Validation of FE Models for Pipelines with Localized Metal Loss
José L.F. Freire, Ronaldo D. Vieira, Jorge L.C. Diniz, Jaime T.P. Castro PUC-Rio – Department of Mechanical Engineering Rua Marquês de São Vicente 225, Gávea, Rio de Janeiro, 22453-900, Brazil
[email protected]
INTRODUCTION A research project was conducted with the purpose of testing pipeline specimens with external corrosion defects and developing a reliable numerical FE model to predict their elastic-plastic and rupture behaviors. In the first phase of this project, burst tests of nine tubular specimens containing single external machined-simulated corrosion defects were carried out. Each of the tubular specimens was instrumented with high-elongation strain-gage rosettes and pressure transducers. These rosettes were bonded in the defect region and also on sites located far from the defects, on the cylindrical surface, so that nominal elastic strains could be measured and compared with theoretically calculated results [1]. The elastic and plastic strain data measured by the high elongation strain gages were compared with a elastic-plastic Finite Element simulation aiming to validate the numerical model and to use it to predict burst pressures. The development of the FE model considered the type and number of elements used, the influence of employing actual specific or average stressstrain material properties, size of the pressure steps used in the non-linear analysis, and the criteria used to consider the numerical bursting failure of each specimen. Agreement between experimental and numerical data for elastic and plastic strains, bulge displacement and burst pressure results were very good, validating the procedure used to construct the numerical model. EXPERIMENTAL ANALYSIS The raw material used in this research consisted of 5 longitudinal welded tubes made of API 5L X60 steel. Nominal outside diameter, nominal wall thickness and length of the tubes were, respectively, D=323.9 mm (12.75 in), t=9.53 mm (3/8”) and 6 m. From this raw material, nine tubular specimens were manufactured and used in the pressure tests. Tensile test specimens were cut from each of the five tubes that originated the tubular specimens in the longitudinal and transversal directions (two for each direction). Clip-gages and special uniaxial strain gages for high elongation testing, type TML YFLA 5, were used. Minimum, maximum and mean yield stresses of the transverse tensile specimens are 437 MPa, 475 MPa and 452 MPa, respectively. The mean yield stress is 9.5% greater than 413 MPa, the SMYS of API 5L X60 steel. Minimum, maximum and mean ultimate stresses are 533 MPa, 556 MPa and 542 MPa, respectively. The mean ultimate stress is 4.7% greater than 517 MPa, the SMTS of API 5L X60 steel. Each of the 9 tubular specimens had one external corrosion defect, fabricated using spark erosion. These defects are corrosion patches, longitudinally oriented, with uniform depth d and uniform width w (circumferential length). All the defects had the same nominal depth of 6.67 mm (70% of the nominal wall thickness) and the same width of 95.3 mm (ten times the nominal wall thickness). They were fabricated opposite to the tube seam weld at a centralized position in relation to the ends of the specimens. The defect lengths and the ratios of the square length to the product of nominal diameter versus the nominal thickness are presented in Figure 1. The tubular specimens were 2 m long. They were closed by specially designed flat heads with crossed reinforcements. These flat heads were welded after the defects were produced. The actual specimen thickness varied up to approximately 4.9% of the nominal wall thickness of 9.53 mm. Minimum and maximum thickness ranged from 9.6 to 10 mm respectively. Minimum and maximum defect thickness ranged from 2.6 to 3.6 mm respectively. The mean defect thickness varied up to approximately 6.8% of the reference defect thickness of each specimen. Each of the 9 tubular specimens was instrumented with 10 high elongation TML YFRA-5 strain-gage rosettes. Nine of these rosettes were bonded in the defect region and one was located far from the defect, on the cylindrical surface, so that nominal elastic strains could be measured and compared with theoretically calculated results.
