Discrete dislocation analyses of circular nanoindentation and its size dependence in polycrystals

Nanoindentation has been extensively used to measure the mechanical behavior of materials at the micro- and nanoscale. However, the material response of nano/microindentation and its intrinsic mechanisms are very complicated, especially when considering heterogeneous polycrystalline materials. In this contribution, nanoindentation in polycrystals, performed with a circular indenter, is studied by numerical modeling based on the two-dimensional discrete dislocation plasticity of Van der Giessen and Needleman [Van der Giessen E, Needleman A. Model Simul Mater Sci Eng 1995;3:689]. The dependence of indentation hardness is investigated with respect to four typical characteristic dimensions: indenter radius, grain size, indentation depth, and the distance between the grain boundary and the indenter. Results show that these characteristic dimensions have considerable influence on the nanoindentation hardness. Further investigation shows that their influence takes effect mainly in two ways, i.e. via strain hardening and the indentation size effect. Although both effects are size dependent, their underlying mechanisms are clearly different. For the present polycrystal case, the strain hardening effect is mainly associated with the constraints of grain boundaries and dislocation obstacles to the dislocation glide, while the indentation size effect is related to the average strain gradient beneath the circular indenter.