Right Stuff: The coyote has described the TT straps pretty well, ie "it anchors the rotor blade to the head/hub." The TT stands for Tension Torsion. The outward forces (centrifugal) of the blade create a tension loading on the straps and when the blade pitch is changed the straps twist with it to allow blade movement, aka torsion.
When the helicopter is flying, the straps are working hard in both tension and torsional directions. The stress and constant movement of the windings would have to be the main factors in the life restrictions of the TT straps, although Bell stipulate that once a strap has been fitted to a helicopter the calendar life commences even if it does not fly.