A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes. Anindya Bhattacharya Senior Engineer (Stress analysis) CEng; [email protected]

Daniel Long Technical Head – Pipe Stress Engineering CEng; [email protected] CB&I UK Ltd, London W2 6LG Phone: +44 (0) 20 7052 5668 Fax: +44 (0) 20 7053 3737 SUMMARY

Bends are the most common type of pipe fittings because of their ability to warp and ovalize under the action of bending moments. They provide added flexibility and hence increased stress with respect to straight pipes. Two parameters are of importance to express the increased stress and flexibility effects of the pipe bends – the stress intensification factor (SIF) and flexibility factor. The stress intensification factor can be defined as the ratio of the bending moment at which a straight piece of pipe fails after a specified number of cycles to that at which a pipe bend of the same diameter and wall thickness fail under the same number of cycles. The flexibility factor is defined as the ratio of rotation of a pipe bend to that of a straight pipe of same diameter, wall thickness and length under the action of the same bending moment. ASME B31.3 [1] and other B31 piping codes present empirical formulas for stress intensification and flexibility factors for different pipe fittings. Stress intensification factors are based on the work of Markl [2] using displacement controlled fatigue tests on piping components. Flexibility factors are based on both analytical solutions by Von Karman and experimental validations [2]. The code cautions against use of these factors for a diameter over thickness ratio of 100. Also, as far as pipe bends are concerned, the code does not address the use of these factors for bends with welded attachments like trunnion supports for piping systems. Pipe stress analysis is usually done using beam based finite element analysis. Stress intensification factors are used to modify the computed stresses at the fittings and flexibility factors are used to modify the stiffness matrix. In this paper, a shell-based finite element analysis (FEA) has been undertaken to: Re-visit the stress intensification factors and flexibility factors for pipe bends for diameter and thickness ratio less than 100, as well as to see the effect of increasing diameter and thickness on these factors. Check for the effect of welded pipe supports on these factors. Provide a technical back-up for simplified methods used in beam-based finite element programmes to simulate the effect of pipe supports welded to bends. Two FE codes, FEBend (a part of FE/Pipe V.4.111) and ABAQUS version 6.9 have been used for the above study.

A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes

1. Elastic stress classification route The concept of stress intensification factor, as used in [1] is based on linear elastic behaviour. The American Piping Codes B31 do not explicitly use the terms primary stress, secondary stress, peak stress etc. (These are outlined in the ASME Boiler and Pressure Vessel Codes Section VIII, Division 2 and Section III [3] [4]) although the concepts are inherent in the specification of different allowable stresses for load and displacement driven stresses.) The concepts are important to develop the methods to be used in computing such factors using FEA. To define these terms in a nutshell: primary stress is load driven and does not reduce due to redistribution; secondary stresses develop to maintain displacement compatibility and are self limiting; and peak stresses are significant only from the fatigue-failure standpoint. [3][4] The individual stress categories have separate failure modes associated with them. Primary stresses result in gross plastic deformation type failure. Primary plus secondary result in ratcheting (progressive plastic deformation or PD) and peak stresses result in fatiguefailure. Henceforth, in line with ASME Boiler and Pressure Vessel Code terminology [3][4], local primary membrane stresses will be termed as Pl, primary bending stresses as Pb, Q as secondary stresses and F as peak stresses. The stress intensification term as used in [1] is for peak stress only under flexural loading. ASME Boiler and Pressure Vessel Code Sec III [4] addresses stress indices (a term not exactly equivalent to stress intensification factor) for other types of stresses as well. B31.3 factors are applicable for both in- and out-plane bending moments with the corresponding stress intensification factors termed as in-plane SIF and out-plane SIF. Flexibility factors can also have similar terminology, although ASME B31.3 expresses single flexibility factor for both types of loading. The flexibility factors computed in this study are for in-plane only. Stress intensification factors are, however, for both in- and out-of-plane loading. 2. The origin of the stress intensification and flexibility factors in the American piping codes In the late 1950s, A.R.C. Markl and his team [2] conducted a series of experiments using displacement controlled fatigue tests to evaluate stress intensification factors. Details of the experimental set up and method can be found in [2] [5] [7] [8] [9]. Markl’s original work, based on which stress intensification factors were derived, was based on the following eqn (in psi). i.Sf = 490000N(-0.2)

eq.1 [2]

where i=stress intensification factor, Sf= stress range to failure, N=no. of cycles to failure 3. A finite element based approach on computation of flexibility factors [6] Simulating the flexibility factor using FEA will involve the following steps (element to be used – 8-node reduced integration shell element in both the FE codes;. in ABAQUS [10] this element is designated as S8R):

