Determination of Mechanical Properties of Thin Films and Functional Gradient Materials Using Inverse Technique

This paper describes a method for evaluating material properties of multi-layered system and functional gradient materials from data obtained from indentation testing. The measurement data collected from the penetration force-depth curves is employed for identifying elastic moduli of thin films and functional gradient materials. An axisymmetric indentation problem is first analyzed on the basis of the three-dimensional axisymmetric theory of elasticity. Two analyses of elastic contact problems, in which an elastic axisymmetric indenter is penetrated into an elastic half-space coated with multilayered films and into functional gradient materials, are presented. An inverse procedure for determining Young’s moduli, Poisson’s ratios and radii of the contact area is described under the assumption that the elastic moduli of the substrate and the indenter, and thicknesses for layers are known. When the complex method is used for minimizing an objective function composed of errors, effective sampling of data obtained by penetrating indenters with various radii of curvature into the coated substrate and functional gradient materials is presented. INTRODUCTION Modern electric devices and mass storage devices have frequently multilayered structures to achieve a high performance and functionality. Furthermore, such devices are coated often by metal thin films to protect from the damage of external dust and environment. It is important to estimate the mechanical properties for improving the reliability of devices and machines. Generally, mechanical properties of thin films deposited on a substrate are different from those of bulk. Hence, we need to know the mechanical properties of deposited films. However, it is very hard to carry out a test for evaluating the mechanical properties of films with a sub-micrometer thickness. Indentation test is one of methods for evaluating the mechanical properties of such thin films, which is a method estimating elastic moduli of thin films using experimental data of the force and the depth of an indenter penetrated into a multi-layered system. In the present paper, when data of the indentation force and depth are used, a method for identifying the mechanical properties of thin films and the distribution function of mechanical properties in functional gradient materials will be presented. ANALYSIS OF INDENTATION PROBLEMS In the present analysis, an axisymmetric elastic indenter with a cross section of f(r) will be penetrated to an elastic half-region composed of layers with various mechanical properties as shown in Figure 1. This contact problem is analyzed using the theory of threedimensional axisymmetric elasticity. Then, displacements and stresses in the layers, the indenter and the elastic half-region can be deduced by substituting Boussinesq’s potential functions, ψ and φ 3 , into the following relationships (Miyamoto 1977, Gladwell 1980).