MODEL SIMPLIFIES ESTIMATE OF BENDING STRENGTH IN CORRODED PIPE
Hong O. Kim
BP Pipelines (Alaska) Inc.
Anchorage
A simple method has been developed for assessing bending strength of corroded pipe subjected to combined loading of internal pressure and moment.
It is as useful as the more complex finite element (FE) analysis method which can be costly and time-consuming.
The new method consists of using:
- Axisymmetric modeling to determine hoop stress occurring in a corroded region due to pressure loading.
- Von Mises failure criterion to determine the axial stress limits which vary with hoop stress.
- The elastic limit and the plastic limit moments of corroded pipe to determine the bending strength.
The experimental cases used to validate the new method as well as the FE method are specifically for 48-in., X-65 pipe. Therefore, the approach should be used with discretion for different parameters.
STRENGTH EVALUATION
Metal loss due to corrosion is a chronic problem in gas and oil pipelines. Criteria currently available for evaluating remaining pressure strength of corroded pipe are found in ANSI/ASME B31.G1 and RSTRENG.2
These criteria are developed empirically for longitudinally (axially) oriented corrosion. Very recently, Kanninen has proposed an alternative approach for determining pressure strength based on elastic axisymmetric analytical modeling of corrosion. 3
Metal loss due to corrosion usually results in randomly located pits, often resulting in large areas of overlapping defects. Because of the geometrically complex nature of metal loss, a rigorous analysis of corroded pipe to predict its structural failure condition requires use of a numerical approach such as the finite element (FE) method.
Bubenik has used the FE method to analyze the pressure strength of corroded line pipe.' The method permits a rigorous analysis of geometrically or materially complex structural problems. Applying it to the corrosion problem, however, can be costly and time-consuming.
A simpler approach that is theoretically sound and expedient is, therefore, desirable and precisely what is offered here.
As an approximation, it is proposed that the bending strength of corroded pipe be taken as the mean value of the elastic limit and the plastic limit moments. The strength values thus determined are compared with several experimental data. 5
The comparison shows good agreement between the results of the two different methods. They are also compared with the FE simulation results based on the general purpose FE program ABAQUS.
The comparisons show that the simple approach proposed here is as viable for predicting the bending strength as complex FE analysis.
HOOP STRESS MODELING
The principal stresses occurring in a corrosion defect consist of hoop stress primarily as a result of pressure loading and axial stress from the bending moment and net axial force.
The current criteria (B31.G and RSTRENG) calculate a safe operating pressure for a piece of corroded pipe but are not intended for defining the hoop-stress distribution in the corroded region.
On the other hand, rigorous determination of the hoop stress in the defect which uses the FE method is by no means simple. But such a determination can use an elastic axisymmetric model as proposed here.
As a means of investigating behavior of hoop stress in a corroded region, two extreme models of corrosion defects may be considered: axisymmetric and plane-strain.
Axisymmetric modeling consists of an axial corrosion profile which remains unchanged around the pipe circumference. The axisymmetric model characterized by an axially uniform corrosion profile is shown in Fig. la.
Plane-strain modeling consists of a circumferential corrosion profile which remains unchanged along the pipe axis. The plane-strain model characterized by a circumferentially uniform corrosion profile is also illustrated in Fig. lb.
These two models were initially conceived and analyzed by Kanninen.'
The axisymmetric solution for the illustrated case indicates that the hoop stress in the corroded region depends on the remaining wall thickness (t*) as well as the axial corrosion length (L), unless the L is sufficiently large.
On the other hand, the plane-strain solution indicates that the hoop stress in the corroded region is virtually independent of circumferential corrosion length (Lc).
For the axisymmetric case, the hoop stress in the corroded region approaches that of the undamaged pipe as the axial corrosion length (L) becomes smaller.
This investigation indicates that the parameters which govern the hoop stress in a corroded region are the remaining wall thickness and corrosion profiles along the pipe axis.
