These are just thoughts. Artichokes are not on my grow list up here so
take my advice with a grain of salt.

You mentioned that your "not doing
anything to them" and that you live in UT.

I would agree w/ David, these are most likely underfed and probably heat
stressed so the energies of the plant are focused into maintaining growth
right now.

In choosing a nutrient and schedule, understand a flowering/bloom
fertilizer mix will enable the plant, but it will not trigger flower/seed
production in plants. The plant's specific conditions must be met, such as
the light cycle which is a trigger. If interested,
http://ucanr.org/freepubs/docs/7221.pdf
has a reference to gibberellic acid, a growth regulator .

Follow the USU recommendations of heavy N and water;
http://extension.usu.edu/files/publi...HG-2003-03.pdf .
There is also the recommendation of cutting back in both of these
references.

BTW, have you checked your pH? SW soil types and waters tend to be
alkaline, usually much harder to keep in check unless you stay on top of it.
This makes proper nute uptake more difficult. I did see an Extension paper
( a CA paper, I believe) where the recommended pH was 6.5 -7.0. On Dave's
Garden website, they have Artichoke (variety unk) listed up to 7.6. ( a bit
much I feel). There is more arid production towards SE CA that may be
closer to your soil/climate if you wish to look for other clues.

I read where certain varieties will flower up until fall under certain
conditions so you may still have a chance.

Good luck and let us know.