Size effect investigation of indentation response of stiff film/compliant substrate composite structure

Abstract

The stiff film/compliant substrate composite structure with a high modulus ratio finds a wide range of applications in production and in scientific research, and its indentation behavior cannot be described by the traditional theory when the film thickness is reduced from the millimeter scale to the micrometer or nanometer scale. In order to better understand the trans-scale indentation response of the composite structure caused by the reduction in the film thickness, this problem is solved analytically with the strain gradient theory and integral transformation. The gradient effect on the indentation response of the system is assessed in detailed from three aspects: load-displacement relationship, surface topography and distribution of bending moment on the film. In addition, the influences of film thickness, modulus ratio of the film to the substrate, contact radius and Poisson's ratio on the gradient effect are investigated. It is found that the gradient effect on the indentation response of the system, which is not sensitive to the contact radius and Poisson's ratio, is related not only to the film thickness but also to the modulus ratio of the film to the substrate. Based on the above analysis, a dimensionless number (g/l) is proposed to evaluate the gradient effect on the indentation behaviors of the system. And with the help of the dimensionless number, a new simple and accurate method for measuring the material length scale is proposed. Our research provides a theoretical basis for an in-depth understanding of the gradient effects on the indentation response of the stiff film/compliant substrate system and for the measurement of the material length scale.