Finite Element Analysis of Bolted Flange Connections

by Jo Pemegger, Flexitallic Group Inc.

A method of engineering design known as finite-element analysis (FEA) has progressed rapidly in recent years. Traditionally, it is used by structural or mechanical engineers to analyze the stresses or flows of fluids in equipment or systems. Now, however, it is becoming widely available for more focused analyses, such as flange connections in process equipment.

FEA offers considerable advantages for this application. It can be a tool to solve nagging process problems such as leaking flanges, which are now important performance issues with the regulation of fugitive emissions. More importantly, it can be used to predict performance, thereby avoiding problems once a process unit is built and put into operation. Flexitallic Group, a leading supplier of industrial sealing systems, now offers FEA analysis as a service to its clients. This has resulted in several notable cases where processing problems have been reduced or avoided.

What is FEA?
FEA is a computer-aided numerical technique for the prediction of performance of structures under static, dynamic or thermal loads. FEA is a process whereby the response of a physical object exposed to some stimulus is numerically simulated. For example, the compression (response) of a gasket (physical object) as a result of loading (stimulus) by the flanges can be predicted using the FE method (Figure 1).

Figure 1. FEA calculates the stress/strain response to loading

Crucial to the accuracy of this predicted response is the mathematical model or set of equations selected to mimic the object's behavior. These equations are termed the material model. There are numerous types of stress-strain relationships to which mathematical equations can be fitted or for which material models can be defined, the most common being elastic and elastic-plastic. Typically, gasket material exhibits a non-linear visco-elastoplastic relationship as shown in Figure 2.

The FEA Procedure
FEA involves three essential stages; pre-processing, solving and post-processing. During preprocessing, a computer model of the structure is generated and divided up into smaller blocks or elements, appearing as a "discretized" mesh superimposed over the structure. These elements are defined in space by nodes, at which the stress strain computations occur. The greater the number of computation points (nodes), the more closely the solution approaches a unique solution. During solving, the FE solver generates a stiffness matrix for each element, the displacements due to an applied load, and then assembles each element's contribution to form a response matrix for the whole model. Once an equilibrium condition has been achieved, the results can then be imported into a "post-processor" for interpretation.

Figure 2. Stress/strain curve describing the non-linear visco-elastoplastic response of a material

FEA Assumptions
The generation of a 3D model is a complex and time consuming process, often taking days or weeks of work. Depending on the symmetry of a 3D structure, reductions in the model geometry about any planes of symmetry will invariably be made. This can result in ½, ¼ or even 2D models. Circular structures, such as weld neck flange assemblies, for which any radial section can be regarded as being the same as any other, can be reduced to 2D sections know as axisymmetric models (Figure 3). Such axisymmetric models, when compared to their 3D counterparts, have the advantage that mesh densities can be increased, thereby increasing the potential accuracy of the results.

Figure 3. Model definition of a circular flange can be simplified using the principal of axisymmetry

Since an axisymmetric model assumes a state of symmetry in a radial sense, the effect of external bending moments cannot be accounted for. Assumptions about the distribution of the bolts in an axisymmetric representation have to be made. The representation of bolts in this manner has been verified against full 3D models for 4 and more bolts.

Similarly, a series of assumptions must be made to model material properties of bolts, flanges and gasketing materials. For SWG and sheet gaskets, the stress/strain behavior is known to be complex. Material models currently available in commercial software codes are not able to accurately model this visco-elastoplastic behavior. In order that FE analyses involving Flexitallic gaskets can accurately predict their response, a specific customized material model has been developed.

Lastly, the model must be loaded and constrained by a series of loads and boundary conditions, which are representative of the loads and restraints on the real structure. Contact conditions between all discrete entities, such as between the sealing element and inner-ring or flange face, need to be defined if realistic solutions are to be calculated. Contact conditions include friction and thermal conductance properties.

FEA Results
The solution of the FE model generates results that include displacements and stresses that are stored in binary files for post-processing. The results are usually represented in the form of contour plots, deformed shape plots and line graphs. Such graphical representation aids an experienced engineer in interpreting the results. Common results for FE analyses of bolted flange connections include:

• degree of flange rotation
  
• variation of stress in flange
  
• variation of stress across the gasket/flange interface
• the above as influenced by operating conditions (temperature and pressure)

Application examples
FEA analysis has been successfully implemented in a variety of situations. Three are presented here:

1. Yielding Flange
   A large oil company wanted to assess a sub-sea, safety-critical flange assembly. The assembly was made up of ANSI B16.5 24-in. Class 300 flanges, each with an XS pipe schedule. The assembly was subject to an operating pressure of 50 bar. Initially, a standard 300 CGI SWG gasket was specified.

   The initial FEA showed Von Mises stress in the region of the weld neck to be critically close to yield under operating conditions. Given that external bending moments were expected as a result of high swells, such high levels of yield criterion stress questioned the safety and implied likely failure of the assembly. Investigation of the gasket for this case also showed excessive loss of axial stress under operating conditions. The loss of this stress is due to large flange rotations (Figure 4). Flange rotations of up to 1.5mm were predicted for each flange.

   
   Figure 4. Overlay of deformed mesh over the original showing a large degree of flange rotation (magnification = 1)

   An alternative assembly more suited to this application was determined by an FEA sensitivity study. The most favorable Von Mises stress result was demonstrated by a Class 600 flange (pipe schedule 80) with hub length increased to 10 in. The extension of the hub reduces the sharpness of the stress raiser in the region of the weld. The reduction of the Von Mises stress is due to a reduction in the amount of flange rotation. The net result is that the assembly can tolerate bending moments, while satisfactory gasket stresses can be maintained.

