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Failure pressure of a pressurized girth-welded super duplex stainless steel pipe in reverse osmosis desalination plants Chin-Hyung Lee, Kyong-Ho Chang* Department of Civil and Environmental & Plant Engineering, Chung-Ang University, 84, Huksuk-ro, Dongjak-ku, Seoul 156-756, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 April 2013 Received in revised form 25 August 2013 Accepted 28 August 2013 Available online 27 September 2013

Pressurized super duplex stainless steel grade S32750 pipe is the most important element in SWRO (Sea Water Reverse Osmosis) plants. This paper presents FE (ﬁnite element) analyses to investigate the residual stress distributions produced by the girth welding of the thin-walled super duplex stainless steel pipe and the failure pressure of the girth-welded super duplex steel pipe under internal pressure. FE simulation of the girth welding process was ﬁrst performed to predict the weld-induced residual stresses employing a sequentially coupled three-dimensional (3-D) thermo-mechanical FE formulation. The residual stresses were then incorporated into the 3-D elastic-plastic FE analyses to explore the failure behavior of the girth-welded super duplex steel pipe subjected to superimposed internal pressure. GPD (Global Plastic Deformation) was used as an indicator of the failure pressure. The FE results have shown that the failure of the girth-welded thin-walled super duplex stainless steel pipe under internal pressure occurs when the effective stress approaches at a certain level which is much lower than the ultimate tensile strength and the burst pressure is weakly inﬂuenced by the weld-induced residual stresses. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Girth-welded super duplex stainless steel grade S32750 pipe Weld-induce residual stresses 3-D FE analysis Internal pressure Failure Burst pressure

1. Introduction Water shortage is one of the most serious global challenges of our time. Currently, a large proportion of the world’s population lives in water-stressed countries, and climate change and population growth will probably add to these numbers. One way to circumvent the limited supply of fresh water dictated by hydrologic factors is to remove the salt from seawater, i.e. seawater desalination. Seawater desalination offers a seemingly limitless, steady supply of high-quality water, without impairing natural fresh water ecosystems. Indeed, seawater desalination plants have already been in operation as a means to augment water supply around the world. Early desalination plants were based on thermal desalination, where the seawater is heated and the evaporated water is condensed to produce fresh water [1]. Such plants consume substantial amounts of thermal and electric energy, which result in a large emission of greenhouse gases [2]. Recently, the vast majority of seawater desalination plants have been constructed based on reverse osmosis technology, where seawater is pressurized against a semipermeable membrane that lets water pass through but retains salt. The development of high rejection, low energy membrane products and high efﬁciency energy recovery devices has * Corresponding author. Tel.: þ82 2 820 5337; fax: þ82 2 823 5339. E-mail address: iﬁ[email protected] (K.-H. Chang). 0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.08.056

made SWRO (Sea Water Reverse Osmosis) technology very competitive [3]. At present, reverse osmosis is the most energyefﬁcient technology for seawater desalination [2,4]. Desalination plants are known to be very severe environments due to the high chloride, high pressure conditions [5]. In the past, austenitic stainless steels in the ASTM (American Society for Testing and Materials) 300 series tended to be the material of choice in desalination plants. However, experience from a lot of SWRO plants already in service has revealed that there is a high risk of corrosion if the wrong stainless steel is used in the high-pressure piping needed for the environment. The 316L (EN 1.4404) and 317L (EN 1.4438) grades do not possess sufﬁcient corrosion resistance properties to withstand the environment. Consequently, highly alloyed austenitic steel grades of 6Mo such as 254 SMO (EN 1.4547) were deemed more or less mandatory for large SWRO plants [6]. However, the high cost of alloying elements, such as molybdenum and nickel, has presented a need to look for more effective options. One solution is a super duplex grade S32750, i.e. SAF 2507 (EN 1.4410). It has almost the same resistance to pitting and crevice corrosion as 254 SMO and thus has a similar shelf life. Moreover, it has twice the strength, and the cost is far lower. S32750 is used for the high-pressure piping that feeds the incoming seawater through the initial SWRO pass for the plant [7]. In practical situations, girth welding of the super duplex stainless steel pipe is frequently required owing to the long geometry

