SIMULATION OF MULTIPASS WELDING OF A STEEL PIPE INCLUDING MODELLING OF HYDROGEN DIFFUSION AND FRACTURE MECHANICS ASSESSMENT

Transcription

1 To appear in: Modelling of weld phenomena 10, 2013 SIMULATION OF MULTIPASS WELDING OF A STEEL PIPE INCLUDING MODELLING OF HYDROGEN DIFFUSION AND FRACTURE MECHANICS ASSESSMENT H. G. FJÆR*, S. K. AAS**, V. OLDEN***, D. LINDHOLM* and O. M. AKSELSEN*** * Institute for Energy Technology 2027 Kjeller, Norway **Instituto SINTEF do Brasil, CEP Rio de Janeiro, Brasil *** SINTEF Materials and Chemistry, 7456 Trondheim, Norway ABSTRACT Hydrogen induced cold cracking is a critical issue for hyperbaric welding of pipelines on the sea bed. The susceptibility to cracking is influenced both by the microstructure, the hydrogen content and the stress state. In order to investigate these complex phenomena a hydrogen diffusion model has been included in the FEcode WELDSIMS. Here, the hydrogen diffusion is dependent on both the temperature, the hydrostatic stress and the phase composition, and the effect of reversible traps is included. The model has been applied on a case involving 14-pass butt welding of a ferritic steel pipe. The hydrogen concentration and stress state in the vicinity of a weld root defect is investigated. The effect of possible interpass and post weld heat treatment on the hydrogen concentration is predicted. 2D simulations with a good spatial resolution and numerical accuracy are accompanied with 3D simulations on a sector of the pipe. A cohesive element model is used to predict whether hydrogen induced cracking will occur in the HAZ after welding. Residual stresses and hydrogen concentrations from the welding simulation are imported into an ABAQUS model, where the hydrostatic stress field is used as a driving force in an isothermal analysis of hydrogen diffusion. This procedure allows fracture mechanics assessment of both cold cracking and fracture due to mechanical loads, e.g. during reeling operations. INTRODUCTION Integrity of pipelines is a critical issue for the oil and gas industry. Especially for underwater installations a failure will have huge environmental and economical consequences. The most used materials in pipelines are X65 and X70 microalloyed ferritic steels. The heat affected zone (HAZ) adjacent to welds in such pipelines tends to be brittle and prone to hydrogen induced cold cracking. When the offshore activities move to deeper water, several aspects become more difficult. Welding operations on the sea bed, repair welding, and hot tapping,

2 i.e. establishing of a connection between a branch pipe and a main pipe without stopping the flow in the main pipe, must be carried out with remote control, as diver operations are restricted to depths less than 180m (Norwegian waters) [1]. The cold cracking phenomenon is believed to be a result of a combination of the stress state, the brittleness of the weld metal and the HAZ and the concentration of hydrogen. At hyperbaric conditions the weld beads are smaller than in welding at 1 atm, leading to faster cooling and high hardness values in the weld metal and HAZ. Presence of moisture in the welding atmosphere or contamination of the base metal surface may lead to hydrogen embrittlement problems. Preheating to remove moisture and post weld heat treatment (PWHT) to enhance the expulsion of hydrogen to the environment are procedures that are used as remedies for hydrogen induced cold cracking. In order to predict such conditions in a ferritic steel, the evolution of temperature, metallurgical state, stress and hydrogen concentration must be simulated through the process of multipass welding. Still, the accuracy of such efforts are limited by lack of accurate material data, modelling approximations and limited computational resources, but the potential of available models now is believed to be able to provide useful information. Others have addressed hydrogen diffusion in welds with a temperature dependent heat diffusion coefficient [2,3]. Models that include the effect of stress (lattice pressure), trapping of hydrogen [4], and straining on the hydrogen diffusion have also been presented [5,6], but this modelling considered only isothermal conditions. We have not found any examples in the literature where hydrogen diffusion under the influence of trapping and stress development have been simulated during a non-isothermal process like welding. This paper presents a model where the hydrogen diffusion problem is solved together with a computation of temperatures, stresses and phase transformations in steel by the model WELDSIMS [7,8]. This model has been applied in a case study involving the simulation of a 14-pass girth weld on a pipe where a back bead has a defect induced by a cold lap. Residual stresses from welding and the hydrogen concentration field are exported to a fracture mechanical analysis using cohesive elements for the crack path. The model is described in the following section. Next follows a description of the case study with a discussion of the results. MATHEMATICAL MODEL As the computations of temperature, phase fractions and stresses with the WELDSIMS model have been explained elsewhere [7,8], we will here mainly consider the modelling of the hydrogen diffusion. However, some other details and extensions of the modelling capabilities are explained in this section. THERMAL MODELLING For a ferritic steel, thermophysical data are specified for each phase, e.g. austenite, ferrite, pearlite, bainite and martensite, and a simple law of mixture is used to evaluate the

