I found this[0] chart at a NASA site a while ago purporting to say that, given the limitations of reaction-based rockets, a fusion rocket is still nowhere near good enough to reach even the closest star system in a reasonable time. The mass to drive a Shuttle cargo bay sized canister past Alpha Centauri in 900 years using Fusion power is supposedly 1000 supertankers of propellant. That's the closest star system, and doesn't count stopping, much less getting there in under a millennium. Even anti-matter, the best reaction-based rocket we can conceive of, is supposedly wildly impractical.
Given that, I'd like to see some quality calculations on exactly how they plan to get around the reaction mass problem before it makes sense to worry about stuff like materials in high radiation environments, and I don't see anything like that on their site. They seem to just kinda hand-wave it away, as far as I can tell. It seems likely that to build a practical starship, we'll need a propulsion system far beyond anything we can imagine today. Well, more realistically, calculations by people who seem to be qualified to perform them, since I'm probably not smart or well-versed enough to really understand it.
[0] http://www.nasa.gov/centers/glenn/images/content/84509main_w...