Composite in itself is a big world. You have to first narrow down to your interest of topic whether you want to work on PMC, MMC, Ceramics etc or you want to work on mathematical modelling or fabrication. Choose a specific branch or field within composite and read a lot of review papers that would give you initial idea to define your problem.
Composite itself is one of the most interesting and advanced topic. I suggest you to have a look on Additive Manufacturing area on composite material (foreseen a high demand).