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Nomenclature bi body force c speciﬁc heat E0 initial Young’s modulus E0.2 tangent stiffness at the 0.2% proof stress h temperature-dependent heat transfer coefﬁcient I arc current Kx, Ky, Kz thermal conductivity m additional strain hardening exponent n strain hardening exponent P magnitude of internal pressure Pb burst pressure Q rate of moving heat generation per unit volume Q(t) heat ﬂux distribution QA heat input from the welding arc QM energy induced by high temperature melt droplets Ri inner radius Ro outer radius r(t) radial coordinate with the origin at the arc center on the surface of work piece

relative to the diameter and the wall-thickness. When two steel pipes are welded together, a non-uniform temperature ﬁeld induced during the welding process produces undesired residual stresses and deformations. The presence of weld-induced residual stresses originated from the elastic-plastic response of the material during the thermal cycles can be a major concern in structural integrity assessment of the pressurized girth-welded steel pipe [8]. These stresses, especially tensile stresses within and near the weld area generally have adverse effects, increasing the susceptibility to fatigue damage, stress corrosion cracking and brittle fracture [9]. When combined with service loads, welding residual stresses can reduce the fatigue life, accelerate growth rates of pre-existing or service-induced defects in pipe systems [10]. Accurate estimation of the weld-induced residual stresses, and understanding the service behavior of the girth-welded super duplex stainless steel pipe under internal pressure are therefore very crucial for the effective operation of the high-pressure piping system, production of an efﬁcient and economic design and safety of the structure. Validated methods for predicting welding residual stresses are desirable because of the complexity of welding process which includes localized heating, temperature dependence of material properties and moving heat source, etc. Accordingly, FE simulation has become a popular tool for the prediction of welding residual stresses [11e16]. Over the last three decades or so, there have been a signiﬁcant volume of research activities on the FE simulation focusing on welding residual stresses in welded shells including girth-welded steel pipes [9,17e22]. However, limited works have addressed the 3-D features of the residual stresses induced by the traveling arc and welding start/stop effects during the girth welding process [23]. For example, Karlsson and Josefson [24] calculated the residual stresses in a single-pass girth-welded pipe using the FE code ADINA, Dong and Brust [25,26] employed the special shell element and moving welding arc to simulate the residual stresses in stainless steel pipe weld, and Fricke et al. [27], Duranton et al. [28] and Deng and Murakawa [29] developed 3-D FE models based on the SYSWELD software and the ABAQUS code to predict the residual stress distributions in multi-pass girth-welded stainless steel pipes. Recently, Lee and Chang [30] predicted the axial and hoop residual stresses produced in high strength carbon steel pipe weld

r0 T U Vp ε εt,0.2 εu dεij dεeij

arc beam radius temperature arc voltage considered weld pool volume engineering strain total strain at the 0.2% proof stress plastic strain at the ultimate strength total strain increment elastic strain increment

dεpij

plastic strain increment

dεth ij

thermal strain increment

h s s0.2 sy su sij r

arc efﬁciency factor engineering stress 0.2% proof stress yield stress ultimate strength stress tensor density

incorporating solid-state phase transformation during the girth welding by employing a sequentially coupled 3-D thermal, metallurgical and mechanical FE model, and Lee et al. [31] estimated the magnitude and distribution of the residual stresses in dissimilar steel girth-welded pipe joints using 3-D thermo-mechanical FE analysis method. Further investigation on the 3-D FE analysis is then needed to comprehensively understand the characteristics of welding residual stresses in girth-welded steel pipes. Moreover, to the knowledge of the authors, very few works have been published on the analysis of welding residual stresses in girth-welded super duplex stainless steel pipes. As a matter of fact, Jin et al. [32] evaluated the axial and hoop residual stresses in circumferentially butt-welded 2205 (EN 1.4462) duplex stainless steel pipe through the numerical simulation based on the nonlinear thermo-mechanical FE analysis. Nevertheless, their work was conﬁned to axisymmetric model which was not capable of predicting the 3-D effects induced by the girth welding process. Much work has been devoted to investigating the failure response or pressure of internally pressurized steel pipes with or without ﬂaws. Ozaki et al. [33] examined the mechanical strength of steel pipes suspended vertically from a ship-type ﬂoating base for CO2 sequestration in the ocean considering the static tension due to the weight of the pipe itself and buoyancy of additional ﬂoaters as well as the dynamic tension due to wave-induced motion of the ﬂoating base. Christoper et al. [34] analyzed existing test data on the failure pressure of different steel pipes subjected to internal pressure in the context of various theories and procedures in order to estimate the maximum pressure in end-capped unﬂawed cylindrical pressure vessels. Brabin et al. [35] evaluated the failure pressure of thin and thick-walled steel cylindrical pressure vessels by employing the axisymmetric FE models based on the GPD (Global Plastic Deformation). In another study, Jayadevan et al. [36,37] numerically investigated the fracture response of an offshore pipeline segment with an external, circumferential part-through surface crack under axial tension or bending combined with internal pressure using the evolution of CTOD. Kamaya et al. [38] assessed the failure pressure of steel pipes containing wall thinning under internal pressure by using 3-D elastic-plastic FE analyses. Three kinds of steel pipes, i.e. line pipe steel, carbon steel pipe and stainless steel pipe were considered and the

