The influence of indenter tip radius on the micro-indentation hardness

The micro-indentation experiments have shown that the indentation hardness depends not only on the indentation depth but also on the indenter tip radius. In fact, the indentation hardness displays opposite dependence on the indentation depth h for a sharp, conical indenter and for a spherical indenter, decreasing and increasing, respectively, with increasing h. We have developed an indentation model based on the theory of mechanism-based strain gradient plasticity to study the effect of indenter tip radius. The same indentation model captures this opposite depth dependence of indentation hardness, and shows the opposite depth dependence resulting from the different distributions of strain and strain gradient underneath a conical indenter and a spherical indenter. We have also used the finite element method to study the indentation hardness for a spherical indenter as well as for a conical indenter with a spherical tip. It is established that the effect of indenter tip radius disappears once the contact radius exceeds one half of the indenter tip radius.