Determination of properties of graded materials by inverse analysis and instrumented indentation

In this paper, a new measurement procedure based on inverse analysis and instrumented micro-indentation is introduced. The inverse analysis is utilized to extract information from indented load-displacement data beyond usual parameters such as elastic modulus. For the initial implementation of this procedure, determination of non-linear functionally graded materials (FGMs) parameters is considered. In FGMs, the compositional profile and the effective mechanical property through the thickness are essential in verifying the fabrication process and estimating residual stresses and failure strengths. However, due to spatial variation of their properties, it is often difficult or costly to make direct measurements of these parameters. In order to alleviate the difficulties associated with testing of FGMs, we propose an effective but simple procedure based on the inverse analysis which relies solely on instrumented micro-indentation records. More specifically, the Kalman filter technique, which was originally introduced for signal/digital filter processing, is used to estimate FGM through-thickness compositional variation and a rule-of-mixtures parameter that defines effective properties of FGMs. Essentially, the inverse analysis processes the indented displacement record at several load magnitudes and attempts to make best estimates of the unknown parameters. Our feasibility study shows promising results when combined data from two differently sized indenters are employed. The procedure proposed is also applicable in estimating other physical and mechanical properties of any coating/layered materials.