Nouns

(n)splinter, slivera small thin sharp bit of wood or glass or metal“he got a splinter in his finger”, “it broke into slivers”

Verbs

(v)secede, splinter, break awaywithdraw from an organization or communion“After the break up of the Soviet Union, many republics broke away”
(v)sliver, splinterdivide into slivers or splinters
(v)splinter, sliverbreak up into splinters or slivers“The wood splintered”