Non-Cyclic Methods for Shakedown Analysis of Cracked Structures

Fatigue calculation of nuclear components under cyclic loading in the inelastic domain is a complex task involving nonlinear material models capable of predicting the strain-stress relationship beyond the yield limit. In this context, the ratcheting boundary that is the cyclic plastic strain accumulation under primary and secondary cyclic loads is a key criterion for structural design. A cyclically loaded structure made of elastic-plastic material is considered elastic shakedown if plastic straining occurs in the first few cycles and the sequent response is wholly elastic. In this paper the finite element calculations of a straight pipe with a notch is used to develop upper and lower bounds limits for the elastic shakedown of structures under periodic loading conditions. Linear methods using elastic compensation approach and the residual stress method derived from Melan’s theorem are used to generate the lower bound limit for the shakedown load while the upper bound is found through a method derived from Koiter’s theorem. Furthermore, the global classical theorems are complemented by local shakedown calculations within the regions near the cracks in terms of stress intensity factors that are evaluated from fracture mechanics theory. The presence of the stress singularity in a cracked structure is breaking down the classical shakedown theory and the conventional shakedown limit for a cracked structure should be zero due to the singularity within the stress field. In this methodology it is considered that the plastic deformation is confined to a relatively limited region around the root of a stationary crack and the energy released rate is associated with the change in the elastic stress field outside of the plastic flow region. Furthermore, probabilistic methods are employed for presenting the response surface plots of the shakedown limit in terms of the maximum accumulated strain and fatigue life against the strain hardening and yield limit.