COMPARISON OF CYCLIC AND BURST TEST RESULT WITH FE SIMULATION OF A LOCALLY
THINNED PIPE BEND
Wolf Reinhardt Atomic Energy of Canada Ltd. Mississauga, Ontario, Canada
Ali Asadkarami Atomic Energy of Canada Ltd. Mississauga, Ontario, Canada
ABSTRACT
Thinning of Carbon steel pipe subjected to water flow has been observed in many piping systems. The feeder pipes in CANDU? 1 reactors have been found susceptible to this degradation mechanism. In response, an industry program has been initiated to investigate the effect of local thinning on structural integrity.
A CANDU? feeder pipe bend specimen was thinned locally to about 70% of pressure based thickness near the weld at the onset of the bend. The test specimen was subjected to severe pressurized cyclic bending for over 1600 cycles, and was subsequently pressurized to failure under a constant applied bending deformation. The failed specimen was subjected to metallurgical examination.
The present paper reports the results of a finite element analysis of the cyclic part of the test and an elastic plastic analysis for failure under pressurization. The results are compared with the experimental outcomes. The conclusions address specifically the test, more generally the failure of thinned pipe and the use of elastic-plastic finite element analysis to predict failure due to pressurization. INTRODUCTION
In a CANDU? reactor, small-bore feeder pipes (feeders) connect the large-bore primary piping to the pressure tube that form the reactor core. Feeders range from 1?-inch (DN 40) through 3?-inch (DN 90), size with lengths from 20 feet
1 CANDU is a registered trademark of Atomic Energy of Canada Ltd. (6.1 m) through 60 feet (18.3 m)., The feeder nominal wall thickness is between 5 mm (1?-inch pipes) to 8 mm (3?-inch pipes). The material in existing plants is unclad SA-106 Grade B carbon steel. The feeders are designed in accordance with NB-3600 of Section III of the ASME Boiler and Pressure Vessel Code (B&PV Code), [1].
Due to high flow velocities, local wall thinning caused by Flow-Accelerated Corrosion (FAC) is an active degradation mechanism. Inspection results from plants and examinations of removed feeders indicated the presence of localized thinning near the reactor end of these pipes [2]. By design, the pipes have about twice the wall thickness required to contain the pressure by NB-3640. Therefore, wall thinning is not an immediate concern. However, near the end of the design life, local thinning may approach or even pass below the NB-3640 thickness.
The very significant margin to failure of thinned feeders was demonstrated in an industry-funded targeted test program (Feeder Bend Testing Program, FBTP). As a design Code for piping, NB-3600 does not address local wall thinning, and its methods are not directly applicable to this type of service-induced phenomenon. Fitness-for-service evaluation methods are better suited for this specific degradation mechanism. Degraded feeders are expected to maintain the nominal margin to failure required by the design code.
Suitable advanced analysis methods have been included in the Fitness-for-Service Guidelines for Feeders in CANDU?Reactors (Feeder Fitness-for-Service Guidelines or FFSG for short, a proprietary document of CANDU Owners Group
Proceedings of the ASME 2011 Pressure Vessels & Piping Division Conference
PVP2011
July 17-21, 2011, Baltimore, Maryland, USA
PVP2011-58005
(COG)) for a more realistic evaluation of local thinning. Methods include limit analysis similar to Section III Article NB-3228.1 (Limit Analysis) [1], and elastic-plastic stress analysis similar to that described in Annex B1.2.4 of ASME FFS-1 [3]. These methods may predict significantly greater margins to failure for a given state of thinning than the traditional elastic analysis methods. Hence, the performance of these methods has to be evaluated carefully and a strong technical basis needs to be established.
The existing FBTP tests concentrated on demonstrating structural margin for realistic thinned feeder pipes with bends under cyclic loading and under pressurization to burst. The main objective of these tests was to incorporate an idealized representation of the local and general wall thinning observed in actual feeders, and to demonstrate that the operation of such feeders is safe due to significant margins to failure.
