Shakedown working limits for circular shafts and helical springs subjected to fluctuating dynamic loads

Abstract

Under quasiperiodic fluctuating dynamic loads, a structure made of elastic plastic material may fail by incremental collapse (ratcheting) or alternating plasticity (fatigue). For the kinematic hardening materials considered, the only two crucial material parameters needed are the initial and ultimate yield stresses, but not the generally deformation-history-dependent hardening curve between them. With the high-cycle loading we suggest taking the fatigue limit as the initial yield stress, and taking the stress corresponding to a certain allowable amount of plastic deformation from the empirical Ramberg-Osgood curve (or the particular cyclic yield strength corresponding to the amount 0.2% of plastic deformation) as the ultimate yield stress in our shakedown analysis of structures. The approach is practical and well founded within our shakedown theory, while the small deformation assumption framework of the classical plasticity theory is kept. As illustrations, we derive explicit expressions of the working load limits for the circular shaft and helical spring, which are based on the shakedown analysis and can be used for safety design of the structures with given loading conditions.