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inﬂuence of the material and the length of wall thinning on the failure pressure was examined. Recently, Ma et al. [39] explored the failure pressure of high strength line pipes with or without corrosion defects subjected to internal pressure through 3-D nonlinear FE models. However, these works have been generally related to hot-rolled or cold-formed steel pipes. As for the failure behavior of girth-welded steel pipes under internal pressure, very little attention has been received to date due to the truly complex analysis procedure involved in welding and subsequent loading problems and therefore deserves special attention. This paper focused on the numerical investigation of the residual stress distributions in a thin-walled super duplex stainless steel grade S32750 pipe with girth weld employed in SWRO plants and the failure pressure of the girth-welded super duplex steel pipe under internal pressure, which is of great importance for the structural safety and the efﬁcient operation of the reverse osmosis desalination plants [3,4] but has not been implemented yet due to the complexity of the processes involved. A sequentially coupled 3-D thermo-mechanical FE analysis which simulates the girth welding process to identify the weld-induced residual stresses was ﬁrst performed. 3-D elastic-plastic FE analyses in which the failure behavior of the girth-welded super duplex steel pipe subjected to superimposed internal pressure was explored incorporating the residual stresses were next carried out. Finally, the paper concludes from the discussion of the analysis results. 2. FE simulation of the girth welding process Welding is a very complicated phenomenon in which coupled interactions between heat transfer, metallurgical transformation and mechanical ﬁeld exist. Complex numerical approaches are then needed to accurately simulate the welding process. However, as far as welding residual stress modeling is concerned, numerical procedures can be signiﬁcantly simpliﬁed, as discussed in Ref. [25]. The welding process is essentially a coupled thermo-mechanical process. The thermal ﬁeld strongly affects the mechanical ﬁeld. On the other hand, the structural ﬁeld has a weak inﬂuence on the thermal ﬁeld. Therefore, sequentially coupled analysis works very well [40]. In this study, the girth welding process was simulated using a sequentially coupled 3-D thermo-mechanical FE formulation based on the in-house FE code [41], which has been extensively veriﬁed against numerical results found in the literature and experiments [42], in order to accurately capture the residual stress distributions in the girth-welded super duplex stainless steel pipe. The procedure for welding residual stress analysis can be split into two solution steps: a transient thermal analysis followed by a transient thermalemechanical analysis. At the ﬁrst step, a transient heat transfer analysis solves for the temperature distribution and its history associated with the heat ﬂow of welding. The thermal analysis is based on the heat conduction formulation with the moving heat source. Then, the resulting temperature history solutions are fed into the thermalemechanical analysis as the thermal loading for thermal stress evolution. Welding residual stresses are the ﬁnal state of the thermal stresses after all welding passes are over and the work piece is cooled down to the ambient temperature. The FE meshes and time steps for both the heat ﬂow analysis and structural analysis are identical. 2.1. Thermal analysis The spatial and temporal temperature distribution during welding satisﬁes the following governing partial differential equation for the 3-D transient heat conduction with internal heat generation and considering r, K and c as functions of temperature only.

v vT Kx vx vx

þ

v vT Ky vy vy

567

þ

v vT Kz vz vz

þ Q ¼ rc

vT vt

(1)

According to the nature of arc welding, the heat input to the work piece can be divided into two portions. One is the heat of the welding arc, and the other is that of the melt droplets. The heat of the welding arc is modeled by a surface heat source with a Gaussian distribution, and that of the melt droplets is modeled by a volumetric heat source with uniform density. At any time t, points lying on the surface of the work piece within r0 receive the distributed heat ﬂuxes according to the following equation:

Q ðtÞ ¼

3QA rðtÞ 2 exp r0 pr02

(2)

where

QA ¼ hIU QM

(3)

The heat from the melt droplets is applied as a volumetric heat source with a DFLUX (distributed heat ﬂux) working on individual elements in the fusion zone.

DFLUX ¼

QM Vp

(4)

where Vp can be obtained by calculating the volume fraction of the elements in currently being welded zone. The heat of the welding arc is assumed to be 40% of the total heat input, and the heat of the melt droplets 60% of the total heat input [43]. The arc efﬁciency factor is assumed as 0.7 for the GTA (gas tungsten arc) welding process used in the present analysis. The heat ﬂux is applied during the time variation that corresponds to the approach and passing of the welding torch. As for the boundary conditions during the thermal analysis, convection and radiation are both taken into consideration and their combined effect is represented by h. In this work, the heat transfer coefﬁcient was assumed to be the same as that for austenitic stainless steels given by Ref. [19]

h ¼

0 < T < 500 0:0668T W=m2 C 0:231T 82:1 W=m2 C T > 500 C

(5)

In addition to the use of latent heat properties to describe heat effects relevant to the molten metal of the weld pool, an artiﬁcially increased thermal conductivity, which is three times larger than the value at room temperature, is assumed for temperatures above the melting point, to allow for its convective stirring effect, as suggested in Ref. [44]. The latent heat and melting temperature for duplex stainless steels are 500 J/Kg K and 1773 K, respectively [45].

