Abstract:
The indentation size effect (ISE) is a central problem in nanoindentation techniques. However, existing models often overlook the differences in deformation mechanisms at nano- and micro-scale indentation depths. This study constructed a modified model tailored to different scales: at the nano-scale, a decay function
f that decreases monotonically with depth was introduced to modify the storage region of geometrically necessary dislocations (GNDs), characterizing the dislocation propagation effect and the influence of elastic deformation; at the micro-scale, the coefficient
β was defined to quantify the nonlinear coupling between GNDs and statistically stored dislocations. Validated by nanoindentation experiments of CoCrFeNiMn, CoCrFeNiAl
0.3 and CoCrFeNiAl
0.6 high-entropy alloys, the model accurately describes the ISE behavior over depths of 50 nm-2000 nm and can degenerate to the classical Nix-Gao model when the cross-scale deformation mechanism differences are neglected. Combined with electron backscatter diffraction analysis, the grain size is found to significantly influence the ISE by regulating dislocation interactions. This work provides a modified theoretical framework and experimental basis for advancing the understanding of the ISE.