Microsoft Word - 04-p4432-e130529J. Cent. South Univ. (2014) 21: 4432−4437 DOI: 10.1007/s11771-014-2445-y
Simulation of hydrogen diffusion in welded joint of X80 pipeline steel
YAN Chun-yan()1, LIU Cui-ying()2, ZHANG Gen-yuan()1
1. College of Mechanical and Electrical Engineering, Hohai University, Changzhou 213022, China; 2. School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China
© Central South University Press and Springer-Verlag Berlin Heidelberg 2014
Abstract: Hydrogen diffusion coefficients of different regions in the welded joint of X80 pipeline steel were measured using the electro-chemical permeation technique. Using ABAQUS software, hydrogen diffusion in X80 pipeline steel welded joint was studied in consideration of the inhomogeneity of the welding zone, and temperature-dependent thermo-physical and mechanical properties of the metals. A three dimensional finite element model was developed and a coupled thermo-mechanical-diffusion analysis was performed. Hydrogen concentration distribution across the welded joint was obtained. It is found that the postweld residual hydrogen exhibits a non-uniform distribution across the welded joint. A maximum equivalent stress occurs in the immediate vicinity of the weld metal. The heat affected zone has the highest hydrogen concentration level, followed by the weld zone and the base metal. Simulation results are well consistent with theoretical analysis. Key words: numerical simulation; hydrogen diffusion; temperature field; stress field
1 Introduction
With a future increase of natural gas and hydrogen demand, pipelines are required to store and transport higher quantities of gases. High-strength steels, such as X80 steel, enable the energy and pipeline industries to realize significant savings in the total cost of long-distance oil/gas transportation in view of the reduced wall thickness and increased operating pressure in pipelines [1−2]. However, hydrogen can be introduced during welding of the pipelines. With the elevated transportation pressure, hydrogen induced cracking (HIC) is a major issue as even a microscopic crack can cause catastrophic events.
HIC is also one of the major challenges regarding the structural integrity of offshore installations and subsea pipelines. It is also called “delayed cracking” due to the incubation time required for crack development. Diffusible hydrogen in the weld metal, as well as a susceptible microstructure and residual stress in the weld joint, is one of the main factors for the cold cracking. Therefore, further study of the hydrogen diffusion behavior in the welded joint and various influencing factors is of great importance for better understanding of the HIC mechanism.
Since welding process is a rapid and quite non-uniform physicochemical metallurgy process,
microstructures are quite different in base metal (BM), heat affected zone (HAZ) and weld metal (WM), and the formation of residual stress and strain is inevitable in the welded joint. The complex and inhomogeneous conditions result in increasing complexity of predicting the hydrogen diffusion and accumulation behavior. The determination of the diffusible hydrogen content of welding products is problematic because the hydrogen atom diffuses easily and escapes from steel even at room temperature due to its small size. Therefore, it is impossible to know the exact quantity of hydrogen introduced during welding [3−8]. Faced with this difficulty to determine local hydrogen concentration by laboratory experiments due to the inhomogeneity of the welding zone, finite-element based (FE-based) numerical simulations have gained considerable popularity in investigating hydrogen behavior in the welding zone. However, few analysis procedures have been developed including taking into account the interaction of transient stress−strain fields, microstructure and hydrogen diffusion.
In this work, a combined experimental and FE-modeling approach for an effective study of hydrogen behavior in the welded joint of X80 pipeline steel was carried out. Hydrogen diffusion coefficients were measured in base metal (BM), heat affected zone (HAZ) and weld metal (WM) using the electro-chemical
Foundation item: Project(BK2011258) supported by the Natural Science Foundation of Jiangsu Province, China Received date: 2013−08−07; Accepted date: 2013−11−04 Corresponding author: YAN Chun-yan, Assistant Professor, PhD; Tel: +86−519−85191938; E-mail: yancy_hhu@163.com
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permeation technique. A comprehensive 3D modeling considering coupling of hydrogen diffusion, transient stress−strain and microstructure was established to perform transient hydrogen analysis in the welded joint of X80 pipeline steel. 2 Experimental
The material in this work is the grade API X80
pipeline steel. The chemical compositions and mechanical properties of the X80 steel are presented in Table 1 and Table 2, respectively. Using conventional shielded metal arc welding (SMAW) process, bead-on- plate welding was carried out on plates of 80 mm× 25 mm×12 mm (thickness). Pipeliner 19P AWS A5.5-96 electrodes of 4 mm in diameter were used. The experimental welding parameters are given in Table 3.
