If you haven't already, try having a look at the type certificate for the CFM56-5C2. Should be some data here. The title should be free for the viewing and printing at
www.faa.gov.
Of course, FCOMs would not have much tech data on the engine, but an AMM/EMM (Aircraft/Engine Maintenance Manual set) would. A google for A320 AMM "tech manual" revealed a couple of hits for AMM resources.
Otherwise an email describing your project and student status to CFM
may get you some access.