Depth-dependent mechanical properties of enamel by nanoindentation

Nanoindentation has recently emerged to be the primary method to study the mechanical behavior and reliability of human enamel. Its hardness and elastic modulus were generally reported as average values with standard deviations that were calculated from the results of multiple nanoindentation testing. In such an approach, it is assumed that the mechanical properties of human enamel are constant, independent of testing parameters, like indent depth and loading rate. However, little is known if they affect the measurements. In this study, we investigated the dependence of the hardness and elastic modulus of human enamel on the indent depth. We found that in a depth range from 100 to 2000 nm the elastic moduli continuously decreased from approximately 104 to 70 GPa, and the hardnesses decreased from approximately 5.7 to 3.6 GPa. We then considered human enamel as a fiber-reinforced composite, and used the celebrated rule of mixture theory to quantify the upper and lower bounds of the elastic moduli, which were shown to cover the values measured in the current study and previous studies. Accordingly, we attributed the depth dependence of the hardness and modulus to the continuous microstructure evolution induced by the nanoindenter tip.