I would like to bolt a bracket to a steel pipe (1.5 inch diameter), with the nut located inside the pipe. Since the application needs to support a considerable amount of weight, I need some kind of washer or spacer that is flat on one side but spherical (or cylindrical) on the other side, to match the inside surface of the pipe. I'm afraid that a regular washer will buckle and/or crack under the pressure, since the force would not be distributed evenly. What can I use to solve this problem?
Most washers will flex somewhat, so unless it's a really small pipe, or you're installing in really cold temperatures, you shouldn't worry ... but I'd be more concerned with being able to hold the nut still while you're trying to bolt to it in a smaller diameter pipe. (I don't know if the 1.5" is ID or OD, but if it's outer diameter, and it's got any significant wall thickness, it's going to be tight)
If you're really concerned, you should be able to find a rubber gasket to put in there to take up some of the gap; you could also cut down a rubber grommet or bushing to fit in there. You could also use multiple thinner washers which will flex more easily than a single thick one.
Another option would be to take a hole saw that's got a similar inner diameter to the pipe, cut a plug of wood, then slice a chunk off to make the flat-on-one-side-curved-on-the-other piece you're looking for. (and then use a fender washer or similar so the nut doesn't dig into the wood).
I also needed to attach a flat steel plate to the exterior of a thin walled tube (it is a shelf attachement). The thin walled tube is more or less oval, and the inside diameter is about 40 mm (1 37/64"), and the washers are about 39.5mm ext diam., 10 mm internal diam., and about 2 mm thick (about 5/64" thick).
So, I needed to curve the washers and grind one end of the nut to conform to the bent washer, so that it could clamp the thin walled oval tube without deforming or tearing a hole in it...
Therefore, I heated the washer, clamped it on a bench vise and pounded it with a hammer. It ended up curved but not in a smooth curve. And it was tedious, as I needed twelve curved washers.
Later on, I choose to grind a pair of pieces of steel, to form a concave and a convex surfaces, with the approximate desired 20 mm curvature radius (about 3/4"), and used a large bench vise to press the washers into a better, more uniform shape. Using a 3/4" cilindrical stone in my Metabo GE 710 Die Grinder was easy and relatively fast for the concave shape, but tedious for the convex one. Still, it ended up being somewhat time consuming, but produced some quite good results.