Is there a connection between UV-degradation and the photoelectric effect Recently I've been learning about the photoelectric effect in my physics classes.

I only have a rudimentary understanding of chemistry, but I've been wondering what the connection is between the photoelectric effect and UV degredation.

For the sake of simplicity let's focus on the degredation of polypropylene.

My hypothesis is, that the UV light frees some electrons from the material. These will either weaken or break the bond between two molecules or atoms in the molecule itself.
I would ultimately except the molecule chains to be broken into smaller pieces due to this.

Is that a reasonable assumption or does the process work completely different?
Yes and no. 

In a metal, the photoelectric effect is when a UV photon has enough energy to push an electron from it's current energy level to at least the $n=\infty$ level. Extra energy goes into electron kinetic energy.

For UV degradation, we are promoting elections to higher energy orbitals in an analogous way. This produces an energized state that is highly reactive and may undergo radical reactions that ultimately lead to the formation of different species.

The difference is that we assume the electron is essentially removed from the atom in the photoelectric effect. Elections are weakly enough bound in a metal for a UV photon to achieve this. But in general, for UV degradation, the UV photon can't actually remove the electron from the molecule. But the photon can energize electrons that lead to degradation reactions.