Two opposite size effects of hardness at real nano-scale and their distinct origins

Although it has been well known that hardness of metals obtained with conical indenter remains a constant of about 3 times yield strength in conventional tests, and hardness will show a size effect of increasing hardness with decreasing indentation depth in micro-scale beyond 100 nm, the nano-indentation hardness experiments within 100 nm indentation depth usually show a large deviation and unclear trends. We report the cross-validated experimental and numerical results of two opposite depth-dependences of hardness at real nano-scale. That is to say, the indentation size effect (ISE) of hardness of single-crystal copper shows a rapid increase and then a slow decrease with increasing indentation depth within 100 nm depth. All of the results were coss-checked by means of both elaborated nano-indentation experiments with calibrated indenter tips and large scale molecular dynamics (MD) simulations. Further analysis of the MD results and experimental data reveal that the two opposite ISE of nano-hardness should be attributed to the finite roundness of the indenter tip and the intrinsic transition governing property of the material.