Toughness: When a huge external force is applied on a metal, the metal will experience fracture. Toughness is the ability of a metal to resist fracture. The ability of a material to resist fracture due to high impact loads, is called toughness. 

Hardness: Hardness is the ability of a metal to resist permanent change of shape caused by an external force. 

Brittleness 
Brittleness is a property of material which breaks with little or no deformation. 

Ductility: Ductility is the property by which a metal can be drawn into thin wires. It is determined by percentage elongation and percentage reduction in area of a metal. 
 

Elasticity of a material can be defined as the ability of a material to regain its original shape after an external force is applied on it. The ratio of stress applied on a body to the strain produced in it is defined as the Young’s modulus of that material.

Now, when we apply equal amounts of stress on steel and rubber having the same cross-sectional area, we notice that compared to steel, rubber gets stretched. The strain produced in rubber is much larger compared to that in steel. This means that steel has a larger value of Young’s modulus of elasticity and hence, steel has more elasticity than rubber.