FEA of in-Service Welding T Joint Pipe Connection

European Journal of Scientific Research ISSN 1450-216X Vol.40 No.4 (2010), pp.557-568 © EuroJournals Publishing, Inc. 2010 http://www.eurojournals.com/ejsr.htm

Finite Element Analysis of the In-service-Welding of T Joint

Pipe Connections

Farid Vakili-Tahami Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran

E-mail: [email protected] Tel: 0098(0)411-3392463; Fax: 0098(0)411-3354153

Mohammad Zehsaz

Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran E-mail: [email protected]

Tel: 0098(0)411-3392463; Fax: 0098(0)411-3354153

Mohammad-Ali Saeimi-Sadigh Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran

E-mail: [email protected] Tel: 0098(0)411-3392463; Fax: 0098(0)411-3354153

Seyedreyhani

Tabriz Refinery Company, Tabriz, Iran E-mail: seyedreyhani @yahoo.com

Tel: 0098(0)411-4293277

Abstract

In this paper the effects of two major parameters (a) main pipe thickness; and (b) the amount of heat input (electrode diameter) have been investigated on the burn-through risks during the in-service welding of an AISI-316 pipe branch connection on a steam pipeline at full line pressure to perform hot tapping. A 3D Finite Element (FE) based thermo-mechanical analysis has been carried out to model the in-service welding. To assess the burn-through risks, current recommendations only rely on the observation of the main pipe inner wall surface temperature. However, this criterion does not take into account the effect of mechanical stresses due to the inline pressure. In this study, the thermo-mechanical stresses and temperature distribution along the main-pipe wall-thickness have been obtained and values of the effective stress have been compared against the temperature dependent yield stress of the material. The results show that this is a more accurate criterion to check the burn-through risks. It has been shown that thickness of the main pipe has a major role in the occurrence of burn-through. By increasing the pipe thickness, heat wave from the weld-pool does not penetrate in the pipe thickness and therefore the risk of burn-through reduces significantly. In addition, the results show that the amount of heat input which is related to the electrode diameter plays a major role in burn-through. Keywords: In-service Welding, Burn-Through, Finite Element Analysis, AISI-316

Finite Element Analysis of the In-service-Welding of T Joint Pipe Connections 558

1. Introduction Nowadays in-service welding of branch connections on pipelines while they are operating at full line-pressure is becoming a necessity in industrial plants. In addition, branch connections to perform hot-tapping or repairing defects in pipelines are becoming common industrial problems. Although, welding at full line pressure is a preferred technique, but it requires careful selection of the welding parameters; otherwise burn-through may cause severe human damages or financial losses. Therefore, the mechanism of burn-through or failure during in-service welding and its affecting parameters need to be examined carefully. To carry out these operations safely, weld parameters must be selected so that heat inputs remain low enough to avoid burn-through yet not so low that hot cracking occurs (API, 1995). When the heat input is too low, hot cracking of the heat-affected zone (HAZ) may occur (Oddy, et al., 1999). On the other hand, when the amount of heat input is high, although the main pipe wall may not melt through completely, but it could soften locally, leak or rupture, which is called burn-through.

According to the description of the American Petroleum Institute (API) burn-through will occur if the un-melted area beneath the weld pool can no longer contain the pressure within the pipe. Figure 1 shows the type of wall failure (burn-through) due to the in-service welding. In industry, current practice is to follow empirical guidelines to prevent burn-through which imply that “burn-through does not occur as long as the temperature level on the inside surface never exceeds a critical level of 980°C (API, 1995)”. While the empirical guidelines highlight the principal role of the welding heat input, they neglect the influence of the existing thermal stresses or the mechanical stresses due to the internal pressure. Rupture of the main pipe can occur even when the fusion zone only penetrates partially through the main-pipe wall. This is mostly because of the internal pressure and existing thermal or mechanical stresses. Series of experiments have been carried out with short welds on water filled, pressurised vessels. In these tests, slight thinning of the vessel wall has been observed with a fusion zone penetration of only 1/3 of the main pipe wall-thickness (Oddy, et al., 1999). In another case, partial rupture and incipient failure has been observed with a penetration of fusion zone in half of the wall thickness (Oddy, et al., 1999).