The greatest wall thinning is observed near the reactor end of outlet feeders where coolant that has been heated by the reactor and is undersaturated in iron enters the feeder. The attachment point is a hub that is followed by a single or double bend. Due to flow turbulence and the uneven wall thickness distribution in the bends, these tend to contain the thinnest wall sections. Reference [2] gives a summary of the industry experience with feeder wall thinning.
Guided by the operating experience, the bend tests have included general wall thinning that was roughly uniformly distributed throughout the tested piece, and local regions with further thinning to below the NB-3640 pressure based design wall thickness near the bend. Tests were performed at operating temperature and pressure, and included severe cyclic bending loads well in excess of the bounding (seismic) loads. After applying a cyclic loading program, the feeder bend specimens were pressurized further, mostly to failure.
This paper describes FE analysis of one such test that was performed to obtain additional information about the failure mechanism, and to apply the advanced analysis methods provided in the Feeder Fitness for Service Guidelines.
PIPE BEND TEST
Geometry and Material
The test specimen represented a typical feeder pipe hub and bend with an attached piece of straight pipe, Figure 1 The NPS 2? Schedule 80 pipe was made from SA-106 Gr. B material. The entire pipe specimen was thinned uniformly from the inside to about t un = 4.1 mm wall thickness in the straight section by a chemical process. Using Electrical Discharge Machining (EDM), a rectangular patch was then further thinned from the inside to 2.3 mm wall thickness, or about 70% of the ASME Section III NB-3640 pressure based thickness at Design temperature, which is slightly above 3 mm. The thin region had an axial extent of 12 mm (or approximately ·
45?. It was located in the short straight piece between the hub and the bend (Figure 1), partially under the hub weld. The location of the thinned patch reflects one of the locations of relatively thin walls observed in service.
The pipe specimen was bent using the procedure for feeder warm bending. As in real feeders, the bend radius is 1.5 times the nominal pipe diameter (equal to a “long” pipe elbow). Due to the bending process, the material in the bend region is significantly work hardened. The bend angle in the test specimen was 73?. An ANSI Class 2500 welding neck flange was welded on. The approximately 800 mm long straight pipe adjacent to the bend was closed with a weld cap. Testing Procedure and Results
The experimental setup allowed the pipe to be pressurized with heated water. An in-plane bending load (shear force) could be applied through a load collar located at about 700 mm from the bend as shown in Figure 1. The test temperature was 300°C. The test setup is shown in Figure 2
The test program consisted of a very severe cyclic loading phase where a stroke controlled closing bending was applied with a simultaneous internal pressure. In total about 1600 bend cycles were applied. During the first phase a single cycle from 0 to 8.7 kN·m was applied, followed by 1026 cycles with the same displacement range (load point range 33 mm, maximum displacement relative to initial position 80 mm), The pressure was held constant at 10.3 MPa (the approximate feeder operating pressure). The specimen did not fail. The internal pressure was increased to 18 MPa while maintaining the maximum vertical displacement. After 53 cycles with this level of pressure, the load-point displacement range was increased over three cycles. For the subsequent 221 cycles, the range of load-point displacement was increased from 33 mm to 36 mm (107 mm maximum displacement). The corresponding bending moment range was 0 to 10.1 kN?m. No failure was observed. As in the previous cycles, shakedown occurred. The displacement range was then increased to 39 mm (117 mm maximum displacement), or a corresponding bending moment range from 0 to 10.7 kN?m, for a further 300 cycles of alternating, displacement-controlled bending. Again, no failure was observed.
Subsequently, the bending displacement was increased to 120 mm and held at this value, followed by a slow pressurization to failure. Failure of the pipe specimen occurred through ductile tearing starting at the bend cheek at 66.1 MPa (Table 1). The pipe suffered a complete failure with part of the bend extrados torn off; see the lower picture in Figure 2.
FE ANALYSIS
Scope
Two different analyses: were performed:
?An elastic-plastic analysis under coincident bending and internal pressure was conducted following the
Feeder Fitness-for-Service Guidelines using a stress-
strain curve based on best-estimate tension test results
of the material.
? A (elastic) fatigue analysis to determine the potential for crack initiation.
