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Where have you found the materials from the title to be usefull? I ask because I have obtained a significant amount of plexiglass and I am stuck as drilling it or cutting it leaves nasty fractures and I am afraid that said fractures will over time expand and wreck the model.

All sorts of uses. Very handy things to have around for terrain. Are you sure about exactly what you have, though?

"Plexiglass" is frequently used as a catchall term, simply meaning "clear plastic sheet." Clear polystyrene has rather different working properties than clear acrylic or urethane resin, though. The sort of plexiglass sold in hardware stores is often used to make guards and jigs for power tools, specifically because it's easy to cut and drill, as well as flexible enough to resist fracturing. You can score and snap it, drill it with normal twist bits, saw it, tap holes in it, sand it, etc. Sounds like what you have is significantly more brittle, as is often the case with clear polystyrene (much more than the white HIPS we call 'plasticard'). If you have any solvent cement for styrene models, you can always lay down a little test patch to see if it melts - that'd be a quick way to see if it's polystyrene.

Also consider your cutting methods. Scoring and snapping thin sheet often gives cleaner results than, say, using scissors or shears that flex the material while it's under cutting stress. When drilling, use a sacrificial backing board that you can drill right into - it'll support the material to reduce flexing and keep the bit from biting and screwing itself in, instead of cutting. In extreme cases, you might even need a sacrificial top, as well.

It definetely appears to be clear polystyrene but I'll have to check it. Since acetone melts polystyrene would softening the material with a drop of acetone work? Sacrificial plates aren't an option because I am cutting curved surfaces.

Chemically softening before cutting/drilling will just make a mess, I'm afraid. Instead of the drill bit shaving away and leaving a hole, it would just pull at the soft material and leave a torn, tangled, melted mess. Same with sawing or scoring. Solvents work from the outside in, remember - you won't soften ALL the plastic before you melt the outside, leaving the inside just as brittle as it was, before.

Any more information you can give? Perhaps pictures, if your material is odd scrap? It's hard to give any advice beyond "experiment, a bit," without either knowing more or just resorting to the usual tips for working with plasticard or stock model kits... I'd have very different suggestions if I found out you were working with model airplane canopies/car windows than I would if you were working with old product packaging, off-cuts from a sign-maker, industrial drops, etc.

 oadie wrote:
The sort of plexiglass sold in hardware stores is often used to make guards and jigs for power tools, specifically because it's easy to cut and drill, as well as flexible enough to resist fracturing.

That sounds like polycarbonate rather than plexiglass. Plexiglass is acrylic sheet, and it is somewhat brittle. It can be cut/machined without it cracking or chipping, but if you’re not gentle it will chip/crack.

The softer stuff used for impact resistance is polycarbonate, with the trade name Lexan.

As it has been said before it might not be acrylic glass (plexiglas is just a brand name).
Even if it is acrylic glass, there are two kinds XT and GS - Extruded and Cast.
Cast is easy to drill, saw or mill.
XT is prone to chip and fracture when drilled or sawed and melts faster when milled.
A very good tool for cutting both kinds of acrylic glass is a laser cutter.
There are many other transparent plastics. Some are only available as foils (thinner than 1mm). But I'm not aware - that doesn't mean that there is none - of any transparent plastic other than extruded acrylic glass that would fracture when drilled, the others would melt.

If it is some acrylic glass XT try cooling the drill and don't push too fast. If you have a drill rig, use it.

One trick I've learned with cutting acrylic (I use a bandsaw with a fine toothed blade as I don't have a lasercutter) or drilling it is to tape the areas you are drilling. I also adjust the speed down a little, like for metal.

Just put a piece of masking tape down on the surface where you want the hole, or the line where you are cutting (so you cut through the tape AND the acrylic). Similar techniques are used to drill tile (the tape is to stop the drill bit slipping.)