Figure 1: Type of pipe or canal-wall failure (burn-through) during to the "in-service" welding

Due to the enormous expenses of experimental tests, there is a general trend to develop and use numerical methods to model welding processes and also the strength or mechanical behaviour of the weldments. These models can be divided in three different fields: a) models which study the welding process itself; b) models which study the mechanical behaviour of the weldments; and c) models which study the mechanical behaviour of the surrounding parts during the welding process. First and second fields have been the subject of many research works in the past decades. However, despite its importance, the third field or burn-through analysis have been the subject of a few works. The following paragraphs provide a brief review of these research works.

559 Mohammad Zehsaz, Farid Vakili-Tahami, Mohammad-Ali Saeimi-Sadigh and Seyedreyhani

In 1930, an analytical method using Fourier's heat transfer equation has been developed to study the temperature distribution for the butt-welded infinite plates (Parmar, 2002). In this model, the governing heat transfer equations have been solved in quasi-stationary condition. Due to the simplifying assumptions in this model, the results were significantly different from those obtained using experimental observations. To overcome these shortcomings and to allow for the complicated boundary and initial conditions, Hibbitt and Marcall (1973) have used a FE based numerical method to model a single pass butt-weld. They have also studied the effect of temperature gradient on the stress distribution for butt-welds. Goldak (2005) has used Double Ellipsoidal Power Density Distribution method to model the heat input during the welding process. Brickstad and Josefson (1998) have obtained the due weld residual stresses in multi-pass butt-weld using FE based computer code ABAQUS and Element Birth and Death technique. Deng (2009) has employed Goldak’s model in computer code ABAQUS and has shown that this model can predict the weld pool shape properly. In addition, the effect of phase change on the residual stresses has been taken into account in their model. Vakili-Tahami et al. (2009) have also used the Element Birth and Death technique to estimate the due weld residual stresses in a 3D-FE based model.

Goldak et al. (2005) have investigated the risk of burn-through during the welding of pressurized gas pipe lines. For this purpose, they have obtained the temperature gradient in a transverse T joint welding using FE analysis and have shown that the weld bead size and the fillet radius have significant effect on the size of the weld pool and fusion zone (FZ) penetration depth. They have shown that the weld pool size and FZ penetration depth have major role in burn-through. Thermo-elasto-plastic analysis has been used by Wahab et al. (2005) and Sabapathy et al. (2001) to predict the burn-through of pipeline welding. They have used empirical relationships to estimate the weld pool size. They have also investigated the effect of different welding parameters. Vakili-Tahami et al. (2009) have used a 2D-FE model to study the burn-through risk in welding process. They have shown that the risk is high during the first pass of the welding process and this risk reduces at subsequent passes. They have shown that this is because of the weld bead size and its location.

The main purpose in investigating the risk of burn-through is to assess the strength of the main pipe wall to sustain the existing thermo-mechanical stresses during the in-service welding. This task is completely different from those works that investigate the strength of the weldment itself to carry the applied loads while the structure operates under applied loads. All the experimental observations and recent studies have confirmed that over-heating plays a major role in burn-through occurrence (Oddy, et al., 1999). To reduce the over-heating, electrodes with smaller diameters can be used which in turn may lead to hot cracking due to the rapid cooling of the welding pool and HAZ. However, the mutual effect of the thermo-mechanical stresses has not been addressed in these research works and this aspect is the main achievement of the present study.

In this paper, the results of a numerical study have been presented for a 3D thermal-mechanical finite element analysis of an in-service welding process on a pressurized pipeline T joint. In this work, the in-service welding process and burn-through risks have been studied for welding of a T shape branch connection on a super-heat steam pipeline while it is operating at full line pressure. Also, the effect of electrode diameter size and the main pipe thickness have been investigated. For this purpose, a 3D FE model of the T branch has been developed and the movement of the electrode has been simulated using Element Birth and Death technique. In this model, the risk of burn-through has been checked by comparing the temperature level at the inner wall of the main-pipe with the critical temperature level; and also, by comparing the thermo-mechanical effective or Von-Mises stress level along the pipe wall against the yield stress at the associated temperature. 2. Materials and Models In this model, a T joint branch with the inner diameter of 152.4 mm is welded on a main pipe with the diameter of 219.1 mm to perform hot tapping. Table 1 shows the variation of the physical and mechanical properties of 316 Stainless Steel with temperatures (Vakili-Tahami, 2002). During the


welding process, the main pipe conveys superheated steam flow of 76 ton/hr at 480oC and 10.2 MPa, while, the branch pipe is open-ended and is not under pressure or external loads.

