Effect of surface energy on the indentation response of hard nanofilm/soft substrate composite structure

Abstract

The indentation behaviors of hard nanofilm/soft substrate composite structures which are widely used in production and in scientific research cannot be described by the conventional continuum theory due to the influence of surface energy under the micron scale. To better understand the indentation response of this composite structure under the influence of surface energy, an analytical indentation solution is obtained with the Hankel transform and the surface elasticity model developed by Gurtin and Murdoch. Based on the analytical solution, the influences of surface residual stress and surface elastic constant on the distribution of the bending moment in the nanofilm, the load-displacement relationship, and the surface morphology are investigated in detail. In addition, the influences of the film thickness, modulus ratio of the film to the substrate, contact radius and Poisson's ratio on the surface effect are studied. The results show that the influence of the surface effect on the indentation response of the system, which is insensitive to the Poisson's ratio and the contact radius, is not only sensitive to the thickness of the film, but also to the modulus ratio of the film to the substrate. Based on the above analysis, a dimensionless number (K2/(λ+6K1)1/3) is proposed to evaluate the influence of the surface effect on the indentation response of this composite structure. Our study sheds light on the understanding of the indentation behaviors of this composite structure under the influence of the surface effect and provides a theoretical guidance for the application of this composite structure.