Tabor’s relation

The question whether hardness is a property related to modulus (E) or yield stress (Y) is a problem which has been commented before by Bowman and Bevis 13). These authors found an experimental relationship between microhardness and modu-lus/yield-stress for injection-moulded semicrystalline plastics. According to the clasical theory of plasticity the expected indentation hardness value for a Vickers indenter is approximaterly equal to three times the yield stress (Tabor s relation). This assump-... 

Fig. 16. Correlation between microhardness at 0.1 min and true yield stress of PE M = 170000 (O) Mw = 2x 106 (A). The solid line is drawn according to Tabor s relation 28 )...

For the yield stress in compression, deviations from Tabor s relation giving values of 2Yc are found. This is presumably due to the elastic strain of the indented material. A detailed analysis of the H/Yc ratio on the basis of mechanical models of elastoplastic indentation reveals that H/Yc linearly increases with ln[(tan/3Ec)/Yc]. Compression-moulded (chain-folded) PE samples, which present the lowest crystallinity of all the samples investigated, also show the lowest H/Yc ratio as a consequence of the comparatively large elastic strains. 

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