In order to investigate the effect of the main pipe thickness in burn-through, two different wall thicknesses of 8.2 mm and 2.8 mm have been considered. In addition, to study the effect of heat input the welding process has been modeled using 4 and 8 weld-passes. Table 1-a: Thermal, physical and mechanical properties of AISI 316 stainless steel (Vakili-Tahami, 2002)

Temperature (0C)

Specific Heat

(J/Kg.oC)

Conductivity (W/m.oC)

Density (Kg/m3)

Yield Stress (Pa)

Thermal Exp. (1/ oC)

Young Modulus

(Pa)

Poissons ratio

20 470 13.31 7966 480e6 15.24e-6 195.1e9 0.267 100 487 14.68 7966 445e6 15.80e-6 191.2e9 0.273 300 529 17.93 7966 420e6 16.97e-6 179.6e9 0.310 500 571 20.96 7966 351.3e6 17.85e-6 164.5e9 0.313 700 613 23.76 7966 254.2e6 18.54e-6 144.1e9 0.282 900 655 26.33 7966 80.7e6 19.11e-6 116.8e9 0.240 1100 698 28.67 7966 80.7e6 19.66e-6 100.0e9 0.223 1300 719 29.76 7966 80.7e6 19.95e-6 100.0e9 0.223 1460 765 64 7966 80.7e6 20.70e-6 100.0e9 0.223 1780 765 320 7966 80.7e6 20.70e-6 100.0e9 0.223

Table 1-b: Temperature dependent Hardness Modulus of AISI 316 stainless steel (Vakili-Tahami, 2002)

Temperature(K) 298 302 399 482 566 1073 Hardness Modulus

(Pa) 5.60e9 5.64e9 6.e9 7.65e9 4.65e9 2.35e9

2.1. Finite Element Model

A 3D FE model of the T branch has been developed and the movement of the electrode has been simulated using Element Birth and Death technique. The heat dissipation through the in-pipe steam flow has been taken into account by imposing convection boundary conditions along the inner wall of the main pipe. In addition, the mechanical loads due to the internal steam pressure have been taken into account. Since the temperature gradient near the weld pool is severe, material constitutive model takes into account the temperature dependency of the physical parameters and they have been considered temperature dependent. In this model, the risk of burn-through has been checked by comparing the temperature level at the inner wall of the main-pipe with the critical temperature level; and also, by comparing the thermo-mechanical effective or Von-Mises stress level along the pipe wall against the yield stress at the associated temperature.

Figure 2 shows the 3D model of the T joint. The FE model has been developed using FE based computer code ANSYS. Due to the thermo-mechanical properties of the solution, tetrahedral coupled-field element type SOLID98 with 10 nodes has been used to create the FE mesh. This element has four degrees of freedom for each node: three for displacement and one for temperature and therefore is capable of solving coupled thermo-mechanical analysis. Total number of elements in the FE model is 15957 with 63828 degrees of freedom including the temperature. To investigate the mesh sensitivity of the model and also the mesh independency of the results, two other meshes have also been used in which the number of elements have been increased and decreased by 10%. The maximum difference of 7.4% has been observed in temperature level for nodes using these FE meshes. To simulate the movement of electrode, Element Birth and Death technique has been used. For this purpose, the whole saddle shape of the weld has been divided into 60 blocks in each pass. In this way, each block has 8 mm length which is in accordance with Rosenthal’s model (Parmar, 2002). At first, the blocks are deactivated and excluded from the global FE mesh. Once the welding starts, blocks have been activated


successively (birth of elements) each one after 2 or 2.67 seconds to accommodate the predefined welding speeds of 20 cm/min or 15 cm/min respectively.