The hydrogen concentrations and diffusion coefficients of BM, HAZ and WM were measured by means of the electro-chemical permeation technique. Test specimens were prepared and conducted according to ISO17081—2004. The hydrogen permeation measurements were performed in a two-cell system based on the Devanathan-Stachurski technique [9]. The experimental results are summarized in Table 4. Table 1 Chemical composition of X80 pipeline steel (mass
fraction, %)
Al N Ceq Pcm
0.030 0.0005 0.429 0.153
Yield strength/
investigation
Welding
voltage/V
Welding
current/A
Location Diffusivity/(m2·s−1)
Heat affected zone 3.5×10−3exp(−46000/RT)
Weld metal 2.3×10−3exp(−40000/RT)
3 Numerical modeling 3.1 Model for hydrogen diffusion
Considering hydrogen diffusion in a body with volume V and surface S, mass conservation requires that the rate of total hydrogen inside V is equal to the flux through S:
d
C V S
t J n (1)
where C is the hydrogen concentration, J is the hydrogen flux and n is the outward-pointing unit normal vector.
The hydrogen flux J is driven not only by the gradient of the hydrogen concentration at the lattice sites CL but also by the gradient of the hydrostatic stress σh, so J is given by
L L H L L h
D C V D
RT J C (2)
where DL is the diffusion coefficient of hydrogen at the lattice sites, VH is the partial molar volume of hydrogen, R is the gas constant, i.e., 8.314 J/(mol·K), and T denotes the absolute temperature. Using the relations above, hydrogen diffusion equation can be derived as follows:
* L L L H L L h( ) ( )
D C V D D
t RT
(3)
where D* is the effective diffusion coefficient, θT is the occupancy of trap sites, NT is the trap site density and εp is the equivalent plastic strain.
The finite element hydrogen diffusion equation [10−13] is derived according to the standard finite element formulation as follows:
1 2 1 2[ ] ([ ] [ ])L
L
t
T *[ ] [ ] [ ]d V
T 1 L[ ] [ ] [ ]d
T L H 2 h[ ] [ ] [ ] [ ]d
V
RT (7)
In the above equations, [N] is the shape function of
a finite element, [B] is the gradient of [N], {f} is the
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hydrogen flux vector on the surface with an outward normal unit vector n, {σh} is the Nodal hydrostatic stress vector and {θT} denotes the Nodal vector for occupancy of the trap site.
A transient hydrogen diffusion analysis can be carried out by solving Eq. (4). 3.2 Numerical approach
In this work, all analyses were performed using ABAQUS code. Based on the realistic welded joint, a three-dimensional FE model of the welding piece was established for the hydrogen analysis. The three-step calculations were performed including coupled thermal calculation, mechanical calculation in consideration of temperature field and final calculation of hydrogen diffusion in consideration of temperature field, stresses and strains. The elastic-plastic stress analysis was performed using the standard Mises material model in ABAQUS Standard. The same model mesh was applied for all the three calculation steps. Figure 1 shows the modeling of the welded joint and corresponding meshing. Since welding is a localized heating and cooling process, the meshes of the weld bead and adjacent heat affected zone are refined to model the gradients of concentration and stress.
Fig. 1 3D finite element model
In the FE simulation, temperature-dependent
thermo-physical and mechanical properties of the base metals and weld materials are involved, i.e., thermal conductivity, specific heat, density, thermal expansion
coefficient, Poisson ratio and yield stress. These parameters governing the behavior of the FE model should be specified accurately so that the FE elements can simulate the welding procedure. Temperature- dependent thermal and mechanical properties of the base materials considered in this work are presented in Table 5. The hydrogen diffusion coefficients of different regions (BM, WM and HAZ) were calculated using the tested diffusion coefficients shown in Table 4. A Goldak double ellipsoid heat source was applied in the simulation to capture the heating effect of the welding arc and achieve high consistency with the practical situations. 4 Numerical results and analysis
Hydrogen diffusion analysis considering the interaction with transient stress−strain and microstructures was carried out. The transient temperature field, stress field, and hydrogen distribution were investigated. 4.1 Thermal analysis
It is of great importance and necessity to perform preliminary thermal analysis during welding and subsequent cooling for FE structure and diffusion analysis. In the thermal analysis, heat sources in accordance with welding practice, temperature dependent thermal properties, and heat loss due to convection and radiation were taken into account.
