Nanohardness of high purity Cu (111) single crystals: The effect of indenter load and prior plastic sample strain

Abstract

Experimental investigations have been carried out in which nanohardness of single crystals of Cu (111) samples containing prior plastic strains of 0, 0.06, 0.24, and 0.61 has been measured using a Berkovich diamond indenter of tip radius of ∼200 nm. The projected contact areas of nanoindentations were determined using a calibrated atomic force microscope and these were used for determining the nanohardness values. It has been found that for every sample, the nanohardness was the highest for the lowest indenter load of 0.625 mN. At the lowest applied indenter load the overall highest hardness was obtained in crystals with the lowest prior strain of 0 or 0.06. At higher indenter loads in the range 40–125 mN, the hardness increased with increasing prior plastic strain in the sample. It is also shown that the indentation hardness H data are not fitted by the relation H2∝1/a, where a is the equivalent radius of indentation. The above relationship is predicted by the strain gradient, lattice rotation around the indentation, and the dislocation slip distance theories. A three-stage qualitative model, previously proposed by us, has been used for explaining the hardness versus indentation load data. In the first stage nucleation of dislocations under the indenter occurs. If the sample is well annealed, the nucleation of dislocations is homogeneous, but for the Cu (111) samples containing prior strains of 0.06, 0.24, and 0.61, the nucleation is heterogeneous. The highest hardness was obtained for a well annealed sample of the Cu (111) using a Berkovich diamond of tip radius of (407±32) nm. The mean normal pressure pm values at the moment of homogeneous nucleation of dislocations when the indenter was loaded on the Cu (111) and Cu (100) surfaces were determined as 16.75 and 9.32 GPa, respectively. From these pm values, the critical resolved shear stress of the copper single crystal has been determined as 4.56 and 3.80 GPa, respectively. The mean of these two values is 4.18 GPa, which is about 58% higher than the theoretically calculated ideal shear strength of copper of value 2.65 GPa. An alternative method using the maximum shear stress under a hard spherical indenter gives the value of the critical resolved shear stress as 1.945 GPa, which is ~26% lower than the theoretical value. Young’s modulus values along the normals to the Cu (111) and Cu (100) surfaces of well annealed and high purity copper crystals have been determined using the “pop-in” loads and the Hertzian elasticity theory. The values thus determined were 170 and 52 GPa for the Cu (111) and Cu (100) surfaces, respectively. These values are close to the literature values of 190.3 and 66.7 GPa. Young’s modulus values were also determined using the unloading curves and the ISO 14577 method; these determinations were 135 and 110 GPa for the Cu (111) and Cu (100) surfaces, respectively, and are significantly different from the literature values, which indicates the inherent erroneous nature of the ISO 14577 method of nanoindentation data analysis.