AXISYMMETRIC MODELING
Based on this conclusion, application of axisymmetric modeling as described in the following discussion will serve the current purpose of approximating the hoop stress occurring in the corroded region for the subsequent calculation of the pipe-bending strength.
When the defect in a pipe cross-section is random, the circumference of the corroded pipe cross-section must be subdivided into many equal sub-arcs to determine bending strength of the cross-section.
If the sub-arcs are made sufficiently small, it may be assumed as an approximation that hoop stress remains constant along each sub-arc.
The hoop stress may then be assumed to depend on the corrosion profile along the pipe axis only, enabling use of axisymmetric modeling to determine stress. The profile is perpendicular to the sub-arc at its midpoint.
The same assumption and modeling may proceed to the next sub-arc if its corresponding corrosion profile differs from the current one.
It is important to note that axisymmetric modeling need not be limited to the uniform corrosion profile case analyzed by Kanninen.' It can be extended to a variable profile case, a typical example of which is shown in Fig. 2.
The variable-profile modeling allows more-accurate simulation of any complex corrosion geometry in the pipe axial direction, thus enabling investigation of interaction between discrete damage regions in the axial direction.
Analysis of an axisymmetric model consisting of a variable corrosion profile requires a numerical approach. This numerical analysis involves considerably less effort, however, than the rigorous FE analysis of the actual corrosion defect.
As an effort to validate the use of axisymmetric modeling to determine the hoop stress occurring in the corroded region, failure pressures are predicted from this modeling, the predictions using the weakest-link principle. This principle states that pipe failure occurs when the maximum hoop stress in the region reaches the pipe material flow stress.
RSTRENG
The flow stress is the empirically observed failure stress level of a ductile material. The flow stress levels defined for the current criteria are shown in Equation 1 for B31.G, Equations 2 and 3 for RSTRENG (box).
RSTRENG is a modified version of the B31.G for more accurate predictions of corroded-pipe failure pressures. Kiefner and Vieth published the failure pressures predicted from the current criteria for the experimental cases shown in Table 1.2
Information provided by Kiefner and Vieth indicates that the RSTRENG values based on Equation 3 are less conservative and show the best agreement with the observed failure pressures. The axisymmetric predictions in the following discussion are, therefore, based on use of Equation 3 for the flow stress.
Kiefner and Vieth's work contains 86 experimental data points which include both leak and rupture failures. Only the rupture data points are shown in Table 1, however, because they are considered to be more practically important.
The rupture data for pits that are deeper than 80% W.T. are excluded from Table 1 on the assumption that pipe damaged to this degree would be repaired or replaced for continued service. The actual corrosion profiles of the test specimens are currently unavailable, except for the maximum pit depths and the damage lengths, as shown in Table 1.
Therefore, various polynomial profiles such as triangles, parabolas, ellipses, and rectangles are defined from the given information to construct axisymmetric modeling. The profiles defined have their maximum heights located at their centers, and the heights are equal to the maximum pit depths.
Additionally, tiered profiles are also assumed from the information, considering the possibility that the actual defects may consist of single pits with the maximum depths which are confined at the middle of the damage lengths. The tiered profiles assumed are illustrated in Fig. 3.
The failure pressures resulting from the axisymmetric analysis based on these assumed corrosion profiles are shown in Table 2. The results indicate the following:
- Overall, the predicted values are conservative.
- Agreement between the predicted values and the actual failure pressures are better for shallower damages.
- For relatively short damage, the predicted values are sensitive to the profiles assumed.
- As the damage length increases, the predicted values become 'Really independent of the profiles assumed. In this case, the predicted values are overly conservative.
It is not surprising that the predicted values are conservative because the axisymmetric modeling of complex corrosion geometry is a conservative simplification of the problem. Besides, application of the weakest-link principle to the prediction is partly responsible for the conservatism.
For all this conservativism, the predicted failure pressures are generally acceptable. When the circumference of a corroded pipe cross-section is subdivided into small sub-arcs to determine the hoop stress occurring in each sub-arc for the subsequent calculation of the bending strength, the weakest-link principle is no longer used.
