I would like to know if there is an established theory to determine the fatigue behavior of materials if the loading is stopped due to time limitations before the sample fails. Due to the application of loading (tension-compression or bending or cyclic loading), some damage will occur in the material internally. Are there any well-known procedures to determine the damage variable when the loading is halted before the failure of the material occurs? How can we determine the damage variable when the material experiences plastic shakedown (no ratcheting)?
Could you kindly share with me your idea, well-known publication lists, and so on? Thanks a lot for your precious time and kind attention.