Are hardness, strength and toughness of materials not the same thing in a way? I had to look through several videos and re-read Wikipedia statements about these material properties several times before I could even begin to differentiate them. However, now that I have found out this is what I understand:


*

*Hardness measures the pressure needed to cause permanent change.

*Strength measures the load that can be withstood before permanent change.

*Toughness measures the stress needed before fracturing.
Overall, all three properties could be generalized to measure the stress needed to cause permanent change whether by fracture, plastic deformation or any other form of failure or no? Are their only differences the specific type of stress applied and the specific failure when the amount of said stress exceeds the property measurement?
 A: Strength and Toughness


Image source: Materials Group - University of Cambridge

We need the separate words "strength" and "toughness" because sometimes materials with high toughness and high strength are very different, like rubber and ceramic. Let's say you are designing a chair so that can support a person of a certain weight. Why not build it out of glass right? As long as the strength is high enough, it will support that person, you reason. The problem is if a person of weight above the design weight sits on the chair, it will shatter immediately because of its low toughness. Whereas a chair made out of polymers (plastic) may have the same strength as the glass but also have some toughness so that it would deform a bit before breaking. Final example: steel and ceramic both have high strength but very different toughness, so you need both words to distinguish their behaviors.
Strength and Hardness
While they do seem to be correlated, they are not exactly the same:


Image source: "Predicting the compressive and tensile strength of rocks from indentation hardness index" by Kahraman, Fener, and Kozman. Journal of the Southern African Institute of Mining and Metallurgy. 2012.

The figure above contains data on rocks but similar correlations are found in metals as well. As with strength and toughness, two materials may have the same strength but different hardness. Maybe people keep dragging sharp plows along your steel bridge and they are slowly scraping material away, so independent of how heavy those plows are (which determines the strength required) you decide to use a harder material.
