I am developing a product that I plan to have injection molded. One of the companies that excels in that kind of work is at Protomold.com. They have a thing you can order for free called the Proto Polygon. It shows different types of injection-moldable plastics along with their bendability and surface appearance properties. I'm looking at mine now. Glass-filled nylon won't bend, the hinge test on it breaks off. Maybe Taulman's nylon would be better.
The materials to do hinge well are TPE, HPPE and... you guessed it, ABS. I have bent the ABS hinge back and forth about a couple dozen times, bending it all the way back on itself. It is starting to split in the middle a bit but still works. I don't know how many times you expect to bend your iPhone case open but I think it would last me for a good while. The thinnest part of the hinge is .68MM.
BTW, I had my wife stitch me up a wallet of Tandy Imitation Alligator cowhide. It holds dollars as well as credit cards, DL etc. and my "pen glasses" (reading glasses the size of an ink pen). It also holds my Android phone. I've used it for three years and love it. It protects the phone from drop-and-breaks, some weather and looks as good as the day it was made.
I put self-adhesive Velco dots on the phone as well as the wallet. I can rip the phone out if I want or, usually, I just bend the wallet backwards and talk with the phone still attached to the wallet. All the checkout counter clerks ask me about it, so hey, you KNOW its cool.
Here's a couple pics without the phone in it (I'm taking the pic with the phone).
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Robox printer, HICTOP (Prusa i3 variant) Model 3DP17 printer, ELEK 2.5W laser engraver, AutoDesk 123D Design, Windows 10