I don't see a pulley or a V-belt in the image you show above, but I will ignore that and answer the question you wrote.
Fatigue is based on cycles. One cycle of stress occurs on each revolution of the pulley. The cyclic stress comes from the tension in the V-belt applying a lateral force to the pulley. A simple way to get the fatigue life of the pulley (and shaft!) is to model the pulley and shaft as flexible bodies. Apply the lateral force to the pulley and ignore the fact that it is spinning. You have SN curves defined for the material of the pulley in Engineering Data, which is required. In the Fatigue tool, it should be configured for Fully Reversed Load Ratio to account for the fact that the lateral force pulls then pushes as the pully rotates relative to a fixed point on the pulley. The Life plot is then read as number of revolutions to failure.
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