Assuming that the joint is solid, there is no prevailing torque, and all torque is used to stretch the external threads (and overcome friction), then yes, there is a straightforward way to calculate the torque that will damage threads. You can use the following equation (uses SI units, so you will need to convert):
M = F/1000*(0.16p+mu(0.58d2+((do+di)/4)))
where
M is the applied torque in N m
F is the preload developed in N
mu is the friction coefficient for the materials involved
p is the pitch in mm
d2 is the pitch diameter
do is the nut outer contact diameter
di is the nut inner contact diameter (most likely the hole size)
p, d2, do, and di are all dimensions that will come from your part drawings. Unless you specify mu, you will need to estimate this (your nut supplier can provide this for you). F will need to be calculated using the materials properties for your parts. Your nut will have a materials specification, and perhaps a load requirement (e.g. Proof Load). For the shaft, you can use this equation:
F = s * A
where
F = force in N
s = material yield stress in Pa
A = cross-sectional area in m^2
for a 7/16"-20 fastener (assumed to be a solid threaded region on the shaft), A = 7.66 * 10^-5 m^2.
Good luck.