Methodology
The burst pressure simulation results are obtained from elastic-plastic analysis following the methodology outlined in E-11.2, Plastic Collapse Load Based on Elastic-Plastic Stress Analysis, of the Feeder Fitness for Service Guidelines. The analysis proceeds as follows:
a)Create a numerical model of the component that
includes all relevant geometry characteristics.
b)Apply boundary conditions, and applied loads for
each load case.
c)Perform the analysis using an elastic-plastic material
model. The von Mises yield function and associated
flow rule are used. A material model that includes
hardening or softening, or an elastic-perfectly plastic
model may be used. A hardening material model
should be based on the true stress-strain curve of the
material of the modelled part, and the hardening
behaviour should be included up to the true ultimate
stress and perfectly plastic behaviour (i.e., the slope
of the stress-strain curves is zero) beyond this limit.
The effect of large deformations with nonlinear
geometry shall be included, and equilibrium shall be
satisfied in the deformed configuration.
d)At any load level where the analysis achieves
convergence, the part is stable under the applied
loads for this load case. The highest load level at
which convergence can be achieved is the collapse
load (or plastic instability load according to NB-
3213.6 of Section III [1]).
In practice, one obtains the plastic collapse load from a finite element model, which incorporates an elastic-plastic material model representing the hardening response. Since the effects of non-linear geometry are considered in this analysis, the true stress-strain curve needs to be used. The plastic collapse load is reached at the point of structural instability. At this point, the FE software is unable to achieve an equilibrium solution for a small increase in load (i.e., the solution will not converge).
In addition to the plastic collapse load, a very simple local failure criterion was also explored. “Local” failure is a term used in ASME Section FFS-1 [3] to describe failure due to ductility exhaustion, such as immediately preceding the final rupture of a tensile specimen. The criterion that is used here is a simple strain limit, which assumes failure when the local equivalent true strain reaches the ultimate true strain from the tensile test (note that this is equivalent to the true stress reaching the ultimate true stress).
Finite Element Model
The finite element model included the flange, hub, and bent and straight pipe portions of the tested specimen up to the plane of load application. A half model was created in ANSYS (Ver. 10.0) and meshed with 8-noded SOLID185 elements. The thin wall at the flaw as well as the straight pipe around the thin patch and the bend were meshed with 5 elements through the thickness. The straight pipe attached to the bend and extending toward the loading plane was meshed with 3 elements through the thickness. The overall model is shown at the top of Figure 3.
The wall thickness distribution of the experimental specimen was measured and applied to the model in the bend region and in the straight pipe regions. The non-uniform wall thickness in the bend is evident in the lower left picture of Figure 3.
The local flaw and the weld cap were included in the model. The lower right picture of Figure 3 shows a detailed zoom-in on the region around the flaw. The weld cap height was estimated to be 1 mm from pictures of the test setup.
Symmetry boundary conditions are applied on the pipe midplane. The bending load or bending displacement is applied at the straight pipe end surface of the model. The pressure blow-off load is applied to this surface as well. The blow-off load was calculated based on the initial geometry and not adjusted; this was based on the observation that the radius change of the straight pipe is relatively moderate.
The elastic material properties used in the model are
Elastic modulus 203,000 MPa (29,400 ksi)
Poisson’s ratio 0.3.
An existing database from testing of the tested material was used to determine the stress-strain curves at 300°C for the model. The true stress-true strain curves are plotted in Figure 4. The tensile properties are significantly higher than the ASME Code minimum properties. This is especially true for the bend, due to the level of cold worked applied to the material during the bending process that was applied.
Results – Burst Pressure Prediction
This simulation employed elastic-plastic material properties in a plastic collapse analysis. To simulate the actual loading sequence at least approximately (excluding the cyclic portion), the FE analysis applied first a pressure of 10.23 MPa, then ramped the displacement to 125 mm while the pressure was held constant, and finally increased the pressure to the point of plastic instability with constant displacement. In total, four of the analyses that were performed are described here, which are characterized as follows:
1.FE model of the beginning-of-test geometry with
loading as described above, and best-estimate tensile
properties.
