Turnitin assignments are created with a start date, due date, and a post date. Once the due date has passed, Turnitin expires the assignment and access is read-only. Therefore, when you click on any of the students' submitted papers you would receive a message stating the 'course has expired'. You as an instructor would not be permitted to grade students' submission, and students would not be allowed to submit to the assignment.
Upon receiving the expiration message, you have two options:
Here is how:
You may also create a new Turnitin assignment and set the due date to the date that the semester ends. Hide the assignment so that students would not be allowed to submit to the assignment. This option ensures that Turnitin assignments would not expire before the semester ends.