Hardness estimation for pile-up materials by strain gradient plasticity incorporating the geometrically necessary dislocation density

A plastic strain gradient theory incorporating the geometrically necessary dislocation density based on the low order displacement finite element method is proposed for calculation of the hardness value by Berkovich indentation. The obtained analysis results by this work are found to be in good agreement with the experimental data. Three-dimensional modeling technique of Berkovich indentation is also suggested. An empirical coefficient that includes the strain gradient effect into the yield stress formula is introduced and determined by reviewing area factors and hardness curves generated from the analyses. As pile-up occurs, classical plasticity theory gives a higher area factor and lower hardness value than those from experiment. However the strain gradient plasticity theory used in this work gives corrected area factor and hardness values. Dislocation density plots are generated that can explain the size effect during indentation and the availability of the three-dimensional modeling of Berkovich indentation.