Nonlinear magnetoelectric effect in PZT/Terfenol-D nanobilayer on a substrate with surface stress

Abstract

Based on a linear piezoelectric constitutive relation and a nonlinear magnetostrictive constitutive relation, a nonlinear magnetoelectric (ME) effect model for lead zirconate titanate (PZT)/Terfenol-D nanobilayer on a substrate has been developed. In this study, the nonlinear ME coefficients at bending mode for two cases (without surface stress and with surface stress) are calculated by using Gurtin-Murdoch theory. The difference between two cases and the influence of residual surface tension are discussed. At the same time, the clamping effect of the substrate on ME effect is studied by altering the thickness ratio of the substrate and selecting different substrate materials. The influences of frequency of the magnetic field, PZT volume fraction on the ME effect are investigated, respectively. Finally, the dependence of ME effect on pre-stress is presented. The results show that for the nanobilayer, both the residual surface tension and surface stress have non-ignored effects on the ME effect. Besides, the resonant frequency of the nanobilayer is very low at the bending mode, which can be enhanced by increasing the thickness ratio of the substrate. Also, the substrate can weaken the ME effect due to the clamping effect, and a more soft substrate material should be selected for large ME effect. In addition, pre-stress plays an important role in the nonlinear ME coupling effect of the model developed.