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 systems and functional gradient materials using data obtained from indentation testing. The measurement data collected from the penetration force-depth curves in the test are employed for identifying elastic moduli of thin films and functional gradient materials. An indentation problem is first analyzed on the basis of the three-dimensional axisymmetric theory of elasticity. Analyses of elastic contact problem, which an elastic axisymmetric indenter is penetrated into multi-layered systems and into functional gradient materials, are presented. An inverse analysis for determining Young’s moduli, Poisson’s ratios and radii of the contact area is performed under the assumption that the elastic moduli of the substrate and the indenter, and thicknesses for layers are known. When 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 dusts and environment. It is important to estimate their 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 in-situ the mechanical properties of deposited films. However, it is very hard to carry out a test for evaluating the mechanical properties of films in a sub-micrometer thickness. Ihara, et al. estimated the material properties of a thin film using surface wave spectroscopy. Matui, et al. examined the accuracy of identified elastic moduli in a multilayered system. Kishimoto, et al. idetified the elastic properties for a bar of functional gradient materials. Indentation test is one of methods for evaluating the mechanical properties of thin films, which is the one 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 into 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).
Measurement of Elastic Modulus of Functionally Gradient Material Using Inverse Analysis.
This paper presents a method to detemine the distribution of the Younng's modulus of function-ally gradient materials by bending testing. In the method, the measured values of the flexural rigidity, which are obtained by reducing the height of the specimen, are used to inversely analyze the distribution of the modulus across the thickness. The solution is obtained through minimizing the residual between measured data and estimated values. The Davidon-Fletcher-Powell method is employed for minimization of the error. The practical applicability of the method is examined through several examples.
Elastostatic Infinite Elements for Layered Half Spaces
The far field behavior of a homogeneous half space and a layered half space is investigated under torsional, vertical, horizontal and moment loadings. Based on the derived far field behavior, three different finite‐element based algorithms, i.e., Ordinary Infinite Elements (OIE), Finite Elements by Singular Contraction (FESC) and Exactly Integrable Infinite Elements (EIIE) are developed to model the far field of multilayered half spaces. The coordinate mapping functions and displacement interpolation functions are selected in accordance with the derived far field model. All three schemes satisfy compatibility and completeness. Excellent results are obtained at a very low computational cost by modeling the near field using a small finite‐element mesh, together with any of the present schemes modeling the domain exterior to the finite elements. Considering the computational efficiency and ease in incorporating FESC into an existing finite element package, FESC is superior to the other two algorithms.