Consider the steel ruler, ceramic mug, rubber strip, and plastic food storage box. It is not useful to describe each one as “strong” when trying to make comparisons. Mechanical behavior is broken down into different properties because a material could exhibit good performance in one situation and poor performance in another. Strength, stiffness, hardness and toughness describe different aspects of the material response to stress, deformation, contact and fracture.
Strength is a measure of how much stress a material can withstand before it yields or fails. It may refer to yield strength, tensile strength or compressive strength depending on the situation. Yield strength identifies the onset of permanent deformation and the tensile strength is associated with the maximum stress in tension. High strength does not require a thick or heavy material. The value of strength can also depend on the component shape, defects, temperature, processing and service conditions.
Stiffness is a measure of the resistance to elastic deformation. Think about the case in which you apply similar loads to a metal ruler and flexible plastic strip to bend them. As long as the materials stay within the elastic regime, the ruler will deform much less under the applied load because it has higher stiffness. Stiffness is usually characterized by the Young’s modulus. A high value for stiffness only means the material deforms elastically for a relatively larger amount of stress. That is, it is possible for a material to be stiff but fail at a relatively lower strain. Conversely, another material may undergo large elastic strains before failing.
Hardness describes a material’s resistance to localized deformation (indentation), scratching or surface wear. A hard coating on a tool may resist the effects of abrasion, but the properties of the bulk material underneath can be completely different. Hardness is measured under controlled conditions using an indenter. So, a simple scratch test is not a good substitute for hardness measurements. It is also possible that a material that is very hard is brittle. Glass and many other ceramics have high hardness values because they resist indentation, but they are not very tough; they may suddenly fracture in the presence of a pre-existing crack.
Toughness is a measure of the amount of energy that a material can absorb in a tensile test up to the onset of fracture. Because toughness is associated with the amount of energy the material can absorb, it depends on both the magnitude of stress and the magnitude of strain. A large area on the stress-strain curve means high toughness. A material with high toughness may still be under high stress when it fails. Also, it may have high toughness if it undergoes significant amounts of strain while absorbing the energy. This is quite different from simply having high strength. High strength is important but materials that undergo very small elastic and plastic deformations will still break. The energy absorbed by the material is proportional to the area under the curve in the elastic and plastic regimes. It is possible for a material that has lower strength and higher deformation to be tougher than a material that has high strength but very little elasticity. It is even possible to have two materials that have the same ultimate strength but a very different amount of plastic deformation that would lead to very different toughness values.
Grab a notebook. Prepare four columns and title them strength, stiffness, hardness and toughness. Identify a common household item, say, a metal spoon, rubber eraser, ceramic plate or plastic storage box lid. List the evidence for each mechanical property. What can you conclude without conducting a material property test? A metal spoon is very good at resuming its shape immediately after small deformation. You can safely infer that it has a high strength, and you can tell that a very large load would be needed to permanently deform the spoon. However, without a tension test on the material, you cannot infer the actual value for the yield strength. You can see that the surface of a spoon or plate has been scratched. Can you infer anything about the hardness of the material? It is clear that material removal has taken place and that the surface has been worn by contact with some objects. A simple scratch on a steel spoon or plate is not a measurement of the material hardness value.
Instead of the vague question “which material is stronger”, identify the purpose of the application more specifically. Are you interested in resistance to permanent deformation, resistance to elastic deflection, resistance to wear, or impact absorption in the presence of a defect? Sometimes several mechanical properties are needed for good material performance. Other design considerations include density, temperature, corrosion, fabrication and manufacturability. There is no simple solution. It is always possible to pick up the phone and talk to an engineering materials supplier about the right material for your application. But the ability to talk about a material more specifically than using the one-word answer to everything is the first step toward identifying what you need in order to make the best choice.