Toughness and Ductility
Toughness: Toughness is an estimate of how much energy is consumed before the material fractures. Energy consumed = work done = force x distance – which you can easily see, is related to the stress and strain. So:
Toughness = the strain energy = area under the stress-strain curve
[Note: to compute toughness, True stress and True strain are used, which measure the instantaneous stress strain at each point in the σ−ε curve.]
Strength of a material is an estimate of the height of the σ−ε curve, while toughness accounts for both, the height and the width of the curve.
Ductility: Ductility is a measure of how much the material can be stretched before it fractures. A simple measure of ductility is:
Ductility = 100 x (Lf – Lo)/Lo
Hardness: There is no precise definition of hardness. We shall take it to mean “resistance to plastic deformation under load”. Under this definition, it is measured by the permanent deformation on the surface of the material being tested, when subjected to a standard loading. There are several different hardness tests that have been developed over the years. One of the earliest is the Mohs scale, which lists 10 materials (diamond = hardest := 10, and talc = softest := 1). If a material has Mohs hardness = n, then it should be able to put a scratch on all materials below hardness n, and not on any materials above harness n 1. It is usually used by geologist who cannot carry testing machines with them in the field. Most common tests for engineering materials are Brinell, Rockwell and Vickers’ tests. The figure below shows how the test works.
Figure 1. Different hardness testing methods [source: Kalpakjiam and Schmid]
The Brinell hardness (HB) test is the best for achieving the bulk or macro-hardness, particularly for those materials with heterogeneous structures. For harder materials, the Rockwell (HRA or HRC) or Vickers (HV) scales are more commonly used, since for such materials, the ball used in Brinell itself deforms significantly, giving unreliable measurements. If the sample is very small and hard, Knoop hardness may be used (HK). In most cases except Brinell, the surface may have to be made smooth by polishing.
Effect of temperature: In most cases, hardness varies exponentially with temperature, as: H = Ae-BT, where A and B are constants for the given material, T is the temperature in Kelvin, and H is the hardness.
Figure 2. Relative mechanical properties in decreasing order for some common materials