin electrodes of the composite were ignored and the piezoelectric pillar arrays were 16 columns × 16 rows. PZT-5 was chosen as the piezoelectric phase material, while 618 epoxy resin and 704 silicon rubber were chosen as the polymer phase material. The PZT-5 and polymer parameters are shown in Tables I and II respectively. Solid5 (3D coupling field solid element) and solid45 (3D solid structure element) were used as the element type of PZT-5 and polymer, respectively. Then, a = 1 mm, b = 0.56 mm, and v_c = 0.41 were set. The composite thickness t was selected as 5 mm.

To study the relationship of the composite performance to silicon rubber volume percentage v_s, the silicon rubber thickness t_s was varied from 0 mm to 5 mm (correspondingly, v_s from 0 to 1). The voltage at the top surface of the composite was set to 1 V, while the voltage of the bottom surface was set to 0 V. Harmonic response analysis was chosen and damping coefficient was set to 0.02 in the simulation. Frequency range and solving method was set to 225 kHz-400 kHz and full, respectively. Through the harmonic response analysis, the vibration modes were obtained and the charges (Q) of surface were extracted. The admittance Y was calculated by Y = 2jπfQ/V (5). In this formula, j, f and V refer to imaginary unit, frequency and the voltage (where V = 1V), respectively. The admittance curves of the composite in different values of v_s were obtained. Figure 3 shows modulus and phase angle of admittance of the composite (v_s = 0.5). Then, the resonant frequency f_s and parallel resonant frequency f_p were determined through the admittance curves. The resonant frequency f_s is the frequency corresponding to the maximum modulus of admittance, as shown in Figure 3A. In Figure 3B there are two frequency points to meet phase angle = 0°. The lower frequency is also f_s, and the higher frequency is parallel resonant frequency f_p.

The electromechanical coupling factor k_t was calculated using Equation 1, and the sound velocity v was calculated using Equation 2. The equivalent density ρ of the composite was determined using Equation 3, and the characteristic impedance z was computed using Equation 4 (6). On the basis of the results of finite element simulation, f_s–v_s, k_t–v_s, v–v_s, and z–v_s curves were plotted, as shown in Figure 4. In Figure 4v_s = 0 refers to the samples filled with only epoxy resin, and v_s = 1 refers to the samples filled with only silicon rubber.

Where ρ₁ = v_c ρ_c + (1-v_c) ρ_e, ρ₂ = v_c ρ_c + (1 - v_c) ρ_s, ρ_c, ρ_e, and ρ_s refer to the piezoelectric ceramic density, epoxy resin density and silicon rubber density, respectively.

Figure 4A shows that the resonant frequency decreased markedly with increasing v_s. This finding can be attributed to the fact that the Young’s modulus of silicon rubber is less than that of epoxy resin. Thus, the stiffness of the composite gradually declined with increasing v_s. Furthermore, the resonant frequency decreased with increasing the stiffness of the composite. Consequently, the greater v_s, the lower the resonant frequency is.

Figure 4B shows that the electromechanical coupling factor k_t increased with increasing v_s. This result indicates that the greater v_s, the better the decoupling effect is. However, a certain amount of epoxy resin must be retained as polymer of the composite to prevent bending deformation.

Figure 4C shows that the sound velocity v decreased before v_s increased to 1. This finding can be attributed to the fact that the sound velocity of silicon rubber is less than that of epoxy resin. Therefore, the greater v_s, the lower the sound velocity is. However, when v_s increased to 1, the sound velocity of the composite increased instead. The reasons of the abnormality are as follows: when v_s is 0 or 1, the composite is the traditional 1-3 piezoelectric composite, and its node plane (the plane of displacement = 0) is in t/2 position (Fig. 5B). However, when v_s is 0-1, silicon rubber and epoxy resin exist in the composite simultaneously, and the node plane of the composite does not lie in t/2 position but in the side of the near epoxy resin (Fig. 5AC). So, the parallel resonant frequency f_p exhibited abnormality because it depends on node position. According to Equation (2) (v = 2f_pt), the sound velocity v also exhibited abnormality.

Figure 4D shows that the characteristic impedance z decreased before v_s increased to 1. As shown in Equation 4, the characteristic impedance z is the product of equivalent density ρ and sound velocity v. Both the equivalent density and sound velocity decreased with increasing v_s. Therefore, the characteristic impedance also decreased. However, when v_s was increased to 1, the characteristic impedance of the composite increased instead. These reasons are similar to those that caused abnormality in the sound velocity v.

To analyze the bending deformation of the improved 1-3 piezoelectric composite, a 15 kPa pressure was applied to the middle position of top surface, and rigid boundary condition was applied to two sides of the improved 1-3 piezoelectric composite, as shown in Figure 6A. The displacement deformation graphs were obtained by using the static analysis of ANSYS, as shown in Figure 6B. The maximum displacement deformation values s_m in different v_s are shown in Figure 7.

Figure 7 shows that when v_s is 0-0.8, the maximum deformations are quite small (lower than 3 μm), but when v_s approaches 1, the deformations rapidly increase. So, v_s must be less than 0.8 to prevent bending problem. Considering electromechanical coupling factor and characteristic impedance, the best v_s should be selected in 0.5-0.8 range.

Experiment and test

The improved composite samples were prepared by cutting and filling methods. Figure 8 shows the preparation technology of the improved 1-3 piezoelectric composite.

The preparation technology steps are as follows:

On the basis of the above preparation technology process, the composite samples were fabricated, and the samples were measured using Agilent 4294A precise impedance analyzer.

On the basis of the test results, f_s–v_s, k_t–v_s, v–v_s, and z–v_s curves were plotted and compared with finite element simulation (Fig. 9). In Figure 9v_s = 0 refers to the samples filled with only epoxy resin, and v_s = 1 refers to the samples filled with only silicon rubber. It can be seen from Figure 9 that the improved 1-3 composite showed a higher electromechanical coupling factor and lower characteristic impedance than the traditional piezoceramic/epoxy resin 1-3 composite. For example, when v_s = 0.8, the electromechanical coupling factor of the improved composite can reach 0.67, and the characteristic impedance can decline to 13 MRayl. The experimental results were in general agreement with the simulation results. However, most experimental values were higher than the simulation results, and the abnormality of the test results was also more obvious than that of the simulation.

Discussion

The research shows that the improved composite has a higher electromechanical coupling factor (can reach 0.67) and meanwhile can reduce bending deformation. Besides, the improved composite has a lower characteristic impedance (can decline to 13 MRayl). While traditional piezoceramic/epoxy resin 1-3 composite can only reach an electromechanical coupling factor of about 0.6, and generally its characteristic impedance is not less than 14 MRayl. Comparison of simulation and experiment shows that most experimental values were higher than the simulation results, and the abnormality of the test results was also more obvious than that of the simulation. These findings may be attributed to slight difference in the material parameters of simulation and experiment.