3 properties in an element. The enthalpy change associated with the phase transformation between austenite and the ferritic phases is taken into account. The welding heat source is basically represented by a Goldak double ellipsoid distribution function. Elements in the weld bead domains become activated when approached by a welding heat source. A density factor, initially zero, is increased simultaneously as heat is added. It is considered to be most physically correct to restrict the volumetric heat input to elements containing liquid metal. In order to replicate experimental fusion lines it is often necessary to superimpose several ellipsoid functions, and to add surface heat sources. There is also an option to specify that a given fraction of the weld heat is to be released in elements containing the melting isotherm, with a radial distribution function with respect to an axis parallel with the weld arc. The model keeps account on the received heat and adjusts a compensation factor each time step in order to balance the prescribed heat input. Melted parts of the base material can be set to become a part of the weld bead domain with weld metal properties. PHASE TRANSFORMATION AND GRAIN GROWTH MODELLING Diffusion-controlled phase transformations are modelled using the JMAK kinetics [9], while the Koistinen-Marburger law is applied to describe martensite formation. Different parameter sets may be used for weld metal and base metal. In the weld metal, however, nucleation of the ferritic phase is not restricted to the grain boundary, and a large number of constituents may form having different mechanical properties (grain boundary ferrite, acicular ferrite, Widmanstätten ferrite, upper bainite, etc.). In addition, the reheated and the primary weld metal will normally have a different mixture of structures. Therefore a simplified modelling approach is used in the weld region where one representative ferritic phase (mixture of different ferritic phases) is considered in addition to martensite. Moreover, the flow stress is scaled with a function dependent of the local cooling time between 800 and 500 C (t 8/5 ) normally used to characterize the weld cooling rate. Such functions can be different for reheated and primary weld metal, and may be based on hardness measurements. The hardness profile across a weld often indicates softening or tempering of the partly transformed HAZ and in the base metal that almost has reached the A c1 temperature. In multipass welding this also applies for the HAZ when it is reheated by the subsequent weld passes. Evolution equations for tempering [10] fit well into the framework of the JMAK kinetics, and transformation from hard ferritic phases into a softer phase is computed in the same way as the transformation between austenite and ferritic phases. As pointed out in [11], the transformation rate from austenite is dependent on the austenite grain size. In the applied model, the time constant is a function of both temperature and austenite grain size as in [12], D DG T, D T n (1)

4 where D G is the reference austenite grain size obtained in the austenization conditions used to establish the reference CCT diagram from which the transformation parameters are derived. The austenite grain size D is often computed by the equation: d a Q D Cexp (2) dt RT where Q is an activation energy, R is the gas constant and a is a time exponent. However, in microalloyed steels different types of precipitates can retard or limit the grain size by the effect of pinning [13, 14]. The evolution of the austenite grain size is here expressed as a1 dd a1 Q 1 1 f i M 0 exp (3) dt RT D k i ri where M 0 is the mobility, is the grain boundary energy, k is the Zener coefficient and f i and r i are respectively the volume fraction and average radius of particle class i. Actual modelling of the local distribution of precipitates could be feasible, but a simpler approach is used where the pinning term fi ri is assumed to be a function only of the local peak temperature, and therefore can be given as a tabular input. STRESS MODELLING Data for constitutive equations are specified for each phase, and as for thermophysical data a simple law of mixture is used to evaluate the properties in a volume element. Volume change associated with the phase transformation between austenite and the ferritic phases as well as transformation plasticity is taken into account. A "normalized" form of the Ludwik-Hollomon equation is used for computing the flow stress of each phase where F, n, m and are temperature dependent functions, 0 is a reference strain rate and is a work hardening parameter that basically corresponds to the integrated plastic strain. This equation reads nt mt FT 0 T 0 T p 0 (4) To account for recovery mechanisms, is set to zero above a chosen temperature, and the second (work hardening) factor on the right hand side in Eqn. (4) is not allowed to increase due to change in the temperature alone. MODELLING OF HYDROGEN DIFFUSION Hydrogen diffusion is governed by Fick's law. Here, we adapt the approach described by Olden et al. [15] where the flux density of hydrogen J is computed from the gradient in normalised concentration C/s rather than from the gradient of the hydrogen concentration C.

