A large number of microhardness measurements (about 350/series) performed at seven different weights on 8 samples of metals and alloys as well as on monocrystals of 19 different mineralogical species have been collected. The property values, which cover the wide range from 9 to $2000 Kg/mm^{2}$, clearly show two different distributions when plotted against the weights applied. A model to explain such a feature is proposed; the model suggests that in some cases a modification of the material behaviour toward penetration may arise when a certain limit of plastic deformation is overstepped. The modification would cause a sharp decrease in microhardness. The paper reports data illustrating the cases in which such a behaviour was observed.