How is the hardness of sandpaper defined? What factors are related to it?

The hardness of sandpaper is a physical feature that tells how well it can hold up against outside forces getting in. You can also think of it as how much energy it takes to make a local change on the surface of the sandpaper. Specifically, when sandpaper has a high hardness, it doesn't deform as easily when there's grinding force, and it can keep being sharp and having a good grinding ability.

1. Type of abrasive
The type of abrasive has a big effect on the hardness of sandpaper. Different types of abrasives have different hardness and how well they can stand wear. For instance, some specially made abrasives are so hard that they make the sandpaper stay sharp and have good cutting performance when grinding.

2. Size of the grains
The size of the grains also has an impact on the hardness of the sandpaper. With the same type of abrasive, the smaller the grains are, the lower the overall hardness of the sandpaper is. That means it's softer. This is because smaller grains are more likely to change shape when there's an outside force, and that makes the overall hardness of the sandpaper go down. On the contrary, the bigger the grains, the higher the hardness of the sandpaper.

3. Concentration of the abrasive particles
Abrasive concentration means the number of abrasive particles in one unit of area. The higher the concentration is, meaning the more abrasive particles there are in one unit of area, the higher the hardness of the sandpaper is. This is because a high concentration of abrasive particles makes the sandpaper better at resisting changes in shape when there's an outside force, and that keeps the hardness high.

4. Backing material
The backing is the material that supports the sandpaper and it has some influence on the hardness too. Different types of backing materials have different hardness and toughness. For example, sandpaper with a cloth backing usually can stretch and is tough, while paper-backed sandpaper is better at being flat and giving a good sanding result. These features can affect how hard the sandpaper is to some degree.

The hardness of sandpaper is a physical feature that combines several factors. When you choose sandpaper, you need to pick the right hardness based on what you need to grind and the material of the thing you're working on. At the same time, you also need to think about things like the material of the sandpaper, the size of the grains, the concentration of the abrasive particles, and the backing material to make sure you get the best grinding result.