5 J sd pp (5) Here, s is the solubility, D is the diffusivity, and p is a stress factor linked to the gradient of hydrostatic stress p. VH p (6) RT 3 VH mm 3 /mol is the partial molar volume of hydrogen in iron-based alloys and T is the absolute temperature. In this way the possibility of "uphill" diffusion towards regions with higher solubility or high tensile stresses is included. Inserting Eqn. (5) into the conservation equation C J (7) t yields C sdpp (8) t Hydrogen diffusion in steels is significantly affected by trapping. This is a generic term for the tendency of hydrogen atoms to reside not only in lattice sizes, but also in vacancies, near solute atoms or at grain boundaries or dislocations. We distinguish between reversible and irreversible traps. Reversible traps are associated with a drop in potential energy that can be overcome by the thermal activation, but they can significantly lower the apparent diffusivity and increase the apparent solubility [16]. Irreversible traps from which the hydrogen is not recoverable will not be treated in this work. Although traps could be expected to have a distribution of energy states, it is commonly assumed that traps in a given material can be associated with a given trap binding energy E T. This approximation is also adapted here. The density of lattice sites in -iron N L has been estimated to be m -3 [16]. The density of traps N T is normally some orders of magnitude smaller. In the presence of traps, the total amount of recoverable hydrogen can be written as the sum of the concentration in lattice sites C L and concentration in traps C T. The flux of hydrogen inside the metal is assumed to origin solely from the diffusion between lattice sites, so that Eqn. (8) can be rewritten as CL CT CL sd pp t t s (9) The equilibrium conditions can be expressed by the site occupancy for lattice sites L = C L /N L and for traps T = C T /N T by T ET exp KT (10) L1T RT Inserting the definitions gives:

6 NC T L CT (11) CL NL KT In [5] it is assumed that the concentration in trap sites is only a function of concentration in the lattice leading to a simple diffusion equation. However, during welding, the temperature is rapidly changing, and the equilibrium constant will also change making it important to include the partial derivative of the concentration in traps with respect to the temperature. CT NTC L CL NTC L T (12) t CL CL NL KT t T CL NL KT t In the case of changing phase composition, also the lattice density, the trap density as well as the trap energy may change. Associated terms in the time derivative of C T involving the time derivative of phase fractions are here neglected. At the temperatures where phase transformation occurs the trap site occupancy can be expected to be very low and the change of total concentration from change of phase is assumed to be small. Trap parameters can also be set to minimize the error introduced by omitting this term. In works especially addressing the condition in front of a crack tip [15,16] a term representing an increase in trap density from plastic strain is included. Numerical investigations generally predict plastic straining during welding to occur at elevated temperature at which material testing show rate-dependent flow stress and little hardening. One could therefore assume that the material undergoes a considerable recovery making it a questionable approach to characterise the state, e.g. dislocation structure, by the plastic strain. Therefore, this term is omitted here. By carrying out the derivation in Eqn. (12), and inserting Eqns. (6) and (11) into Eqn. (9), we obtain: NTNLK T C L VH s 1 2 DCL DCL p KC T L NL t RT s (13) 2 NTNLKT ET RT T 2 KC N t T L L This equation contains only one unknown, C L, and its evolution is seen only to depend on the stress state and the temperature in addition to physical constants and material parameters. T and p are available as results fields during a thermomechanical simulation of a welding process. As we here have applied the convention of a negative trap energy E T it is seen that the lattice concentration as expected will increase from an increase in temperature. Mixture of phases For a steel type undergoing phase transformations a mixture of phases may co-exist. This will occur during local phase transformation, and it will be the case after welding in the

