When grinding steel what causes the convex and concave curvatures?

Answer 1

Heat causes steel to expand until it reaches a point of transformation where the crystal lattice structure goes from a simple cubic (SC) to a body-centered cubic (BCC), in which case it then shrinks, if then quenched it will likely settle as a face-centered cubic (FCC) structure which is even more dense. This can make working with steel, such as knife-making, very challenging especially since most of it is likely quenched to a FCC structure to start with in order to make the steel hard.

What that means is that grinding can heat-up the grinded surface enough that it will anneal at room temp to SC, which will cause it to bow away from the grind. If hot enough however, a quench could possibly return it to FCC and thereby fix it's shape however in that case it's unlikely that the entire piece will get hot enough to do this evenly in which case you're only option to fix it is to heat the entire piece to the austenitic range and quench the entire object.

To avoid such hassles keep the steel as cool as possible throughout the grinding. Repeatedly dip the steel in water as necessary to keep it cool, and you might want to consider slowing the grinder speed. Machining is also an option that generally creates less heat if that's an option but in that case make sure the machinist keeps it cool throughout the process.