In flaw evaluation criteria, the design limits for the secondary stresses is frequently different than the primary stresses. The evaluation procedure for primary stresses are load-controlled based which is independent of pipe deformation. The evaluation procedures for secondary stresses are displacement controlled which are dependent on pipe deformation. Certain stress components such as thermal expansion, thermal striping, welding residual stress, misalignment/cold-springing, dynamic anchor motion are historically considered secondary stresses and their design limits are based on elastic stress analysis. In reality, there can be much more rotation/displacement of the pipe with nonlinear fracture behavior due to nonlinear material behavior and plasticity at the crack plane providing extra margins on the elastically calculated rotation values that come from uncracked-pipe design analyses. In assessing secondary stress margin, a secondary stress reduction factor is defined as the ratio of elastic-plastic moment to elastic moment. This is equivalent to another concept using a Plastic Reduction Factor (PRF) as well as the inverse of structural (or safety) factor (SF) in ASME Section XI flaw evaluation criteria for various service levels.

In this work, the secondary stress reduction factor was determined for a representative pipe system with multiple crack sizes, crack locations, and loading conditions. Nonlinear finite element (FE) analyses of a whole uncracked-pipe system were performed using ABAQUS® under various loading combinations to determine the critical locations for cracks in the pipe system. Next, FE analyses of the cracked-pipe system were carried out using cracked-pipe element — a methodology developed by the authors. Cracked-pipe system analyses were conducted for two loading conditions — one producing contained plasticity or single-hinge system and the other producing larger plasticity in the pipe system. Several analyses were conducted for each loading conditions with a combination of two crack sizes at two key locations. Secondary stress reduction factors were then calculated for both loading conditions in the pipe system. Finally, the margin in secondary stress was assessed for the pipe system by comparing the secondary stress reduction factors with that for straight pipe sections (determined for experimental bend tests) as well as with the recommended equivalent PRF and the equivalent ASME secondary stress correction factors.

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