7 partly transformed HAZ and in a material containing retained austenite. In the current implementation we consider only a locally averaged concentration of hydrogen, and material properties (solubility and diffusivity) corresponding to the weighted sum of the properties for each of the n phases are applied, where f i is the weight fraction of phase i. n n i i, i i i1 i1 (14) s f s D f D The same simple rule is applied for terms in Eqn. (13) containing K T and N T as both the equilibrium constant and the trap density can be different in the different phases. As the solubility is both phase and temperature dependent, we may write the gradient in solubility as s s T sf n i i T (15) i1 Inserting Eqn. (15) into Eqn. (13) gives, when omitting other summations over phases: NTNLK T C L 1 2 KC T L NL t (16) n 2 V 1 1 NTNLKT ET RT H s T DCL DCL p T sifi 2 RT s T s 1 KC N t i T L L Finite element implementation In order to solve the hydrogen diffusion problem by the finite element method, Eqn. (16) is first multiplied with an arbitrary function and then integrated over the domain. NTNLK T CL 1 2 d KC T L NL t n VH 1 s 1 DCL DCL p T sifi d (17) RT s T s i1 2 NTNLKT ET RT T 2 d KC N t T L L By integrating the first term on the right hand side by parts we obtain

8 NTNLK T CL 1 2 d KC T L NL t V 1 s 1 D C C p T sf d N N K E RT T d n H L L i RT s T s i1 2 T L T T 2 KC T L NL t VH 1 s DC ˆ L CL p Tn d RT s T The applied finite element formulation is closely related to what is found in [5]. The main differences are that the model presented here includes a source/sink term originating from the temperature dependent occupancy of lattice sites, and terms related to gradient in the solubility. A simple backwards difference scheme is used for the discretization of time. As an hourglass stabilized midpoint integration rule is used when solving for stresses, the pressure gradient cannot be computed from values in a single element. In order to evaluate this gradient, a polynomial function of second order in the coordinates is fitted to the pressure values in a patch of elements. This method is described in [17]. In a regular 3D mesh with hex elements, a patch of 27 (3x3x3) elements is used. For elements at the boundaries the patch is centred at the closest interior element. If the solution domain has only one or two elements in one direction (e.g. for a thin plate) a reduced polynomial is used for the coordinate axis closest to the thickness direction. (18) Boundary conditions In a state of equilibrium there should be no flux of hydrogen, but in the case of a stationary temperature field, or spatial stress variations, the hydrogen concentration will have gradients due to the pressure and temperature gradient terms in Eqn. (16). If a partial pressure of hydrogen according to Sievert's law is in equilibrium with a surface concentration C ref at a reference temperature and zero pressure, a hydrogen concentration st VH p CT, p Cref exp (19) sref RT where s ref is the solubility at the reference temperature will satisfy the condition of zero flux of hydrogen everywhere. This is accordance with the boundary condition used in [18].

9 SIMULATIONS A case study has been carried out where girth welding of a steel pipe with outer diameter 350 mm and thickness 17 mm has been simulated. The solution domain had a total extension of 800 mm in the axial direction. A total of 14 weld passes filling a u-shaped groove were applied to reflect a realistic welding procedure. For a welding procedure to be robust with full penetration by the root pass a backing material is required [19]. With root penetration and a counterboring a back bead is likely to be formed against the backing material. This will lead to notches and stress localisations. In general, with girth welding of a pipe the residual axial stresses become compressive at the outer surface and tensile at the inner surface. Regions with stress localisation at this back bead are therefore chosen for subsequent cracking analyses. In the simulations, a possible "worst case scenario" is chosen were a cold lap with lack of fusion, e.g. an initial crack, is present on one side of the back bead whereas on the other side the weld metal has undergone complete fusion with the base metal. Multipass welding represents a considerable computational challenge. In order to have a reasonable spatial resolution that can reveal variations of stresses and hydrogen concentrations in the HAZ, an axisymmetric 2D approximation was generally used in the simulations. The 2D mesh in the weld area is depicted in Fig 1. Three levels of mesh refinement have been applied in two regions with expected stress localisation. Fig. 1 Centre part of 2D solution domain and finite element mesh. From the slow diffusion of hydrogen one may expect a 2D approximation to represent a small error source for the prediction of hydrogen concentrations. On the other hand, large gradients in temperature and associated large variations in mechanical properties in front of the weld pool may represent important effects not accounted for in the mechanical 2D analyses. A supplementary 3D simulation on a 30 pipe sector was therefore carried out to check the validity of the 2D assumption. In the simulations, the weld passes were started