Figure 2: The 3D model of the T joint and the saddle shape weldment

2.2. Thermo-Mechanical Boundary Conditions

During the welding process, the input heat melts both the filler material and the parent material surrounding the weld pool. The amount of the heat input can be obtained using (Parmar, 2002):

VIQ η= (1) in which η usually estimated in the range of 0.6-0.7 (Parmar, 2002). According to the welding process documents; for this welding V=30 volts and I= 70 A.

The governing partial differential equation which describes the heat transfer near the weld pool is (Lewis et al., 2004):

),,(),,,(.),,,( zyxQtzyxqtzyxtTc +−∇=∂∂ρ (2)

The generated heat in a welding process will dissipate from the welding zone by thermal radiation, conduction and convection. Radiation losses are dominant at high temperatures near and in the weld zone, while the convection has a major role at low temperatures in the area away from the weld pool. To take into account these two effects, a total temperature-dependent heat transfer coefficient has been used (Brickstad et al., 1998):

⎪⎩

⎪⎨⎧

≥−

≤≤=

CTWhenCmWT

CTWhenCmWTh

o

o

02

02

500)/)(1.82231.0(

5000)/(0668.0 (3)

The above thermal boundary condition has been employed on all free boundaries of the 3D model. The main pipe conveys superheated steam flow of 76 ton/hr (21.1 kg/s) at 480oC and 10.2x106 Pa. Due to the passing steam flow with the velocity of 25.1 m/s, convection heat transfer on the inner side of the pipe-wall has been calculated to be 2000 W/m2K using (Wanger et al 2008):

4.08.0 )()(023.0g

gpg

g

gg

g

g

kCDv

kDh μ

μρ

= (4)

The thermal-physical properties of super heat steam at 480oC and 10.2 x106 Pa to calculate gh are listed in Table 2 (Wanger et al., 2008).

Table 2: Thermo-physical properties of super heat steam at 480oC and 10.2 x106 Pa (Wanger et al., 2008)

Physical property Values Thermal Conductivity Kg=0.075 (Watt/mK) Density ρg=30 kg/m3 Specific Heat Cpg=2600 J/kgK Viscosity gμ =29x10-6 Pa.s


2.3. Thermo-Mechanical Model

The governing equations of thermo-elasticity in terms of displacement components and in the absence of body forces are (Eslami et al., 2009):

..

,,, )23()( iikikkki uTuu ραμλμλμ =+−++ (5) Using the strain-displacement relation, )(21 ,, ijjiij uu +=ε and substituting into equation (5) yields

..

,,, )23()( ijijijkkkkij T εραμλεμλμε =+−++ (6) Substituting for strain from stress-strain relations

ijijkkijij TT δαδσμλ

λσμ

ε )()23

(21

0−++

−= (7)

where (T-T0) is the temperature change. According to the principle of virtual work and the divergence theorem, the equilibrium equations and the constitutive equations can be rewritten in the matrix form as

}]{[}{}{][ e

T

V

UKRdVB ==∫ σ (8)

To model the welding process, it is necessary to solve the equations based on a non-linear isotropic hardening elasto-plastic theory. For this purpose, a bi-linear elasto-plastic formulation of the material behavior has been used. Also, an incremental calculation has been employed to accommodate the nonlinearity of the nodal displacement functions in the elasto-plastic analysis. Using the thermo-elasto-plastic material model, based on the Von-Mises yield criterion and the isotropic strain hardening rule, stress–strain relations can be written as

}]{}[{}]{}[{}{ eth

ep

ee TMCUBD Δ−Δ=Δσ (9) Substituting EQUATION (9) into the incremental form of EQUATION (8) yields

}{}}{{}}{{ 21

11 RTKUK e

me

m Δ=Δ−Δ ++ (10)

where ∫=+

V

pe

Tm }[B]dV{D[B]}{K11 , and ∫=+

V

thTm dV]M}[C{]B[}K{ 21 . The displacement increment

{ eUΔ } and stress increment { eσΔ } can be obtained from equations (9) and (10). With these results, the displacement { eU } and stress { eσ } can be obtained. 3. Results To investigate the effects of heat input and main pipe thickness, the numerical analyses have been carried out using different number of conditions shown in Table 3. For these case studies, temperature profiles and stress distributions along the main pipe wall have been obtained. Results are presented for the critical position of the weldment along the path A-B of the main pipe wall (see in Figure 3). Table 3: Different conditions of model/solution

Case study Weld Passes Electrode Diameter (mm) Main Pipe Thickness (mm) 1 8 2.4 2.8 2 4 4 8.2 3 8 2.4 8.2

Figure 4 illustrates the temperature gradient when electrode reaches to position θ=90 at time

t=30Sec in T joint connection. Due to steam flow in main pipe temperature is 634k in main pipe and temperature in fusion zone is 1673k.

