Effect of cantilever nonlinearity in nanoscale tensile testing

Abstract

Microcantilevers are widely used in micro-/nanoscale mechanics studies. The nonlinear response of a cantilever at large deflection is sometimes overlooked. A general study of cantilever beam nonlinearity under a variety of loading conditions was performed with analytical and finite element analyses. Analytical equations for the applied load and the cantilever deflection were obtained. The cantilever nonlinearity was found to increase with increasing cantilever deflection and/or angle of loading. Tensile tests were performed on templated carbon nanotubes (TCNTs) with a custom-made nanomanipulator inside a scanning electron microscope. Atomic force microscope (AFM) cantilevers were used to load the TCNTs and sense the force. During the tests the AFM cantilevers were loaded to relatively large deflections with nonvertical loads applied at the AFM tip. Based on the slope and the loading angle measurements, the breaking forces of the TCNTs were obtained through numerical integration of the analytical equations. A comparison was made between the load results obtained from linear and nonlinear analyses. The linear analysis was found to underestimate the applied load by up to 15%.