For comparison the polyurethane I was using has the following traits:
Shore D hardness: 85
Tensile Modululs: 370 000 PSI (2.55 GPa)
Ultimate Tensile: 7800 PSI (54 MPa)
This is the polyurethane resin I was able to get locally. One of the interesting parts of moulding in polyurethane is there is a great variety and you can select just about whatever traits you like. For my production run I was considering the below polyurethane:
IE 3075
Shore D hardness: 80
Tensile Modulus: 420 000 PSI (2.90 GPa)
Ultimate Tensile: 10 500 PSI (72 MPa)
I've used tensile modulus for consistency with Dennis, and the fact that for the plastics we're considering the tensile modulus usually close to the flexural modulus. However, I think flexural modulus is probably the more important number for hinge consideration.
It looks like the ultimate tensile of Oak is somewhere between 50 and 100 MPa.
Polycarbonate has a shore D hardness around 80.
For both polycarbonate and polyurethane you could use fibre reinforced versions to get even better numbers, but that may not be necessary or worth the extra trouble.