THE SIGNIFICANCE OF SLOPES OF THE SEMILOGARITHMIC RELATIONSHIP BETWEEN HARDNESS AND SOLID FRACTION OF POROUS COMPACTS

On the basis that the solid fraction theta-r is not a standardized parameter which reflects the degree of three-dimensional bonding in a porous compact, a more appropriate parameter, the normalized solid fraction P, has been proposed. P = (theta-r - theta-rT)/(1 - theta-rT), where theta-r is the solid fraction of the compact and theta-rT is the solid fraction of the powder after transitional restacking (i.e., after the initial extensive rearrangement). In a similar manner, the indentation hardnesses of the porous compacts, H, were converted to relative hardnesses by the following operation: ln H/ln H0, where H0 is the hardness of the compact at zero porosity. Evidence has been provided to prove that the normalized solid fraction P is a more appropriate parameter than the solid fraction to describe the degree of three-dimensional bonding in a compact. The significance of the slopes of the relationships between the logarithm of hardness, ln H, and the relative hardness, ln H/ln H0, on one hand and the normalized solid fraction P, on the other has been clarified. The slope k(s) of the initial portion of the plot of the logarithm of hardness of a compact as a function of its normalized solid fraction furnishes information on the ductility of the substance under test. When the relative hardness ln H/ln H0 is plotted as a function of the normalized solid fraction P, the resulting slope b(s) of the initial portion of the plot is a measure of the fracture propensity of the material. It has also been shown that the relationship between the slopes b(s) and k(s) as functions of the composition of the mixtures exhibits percolation theory attributes.