Figure 2 illustrates the global time dependent temperature field during the welding process in several steps of the calculation. It can be seen that temperature field is unsteady and temperature of the weldment gradually increases at the beginning of welding (t=5 s). The temperature field during welding becomes steady afterwards (t=20 s) and the peak temperature is about 2000 °C. Due to the effect of a preheating treatment, the minimum temperature of the weldment during welding is about 60 °C. The temperature gradient ahead of the heat source is very steep while the gradient behind the heat source is gentle. The torch also preheats a very small area in front of the torch where the heat source is going
Table 5 Thermal physical properties and mechanical properties of X80 pipeline steel
Temperature/°C Specific heat/
Density/
Thermal expansion
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Fig. 2 Temperature evolution during welding process: (a) t=5 s;
(b) t=20 s; (c) t=40 s
to pass. The heat input generated by the moving heat source along the welding line is gradually transferred to the plate in all directions by conduction, convection and radiation. The peak temperature experienced by points at a distance away from the weld is found to be much lower than the peak temperature in the weld pool. 4.2 Mechanical analysis
The subsequent mechanical analysis involves the use of the temperature histories calculated by the preceding thermal analysis for each time increment as an input (thermal loading) for the calculation of transient and residual thermal stress distribution. The equivalent Von Mises stress after welding is displayed in Fig. 3.
It is apparent from Fig. 3 that the residual stress
Fig. 3 Residual stress distribution in weldment
exhibits a non-uniform distribution across the welded joint and base metal due to the localized heating and subsequent cooling. Stress level of HAZ is of higher magnitude than that of the other regions, as would be expected. The maximum tensile stress occurs in the immediate vicinity of the weld metal. However, the high-magnitude residual stresses within the HAZ can be a major threat for the in-service structural integrity of welded structures, since regions of high stresses and strains pose as hydrogen traps and increase the risk of hydrogen induced cold cracking. 4.3 Hydrogen diffusion
The resulting stress field at each applied stress level in the stress analysis step is input as initial conditions in the diffusion analysis. The calculated evolution of hydrogen concentration with time is shown in Fig. 4. It can be seen that the weld pool is saturated with hydrogen at the beginning. Since the diffusivity of hydrogen is the highest in the weld pool and much higher than that in the base metal and the HAZ, hydrogen in the weld pool diffuses toward HAZ and the base metal with a very high speed. After some time, hydrogen accumulates in the HAZ due to low diffusivity of the HAZ. Hydrogen concentration distribution along the transverse direction is illustrated in Fig. 5 after 800 s of diffusion.
By comparing Fig. 3 and Fig. 5, it can be noted that hydrogen concentration in the HAZ is very high where the tensile stress is also very high. This indicates the high tendency of hydrogen diffusing toward high hydrostatic stresses, which is particularly important at low temperatures where stresses are higher and hydrogen diffusivity is lower. Given a sufficient hydrogen concentration and a high enough tensile stress state, together with a sensitive microstructure, HIC is very likely to occur.
The evolution of hydrogen concentration in the weld metal, HAZ, and the base metal is displayed in Fig. 6.
It can be seen from Fig. 6 that hydrogen
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Fig. 4 Evolution of hydrogen distribution in weldment: (a) t=
5 s; (b) t=40 s; (c) t=200 s; (d) t=1000 s
Fig. 5 Hydrogen distribution along transverse direction
concentration in the weld metal reaches a peak in a few seconds just after the end of the deposition, and then decreases during subsequent cooling due to the decrease of the solubility ratio during the bainitic transformation. The high temperature around the welding pool and
Fig. 6 Hydrogen evolution in different regions
existing heat dissipation cause a severe temperature gradient, which change the microstructures of HAZ. In HAZ, hydrogen concentration increases with time. Hydrogen piles up near the interface due to the low diffusion coefficient of the HAZ caused by bainitic transformation [14−16], and high stress level in HAZ also contributes to the hydrogen accumulation as mentioned above. During the transformation in HAZ, the residual stress and number of dislocations will increase, hence the number of trap sites for hydrogen increases as well. As a result, the diffusion rate will slow down and the hydrogen concentration becomes higher. Hydrogen concentration in the base metal also increases with time, but with a relatively slow rate. Compared to HAZ, the final hydrogen concentration in the base metal is much lower. This may be explained by a relatively high level of micro-alloying elements in the X80 steel [17−20], because they tend to form precipitations which slow down the diffusion due to trapping. 5 Conclusions
1) Electrochemical permeation testing has been performed to measure the hydrogen diffusion coefficients in weld metal, heat affected zone and base metal in the X80 pipeline steel welded joint.
2) A coupled diffusion elastic-plastic finite element analysis was carried out to investigate the hydrogen distribution in the welded joint of X80 pipeline steel using a double-ellipsoid heat source. The calculation of hydrogen diffusion in the weldment was carried out using the temperature histories and mechanical analysis results as the input data. Calculation results indicate that hydrogen diffusion and distribution are strongly dependent on the stress state. A maximum equivalent stress occurs in the immediate vicinity of the weld metal. Hydrogen concentration in HAZ increases with time after welding. The final maximum hydrogen concentration is reached in HAZ which coincides with
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