Effect of flexoelectricity on elasticity characterization by nanoindentation

Flexoelectricity is a very common phenomenon in dielectrics and is a size-dependent electromechanical mechanism coupling polarization and strain gradient. Flexoelectric effect is significant due to higher strain gradients at nanoscale. Barium Titanate (BaT iO3) is one of the dielectrics whose flexoelectric properties have been determined by bending tests and nanoindentation technique. These properties estimated from these two tests have good conformance with each other. In the following work, the estimated flexoelectric properties have been used to evaluate the Young’s modulus of a BaT iO3 sample using nanoindentation. The analytical solution for three indentors is available for nanoindentation technique based on Hertz contact theory. The analytical solution for all the indentors is a function of the radius of indentor, indentation depth , applied force, Young’s modulus and Poisson’s ratio. Here we computationally implement the linear theory of flexoelectricity, taking into account only the flexoelectric effect. We compute the change in indentation of the material by varying the flexoelectric constant in range of four orders of magnitude. This variation helps us maneuver from the macroscopic scale to the nanoscopic scale. Using the Hertz contact theory we obtain the Young’s modulus based on the indentation depths computed on account of variation of the flexoelectric constant. The results obtained from this study show that the flexoelectric effect is a scale dependent phenomenon