Pereira
Your question is a little vague, the mechanism of fatigue is very complex. If your pump shaft has been manufactured by the pump manufacturer and you are operating the pump within the specifications stated by the manufacturer i.e fluid, speed, protection, etc then I would expect the pump manufacturer has already considered fatigue as a failure criterion. They will!! have selected an appropriate material, considered the loading applied, accounted for any stress raisers on the shaft etc.
All in all there should be no worries!!
Note that fatigue tests have been carried out for many different materials under various kinds of load, hence engineering practice relies heavily on this emperical data.
I expect your pump shaft will have been conservatively designed to never reach what is known as its "endurance limit" assuming it is made of ferrous material.
Hope this helps
dave1
