Fatigue Assessments of Pressure Vessels
Section VIII, Division 1 of the 2021 Edition of the ASME Boiler & Pressure Vessel Code introduced Mandatory Appendix 47 which specifies the qualification requirements of individuals involved in designing pressure vessels. Within this appendix is the requirement that fatigue assessments of pressure vessels are to be performed by, or under the direction of, a Certifying Engineer. While some may consider this a bit of overreach on the part of the ASME Code, there are a number of considerations when performing fatigue assessments that make this new requirement understandable. This article discusses some of the things that are considered when conducting a fatigue assessment that go beyond being able to follow a procedure or properly use an equation.
The equations and the rules of Section VIII, Division 1 are fairly straight-forward. As a result, it generally doesn’t take a great deal of experience or training before a new Engineer or Designer is designing Division 1 pressure vessels that meet the ASME Code. Fatigue assessments, however, are different in that they generally involve finite element analysis (FEA) which require a greater level of training, experience, and engineering judgement.
Properly conducting a fatigue assessment is more involved than taking a course on how to use a particular FEA program and simply looking at stress results. Most FEA training courses offered by software vendors are not hand-tailored to pressure vessel design but rather take a more general approach that is not specific to any particular product. There are a number of things that need to be considered when performing finite element analyses and fatigue assessments of pressure vessels that can directly affect the accuracy of the results and assessment.
Assuming the fatigue screening procedure has already been performed and a fatigue assessment deemed necessary, the procedure for conducting a fatigue assessment consists of the following steps:
Build a CAD model of the pressure vessel or component
Create a finite element model from the CAD model
Define material properties
Apply loads and boundary conditions
Solve the appropriate load case combinations
Determine the magnitude of cyclic stresses
Calculate fatigue damage and design fatigue life
Perform a ratcheting assessment
Fatigue life of pressure vessels is dependent on the magnitude of local stresses. Finite element analysis is an effective tool in predicting local stresses but requires experience and an understanding of the finite element method to achieve an accurate evaluation. It is very easy for an inexperienced analyst to unknowingly make decisions that result in an incorrect assessment of the pressure vessel’s fatigue life. Achieving a correct fatigue assessment is all about accurately predicting local stresses. With finite element analysis there are several decisions that require sound engineering judgement to ensure the results of a fatigue assessment are valid. These include: what to include in the finite element model, boundary conditions, quality of the finite element mesh, and singularities.
What to Include in the Finite Element Model
The largest stresses in a pressure vessel will occur at locations of stress concentration such as bolt threads, welds, and nozzles. While one might be inclined to include every detail in the finite element model of the pressure vessel, this will usually result in a large finite element model, longer solution run times, and require more computer memory. Including every detail is rarely necessary to achieve an accurate fatigue assessment.
So what details should be included and which ones can be safely ignored? Knowing which details can be simplified or excluded from the finite element model is sometimes not straight-forward or apparent. It is not always easy to determine which detail or component will have insignificant cyclic stresses and can therefore be excluded from the model. Some components can be excluded without further consideration such as the attachment of name plate brackets to the pressure vessel. Others, such as excluding the threads in the modeling of flange bolts will reduce the number of elements in the model but require the cyclic stresses from the FEA to be scaled by a fatigue strength reduction factor to account for the threads not being included in the model. Small nozzles can sometimes be excluded from the finite element model provided the loads on the nozzles do not produce significant cyclic stresses. Ultimately, knowing which details and components can be safely excluded from consideration in a fatigue assessment is something that comes with experience under qualified supervision.
As noted above, the simplification or exclusion of certain details will sometimes require the use of a fatigue strength reduction factor. For example, welds joining nozzles to the vessel shell can be either modeled or excluded when performing fatigue assessments in accordance with the ASME Code. If the welds are explicitly modeled, the total stress in the weld including the effects of stress concentrations is used in the fatigue assessment. Alternately, the weld can be excluded from the model, and linearized membrane plus bending stresses scaled by an appropriate fatigue strength reduction factor can be applied at the location where the weld would be located. There are pros and cons to both of these approaches, some of which are discussed below. An experienced analyst will take the appropriate precautions in their modeling and evaluation to ensure their results are accurate regardless of the approach they take.
Boundary Conditions
The location and details of the boundary conditions applied at the extents of the finite element model can also affect the accuracy of the results used in a fatigue assessment. If the model is constrained close to an area of interest, the magnitude of the stresses may be inaccurately high. Restricting translation or rotation at the boundaries of the model may not be an accurate representation of reality resulting in inaccurate stress results. Understanding the behavior and movement of the pressure vessel at its supports when subjected to loads is important in applying correct boundary conditions and obtaining accurate results.
Quality of the Finite Element Mesh
The accuracy of the predicted magnitude of stress at locations of stress concentration are dependent on the quality of the finite element mesh of the model. Elements too large or poorly shaped will result in inaccurate stress results. There should also be a sufficient number of elements through the thickness of components to accurately predict the bending stresses. If the pressure vessel is subjected to thermal transients such as thermal shock, additional elements through the thickness of the component may be necessary. If a transient thermal analysis is required, an appropriate time increment must also be chosen to accurately predict when the pressure vessel is subjected to maximum thermal stress. An experienced analyst will be able to assess the quality of the element mesh by looking at the stress contours in areas of high stress gradients and/or performing mesh sensitivity studies.
Singularities
Considering all of the above, it would not be unusual for someone to believe that the stresses from a finite element model with a significant amount of elements in the areas of interest are accurate. While this is often true, it may not be so in areas of singularities. For example, if a weld joining a nozzle to the shell of a pressure vessel is not explicitly modeled, a sharp corner will exist between the nozzle and shell. This sharp corner creates a singularity which results in an infinite stress concentration factor at this location. In areas where a singularity does not exist increasing the mesh density will result in a more accurate stress result. The addition of more and more elements will eventually result in less and less of a change in stress. This is not the case in areas of singularities. Increasing the element mesh density in areas of singularities will result in an ever-increasing magnitude of stress. Therefore, the magnitude of the stress at a singularity may be lower than the actual value if the element mesh is coarse, or higher than the actual value if the element mesh is refined.
The problem with singularities is determining the actual magnitude of stress. There are accepted methods of predicting stresses at singularities such as using extrapolation of stress results near the area of interest. However, the main point here is that recognizing areas of singularity and how to deal with them is something that comes with experience.
Conclusion
In conclusion, a fatigue assessment is all about accurately predicting local stresses at areas of stress concentration. While finite element analysis can produce good stress results, modeling simplifications, boundary conditions, and the underlying mathematics of the finite element method can affect the accuracy of a fatigue assessment. Accurately performing a fatigue assessment of a pressure vessel requires an understanding of the finite element method, fatigue, the requirements of the ASME Code, and sound engineering judgement that comes with experience.