1
general::
Open a book to study or read, as in He passed the exam without cracking a book. This expression employs the verb to crack in the sense of "to open," a slang usage that dates from the early 1700s. [Colloquial; c. 1930]
American Heritage Idioms
2
general::
Phrase(s): crack a book
Fig. to open a book to study. (Usually used with a negative.) • I never cracked a book and still passed the course. • Sally didn’t crack a book all semester.
McGrawhill's American Idioms And Phrasal Verbs