This article from CSM Instruments describes the additional material properties which can be obtained from nanoindentation measurements performed with a spherical indenter tip. Although most low load nanoindentation measurements are made using a Berkovich indenter geometry (to minimise indenter tip chisel effects), such a geometry still suffers from a finite tip bluntness which is very difficult to define accurately.
Spherical indentation overcomes many of the limitations associated with pyramidal indenters and allows hardness to be evaluated by following the transition from elastic to plastic behaviour. This also enables the yield stress to be calculated . Indentation behaviour depends on the ratio between the actual strain and the yield strain of the material; low ratios produce elastic behaviour whereas high ratios produce plastic behaviour.
The actual strain can be represented by tanb where b is the angle between the indenter and sample surfaces. Clearly, a spherical indenter will behave in a fundamentally different way from one with a pyramidal geometry: the strain will increase as the indentation depth increases. Therefore, a series of spherical indentations with progressively increasing load will produce stress-strain curves which follow the transition from purely elastic to plastic behaviour.
The example in Fig. 1 shows a plot of stress versus strain for five different material types, produced from multicycle indentations over the range 10 - 260 mN. The stress (y-axis) corresponds to the measured hardness of each cycle in GPa, whereas the strain is calculated by dividing the radius of the residual impression by the indenter radius.
Figure 1. Stress-Strain data for TiN (coating thickness = 3 μm), pure Si, 100Cr6 steel, glass and pure copper calculated from multicycle indentations performed over the range 10 - 260 mN with a spherical indenter of radius 1 μm. Each data set corresponds to the average of five sets of measurements.
The results presented in Fig. 1 clearly show the type of elastic-plastic transition which is observed in hard materials (TiN, Si) and softer materials (Cu). Harder materials tend to exhibit a more pronounced gradient change as the strain is increased.
Although a spherical indenter theoretically produces a uniform stress field around its circumference, severe cracking is nevertheless observed in materials such as silicon, especially when several load-unload cycles are performed on the same area. Fig. 2 shows the cracking and chipping which results after indentation at loads from 30 up to 200 mN using an indenter of radius 1 μm. Scanning Force Microscopy (SFM) is particularly useful for imaging such nanoindentation effects.
Figure 2. SFM images of residual monocycle indentations performed in Si with maximum applied loads of (a) 30 mN, (b) 100 mN and (c) 200mN. The indenter was a spherical diamond of radius 1 μm. Cracking becomes apparent even at low loads with severe chipping occurring at higher loads.
The SFM images shown in Fig. 4 represent residual indents in pure copper and the corresponding cross-sectional profiles are plotted together in Fig. 3. Previous measurements have shown that multicycle indentations produce less pile-up in soft metals such as copper than a monocycle indentation to the same maximum load. This phenomenon can be attributed to the effects of gradual work hardening under the indenter as the load is increased on every subsequent cycle. A careful choice of indenter radius, coupled with a suitable load range, allows a very wide range of materials to be investigated with this technique.
Figure 3. Cross-sectional profiles through the residual imprints shown in Fig. 4. Note the evolution of pile-up as a function of maximum depth and the variations of the profiles due to indenter non-symmetry.
Future work will involve indentation of ceramics, for which Hertzian contact of a spherical indenter can initiate cone fracture (brittle mode) or sub-surface deformation (quasi-plastic mode) if the elastic limit is exceeded.
Figure 4. SFM images of residual spherical indentations in pure copper. The indents correspond to indentation load ranges of (a) 10-60 mN, (b) 60-110 mN, (c) 110-160 mN and (d) 210-260 mN.