2.2. Mechanical (structural) analysis The subsequent thermalemechanical analysis involves the use of the temperature histories computed by the previous heat transfer analysis for each time increment as an input (thermal loading) for the calculation of transient and residual thermal stress distributions. Two basic sets of equations relating to the mechanical analysis, the equilibrium equation and the constitutive equation, are as followings. Equilibrium equation:

sij;j þ rbi ¼ 0 where sij is symmetrical, i.e. sij ¼ sji.

(6)

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Constitutive equation:

600

(7)

The elastic strain increment is calculated using the isotropic Hook’s law with temperature-dependent Young’s modulus and Poisson’s ratio. The thermal strain increment is computed using the coefﬁcient of thermal expansion. For the plastic strain increment, a rate-independent elastic-plastic constitutive equation is considered with the Von Mises yield criterion, temperature-dependent mechanical properties and linear isotropic hardening rule. A large strain formulation is employed in the continuum mechanics. In the thermal and mechanical analyses, a consistent ﬁller activation/deactivation scheme was used to simulate the weld ﬁller variation with time. This scheme keeps track of the movement of the welding torch and updates the status of weld ﬁller (deposited or not). The thermal aspect of the scheme is to change the thermal conductivity of the weld ﬁller. For the weld ﬁller that is not yet deposited at a given time, a value for thermal conductivity equivalent to that of air is assigned. This process is called ﬁller deactivation. After the weld ﬁller is deposited, it is reactivated and the thermal conductivity is made to change from air value to that of the material used. The mechanical aspect of the scheme is to change the stiffness of the weld ﬁller. For the weld ﬁller which the welding torch has not yet approached, a severely reduced material stiffness is assigned [14]. At the time of application of the weld ﬁller deposition, it is reactivated and the temperature-dependent mechanical properties of the material are assigned with no record of strain history to bring it into existence without incurring strain incompatibilities. During the analysis, a full NR (NewtoneRaphson) iterative solution technique [46] was employed for obtaining a solution. During the thermal cycle, temperature and temperature-dependent material properties change very rapidly. Thus, full NR, which uses modiﬁed material properties and reformulates the stiffness matrix at every iteration step, was believed to give more accurate results [47]. 2.3. Veriﬁcation In order to conﬁrm the validity of the FE analysis method adopted in the present investigation, the experimental work by Deng and Murakawa [29] in which the residual stresses in a girthwelded austenitic stainless steel pipe constructed with two-pass GTA welding were measured by the classical sectioning method was simulated due to the scarcity of the experimental data on the residual stress distributions in the girth-welded super duplex stainless steel pipe and compared with the experimental measurements. The speciﬁc details are given in elsewhere [29]. The modeling procedure for the experiment is similar to that given in the forthcoming section except for the temperature-dependent thermal and mechanical properties [29]. The axial and hoop residual stresses calculated by the FE simulation at those locations where the circumferential angle from the welding start/stop position is 180 on the inside surface with respect to axial distance from the weld centerline are shown in Fig. 1(a) and (b). Superimposed, in both ﬁgures, are the experimental measurements performed on the weld specimen using the layering technique. It can be seen that the residual stress distributions predicted by the FE analysis show very good agreement with those determined by the experiment.

Axial stress (MPa)

dεij ¼ dεeij þ dεpij þ dεth ij

450 300 150 0 -150 -300 0

50

100

150

200

250

300

350

400

Distance from the weld centerline (mm)

(a) 600

Analysis Experiment

450

Hoop stress (MPa)

During the welding process, because solid-state phase transformation does not occur in duplex stainless steels [32,45], additive strain decomposition is used to decompose the differential form of the total strain into three components as follows:

Analysis Experiment

300 150 0 -150 -300 0

50

100

150

200

250

300

350

400

Distance from the weld centerline (mm)

(b) Fig. 1. Comparisons of the FE analysis results with the experiment: (a) axial residual stresses, and (b) hoop residual stresses.

