This sections considers the simulation of ion-implanted samples by varying the yield stress distribution as described earlier. The depth of the peak in the strength is varied parametrically, to model deeper ion penetration (higher ion energies). The results of this study are shown in Fig. 2. As expected, the depth of the peak in the hardness increases as the depth of the property distribution increases.
Another result that can be inferred from Fig. 2 is that the height of the hardness peak decreases with the depth of the peak in the properties, even though the height of the yield stress peak does not change. This likely occurs because as the yield stress peak deepens, the effects of this peak on the hardness can be spread over a wider area. (For reference, the relative hardness of a homogeneous material with a yield stress equal to that of the peak in the yield stress distribution used in these analyses is 2.64.) This phenomenon exhibits the ability of the hardness test to spread localized property changes over larger areas. Another notable result is that the hardness at the surface seems to decrease as the depth increases. The curve representing the deepest peak in the yield stress indicates that the normalized hardness is below unity at the surface, which is not an expected result. However, taking into account the errors discussed earlier, these relative hardness values are essentially unity, so no conclusive statements can be made here.