2.FE model with simplified bend flaws from cyclic
loading phase; loading as described above, and best-
estimate tensile properties,
3.FE model of the beginning-of-test geometry with
pressure loading (no bending displacement), and
best-estimate tensile properties.
4.FE model of the beginning-of-test geometry with
loading as described above, and lower bound tensile
properties.
Case 1
The instability pressure (where convergence of the FE analysis is lost) is reached at 77.3 MPa, which is about 16% above the experimental failure pressure of 66.1 MPa. Figure 5 shows the exaggerated deformed shape as well as the plastic strains to allow an evaluation of the location of failure. The bulging of the straight pipe between the hub and bend and the additional bulging of the thin region, as evident through the higher level of plastic strain there, suggest that the thin region is the location of blow-out in the analysis.
The bulging of the straight section of pipe relative to the hub and bend is evidently constrained by the smaller radial deformation of these nearby sections. The smaller deformation of the hub is caused by the increasing wall thickness, while the deformation of the bend is lower due to the elevated tensile properties there. Equally, the existence of the weld crown would reinforce the thin region. However, the small total
volume of the weld crown suggests that the weld crown reinforcing effect is much smaller than that of hub and bend. Since the bend is in the immediate vicinity of the thin region, it is expected to be the major influence on the failure pressure.
To investigate the possibility of a local failure by ductility exhaustion, it is also determined at which pressure the (true) ultimate strain from a tension test is reached. Note that the criterion is evaluated separately for the straight pipe and bend regions. This pressure is 73.8 MPa, or about 10% above the experimental failure pressure. The location where the ultimate strain is reached first is at the thin region as indicated in Table 1. From Figure 5, the highest plastic strain occurs at the bottom radius on the side of the thin region, which indicates the predicted failure location. This failure location is consistent with the previous straight pipe test [5], but not with the observation from the present test.
Case 2
An examination of the bend fragments after the test showed that axially oriented fatigue cracks had initiated at one of the bend cheeks, and that the failure initiation site during the final pressurization was that crack. The FE model without bend flaw indicated failure would occur at the thinned region; therefore the reduction in wall thickness due to the cheek flaw was analysed next. The dimensions of the flaw were based on the measured fatigue crack depth of 1.1 mm and a length estimated from the post-test examination as:
c flaw Total flaw length (axial) = 30 mm
a flaw Total flaw depth (radial) = 1.1 mm.
The FE model incorporates the flaw by having a wall thickness reduction at the cheek circumferential location only, while the original wall thickness was maintained everywhere else. Essentially, a V-notch with a total circumferential extent of 2 element sizes was created. While this is not sufficient for a fracture mechanics evaluation, it allows an evaluation for plastic collapse, since the wall reduction is represented.
An analysis based purely on plastic instability indicated no substantial reduction of the failure pressure relative to for the unflawed model. However, the failure of the crack might be governed by crack propagation and subsequent failure, or by excessive straining of the remaining ligament.
Applying local (strain) criterion indicates a significant drop in failure pressure to 67.2 MPa, or 2% above the experimental value. The predicted location of failure shifts from the thin region to the bend cheek. This is consistent with the experimental observations. The maximum plastic strain occurs at the OD of the bend cheek (at the location of the flaw). At this location, there is no significant mesh dependence of the observed strain.
Case 3
The reference model (without bend flaw) was subjected to pressurization without applying the simultaneous bending deflection. The instability pressure was found to be 25% lower than that of the case with simultaneous bending, Table 1. The region of failure is again near the thinned flaw. Unlike the bending case, the local failure criterion is not reached in this case, and instability failure governs. Case 4
According to the previous simulation of the straight pipe test [5], a trilinear hardening model (elastic-linear hardening-perfectly plastic above the true ultimate strength, Figure 6) based on ASME Code material properties was shown to give lower bound burst pressure predictions. Note that the ASME ultimate strength needs to be converted to true stress before being input as a point on the true stress-true strain curve. The true ultimate strain (tensile instability strain) was chosen to be 0.25, consistent with the straight pipe test material that had low (near-Code) yield and ultimate strengths [5].
