A new insight into the work-of-indentation approach used in the evaluation of material's hardness from nanoindentation measurement with Berkovich indenter

摘要

The work-of-indentation approach employed to extract the hardness of a material from the load-displacement data is often misinterpreted and improperly compared with the Oliver and Pharr method. A theoretical basis is presented to show that the hardness values evaluated using these two methods are fundamentally different, but are interrelated. As such, an expression that relates one type of hardness to another is derived by considering an energy-based relationship between the contact and the maximum penetration depths for an ideally sharp Berkovich indenter. This modified work-of-indentation approach is first validated using the load-displacement data obtained from the finite element simulation of the indentation contact performed with a Berkovich equivalent conical indenter on materials having a wide range of elastic recovery. The real load-displacement data - with and without dwelling - from ceramics oxides and metals corresponding to a peak indentation load lying in the range 20-120 mN are also considered to validate the proposed method. It has been found that a correction due to the amount of work done during dwelling is required if the load-displacement data also feature a dwelling phase. The hardness value so obtained is found to be in close agreement with its Oliver and Pharr analogue for each material considered thereby indicating that the modified approach, in the present form, is applicable even for blunt indenter when the tip radius is very small as compared to the maximum penetration depth. Further refinement of this methodology is, however, required to take the effect of material's pile-up, sink-in, and tip bluntness on the measured hardness into account.