PIPE FAILURE
Hypothetically, consider an elastic, perfectly plastic material behavior with yield stress equal to the flow stress of the pipe material.
Excluding the possibility of brittle fracture, the corroded pipe consisting of this hypothetical material will fail by ductile fracture at a very large strain. This failure is a plastic instability problem involving unrestrained plastic deformation.
The location and orientation of the failure depend on the geometric characteristics of the corrosion defect in conjunction with the applied loading.
When the pipe is subjected to bending as well as internal pressure, the failure may occur either in the axial or circumferential direction. In either case, the ductile failure may be preceded by local plastic buckling of the pipe wall.
The buckling would be characterized by outward wrinkling of the pipe outer fiber region in compression under bending moment. The critical compressive strain at which the buckling initiates is considerably smaller than the fracture strain.
According to Langner, the buckling strain is inversely proportional to the OD/W.T. (D/t) ratio.6
For instance, the critical buckling strain of an undamaged pipe with a D/t ratio equal to 50 is approximately 1.0%, while the strain for D/t equal to 100 is 0.5%. These strains are considerably smaller than the ultimate tensile strain of most pipe materials.
If these pipes are corroded in the compression side of bending, they may buckle at smaller strains. Therefore, regardless of the defect characteristics, local buckling may precede the ductile failure unless the ductile failure has already developed under the applied pressure alone.
Once initiated, the buckling drastically reduces the pipe load-carrying capacity for a further increase in bending moment. This will lead to large local deformations in the pipe, resulting in the ductile failure commencing at the highest tensile strain location and orientation.
BENDING STRENGTH
Based on this perception of pipe failure, the bending strength of the corroded pipe immediately before the pipe failure may be considered to be slightly higher than the critical bending moment at which the buckling initiates.
Buckling analysis of the corroded pipe subjected to the combined loading to determine the critical moment is formidable. However, the elastic and plastic limit moments of the same pipe can be easily determined. The critical moment is bounded by the two moments.
The bounding values may be determined by the following procedure:
- Subdivide the circumference of the corroded pipe cross-section into many equal sub-arcs.
- Determine the hoop stress occurring in each subarc as a result of pressure loading, using the axisymmetric approach described earlier.
- Determine the axial stress (tensile and compressive) limits from von Mises failure criterion and the hoop stress for each sub-arc.
- Determine the elastic axial stress distribution which satisfies the equilibrium condition across the pipe cross-section, using the assumption that the plane cross-section remains plane after bending.
The axial stresses thus determined should not exceed the limit values in tension or compression throughout the entire sub-arcs.
- Determine the limit axial stress distribution which satisfies the equilibrium condition only.
- Determine the elastic and plastic limit moments from the axial stress distributions determined from Steps 4 and 5, respectively.
Depending upon the defect characteristics, the critical moment may be closer to either the elastic or the plastic limit moment. As an approximation, however, it is proposed that the critical moment of the corroded pipe be taken as the mean value of the two limit moments. At the same time, the bending strength of the pipe before failure is taken equal to the critical moment.
The strength values determined from this approach are compared with experimental data in the following section.
EXPERIMENTAL RESULTS
Five experiments were performed on 48-in. OD x 0.480-in. W.T. Grade X-65 steel pipe with simulated corrosion patches.' The flow stress of the steel was determined to be approximately 80 ksi.
The simulated corrosion patches were made by grinding and were duplicated on both sides of the pipe in the plane of bending. The patch dimensions and a summary of the test results are given in Table 3.
The experiments consisted of bursting the pipe under combinations of internal pressure and bending moment.
The test procedure consisted of three steps: The pipe was pressurized to 950 psig; it was loaded in four-point bending until an additional 0.4% strain in the nominal wall thickness was reached on the tension side; and the pipe was further pressurized if burst did not occur (Test 1).