The instability pressure resulting from the run is shown in the last line of Table 1. It is reduced by over 50% relative to the instability pressure obtained with the same model with best estimate stress-strain curve. Failure is predicted at slightly more than 1/3 of the experimental failure pressure, which is very conservative.
Results – Fatigue Analysis
A fatigue analysis was performed using the results of an elastic analysis. Elastic analysis was chosen because any cyclic plasticity that may occur in the component is highly localized, under which conditions an elastic analysis under these conditions is consistent with the ASME Section III NB-3222.4 [1] approach. For localized plasticity, the elastically calculated strain (or stress) is a reasonably accurate measure of the total strain [6].
The elastic analysis was performed for minimum and maximum conditions. The minimum condition had 10.3 MPa pressure applied, while the maximum condition had 10.3 MPa pressure and a bending force of 10.7 kN. These conditions correspond approximately to the first 1000 cycles of load application. Stress component ranges are obtained by subtracting one extreme solution from the other. The stress intensity range is calculated from the component ranges. The subtraction eliminates the effect of constant pressure, and is thus applicable to all loading cycles with the exception of the half cycles during which the pressure changes. Since there are only two such cycles, the effect is deemed negligible.
The stress intensity range distribution identifies two locations where the largest cycling occurs, namely at the flange side corner radius of the thinned region and the bend cheeks, Figure 7. At both of these locations, fatigue cracks were observed after the experiment as shown in Figure 7.
The stress ranges for the experimental loading program were obtained from the recorded values of the applied bending force. The extreme values during each cycle were extracted from the recorded loading history, and a rainflow cycle count [7] was performed to identify the individual load cycles. A total number of 1622 bending moment application cycles was found.
The stress ranges in the model were prorated from the analyzed bending load range to the bending load range of the cycle under consideration. The stress amplitudes, S a, were determined from the stress ranges as described in NB-3222.4. The amplitude spectrum of the entire cyclic history is plotted in Figure 8
The cumulative usage factors calculated using the ASME Section III fatigue curve for carbon steel are listed in Table 2. The fatigue usage factors calculated by ASME Code methods
at these locations exceed unity, indicating that fatigue crack initiation could occur. Since the Design curve used for the fatigue calculation lies a factor of 20 on cycles below the mean curve of the fatigue test data base, initiation may not occur immediately as the Design curve is exceeded. In the experiment, initiation did occur on one side of the tested pipe, but not on the other, nominally symmetric side. This may be due to non-symmetric features in the set up, for example in the load application, in local material properties, or in the geometry (e.g., surface roughness features or wall thickness deviations). These are not reflected in the FE model.
Overall the agreement between experiment and analysis was good. The initiation sites were identified correctly, and the fact that initiation would occur well before the end of the test was also predicted correctly.
DISCUSSION
The analysis of the FE model with unflawed bend predicted that failure through pressure blow-out would occur in the thinned region, and that it would be likely that the failure would occur by local failure or ductility exhaustion (formation of a crack) at a pressure level of 73.8 MPa, which is fairly consistent with (about 5% below) the ultimate pressure at plastic instability, 77.3 MPa. However, in the test the failure occurred in the bend cheek region at a pressure that is 15% below the predicted instability pressure. Therefore, the unflawed model, with or without local failure criterion, cannot explain the experimentally observed failure. The test does not refute the analysis result because the analysis applies to failure at the thin region, but the actual failure occurred in the bend. It is unknown if the specimen could have reached the predicted failure pressure if the bend had not failed.
The FE run with a flaw represented as a local wall thickness reduction in the bend cheek showed no significant reduction in the instability pressure. The local failure criterion, on the other hand, indicated that the bend cheek would be the location of failure, and that the failure pressure would be significantly reduced compared with the instability pressure. The failure pressure given by the local failure, or ductility exhaustion, criterion was about 2% above the experimental failure pressure. Therefore, the model with bend flaw is in agreement with the experiment both in terms of the location of failure and the failure load when the local failure criterion is used.
