My experience with foam (just like what you used) started with me gluing stacks of foam with epoxy for a nose cone project. At the time epoxy was the best glue for the job, until I heard about Glidden Gripper which is a bonding primer and sealer. Unlike epoxy, the “Gripper” is water based which makes for easier clean-up.
The problem with either epoxy or nearly any other adhesive, is that it’s not wise to spread your glue across the whole surface of the foam you’re using. Most any adhesive is going to leave a really thin wafer of glue that shows up when you are turning it or sanding it. The solution was to spread glue more to the inside of the foam and not all the way to the outer edge. Leave yourself at least ½ inch of bare unglued foam so that, when you sand it, you are no longer sanding that hideous wafer of glue. Easy to spot on this foam cone I turned.
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It’s nearly impossible to hide that wafer unless you gouge it out. I accidentally discovered a foam filler that works really well at patching up dings and flaws and sands perfectly. Works great!
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If you are still pondering about glues, there’s a great video that compares adhesion strength on this very same foam.