0　Introduction

Welding is a significant fabrication technique that is used for repair, modification or extension of pipeline. In buried pipeline, defects can occur as a result of corrosion, construction faults and other inescapable damage. Traditional repair method is to vent the gas or liquid within the pipeline and cut out the segment that is found to be defective, which will cause huge economic losses and environmental pollution. While, compared with the traditional repair technologies, the in-service welding repair technology has great social and economic benefits as well as broad application prospect, because it can operate without stopping flow through the pipeline and keep continuity of gas or oil supply to the customer [1]. There are two typical examples of in-service welding, one is the sleeve repair and the other is the hot-tap. Sleeve repair welding is the most common method to reinforce the areas where the local loss of thickness or the gas leakage is detected because of its high efficiency and low pollution. In sleeve repair welding, two semicircular sleeves are attached to the pipeline around the damaged sections and then two types of welds, circumferential fillet weld and longitudinal weld, are performed. As the circumferential fillet welds are welded directly on the pipeline, it seriously affected the mechanical properties and service life of the sleeve and pipeline.

The stress and deformation play determine roles in different failure mechanisms[2]. Unexpected failure may occur with the residual stress and external loadings acting on the pipeline, which have dangerously effects on the safety and integrity of pipeline in service. And numerical simulation has become an important tool for predicting these phenomena. Some studies on the effect of stress and deformation have been performed by simulation in the past. Mato Peric et al.[3] investigated the residual stresses and distortions in a T-joint fillet weld. Through the analysis of numerical simulation and experimental investigation, the stress and deformation have an important effect on the properties of fillet weld. Chapetti et al.[4] revealed the stress distribution in the sleeve repair of gas pipeline by simulation using the same size as the actual pipeline. Lee et al.[5] studied the effect of yield stress of base material on the residual stress and revealed the stress behavior in welding joints. Therefore, stress and deformation are the key factors that determine the quality and service life of welds.

Until now, some researches on fillet weld have been carried out and some knowledge and experience have been obtained. Phelps et al.[6] revealed the reasonable value of inner pressure and the pipeline wall thickness when the longitudinal weld and circumferential fillet weld would not burn through. Goldak et al.[7] found that the shape of the fillet weld have important influence on the burn-through of the circumferential fillet weld in sleeve repair. Wang et al.[8] studied the effect of heat transfer condition and pass sequence on the thermal cycle characteristic of fillet weld. But at present, the study on the reasonable size of fillet weld is rare.

Reasonable size of fillet weld can seriously affect the service life of the pipeline. The coarse grain, decreased plasticity and toughness may occur with large weld leg height. And the deformation and stress may be produced in HAZ zone. Furthermore, the base and weld material may seriously fuse and cause stress concentration. And defects, such as undercut and crack, are easily produced, which can affect the strength of the weld joint. Based on the above theory, there are two different standards[9] for the fillet weld height. TDW operation manual believes that 1.4 times wall thickness is the maximum value of fillet weld leg height. While the shell standard defines 2 times wall thickness is more suitable. At present, there is no clear definition of the size of sleeve fillet weld for in-service welding. Therefore, some more calculation or extensive researches on the size of sleeve fillet weld are needed to make the process of in-service welding more scientific and reasonable.

In this paper, explicit analysis include mechanical calculation, numerical simulation, heat source fitting and evaluation of the stress and deformation are presented to obtain the reasonable range of fillet weld leg height. A precise calculation based on the yield criteria is presented to ensure the strength and bearing capacity of the fillet weld. Furthermore, the mechanical properties decline in heat affected zone, residual stress and deformation are coupled into the pipes due to the repeated heat process. Thus, a numerical simulation of in-service welding for the multi-pass welding is carried out to study the deformation and stress of the sleeve and pipeline. However, numerical simulation of the welding process is not an easy task due to the complex interactions of thermal, mechanical and metallurgical phenomenon[10]. At the same time, the size and complexity of the models increase so that in some cases simplifications and assumptions have to be made to approximate the results[11]. Thus, the results of the simulation can be used as the basis for optimizing the welding parameters and give a precise explanation about the physical essence of some complex phenomena in welding process. Herein, reasonable fillet weld leg height and further knowledge of welding parameters are provided for welding Engineering.

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1　Mechanical calculation

In practical engineering, it is difficult to analysis the stress distribution considering the stress concentration and the residual stress of the fillet weld. Now some following assumptions are presented to simplify the model[12]:

①The stress concentration of the welding seam has no effect on the strength of the weld joint;

If R≥t is not satisfied, for R=kt, hf=mt, then the inequality can be described as

③There is no difference in the strength of the weld between the front fillet weld and the side fillet weld;

Then the force on the pipeline meet the following conditions

⑤It is calculated with shearing stress because the fillet weld is mostly damaged under the effect of the shearing stress;

As the above assumptions, the theoretical calculation is carried out as follows:

⑥The calculated section of the fillet weld is on the minimum thickness, which is equal to the height of the triangle inscribed.

