I am working on a project right now and am really short on time. I can't seem to get the clipping mask (outer highlighted pink circle on iris) to work on the zig-zags to keep them from going past the iris. The zig zags also only seem to be outlined by an inner circle instead of the shape itself. Iv'e tried merging, clipping, switching the order of the zig-zag and clipping mask, and a few other things. I can't seem to be able to fix this problem, and whenever I do try those things the whole zig-zag gets deleted.
I don't know if this helps with diagnosing the problem at all either. I did create the zig-zag from the eclipse tool.
As I (mis)interpret your description and image, what you call zig-zags could also be called rays, and what you call the clipping mask (still) consists of two independent selected ellipses which need to be turned into a Compound Path to form the inner/outer boundary of the iris and and to be used as the Clipping Mask; you can just select both, as you have in the image, and then press Ctrl/Cmd+8. The Compound Path has to be above the zig-zags/rays as seen in the Layers palette, and the safest way of getting it to work is to have all of them outside any Groups.