The current design of materials against wear considers hardness as the sole material property. As a result, the brittleness associated with increased hardness leads to severe damage. The purpose of this research is to understand the nature of conflicts between hardness and toughness of a new alloy composite. First, we designed Al-Cu-Fe alloys containing crystal structures of , , and quasi-crystalline i-phase. These and their combination with others lead to a set of alloys with various hardness and fracture toughness. Experimental study was carried out using a noble and hard tungsten carbide (WC) ball against sample disks. The WC ball did not produce any wear. The wear rate of those alloys was found to be dependent not only on their hardness, but also the toughness, an alternative to the well-accepted Archard-based equations.