10 with intervals of 500 seconds. The welding speed was 4.3 mm/sec and heat input per weld length was 7.0 kj/cm in the 2D simulations. In the 3D simulation a higher heat input of 7.7 kj/cm was used in order to obtain the same weld bead size as in the 2D simulations. The base material was assumed to be a X70 steel with the composition shown in Table 1. In the simulations carried out in this work, generally the same thermal and mechanicial property data have been used as in former simulations of welding of this alloy [8]. A CCT diagram for this steel has been worked out by Onsøien et al. [20] providing data for calibration of phase transformation parameters. However, in the simulations presented here, grain growth parameters and pinning forces in Eqn. (3), have been calibrated to reproduce the actual austenite grain sizes in the coarse grained HAZ. Table 1 Chemical composition in wt-% of X70 steel. C Si Mn P S Cr Ni Al Cu Mo Nb V Ti N Hydrogen diffusion in both the base metal and in the simulated HAZ of this X70 steel, as well as in HBQ Coreweld weld metal, has been studied by the use of the electrochemical permeation technique [21]. From measurements of the effective diffusion coefficient carried out at 25 C, 50 C and 70 C, the density of reversible traps and their binding energy were estimated. These values are listed in Table 2. Table 2 Hydrogen trap data Material N t (sites/cm 3 ) E T [kj/mol] X70 base metal HBQ weld metal Simulated HAZ In the simulations, the same trap density and energy were assigned to the austenite phase as was used for the ferritic phases in both the weld metal and the HAZ. In this way an artificial hydrogen source from change of trapping conditions due to phase change is minimized. The base metal values were used also for a weak phase formed by tempering of the base metal and the HAZ. We considered it most consistent to use the lattice diffusion coefficient used in [21] also in the welding simulation for the ferritic phases. It is shown as a function of temperature in Fig. 2. This diffusion coefficient curve has larger values than the upper limit of a scatter band of diffusivity data reported in [22]. For lower temperatures where trapping leads to a much lower effective diffusion coefficient, this is considered to be reasonable. For higher temperatures, the applied diffusion coefficient may be too large. No data has been found on the solubility of hydrogen in X70 steel as function of temperature. In the simulations, austenite data from [23] and ferritic phase data for 1020 alloy [24] were applied. These solubility curves are shown in Fig. 3. In the governing equations, the hydrogen diffusion is not affected by the absolute level of solubility. It is only affected by the ratio of solubility in different phases and the relative

11 temperature dependency. Moreover, the curves in Fig 3. are in reasonable agreement with data on solubility in iron found in [25]. 1.0E-02 Hydrogen diffusion coefficient (cm²/s) 1.0E E E-05 Ferrite Austenite 1.0E Temperature ( C) Fig. 2 Hydrogen diffusion coefficients as function of temperature. 1.0E+03 Hydrogen solubility (mol H 2/(m 3 MPa 1/2 ) ) 1.0E E E E E-02 Ferrite Austenite 1.0E Temperature ( C) Fig. 3 Hydrogen solubility as function of temperature.

