a "bullet" is the projectile that is fired.
A "shell casing" is the brass case which holds the powder and projectile.
A "cartridge" is the complete unit ready to be loaded into a firearm.
I assume you are asking about the shell casing. If the casing Split after being fired it can be for several reasons. The casing was reloaded to many times and fatigued. It was an excessively hot load, the chamber of the rifle is over sized or damaged, there is excessive head space in the chamber etc etc.
The split casing should be tossed out ( recycle old brass for cash).
if it split in your rifle, check to see if other fired brass show cracks or flaws.
Inspect the chamber.
If in doubt, have a gunsmith take a look at the firearm.
Better to be safe, than lose an expensive firearm, or get injured or worse.
Shoot safe