Hardness is the resistance of a material to localized deformation. The term can apply to deformation from indentation, scratching, cutting or bending. hardness commonly refers to a material's ability to penetrate softer material. An object made of a hard material will scratch an object made of a softer material.In metals, ceramics and most polymers, the deformation considered is plastic deformation of the surface.

For elastomers and some polymers, hardness is defined at the resistance to elastic deformation of the surface. The lack of a fundamental definition indicates that hardness is not be a basic properties of a material, but rather a composite one with contributions from the yield strength, work hardening, true tensile strength, modulus, and others factors. Hardness measurements are widely used for the quality control of materials because they are quick and considered to be nondestructive tests when the marks or indentations produced by the test are in low stress areas.

Toughness: The quality known as toughness describes the way a material reacts under sudden impacts. toughness is the resistance to fracture of a material when stressed. It is defined as the amount of energy that a material can absorb before rupturing, and can be found by finding the area (i.e., by taking the integral) underneath the stress-strain curve. It can be defined as the work required to deform one cubic inch of metal until it fractures. 



Toughness, often expressed as the Modulus of Toughness, is measured in units of joules per cubic meter (J/m3) in the SI system and pound-force per square inch (sometimes expressed as in-lb/in3) in US customary units.

Toughness is measured by the Charpy test or the Izod test.

Both of these tests use a notched sample. The location and shape of the notch are standard. The points of support of the sample, as well as the impact of the hammer, must bear a constant relationship to the location of the notch.

Difference:
The hardness of a metal limits the ease with which it can be machined, since toughness decreases as hardness increases Toughness is a combination of high strength and medium ductility. It is the ability of a material or metal to resist fracture, plus the ability to resist failure after the damage has begun. A tough metal, such as cold chisel, is one that can withstand considerable stress, slowly or suddenly applied, and which will deform before failure. Toughness is the ability of a material to resist the start of permanent distortion plus the ability to resist shock or absorb energy