12 BOUNDARY CONDITIONS In the simulations, a 4 C ambient temperature was assumed to reflect seabed conditions, although the conditions inside a chamber for dry hyperbaric welding is likely to be influenced by heat from the welding equipment. A temperature dependent heat transfer coefficient was used that in a former study had given good fit to thermocouple measurements. A good thermal contact with the backing plate was assumed during the first seconds after the formation of the back bead, with a heat transfer coefficient as high as 9000 W/m 2 K. After 10 seconds it was assumed to be as low as 10 W/m 2 K due to loss of contact. Restraints on the pipe in the axial direction were modelled by a stiffness of 890 kn per mm displacement on the pipe ends of the solution domain representing a cross section area of m 2. This corresponds to a fixation of the pipe at a distance of 4m. In the cold lap region where lack of fusion was assumed, a crack was introduced where the sides were mechanically free to separate, and where hydrogen was free to escape at the outer boundaries. It was assumed that there were no interface stresses at the surface of the backing material. In addition to a reference simulation, another simulation was carried out where additional interpass and post-weld heating was imposed on a 50 mm wide section across the weld at the outer surface. Post weld heating has been reported to significantly reduce the risk of hydrogen induced cold cracking [3]. To investigate the influence of the axial restraints on the welding induced strains and stresses, a simulation with a high axial stiffness of kn per mm displacement at internal boundaries 25 mm from the weld centre was carried out. Regions more than 25 mm from the weld centre were in this case treated as rigid. Hydrogen was added in the weld regions by imposing a lattice concentration of 10 ppm on all computational nodes where the temperature was above 1520 C. By using Eqn (19) the external boundaries were set to be in equilibrium with the surroundings with a surface concentration of 0.01 ppb for ferritic phases at 20 C. FRACTURE MECHANICS SIMULATIONS The fracture mechanics simulations employ cohesive elements that act as an interface between the continuum elements. The constitutive behaviour of the cohesive elements is governed by a traction-separation law, which defines a critical stress and a critical crack-face separation that the element can endure before failing. The traction-separation law chosen in this work is the polynomial equation proposed by Needleman [26]. Pure Mode I fracture is assumed in this case, and triaxial constraint is ignored, thus only two parameters are needed to describe crack-face separation: the cohesive strength and the critical separation distance. The calibration of these parameters for X70 steel has been done by Olden et al. [27]. They performed fracture mechanics testing of SENT specimens in air and in hydrogen charged condition. A user element subroutine was developed based on the work of Scheider and Brocks [28], in which they implemented a traction-separation law that could account for the reduced fracture toughness observed due to hydrogen embrittlement. The same user

13 subroutine is used in the present work. One modification was made on the trapped hydrogen is influenced by plastic strains, p. Whereas Olden et al. [27] used: CT 49.0 p 0.1CL (20) the equation used here, based on estimates from measurements on a X70 steel [29], was CT 8700 p 2000 CL (21) The estimated concentrations in traps, C T, is added to the concentration values, C L, obtained from the diffusion simulations. The influence of hydrogen on the tractionseparation function is shown in Fig. 4. The maximum traction stress is 1850 MPa, and the critical separation distance is 0.3 mm. Normal traction (MPa) Separation (mm) Fig. 4: Traction-separation function used in this work, showing the reduction in strength due to different levels of normalized hydrogen concentration ( p =0). =0 =0.02 =0.04 =0.06 The continuum elements were bilinear quadrilateral elements with reduced integration and hourglass control. The elements in the HAZ region, seen in Fig. 5, were kept to a relatively small size of 0.3 mm to capture the varying residual stresses from the welding passes. Near the cold lap and the root-weld bead (Fig. 5c) an element size of 5 µm was used. The procedure for running these analyses consists of three steps: First a quasi-static mechanical simulation of the un-cracked geometry was performed. The crack faces were connected by surface tie-constraints at this stage. The second step was a dynamic diffusion analysis, where the hydrostatic stresses from the first simulation were used as a driving force in the diffusion process. In the last step, a mechanical simulation was performed again, this time with cohesive elements and hydrogen concentration input from the diffusion analysis. The material was assigned HAZ properties [27], and modelled as elastic-plastic with the von Mises yield criterion and isotropic hardening. Stresses were imported from the welding simulation in the first step, during which the model was restrained in order to preserve the original stress field during equilibrium iterations. The high restraint case was assigned spring elements at 25 mm from either side of the weld center to obtain the same stiffness as applied in the welding simulations. An axial load of 606 MPa was then applied to one pipe end, which corresponds to 1.25 R p0.2. In the diffusion analysis, a boundary condition of 1.5 ppm for the total hydrogen concentration was applied. Two analysis steps were made

