On the Size Effects in Indentation Testing of Elastic Functionally-graded Materials

The size effect in the small-scale indentation testing is studied for a functionally-graded material (FGM) whose shear elastic modulus varies according to the exponential law. Under the simplifying assumption of zero Poisson’s ratio, the asymptotic model of the indentation stiffness for an axisymmetric frictionless indenter is developed in the case when the contact radius is small compared to the inhomogeneity characteristic size. The so-called sample size effect is considered on the example of a simply supported FGM plate indented at the center of its top surface. A certain range of applicability of the first-order asymptotic models has been established by comparison with the approximate analytical solution available in the literature.