Experimental Verification of the Strain-Gradient Plasticity Model for Indentation

The indentation size effect of pure iron samples with various pre-plastic tensile strains has been experimentally investigated and analyzed. With the increase in the strain, the indentation size effect of iron samples becomes weak, accompanied by the multiplication of the statistically stored dislocations. All of the hardness (H) versus indentation depth (h) curves fit the strain-gradient plasticity model for indentation of Nix and Gao well. Two fitting parameters, the hardness in the limit of infinite depth (H0) and the characteristic length (h*), were obtained for each curve. The hardness (H0) of iron samples can also be estimated as the microhardness (H) at a very large depth, h ≅ 10h*. Both the fitted H0 and the measured H0′ increase linearly with the tensile yield stress σy of iron samples, indicating a dependence of H0 on the statistically stored dislocation density through σy. Furthermore, 1/√h* shows a linear increase with the tensile yield stress σy, which also agrees qualitatively with the general prediction of the Nix and Gao theory. Therefore, our experiments and analysis demonstrate that the strain-gradient plasticity model for indentation of Nix and Gao can interpret the indentation size effect with satisfied precision.