I have no idea what's causing it, but I do think if something moves when its not supposed to and hurts, you shouldn't do it.
My elbows pop when I do bicep curls and my knees sometimes hurt during squats. Instead of dynamic exercise that causes the popping/discomfort, I prefer static ones. For example, holding a low squat for 4 1-minute intervals instead of moving up and down.
Perhaps instead of crunches you could do planks? Those are supposed to be much more ergonomically sound, and help engage your back, arm, and leg muscles in the process. Good luck!