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(1)The gap is 0 and just consider the tensile stress then, the two dimensional diagram is shown in Fig.1.

Fig.1　Two dimensional diagram of fillet weld with no gap

For the pipeline, the stress it can withstand meet the following conditions

为保证“两探索一创建”工作顺利进行，青州市人大常委会采取了试点先行的模式，谭坊镇人大专题询问工作率先迈出步伐。经过充分调研，在8月份召开的镇第十九届人民代表大会第四次会议上，谭坊镇人大通过了《专题询问工作办法（试行）》，为此次探索打牢了制度基础。为选好专题询问的议题，镇人大向市镇两级人大代表广泛征求意见，将征集到的20余条题目提交镇人大主席团会议研究。主席团先后召开两次会议，本着“询”大局、“问”大事，“询”重点、“问”热点的原则，最终确定将社会普遍关注、与人民群众息息相关的教育工作作为首次专题询问议题。

(1)

where, σ is the stress, R is the radius of the pipeline, t is the wall thickness of the pipeline, F is the load on the pipeline wall, [σ]b is the permissible stress，and hf is the fillet weld leg height.

④It is calculated with average stress although the distribution of working stress in weld joint is uniform,;

邓小平是一个坚定的马克思主义者，在中国建设和改革过程中始终坚持马克思主义的立场观点和方法，正如他所说：“我是个马克思主义者。我一直遵循马克思主义的基本原则。”［1］173马克思主义社会管理思想为邓小平社会管理改革提供了理论支持。

F≤πt(2R+t)[σ]b

(2)

While for the welding seam, the area of it can be described as

(3)

And the stress on the welding seam can be described as

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(4)

Then substituting Eq.(3) into Eq.(4) yields

(5)

(6)

where R≥t,R≥hf, then the inequality can be described as

(7)

(2) The gap g≠0 and just consider the tensile stress, then the two dimensional diagram is shown in Fig.2.

Fig.2　Two dimensional diagram of fillet weld with a gap

For the pipeline, the force it can withstand meet the following conditions

F≤πt(2R+t)[σ]b

(8)

Then substituting Eq.(8) into Eq.(4) yields

(9)

If R≥t,R≥hf,R≥g, then the inequality can be described as

本项目直接效益只计算发电效益，价格不予修正。建设期效益损失、运行期效益增量及分摊计算，同“财务分析评价”。

(10)

②The residual stress has no effect on the strength of the weld joint;

“就感觉到快，有催人跑的意思……”1978年10月，正在日本访问的邓小平，这样生动地形容乘坐新干线的感受。

(11)

Then the inequality (11) can be transformed into (12)

(12)

To get the range of hf, the changing curve of m is needed when the k takes a certain value. Now, a formula for m is defined

(13)

The function curve based on Eq.(13) is gained by entering a large number of values, as shown in Fig.3.

由5名有经验的果酒品评员组成评定小组，根据修正后的猕猴桃酒感官品评标准酒样的外观、色泽、香气和滋味4个指标进行单因素的感官评定，要求品评员必须客观进行评价，评价酒样的时间间隔为5 min，清水漱口，将评定结果汇总入猕猴桃酒感官评价表中（表1）。

As seen from the trend that the function is approaching a fixed value about 1.169. Therefore, when R≥t is not satisfied, hf≥1.169t.

In general, to ensure the strength and bearing capacity of the weld, the minimum weld leg height is appropriately 1.2 times wall thickness.

Fig.3　The function curve

2　Numerical simulation

2.1　Finite element model

The sleeve repair geometry shows in Fig.4. During the welding process, three-dimensional finite element models with various fillet weld leg height are developed as shown in Fig.5 based on the sleeve repair geometry in Fig.4. For consideration of structure symmetry, a half of sleeve geometry is used to reduce computing time. Furthermore, a dense mesh is usually used in the area along the welding line and a coarser mesh for the rest of the structure, which can be the result of compromise between computing time and accuracy [13].

During the simulation of sleeve repair, the pipeline model parameter is defined in Table 1.The chemical composition and mechanical properties of pipeline materials are shown in Table 2 and Table 3 respectively. It is assumed that the materials of the base metal and weld metal have the same thermal and mechanical properties.

