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:
[email protected]
J. Cent. South Univ. (2014) 21: 4432−4437
4433
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
4435
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
J. Cent. South Univ. (2014) 21: 4432−4437
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(Edited by YANG Bing)