Indentation Size effects

Indentation Size Effects

Size effects in depth sensing indentation test are widely observed in metals and in other materials as well, where the measured hardness turns out to be higher than the bulk hardness (the hardness values measured from experiments such as Vickers, Rockwell hardness tests) at very shallow indentation depths. This is usually observed in nano/micro indentation experiments where the depth of indentation is small. However, with increasing indentation depth the measured hardness approaches the value of the bulk hardness. The hardness measured from these indentation experiments shows an increasing trend with smaller depths of indentation. This is commonly referred as Indentation Size Effect (ISE).

Often, ISE manifests itself only below a certain depth of indentation and it is regarded as the characteristic of the material being tested. Thus a certain length scale, specific to a material, exists below which ISE would show up. Naturally, to capture such behaviour, a length scale parameter must be present in the model being used. Conventional plasticity theory is scale independent and does not contain such length scale parameter. Thus conventional theories are incapable of modelling such behaviour. To this point several theories (crystal plasticity, dislocation dynamics and other continuum based models) have been used to model not only ISE but other size effects associated with non-homogeneous deformation. Strain gradient theory is one among those and we have used the same for modeling ISE (you can find an extensive review on such models here Guha et. al, 2015) .

The figure below show a comparison of the load-displacement responses for two materials undergoing indentation by a wedge shaped indenter in plane strain which was obtained from a strain gradient based FE simulations. One following a conventional plastic behaviour and the other following strain gradient plasticity based material model. These results show three interesting features -

• For the gradient plastic material the load experienced by the indenter is larger compared to the same for conventional plastic material at indentation depths where it is comparable to, or less than l*.

• The slope of the unloading curve at such depths are smaller for gradient plastic materials, indicating more elastic recovery and reduced plasticity ! Suppression of plasticity is observed in many other examples where size effect is found to be present.

• However, when the indentation depth is much larger than l*, both the curves coincide, indicating the absence of size effect.

There are many instances where strain gradient plasticity models have shown good agreement (at least qualitatively) with experiments and one such experimental observation by Dahlberg et. al, 2014 is shown in the figure. They performed indentation test on Nickel single crystal with 120 degree wedge indenter replicating a plane strain condition.  If we carefully see the load-displcement plot, it can be identified that there is clear bulging effect at shallow indentation depth (< 50 microns) similar to those obtained in above simulations.