Therefore, the FE analysis method used here can be considered appropriate for analyzing the residual stresses in the girth-welded super duplex stainless steel pipe. 2.4. 3-D FE model FE thermal simulation of the girth welding process was performed on the super duplex stainless steel pipe with an outer diameter (D) of 240 mm, thickness (t) of 6 mm and length (L) of 240 mm using the aforementioned FE technique. The illustration in Fig. 2 shows the geometry and dimensions of the girth-welded pipe. A single pass girth-welded joint geometry with a single groove was constructed. The ﬁgure also illustrates the welding arc travel direction by the arrow and the welding start/stop position (the circumferential angle from the weld start/stop position, q ¼ 0 ). The welding parameters used for the analysis were assumed to be the same as those for the austenitic stainless steel pipe with similar geometry and dimension, which are typical of industrial practice [40] and are as follows: welding method, GTA welding process; welding current, 230 A; welding voltage, 22 V; and welding speed, 1.3 mm/s. The mesh reﬁnement scheme for the 3-D FE model is shown in Fig. 3, which consists of 2576 elements and 3948 nodes. In the FE simulation of the girth welding process, symmetry conditions with respect to the weld centerline can be employed. Hence, only half of the girth-welded super duplex stainless steel pipe was modeled with 8-noded isoparametric solid elements and two layers were employed through the thickness since the residual stress variation through the inside surface or the outside surface is insigniﬁcant for

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569

Fig. 2. Dimensions of the analysis model and the welding direction.

girth-welded thin-walled steel pipes. A ﬁne mesh is used in the welding area in order to apply heat ﬂux more accurately when the moving heat source passes the area at speciﬁc time steps and to capture the anticipated high temperature and stress gradients there. Mesh sensitivity study was conducted to examine the dependence of FE mesh size on the accuracy of the analysis results. As a result, the present FE mesh model with the smallest element size of 0.9 mm (axial) 3.0 mm (thickness) 26.3 mm (circumference) was considered to give sufﬁciently accurate results using a reasonable amount of computer time and memory. In order to facilitate nodal data mapping between thermal and mechanical models, the same FE mesh reﬁnement was used except for the element type and applied boundary conditions. For the thermal model, the element type is one which has single degree of freedom, temperature, on its each node. For the structural model, the element type is the other with three translational degrees of freedom at each node. Since the pipe was assumed not to be clamped during welding, the mechanical boundary conditions were prescribed for preventing rigid body motion of the weld piece.

The detailed boundary conditions used in the FE model are shown in Fig. 3 by the arrows. As described earlier, the base metal used here is the S32750 super duplex stainless steel pipe. Detailed information on the base material is described in Ref. [6]. Temperature-dependent thermophysical (e.g., thermal conductivity, speciﬁc heat and density) and mechanical properties (e.g., Young’s modulus, thermal expansion coefﬁcient, Poisson’s ratio and yield stress) of the base metal were incorporated into the FE simulation. Fig. 4 shows the physical properties at high temperatures of the base metal [45,48] in which the units are organized so that they can be shown on one graph for clarity. Note that only the temperature-dependent thermal conductivity is dissimilar to that of austenitic stainless steels and the other properties are similar [45,48]. For the determination of temperature-dependent thermo-mechanical properties of the base material, the elevated temperature tensile coupon tests were conducted in accordance with Korean standards [49] to obtain the mechanical properties at high temperatures. An universal testing machine equipped with a specially made electrical furnace heated by thermal rays was used for the elevated temperature tensile test. Test specimens were machined as per the speciﬁcations [49] and tests were carried out in the elevated temperature range from 20 C (room temperature) to 900 C at intervals of 100 C with a strain

Fig. 3. 3-D FE model.

Fig. 4. Temperature-dependent thermo-physical constants of the material.

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rate of 1 mm/min, and the temperature was controlled to be within 2 C. In the experiment, thermal expansion was allowed by maintaining zero tension load during the heating process. Each specimen was held for approximately 20 min at the testing temperature before testing began to make sure the temperatures evenly distributed throughout the specimens. Fig. 5 depicts the dependence of the mechanical properties on temperatures based on the elevated temperature tensile test results. Both the yield and tensile stresses and the elastic modulus are reduced to 5.0 MPa and 5.0 GPa, respectively at the melting temperature to simulate low strength at high temperatures [50]. For the weld metal, autogenous weldment was assumed. This means that weld metal, heat affected zone and base metal share the same thermal and mechanical properties [51].

Outer_90º

2400

Outer_180º Outer_270º

2100 1800

Temperature (ºC)

570

1500 1200 900 600 300 0 0

100

200

300

400

(a)

2.5. Residual stress distributions

Weld_Pool 5 mm 11 mm 17 mm

2400

Fig. 5. Temperature-dependent thermo-mechanical properties of the material.

