A long fine crack in the surface of something is called a fissure. If you see a fissure in the ice on a frozen lake, you'll want to take off your skates and head back to the car.
Fissure has its roots in the Latin word fissura, meaning a cleft or crack. If something breaks into fine cracks, you can describe the action with the verb form of fissure. For example, "She watched in horror as the earth fissured beneath her feet, recognizing the signs of an earthquake but powerless to do anything to save herself except throw herself to the ground and hang on."