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University Engineering

Notes by Category University Engineering

Mechanics & Stress Analysis*
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Hardness, Toughness, Creep & Fatigue


The hardness of a material is its resistance to wear or indentation. It is generally measured using one of two types of indentation test.

Brinell Hardness

A 10 mm diameter steel sphere is pressed into the test material by a known force. This causes the sphere to leave a circular impression in the test material. The hardness is given by the following function of force, P, sphere diameter, D and impression diameter, d:

Vickers Hardness

Instead of a sphere, a diamond shaped stud is used to indent the test material. The hardness is then calculated as a function of the force, P, and the diagonal of the square indentation, d₁:


Toughness is related to a material’s ability to resist sudden, brittle fracture under a load. It is defined as the amount of energy needed for a material to fracture. Therefore, its units are Joules, J.

It is related to the area under a stress-strain curve, but is entirely separate to Young’s Modulus:

For fracture to occur, a crack needs to initiate somewhere and then propagate through the material. Often, the crack will initiate at a stress concentration like a screw hole or a bend. Fracture could be brittle or ductile.