Development of semi-empirical formulation for extracting materials properties from nanoindentation measurements: Residual stresses, substrate effect, and creep

Nanoindentation is one of the most popular techniques for characterizing the mechanical properties of micro- or nano-structured metals or dielectric thin films. However, the obtained experimental data can only provide the relationship between the applied load and the penetration depth. Mechanics models are therefore required to convert the test data into the corresponding material properties. In this work, the effect of residual stress, the substrate effect, and the creep of materials subjected to the indentation test are discussed in order to establish appropriate conversion formulas or criteria for extracting the interested material properties. Dimensional analyses are firstly performed to find the governing parameters and to obtain scaling relationships for subsequent finite element analysis. With the described procedure, models have been developed to convert nanoindentation test data into the desired material properties. Those models provide useful tools for extracting specific material properties, such as residual stress, creep exponent, and stress relaxation time constant. Specifically, this investigation also shows that for the situation of soft film/hard substrate combination, the indentation behavior is essentially identical if the modulus of the substrate is 10 times higher than that of the corresponding film and the response deviates consistently from that of bulk material with increasing of indentation depth. For penetration depth less than 10% of the film thickness, the deviation could be acceptable. On the other hand, significant deviation is observed for hard film/soft substrate systems. In summary, by integrating the models proposed by this work and data from standard tests, it is possible to obtain the Young's modulus, hardness, and the viscoelastic properties as well as the residual stress for a specific material through indentation characterization.