Details on the pressurizing system used in the tests can be found in [1]. Loading rates were such that the speed of the piston was 0.08mm/s and the volume rate injection was ~0.2 cm3/s, resulting in a maximum pressure rate of 1.3 bar/min. All data was conditioned and collected by an HP 3852A data acquisition system, controlled by a laptop with an A/D National GPIB PCMCIA card, and a specially written software running in a “Labview” environment. Reference [1] presents the burst pressures of the nine tubular specimens along with those predicted by the ASME B31G, the RSTRENG 085dL, the RSTRENG Effective Area and the DNV RP-F101 (Part B) methods. Reference [1] also presents a detailed elastic-plastic strain analysis of the response from the strain gages that were bonded to the specimens. FINITE ELEMENT ANALYSIS The finite element program ANSYS version 5.3 [2] was employed to predict the elastic-plastic behavior of the nine tubular specimens and their burst pressures. The following points were investigated in order to set up the numerical model: • Material Properties: The actual elastic-plastic uniaxial stress-strain behavior for each tube was fed to the FE program. Care was taken to model exactly the uniaxial stress-strain behavior in the knee region, located between the point where the linear elastic behavior ends and the point that characterizes the yield point (0.2%), and beyond up to rupture. Behavior beyond rupture was simulated by a straight zero-hardening line. • Geometric non-linearity: Visual observation and displacement measurements of the bulge formed at the defect central point (Figure 2) suggested that the use of geometrical non-linearity could be avoided. A benefit of that was the increased speed of the numerical solution. A very good agreement was reached when experimental strain behavior was compared with the FE response determined using small and large displacement calculations. • Finite Element Model: Preliminary numerical solutions using 8 and 20 node brick elements demonstrated that the 8 node elements could be used with the same accuracy and lower solution time. Use and comparison of brick and shell element solutions were recently investigated in [3]. At the corroded region three element layers were used through thickness. At the non corroded region six elements were used. Due to symmetry, only one fourth of the tube specimen was modeled. A preliminary analysis carried out with a complete model indicated that pipe end radial restraints due to the flat heads could be simulated by stiffeners. Axial stresses due to the action of the pressure on the flat heads were also imposed to the boundary solid elements. An approximate total of thirty thousand elements were used in each analysis. • Size of Pressure Steps: The stress-strain behavior of the pipe specimens with pressure was seen to be well represented by three phases: an elastic phase, where only one pressure step is needed for the numerical solution; a second phase, between the beginning of small plastic strains up to the pipe overall yielding (the knee curve of the pipe response and not the stress-strain uniaxial response) where a 0.1 MPa was used; and a third phase, where very small pressure increments (0.001 MPa) had to be used to achieve convergence. Small increments of this magnitude were also recommended in [3]. • Rupture Criteria Experimental evidence has shown that the burst failure of pipe specimens without crack-like defects happen after some spread of a longitudinal neck and under a calculated von Mises stress equal to the true ultimate material strength, Sut. In this investigation, two criteria were used to determine the burst pressure from the numerical solutions. The first uses the simple hypothesis that burst failure will occur when any first element reaches a von Mises stress equal to Sut. The second criterion considers failure when convergence is not achieved even when a small increment pressure step of 0.001 MPa (about 10-5 of the burst pressure) is applied. The present investigation concluded that the onset of non-convergence is achieved when all (three) elements in the through thickness direction reach Sut. RESULTS Due to space limitations the results presented at this section may be seen as typical for all specimens tested. Circumferential (εc) and longitudinal (εl) strains measured with the high elongation rosettes and calculated by the numerical solution are presented in Figures 3 and 4. Figure 3 presents the elastic and plastic strain state behaviors of a point located at the center of the defect. Pressure values P1 and P2 are marked in the plots to indicate respectively the test pressure related to the initiation of plasticity behavior (or elastic limit) and the test pressure that causes a plastic εcp strain of 0.17% (equivalent to 0.2% yield strength using LévyMises theory and considering a uniaxial stress state). Pressure P3 indicates an inflection point that occurs before the rupture. The restriction of the longitudinal side walls is more evident in the elastic-plastic and in the plastic ranges of the strain state behavior. Plastic strain increments of εl, δεlp, are clearly negative, making the total strain εl decrease and reach negative values in the end of the elastic-plastic range. It may be noticed that, as the sum of the plastic increments must be zero, i.e., δεcp. + δεlp + δεrp =0, and as the values of δεcp start to become very large, δεlp and δεrp must assume negative values to keep incompressibility. The longitudinal plastic increments can not reach high values due to the adjacent thick wall restrictions and so the total strain has to be inside the overall elastic strain of the material adjacent to the defect. The strains in the thickness direction are less restrained than the strains in the longitudinal direction. Therefore, the thickness of the defect varies with increments that after P2, will be of the order of δεcp . Measurements show that δεcp >> δεlp . Then, it must happen that δεcp= δεrp .
