Secondary Stress Weighting Factor and Plastic Reduction Factor for Circumferential Surface Cracked Pipe and Elbow Tests at Elevated Temperature and Internal Pressure
Authors: Pothana S. , Wilkowski G. , Kalyanam S. , Hioe Y. , Brust F. , Orth F. , Krishnaswamy P. , Hattery G. , Burger S. , Gilbert S. 
Published: October 2021

Abstract
Current flaw evaluation procedures for piping systems use elastic design analysis for secondary stresses (load-controlled), but fracture analysis is used for elastic-plastic loading behavior. The actual rotations/displacements of the pipe system that occur due to non-linear fracture behavior are much higher than the elastically calculated rotations/displacements. These actual non-linear rotations provide margins on the elastically calculated rotation values that come from uncracked pipe-design analysis. To account for this inconsistency, a Secondary Stress Weighting Factor (SSWF) was established which is the ratio of elastic-plastic moment to the elastic moment calculated through an elastic stress analysis. As long as the remote uncracked pipe stresses are below yield, the SSWF is 1.0, and if the uncracked pipe plastic stresses are above the yield stress, the SSWF reaches a limit which is called the Plastic Reduction Factor (PRF). A PRF was developed in an earlier investigation for outer diameter (OD) surface-cracked pipe tests at room temperature (RT). In this study, a PRF factor was developed for internal diameter (ID) surface-cracked pipes and elbows at an elevated temperature from recently conducted experiments.
This methodology can be used on any pipe size, material, and pipe system geometry. To validate this methodology further, SSWF and PRF values were determined for ID surface-cracked pipes and elbows of two different materials at elevated temperature of 550°F with internal pressure of 2,250 psi. The PRF values at RT (70°F) and 550°F were compared. The two materials used in this study were TP304 stainless steel and Alloy600.
Four-point bend pipe tests and elbow tests were conducted on pipes and elbows with varying circumferential surface crack sizes. The actual PRF value for a cracked pipe/elbow has a lower bound, which occurs when the test section of interest is at uniform stress. The center region of pipe in a four-point bend test is at uniform stress. A lower-bound limiting PRF value can also be calculated from stress-strain curves of pipe/elbow materials. Unlike tensile specimens, actual pipe systems are not uniformly loaded. Hence the reduction in stresses from the plasticity developed in the pipe system can vary depending on 1) loading conditions which determine if the pipe system experiences more elastic stresses or plastic stresses, 2) location of crack; if the crack is in a high strength/low toughness pipe or weld, plastic reduction is less, and 3) pipe size; if the pipe is large enough elastic-plastic conditions occur even for high toughness materials.
Prior to developing SSWF or equivalent PRF, it is important to recognize the relative nonlinear-rotation/displacement contributions from the crack and the uncracked pipe adjacent to the crack. This nonlinear rotation/displacement is key to translating fracture mechanics predictions (that include large plastic behavior) back to elastic pipe-system design stresses. Examination of the pipe test data for different materials and under different operating conditions showed that with smaller flaws, the nonlinear rotation of the uncracked pipe was much larger than the nonlinear rotation from the crack; however, for large deep flaws (with failure stresses closer to potential operating/transient stresses) the rotation/displacement due to the crack was larger than from the uncracked pipe. Hence, both nonlinear rotation/displacement contributions are needed in the SSWF development to avoid excessive conservatisms.