2100

Temperature (ºC)

Fig. 6(a) shows the transient thermal cycles at different circumferential locations on the outer surface of the weld region. The curve with hollow marks represents the temperature history at the location where q is 90 , the broken curve the temperature history at the location where q is 180 , and curve without any mark the temperature history at the location where q is 270 . From the ﬁgure, it can be found that the maximum temperature at the weld pool is 2100 C or so. This result agrees with the welding process in practice. Furthermore, it is clear that the temperature histories at the three locations are almost identical. Therefore, it can be concluded that the temperature ﬁeld is steady when the welding torch moves around the pipe. Temperature distributions at different locations from the weld centerline on the outer surface are also shown in Fig. 6(b), which are at the location where q is 90 . The curve without any mark represents the temperature history at the location which is 1.0 mm away from the weld centerline, the broken curve with solid marks the temperature history at the location which is 5.0 mm away, the solid curve with hollow marks the temperature history at the location which is 11.0 mm away, and the dashed curve with hollow marks the temperature history at the location which is 17.0 mm away. From the ﬁgure, it can be observed that the steep temperature gradient in and around the weld region becomes gradual as the distance from the weld centerline is increased. The axial residual stresses which act normal to the weld line at the four different locations along the circumference on the inside and outside surfaces are depicted in Fig. 7(a) and (b) with respect to axial distance from the weld centerline in order to examine the 3-D effects, i.e. circumferential variations of the residual stresses. The four positions have different circumferential angles from the

500

Time (s)

1800 1500 1200 900 600 300 0 0

50

100

150

200

250

300

350

400

Time (s)

(b) Fig. 6. Thermal cycles during the girth welding process: (a) at different circumferential locations along the girth weld, and (b) at different locations from the weld centerline.

welding start/stop position, which are 0 , 90 , 180 and 270 . From the simulated results, it can be seen that within and near the weld region, the predicted axial residual stresses are tensile on the inside surface and compressive on the outside surface. Residual stresses in girth-welded thin-walled pipes are produced mainly from the circumferential shrinkage due to the radial expansion and subsequent contraction during the welding process, which causes a local inward deformation in the vicinity of the weld region and therefore generates a bending moment through the thickness. This results in tensile axial residual stresses on the inside surface balanced by compressive stresses on the outside surface. A stress reversal from compressive to tensile on the outside surface away from the weld centerline is seen and vice versa on the inside surface. It should also be noted that even though the stress proﬁles along the four locations on both the inside and outside surfaces are similar to some extent, the magnitudes are different among them. It indicates that the axial residual stresses change with the circumferential angle. This is because the internal restraint during the welding process changes spatially due to the sequential deposition of the weld ﬁller material as welding arc moves around the circumference. The welding start/stop effects at the overlapping region (q ¼ 0 ) render the variation severe. Stresses acting parallel to the weld line are known as hoop stresses. Fig. 8 compares the hoop residual stress distributions at the four locations. Regarding the hoop residual stresses, their magnitude is inﬂuenced by the axial residual stresses. This explains why on the outside surface, which is undergoing axial compression, the hoop residual stresses are less tensile at the weld region and its neighborhood compared to those on the inside surface. Similar

C.-H. Lee, K.-H. Chang / Energy 61 (2013) 565e574 1000

600 400 200 0

Hoop_90º Hoop_180º Hoop_270º Hoop_0º

1000 800

Residual stress (MPa)

Residual stress (MPa)

1200

Axial_90º Axial_180º Axial_270º Axial_0º

800

571

600 400 200 0 -200 -400

-200 0

40

80

120

160

200

0

240

40

80

160

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(a)

(a) 400

800

Axial_90º Axial_180º Axial_270º Axial_0º

0

-200

-400

Hoop_90º Hoop_180º Hoop_270º Hoop_0º

600

Residual stress (MPa)

200

Residual stress (MPa)

120

Distance from the weld centerline (mm)

Distance from the weld centerline (mm)

400 200 0 -200 -400

-600 0

40

80

120

160

200

240

Distance from the weld centerline (mm)

0

40

80

trends of stress reversal to the axial residual stresses are observed. Furthermore, through careful observation of the results, it can be found that like the preceding axial residual stresses, spatial variations are present along the circumference due to the moving arc and welding start/stop effects. A rapid change of the residual stresses is also seen at the weld start/stop position. Referring to the above results, it can be known that the axial and hoop residual stress distributions along the circumference are by no means axisymmetric. It is often considered and may be acceptable depending on the circumstances [29] that the axisymmetric model can provide a reasonable prediction of the residual stress distributions. However, in general, a careful interpretation on the axisymmetric results is required in view of its inherent limitation. The underlying assumption is that heat is deposited at the same time around the circumference. As such, axisymmetric model cannot reproduce the rapid change of the residual stresses that can occur in the overlapping region (weld start/stop position) and tends to overestimate the hoop residual stresses in the girth weld [28]. Therefore, the results obtained by the axisymmetric model cannot be interpreted, strictly speaking, as a representation of a cross section away from the weld start/stop position. Moreover, in reality, welding is a 3-D procedure, i.e. an axisymmetric weld formation almost never occurs in practice as far as arc-welding processes are concerned. As demonstrated in this investigation, both the traveling arc and weld start/stop effects tend to violate the axisymmetric assumptions by introducing circumferential variations of the residual stresses. Therefore, it is apparent that 3-D FE simulation of the girth welding process is essential to accurately identify the residual stress distributions.

