Application of the Hall-Petch Relation to Microhardness Measurements on Al, Cu, Al-MD 105, and Al-Cu Alloys

The hardness of materials, H, is dependent on grain diameter, d, in a similar way as the flow stress in the Hall-Petch relation: H = Ho + KHd−1/2, where, Ho and KH are constants. The microhardness of 2S-Al (99.5% Al), pure Cu, Al-MD 105 (Al-1% Al2O3), and Duralumin (Al-3.94% Cu) is found to vary with grain size according to the Hall-Petch equation with reasonable accuracy. The grain boundary hardening KH of Al-MD 105 is found to be the highest although this material recrystallizes to larger grain sizes than those for the other materials; this is attributed to the resistance of boundaries to deformation arising mainly from the presence of hard, second phase alumina particles. However, the contribution of solution, precipitation, and dispersion hardening may be added to grain boundary hardening according to Hansen and Lilholt.