Fig.4　The sleeve repair geometry

Fig.5　Three-dimensional model

Table 1　Model parameters

Table 2　Chemical composition of pipeline materials (wt%)

Table 3　Mechanical properties of pipeline materials

2.2　Heat source fitting

2.2.1　Double ellipsoidal heat source

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For the MIG welding, the heat flux distribution of the welding heat source shows the characteristics of volume distribution on the surface and thickness direction of weld structure. The double ellipsoidal heat source proposed by Goldak[14] was employed in this simulation, which use two different ellipsoids to describe the heat flux distribution before and after the arc.

The double ellipsoidal heat source is divided into two different length parts, the front and rear semi-ellipsoid, to better simulate the different temperature gradient distribution of the moving heat source in welding process (the front is steeper, the back is slow). The heat density is represented by or , which is described as follows:

通过Langmuir方程计算出不同压力下储层饱和吸附气体时的气体含量，如图1所示，饱和气体吸附体积随压力增加而增加，当压力超过15 MPa后，气体含量增加幅度逐渐减小。然后使用式(2)计算不同气体含量(包括相对应的压力)时的平均密度和平均体积模量，计算结果如图2所示，可以看出，平均密度和平均体积模量都随着气体含量增加而减小，其中平均密度减小幅度较小，而平均体积模量的减小量在初始吸附气体时下降较快，之后下降量逐渐减缓。

(15)

(16)

where af, ar, b and c are the parameters of double ellipsoid. af and ar are the length of the front and the rear semi-ellipsoid respectively. and express the width and depth of double ellipsoid. f1 and f2 represent the energy coefficient corresponding to the front and rear ellipsoid heat source, and f1+f2=2. And the heat input Q is calculated as follows:

Q=ηUI

(17)

where T0 is the ambient temperature and T1 is the surface temperature of the welded joint.

2.2.2　Parameters of heat source

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It is indispensable to define an appropriate heat source to predict the deformation and stress on the pipeline. The heat source fitting in SYSWELD software is used to calibrate the parameters of double ellipsoid. The parameters of the model are preliminarily determined on the basis of the magnitude of the b, c, v in Eq.(15) and Eq.(16) which make different depth and with of molten pool. The amendments of the parameters were made repeatedly until the morphology of molten pool calculated agreed well with that of bead welded. The welding parameters of heat source fitting are denoted in Table 4, the calculated heat source figure and its thermal cycle are shown in Fig.6 and Fig.7 respectively. After measurement, the penetration depth and width of the calculated heat source are roughly in agreement with the actual molten pool and its thermal cycling curve is smooth, as shown in Table 5. As a result, an accurate heat source model could be defined.

Table 4　The welding parameters

Table 5　The welding pool size

Fig.6　Heat source figure

Fig.7　Thermal cycling curve

2.3　Boundary and initial conditions

Based on the Fourier heat transfer theorem and energy conservation theorem, the governing equation for transient nonlinear heat transfer analyses[15] is expressed as follows:

(18)

where is the thermal conductivity, ρ is the density, is the specific heat capacity, is the rate of internal heat generation and T is the temperature.

But the heat transfer mechanism between the inner wall of the pipeline and the flowing media is assumed to be forced convection and the convection coefficient is defined as follows:

α=4.536×10-8(546.3+T0+T1)[(273.15+T0)2+(273.15+T1)2]+25

(19)

where U and I are the voltage and current of in-service welding respectively, η is the efficiency.

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During the welding process, the heat exchange between exterior surface of the pipeline and air is assumed to be radiation and natural convection heat transfer[16]. The total heat transfer coefficient is defined as follows:

(20)

where λ is thermal conductivity, is the Reynolds number, is the Prandtl number, μ is the kinetic viscosity, is the diameter of the repair pipeline, is the kinetic viscosity of gas at inner wall temperature, which can be denoted as follows:

μw=μ0(273.15+T2)/273.15

(21)

where T2 is the temperature of inner wall of pipeline, is the kinetic viscosity of the oil at 0 ℃.

3　Results and analysis

3.1　Deformation analysis

During the welding process, due to the localized heating and subsequent rapid cooling, thermal stress in the weld region and its immediate vicinity leads to elastic-plastic deformation of the pipeline. The strength of the pipeline decreases because of the temperature field. Radial deformation may occur under the effect of internal pressure and welding stress. It is considered that when the magnitude of deformation is more than 0.1 times wall thickness of the pipeline, burn through may occur, which has a deleterious effect on the safe service life of the pipeline. In the framework of this study, the magnitude and distribution of the models are presented. The size of weld leg height is 4mm (about 0.56 times wall thickness), 8 mm (about 1.1 times wall thickness), 10 mm (about 1.4 times wall thickness), 12 mm (about 1.7 times wall thickness), 14 mm (about 2 times wall thickness) respectively.

