Tabor’s criterion

Hence, in the present chapter the Hill and Marsch equations fractal analogs are obtained, which has shown, that cross-linked epoxy polymers microhardness is defined by their structure only, characterized by its fractal dimension. Tabor s criterion is only fulfilled for Euclidean (or close to them) solids. The cross-linking degree enhancement results to loosely packed matrix loosening and corresponding reduction of cross-linked epoxy polymers microhardness. The similar results obtained for linear polyethylene and nanocomposites on its basis, filled with organoclay [16]. 

Figure 9.28 The dependences of the ratio HJOy on the structure fractal dimension df. 1,2- the theoretical calculation according to Equations 9.38 (1) and 9.39 (2) 3, 4 - the experimental data for epoxy polymers EP-2 (3) and EP-2-200 (4). The horizontal dashed line indicates Tabor s criterion c = 3 [60]...

Thus, the fractal analogues of the Hill and Marsch equations obtained above have shown that the microhardness of crosslinked epoxy polymers is defined only by their structure, characterised by its fractal dimension. Tabor s criterion is correct for Euclidean (or close to Euclidean) solids only. The degree of increase in crosslinking results in loosening of the loosely packed matrix and to a corresponding reduction of the microhardness of crosslinked epoxy polymers [60]. 

For a simple calculation based on the Lindemann criterion and comparison with experiment see for example Tabor, D. Gases, Liquids and Solids, 1969, Penguin Books, Baltimore, p. 207. The calculation assumes harmonic vibration of the particles, against Young s modulus. Melting temperatures are calculated with reasonable accuracy for metals and even for quartz, but not for organic molecules. 

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