From the above results and discussion, it becomes clear that the defect region behaves as a long strip with high (but not absolute) freedom to deform elastic and plastically in the circumferential and thickness directions. Large restraints are offered by the thick walls parallel to the strip to the longitudinal strains. These restraints are present in the elastic behavior and are increased during the plastic behavior. Figure 4 shows a plot where the ratio εl/εc varies with test pressure. Considering a thin pipe with uniform thickness and a Poisson ratio of 0.3, the ratio between the elastic longitudinal and circumferential strains is 0.24. For all specimens analyzed this elastic ratio is affected by the near thick wall restraints and turn to be different from 0.24. After reaching the pressures P1 and P2 , plasticity takes place and this ratio goes rapidly to zero and oscillates close to this value, being positive or negative. Table 1 presents values of burst pressures for comparison purpose. For each of the nine tubular specimens, FE calculated burst pressures were determined based on the two numerical rupture criteria (first element to achieve Sut or numerical instability) and based on the average or minimum thickness at the defect region. It was seen that the failure pressure difference between the two criteria used was under 5%, being consistently lower for the “first element” criterion. Results for failure prediction using the minimum specimen thickness at the defect region agreed very well with the experimental results. On the other hand, large discrepancies happened when the average thickness was used in the calculations. It must be noted that the defect geometry used in the present investigation, which considers a uniform thickness, is more prone to this type of divergence. Numerical tests using full FE models with accurate thickness for each location at the defect region improved the numerical results but this process is time consuming and seems to not offer much gain in the analysis due to uncertainties in other parameters such as pressure measurement and control (which was in the range of 1%). CONCLUSIONS Test results reported in [1] were used to validate a FE model to be employed to predict elastic-plastic and rupture behavior of tubular pipeline specimens. The numerical results calculated from the developed FE model showed good agreement with the experimental results. In order to achieve the present level of agreement the following conditions should be considered when modeling pipeline behavior: 1. Use the materials actual uniaxial true stress-strain curve. 2. Use the minimum thickness at the defect region for long defects with uniform length. There is an ongoing investigation for actual corroded pipes where the corrosion region presents abrupt thickness variations. 3. Measured actual burst pressures were limited by lower and higher FE boundary values, respectively equal to the pressure that causes the first element to reach a von Mises stress equal to the true ultimate strength and the pressure that causes numerical instability. 4. Eight node solid models (and shell elements for uniform corrosion, [3]) may be used. A large displacement analysis was not needed to achieve good agreement with experimental results. REFERENCES 1. J.L.F. Freire, A. Benjamin, R.D. Vieira, J.L.C. Diniz, E.M. Florence, J.T.P. Castro, “Strain Analysis of Burst Tests on Pipeline with External Corrosion”, SEM Annual Conference on Experimental and Applied Mechanics, 689-692, 2001. 2. ANSYS, “ANSYS Software and User Manual”, version 5.5, ANSYS Inc., 1998. 3. Noronha,D.B., Benjamin, A.C., Andrade, E.Q., “Finite Element Models for the Prediction of the Failure Pressure of Pipelines with Long Corrosion Defects”, Proceedings of IPC’02, 4th International Pipeline Conference, ASME, 2002.
(a)
Rosette locations Defect region t’=nominal thickness = 3mm
(b)
Hydraulic actuator
Pressure transducer
P
Gefran and BLH
Manometer
Figure 1 – Test set up and rosette locations
t
D L 2000 mm L (mm) Rosette position L2/(D.t)
TS5.1 255.6 (b) 21.2
TS1.2 305.6 (b) 30.3
TS2.2 350.0 (b) 39.7
TS2.1 394.5 (a) 50.4
TS3.1 433.4 (a) 60.9
TS1.1 466.7 (a) 70.6
Specimen unloaded
TS3.2 488.7 77.4
TS4.1 500.0 (a) 81.0
TS4.2 527.8 (a) 90.2
Onset of pressure failure
Figure 2: Observation of displacements at the center of the defect region under zero and final burst pressure
a)
Deformação x Pressão - E.T.- 5.1 b) Visão geral Escala Ampliada
160
Pressão (bar)
P (bar)
P3 P3
120
P2
P2
80
P1
P1 40 0 -2000
48000
98000
148000
198000
-2000
0
2000
4000
Deformação (µ ε ) Deformação Circunferencial - and EF Longitudinal Strains at the Deformação Circunferencial Figure 3: Pressure x Circunferential defect central point. - EXP - - - - Experimental Deformação Longitudinal - EXP Deformação Longitudinal - EF ------ FE a) general view, b) enlarged view.
ε l/εε c X Pressure 0,3
ε l/εε
P1
0,2 0,1
P3
P2
0
ε
-0,1 0
40
80
Experimental Exp defeito
120
160
Pressure (bar)
FE
Figure 4: Values of the ratio longitudinal to circunferential strains at the defect central point varying with pressure.
Table 1 – Experimental and Numerical Burst Pressures (bar).
Pipeline Tubular Specimen
Average Thickness
Minimum Thickness
Thickness Variation
Failure for Failure after Failure for Failure after First mm Numerical First Numerical Element Instability Element Instability
%
Experimental Burst Pressure (bar)
E.T. - 1.1
126.4
130.1
122.2
125.7
0.30 10
121.5
E.T. - 1.2
140.7
144.7
-
-
0.19 6
143.4
E.T. - 2.1
135.0
139.4
130.2
134.7
0.60 20
130.9
E.T. - 2.2
139.1
142.7
138.0
141.3
0.37 12
138.4
E.T. - 3.1
127.3
132.6
120.0
125.1
0.40 13
123.6
E.T. - 3.2
119.2
125.1
-
-
0.2
121.4
E.T. - 4.1
126.3
130.4
121.6
127.0
0.60 20
122.2
E.T. - 4.2
130.0
134.4
113.6
115.5
1.00 33
115.2
E.T. - 5.1
143.0
147.8
-
-
0.15 5
146.8
6
