Tear, rip, rend, split, cleave, rive can all mean to separate forcibly one part of a continuous material or substance from another, or one object from another with which it is closely and firmly associated.
Tear implies pulling apart or away by or as if by main force; it often suggests jagged rough edges or laceration.
Rip usually implies a forcible pulling or breaking apart typically along a line or juncture (as a seam, a joint, or a connection).
Rend implies greater violence than tear and either heightens the implication of a lacerating effect or adds that of severing or sundering.
Split implies a cutting or breaking apart in a continuous, straight, and usually lengthwise direction or in the direction of grain or layers. In extended use the term implies force or intensity sufficient to split something.
Cleave , a somewhat rhetorical word, may come close to split , but more often it conveys the notion of laying open by or as if by a stroke of an edged weapon.
Rive is elevated for split .