A surprisingly large difference was found between the instability pressure with and without simultaneous bending displacement. In a plastic limit analysis that uses perfectly plastic material properties and small deformation theory, any imposed displacements would leave the limit load unaffected. In other words, the limit pressure with or without bending displacement would be the same. The results show that this is not the case for the elastic-plastic analysis that was performed here. The two differences between elastic-plastic and limit analysis are that the former includes nonlinear geometry effects, in particular on the equilibrium stress distribution, and that it includes material hardening. Since the geometry of the straight pipe near the hub does not change substantially as a result of the bending deformation, it is concluded that material hardening is the main reason for the higher instability pressure. The deformation of the material during bending increases the strength (resistance to plastic flow)) of the material that provides reinforcement to the thin region during the subsequent pressurization. Reinforcement delays pressure blowout at the thin region as the surrounding thicker wall carries some of the stress. This effect is similar to the strengthening of the bend material during the pipe bending process below the normalization temperature. Other effects, such as the applied bending counteracting the pressure opening of the bend, may have had a contributing role.
During the simulation of the straight pipe test [5], it was noted that the shape of the stress-strain curve had a substantial effect on the instability pressure obtained from FE. This effect is similar to the work hardening effect in terms of the strengthening of the material that reinforces the thinned patch. If the reinforcing material reaches a higher stress for the same amount of deformation (or less deformation for the same amount of stress), it provides more reinforcement effect. These arguments are valid only when bending is applied under deformation control. Load controlled bending of sufficient magnitude would be expected to lower the failure pressure. The use of linear hardening results in a conservative assessment.
During the cyclic portion of the test, crack initiation took place at two of the most highly stressed locations as expected from the analysis. The observable fatigue striations indicated a significant period of subcritical fatigue crack growth. The results of the burst simulation indicate that the subcritical fatigue crack growth at the bend cheek was sufficient to facilitate failure at a lower pressure than what would have been expected otherwise, but it was very far from being in danger of bursting at the operating pressure. In other words, there is a large difference between cycles to initiation versus cycles to failure. Therefore, the test points to a large conservatism of the ASME Code fatigue analysis when applied to notches and other locations with a steep stress gradient, since the extended crack growth phase is ignored. This conservatism was pointed out by Tagart [6] in his paper on the ASME Code local strain approach. Thus, if the fatigue crack initiation criterion is satisfied in the presence of stress concentrations, and if the critical crack size is large due to a ductile material and/or geometry with a low constraint, a high safety margin against cyclic failure is achieved. CONCLUSIONS
Significant conclusions of the present correlation of test and analysis were:
Pressurization to failure:
?Both the test and FE analysis with realistic stress-strain curve indicate high margins to failure (test
failed at six times the Design pressure). The margin
was achieved in the presence of a thin region at 70%
of the pressure based Design thickness and fatigue
cracks in the bend
?The analysis is in agreement with the metallurgical result that the test specimen failed by local failure at
the bend cheek fatigue crack. If actual feeders pass an
analysis for fatigue crack initiation, such flaws would
not be expected
?
Due to the local failure, the plastic analysis (plastic instability analysis) overpredicted the failure pressure (by about 15% in the present case).
? The very high failure pressure in the test seems to be
partly due to work hardening of the material surrounding the thin region due to the bending deformation. The analysis indicates that applying pressure without bending deformation would result in a lower failure pressure (15% below the test failure pressure without even modelling the bend cheek flaw).
? The approach of the COG Feeder Fitness for Service
Guidelines of applying the pressure alone to evaluate pressure blowout is, therefore, shown to be conservative for plastic analysis. Fatigue:
? Analysis for fatigue crack initiation is quite
conservative where there are large stress gradients, such as at local notches and also in pipe bends (elbows) subject to bending loading. This applies in particular in the low-cycle regime. The growth of the initiated crack to a structurally significant size can take much more cycles than the cycles to initiation. Use of elastic-plastic analysis for plastic collapse:
? The use of realistic material data will greatly affect
the plastic collapse pressure. The use of specific lower-bound properties could give more realistic and still conservative predictions compared with the most conservative Code minimum and linear hardening model.
