polyurethane or polyisocyanurate foam

Be sure the foam is "closed cell" foam.

A hollow tube filled with foam, water or cement will weigh more than an empty tube. Filling a tube with foam or helium will not make it float. We are talking about the tubes being sealed; right.

Why is this off topic? It is exactly what I thought.

Only when the frame work is open will the foam maybe make the thing float. Other than that Archimedes tells us how things float.

^{No I do not want an off topic either!}

Sounds like the OP should anticipate some learning curve surprises in using a new (to them) assembly method. Bending any 1/4 inch aluminum alloy plate shows some significant pressure can be developed.

That surprised a lot of experienced engineers, too.

I get the impression the OP wants the hollow tubes to be a sealed frame? To float, it would need to be free-flooding. Some clarification is needed.

I suspect that the OP also wants the advantage of having solid pieces to not worry about water migrating through a machined or accidental hole in the aluminum tube.

To float, it would need to be free-flooding.

RHS = Rectangular Hollow Section. A hollow aluminum section does not have to be free-flooding to float. Just the opposite: if it is free-flooding it will sink. Cap the ends and weld them air tight, or fill the section with foam. In either case, the result will float or not depending upon volume vs weight. (Many aluminium sections will float when foam-filled -- it obviously depends upon the wall thickness vs volume.)

Some clarification is needed.

How is clarification needed? The OP is asking for the name of foamed-in-place plastic: usually called just "two part foam" or "two part urethane foam" etc. Billet foam is usually cheaper when it can be used instead.

The weight of the aluminum plus the weight of the foam must be less than the weight of water of their combined volumes.

(The purpose of the foam is to keep the aluminum from being free-flooding.)

Plus the weight of any passengers or cargo they may have to support.

I think the op wants the Al. injected by the foam to increase the displacement.

Before he does anything with foam he only has to calculate the volume of the "whatever"

and decide upon / find out the weight. If the unit is heavier, than the volume of water

it will displace, - it sinks! If lighter, it floats. (Cannot get more basic.)

jt.

I love it when there is no need to think.

You might search Global Spec (or Google) "Syntactic Foam". This is what we used in Underwater R&D when constructing autonomous vehicles for buoyancy, most of which were free flooding. It can be purchased in various grades, in various densities in lbs/cu.ft. We always purchased in preformed blocks of the appropriate size to allow the foam to be contoured to fit inside of the cavity as required. In your case, you might check for the availability of sections of Syntactic foam that will slip inside of your aluminum frame sections. I've never seen the Syntactic foam in a kit form, but that's not to say that it's not available. I've haven't been involved in Underwater R&D for a number of years.

You can get syntactic foams that are coated with epoxy powder (or other heat curable powders for that matter)that can be poured into place. But, they require heat curing.

My experience is mostly with space craft, not underwater.

If you're going to bolt this together and not weld it, you may be able to use that pink insulating foam they sell at builder's supply stores. Just cut it to size and shove it inside the tubing. I'm pretty positive it's closed-cell, but you should test it to be sure it will do what you want.