I'm not a materials (or IC) guy, but my guess is that fracture toughness isn't going to be huge issue. Once the wafer is made, they're all going to be treated pretty gently. The tricky step is actually making the wafer. My understanding is that silicon wafers are normally manufactured by growing a giant silicon crystal ingot, and then basically slicing them into wafers. My understanding of graphene is that since they more or less have to be grown in sheets, then there isn't much of a subtractive process to put high stress on the material.

Most of the stress comes from expansion and contraction of the graphene when it's heating up and cooling back down again, which can be more or less pronounced depending on the substrate (glass, SiO, etc.). With chemical vapor deposition for example, often the substrate needs to be heated and the graphene has to be transferred from one substrate to another so there is still plenty of room for stress during the process. At this point any poor alignments of graphene sheets or individual atoms (I think there's three classifications for the edge of the sheet alone) can cause cracks.

How much stress would radiation outside the Van Allen belts add?

(I could probably find this out myself, but it was quite a few years ago. I assume a sheet would be damaged by gamma?)

I don't think there is a known material that wouldn't be damaged by gamma rays but it's a statistical process and we just don't have that many gamma rays on our surface.

I was wondering about space applications.

A sheet might maybe self heal after gamma radiation, that is why I asked (depending on environment, there might not be much else to happen?). Most other radiation is charged and might be kept away with strong magnetic fields.

But, as I wrote, this was a long time ago.