Indentation and Hardness of Materials: An Inherently Multiscale-Dependent Problem

The method of indentation of an indenter into a material or substrate is widely utilized to characterize one of the mechanical properties of a material, namely hardness. This method is performed on different scales of indenting force, indenter size/dimensions, and size/dimensions of the indented material/substrate. The different scales do not always yield the same hardness output or reading due to material length scales. One of the length scales in a material is related to its heterogeneity, such as in reinforcing particles or second phases. This work performs 3D non-linear finite element analysis using a purely elastic indenter on a composite material. In addition to the scales above that could affect the results, the parameters of particle size, shape, spacing, and volume fraction are all shown to affect the hardness readout in the current work. One of our new findings is that the length scale effect is more phenomenal, especially at scales when the size of the indenter is comparable to any characteristic length in the material beneath the indented surface.