Figure 5 shows the temperature profile along path A-B for the case study No 1 at 0=θ degrees. This position refers to the starting stage of the welding process. It can be seen that the temperature at the inner surface of the main pipe wall is 987ºC (1260K) which is higher than the


critical level of 980ºC (1250K). According to the API recommendations (API, 1995), there is a high risk of burn-through for this case.

Figure 3: Path A-B along which the results are presented and compared

A

B

Welding start pointθ=0

Path A-B from weld center

Figure 4: Temperature gradient at t=30Sec

Figure 5: Temperature profile distribution at 0=θ degrees for case study No 1

12001250130013501400145015001550160016501700

0 0.5 1 1.5 2 2.5 3 3.5Distane (mm)

Tem

pera

ture

(K)

Temprature

Figure 6 depicts both the temperature and effective stress (Von Mises stress) distributions at θ=0 degrees along path A-B for case studies 2 and 3. It can be seen that for both case studies, the main pipe inner wall temperature is about 537oC (800K) which is lower than the critical level of 980oC (1250K). This shows, by increasing the pipe thickness, heat wave from the weld-pool does not


penetrate in the pipe thickness and therefore the risk of burn-through reduces significantly. However, the weld beads applied in case 2 (with 4 weld passes) are larger than those which have been used in case study 3 (with 8 weld passes). Therefore, in the former (case 2 with 4 weld passes), the amount of heat input is more than the amount of heat which has been imposed in case study 3, and consequently, as it can be seen in Figure 6, the temperature level along the main pipe wall is higher for case 2 comparing with those obtained for case 3. This leads to higher thermal stresses that also can be seen in Figure 6. The effective stress level along the inner side of the main-pipe wall, which is the combination of mechanical and thermal stresses, plays a major role and reflects the ability of the pipe to sustain the internal pressure. Since the pipe is AISI 316 stainless steel, the Von-Mises failure criterion has been used here to investigate the pipe wall failure. At the first 3 millimeters beneath the weld pool, the temperature is above 800oC (1073K) and practically the material is unable to sustain any stresses at this temperature. However, the bilinear isotropic hardening model and cut-off method, which have been used in this study, leads to high values of Elastic and Hardness Modulus at this temperature level (see Table 2) and therefore numerical solution overestimates the stresses at this region. Due to the lack of experimental data which give the mechanical behavior of the material beyond 800oC, there was no other choice to carry out the analysis using the available data (Vakili-Tahami, 2002). To highlight these shortcomings, the stress distribution at “beyond 800oC-zone” is shown using dotted lines in the presented figures. It should be added that the “above 800oC-zone” plays an insignificant role in terms of sustaining mechanical or thermal stresses.

The effective stress distribution along the main pipe wall presented in Figure 6, shows that for case 2, at almost 87% of the main pipe wall, the effective stress is higher than the yield stress and therefore there is a high risk of burn-through. To reduce the risk of burn-through, in case study 3, the number of weld passes have been increased to 8, and as it can be seen in Figure 6, only in the 37% of the pipe wall, the effective stress is above the yield stress level, and therefore there is no risk of burn-through. The lower stress levels in case 3 is due to the lower thermal stresses which in turn is due to the low heat input using smaller weld beads.

