Equivalency of Berkovich and conical load-indentation curves

The Berkovich indenter, which is one of the most commonly used indenter tips in instrumented indentation experiments, requires a tedious 3D finite element simulation. The indenter is widely idealized as a conical indenter of 70.3° half-angle to enable a substantially less demanding 2D axisymmetric modelling. Although the approach has been commonly adopted, limited studies have been performed to investigate possible deviations due to this simplification. The present study attempts to address the equivalency of the two indenters by performing extensively both 3D and 2D finite element analyses to simulate the load-displacement response of a wide range of elasto-plastic materials obeying power law strain-hardening during indentation for both Berkovich and conical indenters, respectively. It is demonstrated that the equivalency between these two indenters in terms of curvature of the loading curve is not valid across the range of material properties under study. However, it is established that if only the ratio of the remaining work done (W_R) and the total work done (W_T) of the load-indentation curve is of interest, this simplification can be adopted with satisfactory results.