Hello Francisco Dominguez,
1) Perhaps the first thing that you should consider is that the stress calculations used in the ASME B31 Codes for Pressure Piping DO NOT CALCULATE true elastic (or plastic) stress. Some people who read this will be shocked by that statement.
It has always been the intention of the B31 Code Committees to provide the most simple methodology consistent with the design of safe piping systems (while also allowing the engineer to employ more rigorous methods if the engineer thinks that these methods are appropriate). The term “simplified method” necessarily mean imperfect – just like the real world. So, what is “the most simple methodology”? Consider that the stress equations in the B31 Codes are based upon beam theory – so the calculation is simply the bending moment divided by the gross section modulus of the beam (pipe). This is M / Z. Of course we know from various practical experiments (e.g., Markl et. al.) that it often happens that the simple bending stress equation will not always calculate the highest stresses in every piping component. For a simply supported straight section of pipe (the “beam”) M / Z would calculate the bending stress at the extreme fiber to an adequate accuracy (although it should be understood that “real world” pipe is not perfectly round and that “real world” materials (e.g., steels) are mot perfectly homogeneous materials – the properties often vary along the pipe wall). Prior to 1950 the B31.1 Code Committee knew that “corrections” would be needed to the simple beam bending stress equation if it were to be applied to “other than straight pipe” type piping components. The list of “other than straight pipe” type piping components would include bends (elbows), branch connections (many and varied types), reducers, and other configurations that included geometric and metallurgical discontinuities. The work done by Markl and his team of “all stars” showed that the effect of fatigue should be included in the consideration of cyclic bending stresses. Stress intensification factors (SIF’s) were introduced to modify the simple beam bending stress equation to address the issue of fatigue in various “other than straight pipe” type piping components. The SIF’s come from the statistics that resulted from cyclic testing of various piping components and they are closely associated with the ratio of cycles-to-failure for the specific piping component to the cycles-to-failure for straight section of pipe WITH A GIRTH BUTT WELD. For this comparison the section of pipe with a girth butt weld was assigned an SIF of 1.0 (Testing of straight pipe with no GBW against straight pipe WITH a GBW shows that the later should have a SIF closer to 1.8 – something to be remembered). Similarly, this testing showed that the flexibilities of various piping components were not the same as that of straight pipe, so flexibility factors were introduces to the calculation of stresses in piping components. Later, the calculation of stresses in components was modified to address a variation in stiffness due to internal pressure. So now we are left with a simple beam bending stress equation with several “Band-Aids” (modifications) having been applied. So while we started with an equation that calculated theoretical elastic stresses in pipe (assuming it was “perfect”) we now have an equation that calculated equivalent stresses (that are not true elastic stresses). It works out fine as long as we compare these calculated equivalent stresses to the allowable stresses that the B31 Code Committees have prescribed.
All of this is reviewed in support of my statement that you cannot directly compare stresses that are calculated by B31 Code (beam theory) methodology to stresses that are calculated by finite element methodology, or to stresses that are calculated by another ASME Code’s shell theory methodology. Each methodology has its own “maximum allowable stress” prescribed and the methods and the allowable stresses cannot be mixed or applied indiscriminately (something else to be remembered). I certainly hope that FEA calculated stresses are not being compared to B31 allowable stresses.
The reality of plastic deformations in pipe bends and elbows (as well as the benefit to the redistribution of deformation energy after “complete shake down” has occurred) is so well documented as to be a non-issue. Much work has been done (and published) in the area of FEA calculations of stresses in piping elbows and bends and the reported results vary greatly. While more FEA studies by individual engineers of stresses in piping elbows and bends may lead to a sharpening of his/her modeling technique the result will be of academic interest only. Many reports indicate a wide variation in results as a function of inconsistencies in modeling technique. There are other reasons beam theory models and FEA models cannot be directly compared. For example, current B31 rules (as currently applied by beam theory piping analysis software) will have the SIF’s and FF’s “turned on” at the point of tangency at a bend (elbow) and “turned off” at the following point of tangency. In fact, because the ovalization of the pipe (which leads to additional uniaxial (unless torsion is present) flexibility and additional stress intensification) carries beyond the curved pipe and into the adjacent straight sections of pipe, typical beam theory models are not completely accurate. Beam theory based software does not attempt to adjust for this “end effect” phenomena. To avoid this issue in FEA models, the “anchors” in the FEA models should be located 8 to 10 diameters away from the tangent points to avoid anomalous “stiffening” the curved section. Questions beyond modeling technique arise in the discussion of the practicality of some FEA evaluations of bends and elbows. The very nature of FEA modeling will assure that the bend or elbow model being analyzed will be perfect in geometry (circular cross section and bent on a perfect radius) and perfect in the homogeneity of the material. Such a piping construct has never been built and consequently the stresses calculated by this model will be theoretical and incorrect. If you determine by using an FEA model (elastic-plastic analysis with an adequate number of time steps and with geometry updates (simulating the continuing deformations) as a function of time and include strain hardening) at what location the first (and subsequent) wall regions will experience plastic deformation you MAY get some insight to the “self springing” phenomena (and it should show residual stresses and residual strains when the analysis ends with no applied loading). If you repeat this analysis ten times you will always get the same results. However if you actually fabricate and test ten specimens of the FEA analyzed piping construct (all fabricated in a laboratory setting as exactly the same as possible) and you cycle these ten specimens in a controlled way in a test fixture with appropriate numbers of strain gages located at exactly the correct places, you will get ten sets of widely varying results. Using “real world” construction tolerances, the variation will be greater. The B31 Codes “live” in the real world and take a decidedly practical approach.
2) I too would be concerned if an assessment of the vibrations (or pressure pulsations) IN CONCERT WITH HIGH STRESS indicated that fatigue failure was likely. Obviously, when looking at the S-N curve the total cycles must be considered in concert with the stress magnitude – the further to the right you go on the S-N curve, the lower the allowable stress should be. The lower the stress the more cycles the piping can accommodate (the greater the service life). The approach to high cycle service, when I cannot be avoided, is to use a lower allowable stress in the assessment. But more to the point, the first thing that should be done is to reduce the vibration as much as possible by any or all of the classic methods. At this time, internal pressure pulsation related fatigue is not explicitly addressed.
3) From a theoretical point of view, you are correct. But if you are pleading for more wall thicknesses to be available than are currently available by the current Standard industry schedule method, your plea will fall on deaf ears. Wiser people than we set the Standards and said “enough is enough”. Really though, there is little economic benefit realized in the use of “custom wall thickness” pipe. For many years the power industry specified “minimum wall specification” pipe for power plants. These “min-wall” thicknesses were often very thick piping in which there was some economic benefit in specifying because the piping was “made to order”. But for general application, the economics of specifying non standard pipe is at best moot. There are manufacturing, inventorying and shipping issues that far overwhelm the apparent benefit of additional wall thicknesses.
Regards, John.
