The role of probe shape on the initiation of metal plasticity in nanoindentation

The dislocation nucleation stress of crystalline materials is frequently estimated from the maximum shear stress, assuming Hertzian contact up to the first “pop-in” event, which is a sudden displacement burst during load-controlled nanoindentation. However, an irregular indenter tip shape will significantly change the stress distribution, and therefore the maximum shear stress from a Hertzian estimation. Here, we assess possible errors and pitfalls of the Hertzian estimation of initial plastic yield at the nanoscale. The near-apex shapes of two Berkovich indenters, one sharp and one worn, were measured by atomic force microscopy and directly input into finite element analysis (FEA) models for “virtual” nanoindentation experiments on single-crystal tungsten. Experiments were also carried out with those indenters. Excellent agreement is found between experimental and FEA force–displacement relationships, but the discrepancies between Hertzian and FEA estimates of the shear stresses are over 25% for the sharp indenter and over 50% for the blunt indenter. This demonstrates that small irregularities in the shape of indenter tips can cause significant deviations from the Hertzian estimation of dislocation nucleation stress.