Theoretical Models Of Microbridge Testing And Cantilever Testing For Low Dimensional Materials Properties

Due to the size and configuration of the low dimensional materials,they are not amenable to testing by conventional means. Therefore, various new mechanical characterization techniques have been developed, among which bending test(cantilever testing and micro-bridge testing) is one of the simplest and most important experimental methods. The traditional bending theory is mainly used to characterize the mechanical properties of purely elastic materials, which is not applicable for piezoelectric materials. What’s more, the traditional model cannot be used to deal with small scalar effect for the lack of intrinsic dimensional parameters in the model.Based on the traditional bending theory, we introduced piezoelectric effect and small scalar effect into the model, studied their effect on the low dimension cantilever beam and micro-bridge under coupled electro-mechanical loading. The thesis mainly contains the following parts:1. Piezoelectric effect in low dimensional cantilever and micro-bridge: Based on the three-dimensional transversely isotropic piezoelectric constitutive equations, the one-dimension constitutive equations for piezoelectric cantilever beam under both plane stress and plane strain state were proposed, which make it possible for us to compare the difference between the traditional result of cantilever beam and macro-bridge. At the same time, the equivalent Young’s modulus and equivalent bending stiffness are obtained based on the constitutive equation. What is more, two electric boundary condition were considered and the effect of their effect on the bending behavior on piezoelectric cantilever beam were studied in our study, which provide a theoretical foundation for the piezoelectric test method.2. Small scalar effect in low dimensional linear elastic micro-bridge: A new theoretical model of strain gradient micro-bridge was established by introduce intrinsic dimensional parameters and strain gradient constitutive into the traditional macro-bridge theory. The equivalent higher order boundary condition was verified by compare the results of full-model macro-bridge and equivalent half-modelmacro-bridge. Meanwhile, the load-deflection curve was given with the considering of the substrate deformations. The new theory was used to analysis the experimental data to obtain the material properties such as Young’s modulus, residual stress and intrinsic dimensional parameters. The obtained parameters were then compared with that got from the traditional nano-bridge theory.