what geologic process takes place in cracks or breaks in the rock

The geologic process is fracturing or faulting if the rock breaks and moves, and fracturing/jointing if it breaks without major movement. In simple geology terms, cracks or breaks in rock are usually called fractures , and they often form from stress, cooling, or tectonic forces.

Quick Scoop

• Fracture = a break or crack in rock.

• Joint = a fracture with little or no movement.

• Fault = a fracture where the rock blocks move relative to each other.

• These can form from tectonic stress , cooling , or other geological forces.

So the best single answer is: fracturing. If movement along the break is included, then it becomes faulting.

TL;DR

Cracks or breaks in rock are generally called fractures ; if the broken pieces move, it is faulting.