Classical and differential hardness – aspects of quantifying the deformation response in indentation experiments

Bodo Wolf (1)

1 IEM

In depth sensing nanoindentation the load – depth-curve F(h) is acquired from which a single value for the hardness H and a second one for the indentation modulus Eind are inferred. This is a very poor output since F(h) is a source of much more information. The paper describes a technique to extract the hardness H(h) as a continuous depth dependent function from the load-depth-curve. This was accomplished by assigning each depth h a corresponding contact depth hC = hC(h) that can be calculated using an iteration algorithm. The hardness is then simply H(h) = F(h)/AC(hC(h)). For very simple area functions AC an analytical solution hC(h; F) can even be found. Furthermore, the differential hardness Hd is introduced as an additional hardness quantity which is obtained when dividing the load increment ÄF by the resulting increase of contact area ÄAC It turns out, that H and Hd are identical quantities for a material of constant hardness only. When the hardness is depth and therefore size dependent, Hd differs from H in a definite way that depends on the hardness evolution with depth, i.e. on the indentation size effect of the material under investigation. The differential hardness proves particularly useful for inhomogeneous samples and situations where the hardness is time – dependent.

Mots clés: Physical Sciences

Bodo Wolf. Classical and differential hardness – aspects of quantifying the deformation response in indentation experiments. Philosophical Magazine, 2006, 86 (33-35), pp.5251-5264. ⟨10.1080/14786430600722367⟩. ⟨hal-00513698⟩