A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes

Model the bend with straight pipe attachments of 1D, 2.5D, 6D, 10D respectively in different models. (D stands for pipe nominal diameter.) Fix one end of the bend in all six DOF; apply bending moments using kinematic [10] coupling at the other end. Add a straight pipe of length equal to the bend, i.e. (2 R)/4 where R=1.5D. As the nominal diameter of the pipe, D has to be modelled of same material, wall thickness and boundary conditions and loading as that of the bend. The boundary condition for the straight pipe will be the same as that of the bend in terms of constraint and loading. End rotation will be computed. Measure the rotation at the free end of the bend (with straight pipe attachments) which will be comprised of the bend rotation plus the rotation of two straight ends. The rotation of the straight ends can be approximated using the formula ML/EI where symbols have the usual meaning. The rotation of the “bend only” will be the magnitude of rotation computed using FEA at the free end, minus the sum of the rotation of the two straight ends (approximately equal to 2.ML/EI). Compute the ratio of the rotation computed in the above two steps. This is the flexibility factor. Since this factor will be a function of the attachment lengths, the actual value to be used in an analysis shall be the one coming close to that using B31 formula for flexibility factor. For an analysis correctly done, the values of flexibility factor come close to that of B31.3 for straight lengths close to 6D. A value at 2.5D is recommended. This will provide the necessary conservatism. This is independent of D/T values. For the correctness of model, check the end rotation for the straight pipe against the value ML/EI. 4. A finite element based approach on computation of stress intensification factors Stress intensification factor can also be expressed in a simplified way as the ratio between peak stresses in a component to that of nominal stress in a component. Nominal stress in a part can be taken as M/Z for the applied bending moment. Stress intensification factors can also be computed for primary and secondary stresses (as required in the ASME SEC III code). For generation of peak-SIF in pipe bends using an FE model, the following procedure was used - ASME B31 piping codes (here, for the purpose of this paper, we refer to ASME B31.3 only) use SIF based on a ratio of actual stress due to application of bending moment to that of the nominal stress in a girth (circumferential) butt weld due to the same bending moment. Hence, B31-SIF = Actual stress in part due to bending moment, M upon stress in girth butt weld due to M. Girth butt welds have stress intensification factors between 1.7 and 2.0 [9] and are material dependent. Thus, conservatively, the true peak stress in a girth butt weld due to a moment, M can be expressed as: Peak stress in a girth butt weld (due to M) = 2(M/Z). M is the moment in the pipe with the butt weld, and Z is the section modulus of the pipe with the butt weld. Therefore in terms of the nominal stress in a straight pipe without a girth butt weld, B31-SIF can be expressed as [9]. B31.3 SIF =

Actual (Peak Stress) due to moment, M Stress in Girth Butt Weld due to moment, M

A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes or, B31.3 SIF =

Actual (Peak Stress) due to moment, M 2 X (Moment, M)/ (Section Modulus, Z)

In terms of ASME Section VIII, Div.2, App-5 and finite element analysis (FEA) work, we could use the following equation interchangeably with the previous equations: SIF =

=

Range of Peak Stress due to M 2 X (Moment, M)/(Section Modulus, Z) 2 X (Pl + Pb + Q + F) 2 X (M)/ (Z)

or, SIF =

=

Alternating Peak Stress due to M (Moment, M)/(Section Modulus, Z) (Pl + Pb + Q + F) (M)/ (Z)

The peak alternating stress, (Pl+Pb+Q+F) is usually determined from finite element analysis. Normally, the peak stress is the product of the secondary stress and a fatigue strength reduction factor (FSRF) [3]. For instance, Pl+Pb+Q+F = FSRF(PL+Pb+Q)/ 2

eq.2

To implement this concept in FE analysis, the steps that were followed are: FE discritization of the piping model. Applying a bending moment at the free end of the model (the model is a cantilever). Compute peak stress in the part. Compute the nominal stress in the attached piping. Insert the peak stress and the nominal stress in the above equation to get the B31-SIF. To remove the effect of boundary conditions on the result, parametric study showed a value of >5D as the minimum required straight pipe length, which has been used in the model. Mesh grading has been done such that the mesh size in the location of interest is less than 0.5 RT where R is the shell mean radius and T is the shell thickness. The computation of the peak stress in the part requires the computation of the secondary stresses in the part and the multiplication of the value with fatigue strength reduction factors (FSRF) at the location of interest. According to [3] load driven stresses at locations of gross structural discontinuity are secondary stresses. Hence the stresses generated at the bend under the action of bending moments belong to the category (Pl+Pb+Q). To generate peak stress amplitude, equation 2 is used. FSRF is 1, as the highest stress locations are not weld locations.

A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes 5. Applicability of ASME B31.3 SIF and flexibility factor formulas. According to B31.3 [1] the validity of stress intensification and flexibility factors has been demonstrated for D/T 100. Also, the code does not address the issue of welded attachments to the bends which are mostly trunnion type supports (pipes or structural members). 6. The finite element model

Figure (1). FE Model for computation of bend flexibility fFctor for a 72 inch pipe with 48 inch trunnion attachment (straight length =2.5D). (ABAQUS)

Figure (2). FE results for computation of out of plane SIF for a bend for a 56 inch pipe with 48 inch trunnion attachment. (ABAQUS)