   At this point, the company confirmed that they had already installed half of the flange on the sea bed and that replacement, although favorable, was not possible. It was then requested to explore any possible novel sealing alternatives with FEA. Flexitallic suggested the use of a controlled-compression gasket with a rotation-limiting outer ring. The results showed that Von Mises stress in the weld neck could be reduced and gasket stresses maintained, as long as the tolerance between the ring and the flange is set to an amount determined from the FEA.

2. Leakage at a Nitrogen Regeneration Process
   Flange leakage was experienced on several high temperature flange connections during a nitrogen regeneration process at a UK based petrochemical refinery. The regeneration process involved a 10-day purge of the particular pipeline using nitrogen at 575°C.

   On evaluation, two modes of joint failure were identified: a) Excessive bolt relaxation of the low alloy B16 bolting and b) Oxidization of the gasket's graphite filler material. It was thus recommended at this stage that the bolts be upgraded to B80A Nimonic material and that the gasket design be modified to include specialized, oxidization-resistant, spiral-wound gasket material.

   Although the modification of gasket design was simple enough, the upgrade of the bolt material would increase the cost of system by over £100,000. In light of this, an FE analysis was requested. The analysis indicated massive bolt stress-relaxation and subsequent gasket unloading during the regen process, which accounts for the leakage. An analysis of the flange assembly using B80A bolts showed reduced bolt stress-relaxation and the maintenance of the required levels of gasket stresses. This verified the initial evaluation and indicated that the assembly bolted down with the Nimonic bolts would be able to maintain joint integrity and therefore flange tightness during the regeneration process.

   The next step was to analyze an alternative to bolt replacement. With this in mind, an analysis on the B16 bolted flange assembly—with the lagging around the flanges removed—was performed. The analysis showed that temperature in the area of the bolts was reduced to within the operating limits, minimizing gasket unloading. Thus, through the application of FE analysis, an inexpensive alternative to bolt material upgrading was found.

3. Leakage at a High-Temperature Conical Reactor
   A newly designed flange assembly was installed in a plant at a conical reactor. The assembly was intended to contain a particularly hazardous chemical. Shortly after commissioning, serious leakage problems were experienced.

   The most probable mode of failure was insufficient strength of the top flange, which resulted in excessive rotation and yielding, leading to deficiencies in joint tightness. The decision was taken to weld up to two existing flanges and introduce a new intermediary flange assembly at the midpoint in the lower conical flange. It was only at this stage that the decision to do a FE analysis was made.

   The modified assembly design incorporating a suitable gasket specification was modeled. The analysis showed that even under test conditions, the flange stresses were maintained below 78 percent of yield, with gasket unloading restricted to well within allowable limits. Had an FE analysis been performed at the design stage, the problem of the yielding flange could have been identified and the assembly designed "right first time" for the intended application. The subsequent modifications could have been avoided.

Conclusion

The effective use of FE analysis means that expensive prototypes and trials can be eliminated and components can be designed right the first time. FE analysis can also be used in identifying and solving problem areas in existing systems.

The Flexitallic Group offers FEA services that can predict the performance of any bolted flange connection across a range of pressure/temperature applications. Flexitallic's FE analysis is a three-step process that relies on two different software programs. The first step of the process uses FAM software to create the model. The second step uses a program called Abaqus for analysis and calculations. The post-processing step, also done with Abaqus, creates graphs and contours. Nastran, Marc, Ansys, Cosmos/M and FEMap are other FEA software programs.

Flexitallic's FEA service includes a thorough understanding of seals and sealing systems, as well as expert capability in the modeling of gasket materials. Two- and 3D modeling of standard or non-standard bolted flange assembly, along with an assessment of operating conditions in terms of pressure and temperature (both thermal steady state and transient type analyses), is also offered. With correct interpretation of the model, an effective FEA can predict the degree of flange rotation, gasket contact stresses, flange stresses, effect of bolt load, and the influence of pressure and temperature cycles.

For more information contact: The Flexitallic Group, 6915 Highway 225, Deer Park, TX 77536. Tel: 281-479-3491; Fax: 281-479-6298.

References

1. Smith, A.C., Briggs, G., Finite Element Analysis of Bolted Flange Assemblies, 4th International Symposium on Fluid Sealing of Static Gasketed Joints, Sept. 1996, Mandelieu - La Napoule, France, p. 181-192.
2. Wright, V., Hoyes, J., Briggs, G., Finite Element Analysis of Bolted Flange Connections, 14th International Conference on Fluid Sealing, April 1994, Firenze, Italy, p. 97-105.
3. Nau, B.S., Computer modelling of the sealing behaviour of gaskets in flanged joints
4. Hibbit, Karlson & Sorrenson, Inc., ABAQUS Standard Example Problems Manual and Users Manual, USA, 1995.
5. NAFEMS, A Finite Element Primer, Dept. of Trade and Industry, National Engineering Laboratory, Glasgow, UK 1986.
6. Beer, G., Watson, J.O., Introduction to Finite and Boundary Element Methods for Engineers., John Wiley and Sons, England, 1992.
7. Ugural, A.C., Fenster, S.K., Advanced Strength and Applied Elasticity, Second SI Edition, Elsevier Science Publishing, New York, 1987.
8. Prager, W., An Introduction to Plasticity, Addison-Wesley, 1959.
9. Bickford, J.H., An Introduction to the Design and Behaviour of Bolted Joints, Third Edition, Marcel Dekker, New York USA, 1995.