Question

What is the difference between hard, tough, strong and stiff materials? Can someone please give me definitions of these terms and examples of materials which show these properties?

They all seem so similar so I'm confused

Answer 1

I think this is a brilliant question (I ask my students something similar!) Off we go ...

Explanation:

Hardness is the ability to resist indentation (or scratching if the indented material moves.) We can test relative hardness by pressing one material into another, the softer material is indented. The scales for hardness are many and confusing, there is no agreed system of units. Diamond is a very hard material, as no other (common) material can scratch it.

Toughness is the amount of energy required to fracture a material. It is commonly the most confusing term for students, and the opposite may help here, which is brittleness. Toughness is a feature of materials with a large region of plastic deformation. It is measured in Joules per `metre^2` so it is a measure of the energy required to open up (two) new surfaces in the material. Polymers, such as shoe soles, are commonly very tough - it would take you much effort to fracture one with a hammer.

Strength is just the maximum force (per unit area) or stress, a material can withstand, measured in `N/m^2`, but be wary - there are many sub-categories (I blame engineers) such as ultimate tensile strength, compressive strength, yields strength etc etc. Steel is strong, but carbon fibre is stronger per unit mass.

Finally, stiffness. This is the relationship between stress and strain. Alternatively, it can be defined as the resistance to extension (the ‘k’ in Hooke’s law was a measure of stiffness.) It is measured in `N/m^2` because stress in `N/m^2` devided by strain in `m/m` (extension over original length.) Alumina, a ceramic, is very stiff, as are glass and most others, but they are brittle.

The units themselves are enough to boggle the mind, so don’t worry! Please feel free to ask follow up questions - this was aimed as being an initial response and others may explain things more to your ‘wavelength’.