In flaw evaluation criteria, the secondary stresses (displacement controlled) may have different design limits than primary stresses (load-controlled stress components). The design limits are based on elastic stress analysis. Traditionally the elastic design stresses are used in the flaw evaluation procedures. But realistically a flaw in the piping system can cause non-linear behavior due to the plasticity at the crack plane as well as in the adjacent uncracked-piping material. 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).
Four-point-bend tests were conducted on pipes with varying circumferential surface-crack lengths and depths. The moment-rotation plots obtained from various pipe tests were used in the determination of PRF. A lower-bound limiting PRF can be calculated from a tensile test, but pipe systems are not uniformly loaded like a tensile specimen. The actual PRF value for a cracked pipe was shown to have a lower bound, which occurs when the test section of interest is at a uniform stress (such as the center region in a four-point pipe bend tests). When multiple plastic hinges develop in a pipe system (a “balanced system” by ASME Section III NB-3650 design rules), this gives a greater reduction to the elastically calculated stresses since there is more plasticity. It was found that the plastic reduction is less when most parts of the pipe system remains elastic, or if the crack is located in the high strength/ lower toughness pipe or welds, or if the pipe size is large enough that elastic-plastic conditions occur even for a higher toughness material. Interestingly, it was shown that the same system with different loading directions could exhibit different actual PRF values if the change in the loading direction changes how much of the pipe system experiences plastic stresses. For smaller cracks, where the bending moments are high, the actual PRF is controlled by plasticity of the uncracked pipe, which is much larger than the plasticity that occurs locally at the crack. However, for large cracks where the bending moments are lower (closer to design conditions), the plasticity at the crack is equally important to the smaller amount of plasticity in the uncracked pipe for the actual PRF. Hence the plasticity of both the uncracked pipe and at the cracked sections is important to include in the determination of actual PRF values.
Efficient and accurate determination of 13C T1 and T1ρ relaxation time constants of high-mobility polymers from limited-resolution spectra with optimized pulse sequences and data fitting