7. Results and discussions 7.1 For pipe bends without attachments The two FE codes used show a similar trend in

A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes behaviour with respect to out-of-plane SIFs. The values computed using shell-based finite element analysis are less compared to those computed using ASME B31.3 piping code equations. The trend is irrespective of diameter over thickness (D/T) ratio. The two FE codes differ in the computed values for in-plane SIFs. ABAQUS results show the values to be less, albeit very close to that of ASME B31.3 than the FE pipe values, which are higher, although the difference is not significant (maximum variance in all the cases considered is 10%) and this trend again is independent of D/T. Regarding flexibility factors (in this paper, only in-plane flexibility factors have been investigated), the results show a similar trend (lower flexibility factor values with respect to ASME B31 code). This is expected as finite element models will be stiffer than real life models. Since the trends for SIF and flexibility factors do not show any significant variation with respect to D/T ratio and the maximum D/T ratio that has been considered in the analysis is 203, it can be concluded that the code equations for bend flexibility factors and stress intensification factors can be used for as high as D/T of 200 (rounded). 7.2 For pipe bends with pipe attachments There is a difference in results between the two FE codes used with respect to stress intensification factors. FE Bend results show, in most cases, an increase in in-plane stress intensification factors when attachments are welded to the bends (for a 72 inch pipe bend with 36 inch pipe attachment this factor goes down); however, the results for out-of-plane do not show any significant changes. Since FE Bend is a code where user intervention is minimum, parametric study (using desired mesh grading, other element types, etc.) could not be conducted to investigate the effect further. One interesting observation was that the variance in in-plane stress intensification factors using FE Bend was significant as d/D (ratio of attachment diameter to that of pipe bend diameter) approaches unity. Since the flexibility factors show good correlation between the two FE codes, it can be concluded that the code FE Bend uses added conservatism when attachments are welded and this effect increases with increase in d/D ratio. Since both the FE codes show comparable values for flexibility factors and the results in FE Bend depend strongly on d/D ratio, it can be concluded that the results shown using ABAQUS demonstrate the correct trend in behaviour with respect to welded attachments at bends. This can be explained from a physical standpoint as such attachments will tend to reduce the tendency of the bend to ovalize and warp, which are the main contributing factors for stress intensification factors for bends. Based on this argument, one is tempted to conclude that simplified methods of simulating such effects in beam based pipe stress programmes (like modelling the bends as “single flanged” or “double flanged” or modelling the bends as “square corners” with ASME B31.3 formulas for stress intensification factors) are acceptable and will not result in any significant error. Based on the differing results between the two FE codes, however, an experimental validation/further analysis using other FE codes is recommended. 8. Conclusions ASME B31.3 formulas for stress intensification factors and flexibility factors can be extended (for pipe bends) for D/T ratio of 200. This is based on shell-based FE results showing that such an extension will not result in negation of the conservative approach built into the codes. Two FE codes used show similar trends.

A Finite Element-based Investigation on Stress Intensification and Flexibility Factors for Pipe Bends within and outside the Limitations of ASME B31 Piping Codes There is a difference in the trend shown by the two FE codes on the issue of stress intensification factors for bends with welded pipe attachments. In light of differing results between the two FE codes, experimental validation/additional FE work using other FE codes is recommended. For trunnion attachments to bends, modelling the weld (modelling using shell elements) did not show any significant effect, i.e. highest stresses were still located at points away from the intersection as was the case with FE models, not including such welds, and also on models without any attachments. To investigate the effect of increasing the applicability of the ASME B31.3 formulas for SIF and flexibility factors for fittings other than bends (e.g. TEE joints with reinforcement, etc.), shell-based analysis will not be adequate and either continuum elements or submodelling [12] techniques have to be used, including modelling of welds. This is because shell-based finite elements do not give accurate results for such connections.[11][12][13] 9. References 1. 2. 3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13.

ASME B31.3 -Process Piping. 2008 edition, Published by American Society of Mechanical Engineers Piping Flexibility Analysis, A.R.C Markl, ASME Transactions 1955 ASME Boiler and Pressure Vessel code SEC VIII DI V2 Part 5- 2007 Edition, published by American Society of Mechanical Engineers ASME Boiler and Pressure Vessel code SEC III Division 1- Rules for Construction of Nuclear Facility Components 2007 Edition, published by American Society of Mechanical Engineers. Program Manual FE/Pie Version V4.111( a product of Paulin Research Group, Houston Texas) Chris Hinnant ( Paulin Research Group, Houston Texas)-Private communication Welding research council Bulletin 335- A Review of Area Replacement Rules for Pipe Connections in Pressure Vessels and Piping, by E.C. Rodabaugh. August 1988 NUREG CR-3243 - Comparisons of ASME Code fatigue evaluation methods for Nuclear Class 1 piping with Class 2 or 3 Piping-E.C.Rodabaugh - June 1983 Markl, SIF's and ASME VIII -2 Fatigue Design available at www.paulin.com ABAQUS Version 6.9-1-A product of HKS Inc RI, now marketed under the SIMULIA brand of Dassault Systems S.A. How to use Beam, Plate and Shell Elements -T.Hellen NAFEMS publication Concepts and Application of Finite Element analysis – Cook, Malkus and Plesha 4th Edition John Wiley and Sons NY 2001 Procedural benchmarks for common fabrication details in Plate/Shell StructuresJ.Wood- NAFEMS Publication