Effect of grain size on the indentation hardness for polycrystalline materials by the modified strain gradient theory

Numerous indentation tests in the micrometer and nanometer scale have shown that the measured hardness decreases significantly with increasing indentation depth, and this is known as the indentation size effect (ISE). However, several other nanoindentation results for polycrystalline materials show that the indentation hardness increases with increasing indentation depth because of the grain boundary (GB) effect. In this work, we propose a new model for the indentation test using the modified strain gradient plasticity theory. The GB effect is considered by evaluating the density of GNDs on the GB. Using the proposed model, the indentation hardness of polycrystalline materials in micrometer-scale structures is investigated, and compared with experimental results from other researchers.