Nanoindentation of embedded particles

We address the effect of elastic inhomogeneity on elastic modulus and hardness determinations made by depth-sensing indentations performed on individual particles embedded within a matrix of different elastic modulus. Finite element simulations and nanoindentation experiments are used to quantify the consequences of particle/matrix elastic inhomogeneity and we propose an adaptation of the Oliver-Pharr method that gives access to particle properties knowing those of the matrix. The method is suitable for any combination of matrix and particle elastic modulus and for any type of indenter, provided that the area of the tested particles along the surface of the sample is measured and that a large number of particles are probed. Further conditions for the implementation of the method are that testing conditions be such (i) that permanent deformation of the matrix is avoided, and (ii) that permanent deformation in each probed particle under the indenter is not affected by the matrix.