? The test failed due to a local mechanism at the bend
flaw that was initiated during cyclic load application. A local criterion was found to be required to predict failure origination from sharp discontinuities. For the application to the present piping material with wall thinning from FAC, which tends to be more gradual, such a criterion is not deemed to be necessary. However, the application of a local criterion would demonstrate that this potential failure mechanism has been considered.
?
Careful benchmarking of numerical models is required. There is a need to develop and document acceptable non-linear analysis procedures.
ACKNOWLEDGMENTS
The reported work was funded under the Chemistry, Materials and Components (CM&C) program of CANDU Owners Group (COG). The pipe experiment described in this paper was performed by B. Mills at Kinectrics, Inc as part of a testing program managed by X. Duan of Atomic Energy of Canada Ltd. Thanks are also due to Y . Shao of Atomic Energy of Canada Ltd. for his contributions to the FE analysis.
REFERENCES
[1] The American Society of Mechanical Engineers, 2007,
ASME Boiler and Pressure Vessel Code, Section III, Division 1, ASME, New York.
[2] Duan, X., Kozluk, M.J., and Li, M., 2009, Comprehensive
Integrity Assessment of Carbon Steel Feeder Pipes/Elbows Subject to Wall Thinning, PVP2009-77060, Proceedings of ASME PVP2009, Prague, Czech Republic.
[3] The American Petroleum Institute and the American
Society of Mechanical Engineers, 2007, API579-1/ASME FFS-1, Fitness-For-Service, API Publishing Services, Washington, D.C..
[4] SAS IP, Inc., 2005, ANSYS, Ver. 10.0 User Manuals,
Canonsburg, PA
[5] Reinhardt, W., and Duan, X., 2010, Comparison of
Elastic-Plastic Analysis and Experimental Result for Locally Thinned Pipe, PVP2010-26090, Proceedings of the ASME K-PVP Conference, 2010, Bellevue, WA, USA [6] Tagart, S.W, 1972, Plastic Fatigue Analysis of Pressure
Components, in: Bohm, G.J., Cloud, R.L., Hsu, L.C., Pai, D.H., and Reedy, R.F., Pressure Vessels and Piping: Design and Analysis. A Decade of Progress, V olume One, ASME, New York.
[7] ASTM E 1049-85., Reapproved 2005, “Standard
Practices for Cycle Counting in Fatigue Analysis”, ASTM International.
Table 1: Pre-Test Prediction, Experimental Result and Post-Test Result of the Failure Pressure Analysis Case
Failure Pressure
Test
– 66.1 MPa
F E A n a l y s i s Pressure/bending, pre-test geometry, best-estimate material
77.3 MPa Pressure/bending with local failure, pre-test geometry, best-estimate material 73.8 MPa Pressure/bending with local failure, bend flaws, best-estimate material 67.2 MPa Pressure only with local failure, pre-test geometry, best-estimate material 57.8 MPa Pressure only with local failure, pre-test geometry, ASME/trilinear material
24.3 MPa
Table 2: FE Results and Cumulative Fatigue Usage Factor at Bounding Locations for Fatigue
Location FE Stress Intensity
Range
Stress History
Cumulative Fatigue
Usage Factor Edge of Thinned Region 1826 MPa 8.6
Bend Cheek 1469 MPa 5.1
Figure 1: Dimensions of Tested Pipe Bend Specimen
Figure 2: Test Specimen before and after Test
Figure 3: FE Model Meshes, Above: Overview, Left: Bend Region,: Right: Local Thinned Region
Figure 4: Multi-linear Stress-Strain Curves at 300°C for FE Elastic-Plastic Analysis,
(Deformation grossly exaggerated to highlight failure mechanism)
Figure 5: Plastic Strain and Deformation at Instability Pressure for Unflawed Bend under Pressure and Bending
Figure 6: Trilinear True Stress – True Strain Curve Based on ASME Code Properties
(a)
(b)
Figure 7: Comparison of Predicted Regions of High Stress Range and Experimental Crack Locations,
(a) Flange Side Corner Radius of Local Thinned Region, (b) Bend Cheek
Figure 8: Stress Intensity Amplitude Distribution Spectrum –Bend Cheek