Analytical solution of indentation response of an elliptical cylindrical indenter on elastic microbeam with surface tension

Abstract

<p indent="0mm">In addition to the measurement of mechanical properties of bulk materials, the indentation technology is widely used to measure the mechanical properties of soft films and microscale materials. As the material scale decreases, surface effects play an important role in the force and deformation in the indentation contact problem. In this paper, the two-dimensional indentation problem of an elastic microbeam under an elliptical cylinder indenter is studied theoretically. For the microbeam with the surface tension, the differential governing equation satisfied by the surface pressure distribution and the normal deflection is solved. The analytical solutions of the surface pressure and surface displacement inside and outside the contact area are obtained, where the undetermined coefficients are determined by the contact zone half-width and the indentation depth. The deformation solution of the microbeam under uniform load and Betty’s reciprocal theorem of the indentation problem are given. Then, the contact zone half-width and indentation depth under different measurement forces are solved, and the analytical solution of the indentation problem of an elliptical cylindrical indenter on elastic microbeam is obtained. The effect of surface tension, elliptical indenter parameters and microbeam size parameters on surface pressure and deformation in the indentation problem is analyzed theoretically. This study helps to understand the surface effect on the indentation behavior of microscale materials, and provides some reference for related indentation testing techniques.