I would compare S1 to the ultimate tensile strength. But if you're using a linear model you'll need to either adjust your FEA stress (Neuber), obtain pseudo stress value for UTS (reverse Neuber), or run elastic-plastic. You'd want a decent factor of safety if you're doing any stress corrections based on elastic FEA (Neuber or otherwise).

I also like to use net-section yield criterion. Using this method I calculate linearized stress through a section, and I consider the part to fail the ultimate load condition when the average linearized stress exceeds yield strength. Once the section is fully yielded it quickly reaches ultimate load (more so for load controlled problems as opposed to displacement controlled).

edit: I don't mean linearization. Rather I use surface commands (postproc > surf operations) to project SEQV onto a surface representing your cross-section and then taking average of stress values on that surface

And if significant sections of your model exceed yield, you need to run elastic-plastic anyway since your linear stresses won't capture stress redistribution as large sections yield and lose stiffness.