160

200

240

(b)

(b) Fig. 7. Axial residual stresses at the four locations: (a) inside surface, and (b) outside surface.

120

Distance from the weld centerline (mm)

Fig. 8. Hoop residual stresses at the four locations: (a) inside surface, and (b) outside surface.

Fig. 9(a) and (b) portray the residual effective stresses at the four locations on the inside and outside surfaces with respect to axial distance from the weld centerline. It is worth noting that the maximum residual effective stress produced at the girth weld is 450 MPa or so in both surfaces, which is below the yield stress of the super duplex stainless steel pipe. The effective stresses also demonstrate the 3-D effects within and near the welded zone. The higher effective stresses decrease as the distance from the weld centerline increases and ﬁnally converge to zero at the region far from the girth weld.

3. Failure pressure of a girth-welded super duplex stainless steel pipe under internal pressure 3.1. FE model for analysis 3-D elastic-plastic FE analyses were performed in order to investigate the failure pressure of a girth-welded super duplex stainless steel pipe subjected to internal pressure employing the inhouse FE code [41]. Similar geometry and material to the residual stress analysis were used, except for the applied loading and boundary conditions. The same FE mesh model was employed due to the symmetry in both the geometry and the residual stresses with respect to the weld centerline, using 3-D eight-noded isoparametric solid elements with three translational degrees of freedom at each node. As in the analysis of the residual stresses, the FE model herein considered both geometrical and material nonlinearity, i.e. an elastic-plastic constitutive material model with the Von Mises yield criterion and large displacements based on the total Lagrangian

572

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Effective_90º Effective_180º Effective_270º Effective_0º

Effective stress (MPa)

400 300 200

ε ¼

s s0:2 E0:2

þ εu

100

-100 0

40

80

120

160

200

240

Distance from the weld centerline (mm)

(a) 500

Effective_90º Effective_180º Effective_270º Effective_0º

Effective stress (MPa)

400 300 200 100 0

m

þ εt0:2 for s > s0:2

(10)

where E0.2, su, εu and εt0.2 are expressed in terms of s0.2, E0 and n [52], and m is given by

m ¼ 1 þ 3:5

0

s s0:2 su s0:2

s0:2 su

(11)

The resulting material model is capable of describing the full stress-strain curve for the super duplex stainless steel pipe by using the three basic parameters s0.2, E0 and n, among which the two former material properties were measured from the tensile coupon test at ambient temperature and the last one was obtainable from Ref. [53]. In this work, failure pressure of the girth-welded super duplex stainless steel pipe was explored for two different loading situations. In the ﬁrst case, the girth-welded pipe was assumed to have ‘open-ends’ (i.e. the axial force at the ends due to internal pressure load is zero: only radial component (force) of pressure load is applied). Secondly, a ‘closed-ends’ situation was modeled by applying the corresponding axial force (end-load) at the ends due to the applied pressure. The ‘open-ends’ simulation was intended to identify the inﬂuence of end-load on the failure pressure. For the ‘closed-ends’ case, the axial force (F ¼ P pR2o ) was applied at the ends along with the internal pressure. No mechanical boundary condition except those to prevent rigid body motion of the pipe weld was applied.

-100 40

80

120

160

200

240

3.2. Results and discussion

Distance from the weld centerline (mm)

(b) Fig. 9. Residual effective stresses at the four locations: (a) inside surface, and (b) outside surface.

formulation were used in the FE modeling. The residual stresses and plastic strains of magnitudes and distributions as given by the FE simulation of the girth welding process were introduced as initial conditions into the FE model, i.e. the residual stresses and plastic strains of each brick element in the thermalemechanical model were mapped into the integration points of corresponding solid element in the structural model. Then, pressure load was applied on the inside surface as a distributed load. In the analyses, the internal pressure was increased until reaching a condition of the GPD. FE technique based on the GPD has been used to evaluate failure pressure and its results were found to be in good agreement with test results [35]. GPD indicates the pressure level to cause complete plastic ﬂow through the pipe wall thickness, which was assumed to correspond to the burst pressure obtained in the experiment [35]. Burst pressure of an unﬂawed pressurized closed-ended steel pipe with no residual stress can also be estimated as [35].