While the basic procedure was followed, the internal pressure and strain requirements were altered by circumstances arising in some tests. For instance, in Test 4 the pipe pressure was increased to only 800 psig because the strains in the patch indicated yielding at 600 psig.
After the applied bending moment was increased to achieve a 0.2% axial strain in the cross-section of the tension side, the internal pressure was increased until the pipe burst at 840 psig.
The burst moments and pressures of the tests are shown in Table 3.
Tests 1, 3, and 4 all produced axially oriented burst failures on the compression side, while Test 2 produced a circumferentially oriented burst failure on the tension side.
Test 5 was performed to validate the results of Test 2 and was an exact replication of Test 2. Test 5 showed the same failure pattern, except for the difference (3,532 vs. 3,155 ft-kips) in the burst moments observed. Bulges were Observed for all the test cases before the pipe burst. They were always seen at the patches on the compression side.
With the test pressures shown in Table 3, the elastic and plastic limit moments are calculated by use of the approach described previously. The two limit moments and their mean values are shown in Table 4.
The FE simulation results based on the FE program ABAQUS are also included in Table 4 for comparison. The elements used to simulate the artificial corrosion geometries were twenty-noded brick elements. The FE analyses took into account the elastic-plastic strain hardening behavior of Grade X-65 steel as well as the large plastic deformations before the failure.
Comparing all the analytical results shown in Table 4 with the experimental results in Table 3 leads to the following observations:
- The experimental failure pressures are lower than the plastic limit moments calculated for all the test cases.
- The mean values are lower than the test pressures for all the test cases.
- For the cases of Tests 1, 3, and 5 in which the corrosion extents are greater in the pipe axial direction than in the hoop direction, the mean values are as good as the FE results and are considered to be in good agreement with the test results.
- For the case of Tests 2 or 5 where the corrosion extent is smaller in the pipe axial direction than in the hoop direction, the corresponding mean value is in poorer agreement with the test results.
For the same case, the FE results are also in poorer agreement with the test results. In fact, the mean value appears to agree better with the test results than the FE analysis results.
These observations suggest that the simple approach proposed here is as viable as the complex FE analysis for predicting bending strengths of corroded pipes. Based on the previous comparison, the mean value approximation appears conservative, while the plastic limit moments constitute the upper limit values of the bending strength.
ACKNOWLEDGEMENT
The author wishes to thank the management of BP Pipelines (Alaska) Inc. and Alyeska Pipeline Service Co. for their permissions to publish this article.
REFERENCES
- "ASME Guide for Gas Transmission and Distribution Piping Systems. B31.G Manual for Determining the Remaining Strength of Corroded Pipelines," ASME, New York, 1986.
- Kiefner, J.F., and Vieth, P.H., "A Modified Criterion for Evaluating the Remaining Strength of Corroded Pipe," American Gas Association, Pipeline Research Committee Report on Project PR3-805, Dec. 22, 1989.
- Kanninen, M.F., Pagalthivarthi, K.V., and Popelar, C.H., "A Theoretical Analysis for the Residual Strength of Corroded Gas and Oil Transmission Pipelines," Symposium on Corrosion Forms and Control for Infrastructure, San Diego, Nov. 3-4, 1991.
- Bubenik, T.A., Olson, R.J., Stephens, D.R., and Francini, R.B., "Analyzing the Pressure Strength of Corroded Line Pipe," Proceedings of 11th International Conference on Offshore Mechanics and Arctic Engineering-1992, Vol. 5, Part A-Pipeline Technology, Calgary, 1992.
- Kanninen, M.F., Crouch, A.E., Kwun, H., Grigory, S.C., Roy, S., and Pagalthivarthi, K.V. "Development of Methodologies for Determining the Integrity of Corroded Pipelines," Phase 2, Final Report submitted to Alyeska Pipeline Service Co., Southwest Research Institute, San Antonio, Apr. 27, 1992.
- Langner, C.C., "Design of Deepwater Pipelines," TNO-IWECO 30th Anniversary Symposium of Underwater Technology, The Hague, May 1984.
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