Assuming the bolt sees only torsional shearing and not a complex stress pattern from bending as well, the torsion formula should work as a good approximation, assuming the head shears off of the body.
The material's tensile strength is 586 MPa. The transition radius under the head should be 0.6mm, the head is 13mm in dia, and the body diameter looks to be 8mm.
Stress concentration ~ 1.46
max Shear stress = K * T*c/J
c = 7.78mm
J ~ pi*(d^4)/32 = 402 mm^4
max stress = 586 MPa
K ~ 1.46
586 MPa = 1.46 * T * 8mm / (402mm^4)
T ~ 20.2 N-m ~ 14.9 lbf-ft
Your mileage may vary, and my calculations may be wrong, so you'll probably still want to shear a screw to find out.
I think that we need to know if the head of the fastener is going to be seated on the surface when the torque is applied or if this will be a blind hole torque. If the head is not on the bearing surface, then Istre's numbers will be fairly close. If the head is seated on the surface, you need to remember that about 40-50% of your applied torque to the head is going to friction under the head of the screw, resulting in much less torque acrually getting to the shank of the part. It is common for seating torque values to be higher than blind hole torque values.
Best way to find out is to take a handfull of parts and test them to failure.
Actually, good catches by both of the follow-ups. I read the wrong line for material strength, and I only gave the torque required for a direct shear of the shaft at the head, not for torque required to shear PLUS frictional seating torque.
I guess the lesson is that these forums are a useful place to get starting information, but anything said should be verified before use.
