Lateral and vertical size effects on nanoindented microstructures

In this paper we study numerically the size effect of different constitutive relationships based on bulk silicon subjected to nanoindentation. The constitutive relationships of multilinear kinematic hardening rules are considered in order to capture elastic-perfectly plastic to strain-hardening characteristics. The size effect is estimated from the hardness of the varied contact depths normalized by that of the standard size sample that has been previously validated. Both lateral and vertical sample size effects of the microstructure are evaluated by varying respective size with an identical indentation depth. The contact depths equaling to 1/10th of the sample thickness bring around ±10% of the vertical size effect, while those equaling to one quarter lead to approximately ±20%. A softer material with an elastic-perfectly plastic characteristic generates a smaller vertical size effect because of the continuum mechanism occurs only at the near field. Narrowing down the lateral width, leads to lower loads due to no lateral boundary could conduct. Hard samples are less affected by the lateral size effect than soft ones.