General relationship between strength and hardness

Both hardness and strength are the important properties of materials, and they often obey the three times empirical relationship in work-hardened metals and some bulk metallic glasses (BMGs). But the relationships between strength and hardness are quite different for those coarse-grained (CG) and ultrafine-grained materials, brittle BMGs and ceramics. In the present work, some Cu alloys with different microstructures, Zr-, Co-based BMGs and Al2O3 were employed to analyze the general relationship between hardness and strength. Several different relationships could be gotten from the experimental results of different materials available, and three types of indentation morphologies were observed. Indentation with “sink-in” morphology always represents a state of material and one third of hardness is in the range from yield strength to ultimate tensile strength. The other two indentation morphologies induced the fully hardening of material, so hardness could represent the intrinsic mechanical property of materials. The ratios of hardness to strength are found to be affected by the piled-up behaviors and their ability of shear deformation. Combined effect of the two aspects makes hardness approximately be three times of strength in the work-hardened crystalline materials and the shearable BMGs, but higher than three times of strength in the brittle-, annealed BMGs and ceramics.