1 Ro Pb ¼ pﬃﬃﬃ sy þ su ln Ri 3

(8)

As indicated earlier, autogenous weldment was employed during the girth welding. As such, representative stress-strain relations for the girth-welded super duplex stainless steel pipe can be used to capture the material response. In this study, to replicate the nonlinear behavior of the super duplex stainless steel pipe, the modiﬁed Ramberg-Osgood stress-strain expressions [52] given by Eqs. (9) and (10) were incorporated into the numerical model.

ε ¼

s E0

þ 0:002

s

s0:2

n

for s s0:2

(9)

Results are ﬁrst prepared for the ‘closed-ends’ case. Fig. 10 shows the variation of the maximum effective stress of the girthwelded super duplex stainless steel pipe under the applied internal pressure up to the GPD. For comparison, the maximum effective stress evolution with the applied internal pressure up to the failure for the super duplex stainless steel pipe with no girth weld is also included. The ultimate tensile strength of the base material is superimposed on the ﬁgure as well. It is immediately obvious that the effective stress change across the thin-walled pipe thickness in both the pipes with and without residual stresses is not signiﬁcant, which is in good agreement with the results reported in the literature [35]. Moreover, the failure pressure of the virgin pipe which has no residual stress is estimated to be 43.3 MPa, which coincides very well with the analytical burst pressure calculated by Eq. (8) of 43.8 MPa, while the design pressure is computed as 27.2 MPa [37].

900

Without_Residual_Internal Without_Residual_Outer With_Residual_Internal With_Residual_Outer Ultimate_Stress

800 700

Effective stress (MPa)

0

600 Failure

500 400 300 200 100 0 0

5

10

15

20

25

30

35

40

45

Internal pressure (MPa) Fig. 10. Variation of the maximum effective stress of the end-capped super duplex stainless steel pipes with or without residual stresses under the applied internal pressure.

C.-H. Lee, K.-H. Chang / Energy 61 (2013) 565e574 900

Without_Residual_Internal Without_Residual_Outer With_Residual_Internal With_Residual_Outer Ultimate_Stress

800 700

Effective stress (MPa)

It must be recognized that the failure occurs when the effective stress approaches at a certain level which is far below the ultimate tensile strength and the failure pressure is nearly identical for both the pipes. Possible explanations for the similar effective stresses at the GPD include the premature yielding and the residual stress redistributions of the girth-welded pipe during the application of internal pressure. The numerical failure mode of the pipe model which does not contain girth weld is given in Fig. 11 and compared to the deformed pipe model with girth weld at the GPD, where displacements are ampliﬁed with a coefﬁcient of 5 in order to allow a better visualization of the deformations. As can be seen in the

573

600 Failure

500 400 300 200 100 0 0

5

10

15

20

25

30

35

40

45

Internal pressure (MPa) Fig. 12. Variation of the maximum effective stress of the open-ended super duplex stainless steel pipes with or without residual stresses under the applied internal pressure.

ﬁgures, the pipes share similar failure modes, i.e. they exhibit plastic collapse near the ends. The plastic deformations accompanied by the local bulges hinder the attainment of further resisting pressure. Fig. 12 compares the variation of the maximum effective stress of the girth-welded pipe and the virgin pipe under the applied internal pressure up to the GPD for the ‘open-ends’ case. The results corroborate the previous ﬁndings, i.e. the effective stress change across the pipe thickness is insigniﬁcant and the burst pressure of the steel pipes is nearly the same. Nevertheless, it is signiﬁcant to note that the failure pressure is considerably lower compared with the closed-ended pipes. This is most likely due to the fact that the axial tensile stresses induced by the applied internal pressure at the closed-ends delay the bursting of the pipes near the ends. 4. Conclusions In this study, the failure pressure of a girth-welded thin-walled super duplex stainless steel grade S32750 pipe under internal pressure was investigated by FE analysis method. FE simulation of the girth welding process was ﬁrst carried out to identify the weldinduced residual stresses employing a sequentially coupled 3-D FE model. 3-D elastic-plastic FE analyses in which the failure behavior of the girth-welded pipe subjected to internal pressure was explored taking the residual stresses and plastic strains obtained from the thermo-mechanical analysis as initial conditions in order to clarify the effects of internal pressure on the failure pressure were next performed. Based on the results in this work, the following conclusions can be made. a) 3-D FE simulation is apparently necessary to accurately predict the residual stress distributions in the girth-welded super duplex stainless steel pipe which can incorporate the 3-D effects. b) In designing a pressurized girth-welded thin-walled super duplex stainless steel pipe component in SWRO plants, the inﬂuence of the weld-induced residual stresses on the failure pressure may be ignored. c) The failure pressure of the girth-welded super duplex stainless steel pipe with open ends under internal pressure is remarkably lower compared to the girth-welded closed-ended pipe. References Fig. 11. Deformed shapes of the FE models at the failure: (a) pipe model without girth weld, and (b) pipe model with girth weld.

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