Having already done this once, I decided to go with a lighter material for the core, and a smaller haft for the axe. Still PVC with an Oak dowel core, but 1" versus 1.5".
You'll still need some form of material for the core, that big rubber sheet in this case. A few bolts, a haft and padding are the rest of what you'll need.
Step 1: Cutting and Attaching the Core
So, first thing is to come up with a vague design for the axe head. Mine's going to be a stocky bearded axe, so, I cut out that part of the shape. Tagged in the first picture.
To give it a little more rigidity, I added enough for a fold over the top. In pictures 3 and 4, you can see how it was folded, then drilled and bolted through.
Since this was a little more finicky than the last one, I had to clamp down the rubber and the handle, then use a hand drill to get it in roughly the correct spot. It did not want to stay on a drill press table long enough to clamp properly.
Four bolts and corresponding washers should keep the core together with little movement or tearing.