Fig.8 shows the radial deformation distribution of models with various size of weld leg height respectively. It is obviously that there is no significant difference in various models. Due to an increase of instantaneous temperature in the weld region and faster cooling of the pipeline, the temperature difference between the weld region and pipeline leads to the radial deformation[10]. As seen from the following figures, it can deduced that the sleeve shows an outward concave feature and the pipeline shows an inward concave feature. The magnitude of radial deformation is larger in the middle section of the weld. Welding is a transient phenomenon. At the beginning stage, the temperature is rising with the movement of heat source. And at the end stage of weld, the temperature decreases when the welding is finished. Due to the rigid body boundary and transient heating and cooling at the beginning and end stage respectively, the magnitude of radial deformation is smaller at the start and end position of the weld line. And the deformation in sleeve is also concentrated on the middle section. Furthermore, the radial deformation is small in the weld and far away from the weld. The welding seam shows longitudinal deformation due to the shrinkage in the course of cooling. And the area far away from the weld undergo a lower effect of the thermal load.

Fig.9 shows the selected point on the inner wall for the measurement of radial deformation and residual stress. Fig.10 shows the comparison of magnitude of the maximum radial deformation on the inner wall of the pipeline with various fillet weld leg height. It is obviously that the deformation mode of the pipeline shows concave feature. The maximum value is about 0.11 mm when the fillet weld leg height is 4 mm. With the increase of the fillet weld leg height, the magnitude of deformation increases. It increases to about 0.72 mm when the fillet weld leg height is 8 mm, which reaches the critical value of burning through. Then when the fillet weld leg height increases to 14 mm, the magnitude of deformation reaches the minimum value, approximately 0.41 mm.

Fig.8　Deformation distribution of models(a)Model with 4 mm weld leg height (b) Model with 8 mm weld leg height (c) Model with 10 mm weld leg height (d) Model with 12 mm weld leg height(e) Model with 14 mm weld leg height

Fig.9　Selected point for measurement

3.2　Stress analysis

Welding stress is affected by the interaction of various factors. The local uneven heat input during welding is the decisive factor affecting the welding stress[17]. The stress is modeled using the von Mises yield criterion. Fig.11 shows the residual stress distribution in models with different size of weld leg height described previously.

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A steeper temperature gradient occurs at the heating period and is smoother at the cooling stage, which results in the residual stress in welded structure. From the above figures, there is no significant difference for the residual stress distribution in various models. It is clearly that the magnitude of residual stress is larger in the vicinity of the weld, where undergo higher temperature than that of farther areas. And it is smaller in the last finished weld than the above, since there is not enough time to be cooled for the last weld. Further-more, the residual stress is also concentrated on the welding gap, which have a deleterious effect on the properties of welded joint. By comparison, the magnitude of residual stress in pipeline is larger than that in sleeve because of the wall thickness and less thermal cycle load in the sleeve.

Fig.10　Comparison of the maximum radial deformation

Fig.11　The stress distribution in each welding seam(a) Model with 4 mm weld leg height (b) Model with 8 mm weld leg height(c) Model with 10 mm weld leg height (d) Model with 12 mm weld leg height(e) Model with 14 mm weld leg height

Fig.12　Comparison of the maximum residual stress

Fig.12 shows the magnitude of residual stress in models with various size of weld leg height. As seen from the figure, the magnitude of residual stress increases from about 528.5 MPa to 601.3 MPa with the increase of the fillet weld leg height from 4 mm to 8 mm. Then it decreases with the increase of the fillet weld leg height. It is about 474.7 MPa when the fillet weld leg height increases to 12 mm. Then it decreases to the minimum value about 189.388 MPa when the fillet weld leg height is 14 mm.As seen from the above, there is minimum values of the radial deformation and residual stress in the fillet weld with 14 mm leg height (about 2 times wall thickness). It can be deduced that the fillet weld with 14 mm leg height shows better mechanical properties, which is an appropriate size for sleeve repair of in-service weld. Thus, the maximum value of fillet weld leg height is 2 times wall thickness, which agrees well with the shell standard.

4　Conclusions

(1) According to the request of the strength theory, 1.2 times wall thickness is the minimum value of the fillet weld leg height.

(2) The effect of fillet weld leg height on the the radial deformation and residual stress are performed in this work. The sleeve shows an outward concave feature and the pipeline shows an inward concave feature. The residual stress mainly exists in the weld gap and vicinity of the weld. The maximum value of the fillet weld leg height is 2 times wall thickness, which agrees well with the shell standard.

(3) From the mechanical calculation and numerical simulation results, 1.2-2 times wall thickness is the reasonable range of fillet weld leg height for sleeve repair， which can be provided for the welding projects and of great significance.

References

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M, Z, A, et al. Numerical analysis and experimental investigation of welding residual stresses and distortions in a T-joint fillet weld. Materials & Design, 2014, 53(1):1052-1063.

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