Figure 6: Temperature profile and effective stress distribution at θ=0 degrees for case study No 2 and 3

0100200300400500600700800900

1000

0 1 2 3 4 5 6 7 8 9Distance from weld center (mm)

Stre

ss (M

Pa)

020040060080010001200140016001800

Tem

pera

ture

(k)

stress_4passStress_8passyeild stressTemperature_4passTemperature_8pass

Figure 7 illustrates both the temperature profile and effective stress distributions at θ=90 degrees or 30 seconds after the start of the welding. This figure shows that the inner wall temperature does not change significantly for both case studies and it remains below the critical level. The effective stress level for case study 2 is almost 35% larger than that obtained for case study 3. This figure also shows that burn-through is inevitable at case study 2 because in this case study, the effective stress


along the main pipe thickness is higher than yield stress. However, for case study 3, at 51% of the main pipe thickness the effective stress is lower than the yield stress and therefore, the risk of burn-through is very slim and the pipe can withstand the internal pressure during the welding process.

Figure 7: Temperature profile and effective stress distribution at θ=90 degrees for case study No 2 and 3

0100200300400500600700800900

1000


Stre

ss (M

Pa)

020040060080010001200140016001800

Tem

pera

ture

(k)

stress_4passStress_8passyeild stressTemperature_4passTemperature_8pass

Figures 8, 9 and 10 also show the temperature profile and effective stress distributions for case study 3 at θ=180, 270 and 360 degrees respectively. It can be seen that at θ=180o, in the range of 5.2<t<8.2mm (36.6% of the pipe wall) and at θ=270o in the range of 3.4<t<8.2mm (58.5% of the pipe wall) the effective stress is below the yield stress. Figure 10 presents the data for the end of the welding process i.e. θ=360o. It can be seen that at this position, in the distance of 5.4<t<8.2mm (34.1%) along the main pipe-wall, the effective stress is below the yield stress. The results shown in these figures imply that the end position of the weld in each pass (position θ=360o) is the most critical situation. This is due to the accumulation of the existing thermal stresses during the welding process.

Figure 8: Temperature profile and effective stress distribution at θ=180 degrees for case study No 3

0100200300400500600700800900

1000


Stre

ss (M

Pa)

020040060080010001200140016001800

Tem

pera

ture

(k)

Stress_8passyeild stressTemperature


Figure 9: Temperature profile and effective stress distribution at θ=270 degrees for case study No 3

0100200300400500600700800


Stre

ss (M

Pa)

020040060080010001200140016001800

Tem

pera

ture

(k)


The percentage of the main pipe thickness at which the effective stress is below the yield stress for two case studies has been given in Table 4. Comparing these results and also those shown in Figs. 6-10; leads to the conclusion that by increasing the number of weld passes (decreasing the size of the weld bead and amount of the heat input) the risk of burn-through reduces significantly and also the positions of θ=360o and θ=180o are the critical ones in terms of burn-through possibility. Despite the fact that the inner wall temperature for case study 2 is below the critical level of 980oC, the results show a high risk of burn-through at this case.

Figure 10: Temperature profile and effective stress distribution at θ=360 degrees for case study No 3.

0

200

400

600

800

1000


Stre

ss (M

Pa)

020040060080010001200140016001800

Tem

pera

ture

(k)



Table 4: Percentage of the main pipe thickness in which the effective stress is below the yield stress

Position =θ 0 90 180 270 360 Case Study 2 (4 weld pass) 13% 0% 0% 0% 0% Case Study 3 (8 weld pass) 63% 51% 36.6% 58.5% 34%

5. Conclusion In this study, the thermo-mechanical stresses as well as the temperature distribution along the pipe wall thickness have been obtained. The results highlight the fact that to evaluate the risk of burn-through, not only the inner wall temperature of the main pipe should be checked against the critical level of 980oC, but also the level of the effective stresses must be compared against the temperature dependent yield stress of the material. The results and industrial observations show that this is a more accurate criterion to check the risk of burn-through.

According to the results, the following points can be concluded: 1) The thickness of the main pipe has a major role in the occurrence of burn-through. By

increasing the pipe thickness, the Fusion Zone and the heat wave from the weld-pool does not penetrate in the pipe thickness and therefore the risk of burn-through reduces significantly.

2) The results shown in these figures imply that the end position of the weld in each pass is the most critical situation.3) The results also show the importance of the amount of heat input during the welding process. In excessive heat input, the risk of burn-through increases drastically.

3) By increasing the number of weld passes, the size of the weld beads and consequently the amount of heat input reduces which all lead to lower risk of burn-through.

