Hardness length-scale factor to model nano- and micro-indentation size effects

In this paper, we show that nano- and micro-indentation hardness data can be represented adequately by the strain gradient plasticity (SGP) theory if the uniformity of the dislocation spacing is taken into account. To give relevant information on the plastic deformation process, we suggest to use a hardness length-scale (HLS) factor equal to Ho⋅h*, where Ho is the macro-hardness and h* the characteristic scale-length deduced from the hardness–depth relation of the SGP theory. Theoretically, the HLS factor is proportional to both the shear modulus and the Burgers vector, depending on the dislocation spacing. Applied to various crystalline metals, the representation of the experimental HLS factor as a function of the theoretical one shows two distinct linear behaviours related to the micrometer and nanometer depth regimes associated with a uniform dislocation organisation beneath the indenter and with dislocations located at the vicinity of the indenter tip in a largest plastic zone, respectively.