4) To prevent burn-through, in addition to the main pipe inner surface wall temperature, the effective stress along the main pipe wall should be checked against the yield stress at the same temperature.

Acknowledgement The authors would like to express their gratitude for the technical and financial support provided by the Tabriz Refinery Company and for the help of R&D centre of this plant for providing valuable information, infield observations and technical data. Symbols

[B] Operator matrix {Ue} Nodal displacement c Specific heat (J/kgK) V Voltage (V)

{Cth} Thermal stiffness matrix vg Velocity of steam (m/s) D Diameter(m) α Thermal expansion coefficient (K-1)

{Dp} Plastic stiffness matrix {ΔT} Temperature increment matrix h Heat transfer coefficient (W/m2K) {Δσe} Nodal stress increment matrix I Current (A) {Δεe} Nodal strain increment

[K] Stiffness matrix η Welding efficiency kg Thermal conductivity (W/mK) λ Lame constant (Pa)

[M] Temperature shape function μ Lame constant (Pa) Q Heat generation (J) μg Viscosity (Pa.s) t Time (s) ρ Density (kg/m3) T Temperature (K) ε Strain u Displacement (m) δ Kronecker delta


References [1] American Petroleum Institute (API), 1995. “Procedures for Welding or Hot-Tapping on

Equipment in Service: Recommended Practice 2201”, 4th Edition, Northwest, Washington. [2] ASM (American Society of Metals) Handbook, 2005. “Properties and Selections: Irons, steels

and high performance Alloys”, ASM International, Vol. 1, USA. [3] Brickstad B., B.l., Josefson, 1998. “A parametric study of residual stresses in multi-pass butt-

welded stainless steel pipes”, Journal of Pressure Vessel and Piping 75, pp. 11-25. [4] Deng D., 2009. “FEM prediction of welding residual stress and distortion in carbon steel

considering phase transformation effects”, Journal of Material Design 30, pp. 359-366. [5] Eslami M.R., R.B., Hetnarski, 2009. “Thermal stresses advance theory and applications”

Springer, Netherlands. [6] Goldak J.A., M., Akhlagi, 2005. “Computational welding mechanics”, Springer, New York; 22-

35. [7] Hibbitt H.D., P.V., Marcal, 1973. “A numerical thermo mechanical model of welding and

subsequent loading of fabricated structure”, Journal of Computers and Structures 3, pp. 1145-1174.

[8] Incropera F.P., D., Witt, B., Bergman, J., Lavine, 2006. “Fundamentals of heat and mass transfer”, Wiley & Sons, New Jersey.

[9] Lewis RW, P., Nithiarasu, K.N., Seetharamu, 2004. “Fundamentals of finite element method for heat and fluid flow” John Wiley & Sons, New Jersey.

[10] Oddy A.S., J.M.J., Mcdilll, 1999. “Burn-through prediction in pipe line welding”, International Journal of Fracture 97, pp. 249-261.

[11] Parmar R.S., 2002. “Welding engineering and technology”, Khanna Publishers, Delhi. [12] Sabapathy P.N., M.A., Wahab, M.J., Painter, 2001. “Numerical models of in-service welding of

gas pipelines”, Journal of Material Process Technology 118, pp. 14-21. [13] Vakili-Tahami F, H., Masoumi, 2009. “A two dimensional thermo-mechanical analysis of burn-

through at in-service welding of pressurised canals”, Journal of Applied Science 9, pp. 615-626. [14] Vakili-Tahami F., A.H., Daei-Sorkhabi, M.A., Saeimi, A., Homayounfar, 2009. “3D finite

element analysis of the residual stresses in butt-welded plates with modeling of electrode- movement”, JZUS 10, pp. 37-43.

[15] Vakili-Tahami, F., 2002. “CDM analysis of damage and creep crack growth in weldments”, phD thesis, UMIST University.

[16] Wahab M.A., P.N., Sabapathy, M.J., Painter, 2005. “The onset of pipe-wall failure during in-service welding of gas pipe line”, Journal of Material Process and Technology 168, pp. 414-422.

[17] Wanger W., H.J., Kvetzschmar, 2008. “International steam table”, Berlin Heidelberg, Springer-Verlag.

Documents

FEA of in-Service Welding T Joint Pipe Connection