14 consecutively, the first step of 24 minutes with residual stresses, and the following step of 24 minutes with 606 MPa axial loading. (a) (b) (c) Fig. 5: Cohesive elements were introduced in the model, seen as vertical lines in Figure (a). The largest element size for the HAZ region was 0.3 mm (b). The cold-lap crack and the notch at the root bead had elements sizes of 5 µm near the stress concentrations (c). RESULTS AND DISCUSSION HYDROGEN DIFFUSION Fig. 7 shows the computed concentration field of hydrogen both in the lattice and in traps together with the temperature field at 3 different stages after the deposition of the 6th weld bead. At 5 seconds after welding the temperatures are so high that almost all hydrogen is in the lattice, leading to a fast diffusion. The concentration in traps is only significant in the HAZ at the far side of the weld groove. After 120 seconds, the temperature field is quite homogeneous at a level of about 130 C. At this stage, the concentration is significant both in the lattice and in traps. A noticeable observation is that the total concentration in the HAZ is predicted to rise to a level higher than the initial concentration in the weld metal. This is

15 (a) (d) (b) (e) (c) (f) (g) (h) (i) Fig. 6 Hydrogen concentration (ppm) in lattice (a)-(c) and in traps (d)-(f), and temperature field (g)-(i) computed respectively 5, 120 and 500 seconds after the 6th weld pass. Note that the contour levels are different in the figures. caused by a combination of a higher trap energy in the HAZ than in the weld metal, and a higher solubility in the HAZ than in the weld metal due to a more pronounced supercooling

16 of the γ-phase in the HAZ. After 500 seconds, corresponding to the start time for the subsequent weld pass, the temperatures has dropped to 57 C, and the amount of diffusable hydrogen in the lattice is significantly reduced. The highest concentrations are found in the last weld bead and in the adjacent coarse grained HAZ, where a small fraction of retained austenite has been predicted. The first 6 plots in Fig. 7 show the predicted concentration of hydrogen when respectively the 1st, 2nd, 6th, 11th and 14th weld bead has cooled for 500 seconds. The last two plots show the concentration field predicted respectively and seconds after start of welding. Each new weld bead deposited next to the base material is seen to locally raise the concentration in the HAZ to a level that corresponds to a complete filling of the traps. In HAZ regions at a longer distance from the new weld bead the concentration is reduced, indicating that the effect of heating, leading to faster diffusion as the hydrogen is temporarily recovered from the traps, is stronger than the effect of adding more hydrogen. Between 7000 and seconds the concentration in traps is actually predicted to increase due to slow diffusion and cooling to the ambient temperature of 4 C that allows an even smaller fraction of the hydrogen to reside in lattice sites. When the weld is kept at 4 C the concentration is seen to slowly decrease in the weld metal whereas the concentration in a large part of the HAZ is at 3-4 ppm. It is at some places even increasing between and seconds. The very slow evolution of the predicted concentration in traps is due to a very low concentration of hydrogen in lattice at low temperatures, shown in Fig. 7, when any surplus of hydrogen with respect to the number density of traps has disappeared. By interpass and post weld heating, where the temperature in the weld is kept at about 115 ºC, the hydrogen is in a simulation effectively expelled. Fig. 9 shows that a significant amount of hydrogen remains in traps after a about 3000 seconds of heating, but at seconds after start of welding almost all hydrogen has disappeared. The evolution of different result fields are often better presented by time plots. Here plots are made for the three positions A, B and C shown in Fig. 9. Point A is close to the cold lap crack tip. Point B is in the heat affected zone in the root area, and point C is inside the 4th weld bead. The thin lines in Fig. 10, which are also visible in other contour plots, are weld bead domain boundaries, extension of melted areas for each weld pass, and boundaries of mesh refinement regions. The evolution of hydrogen concentration and temperature in these log points are shown in Fig. 11. During welding the strong temperature variations repeatedly move the hydrogen into and out of traps. As points A is positioned close to an outer boundary, the boundary condition quickly reduce the hydrogen concentration to a low level. In the case with no extra heating, the concentration in point B is brought down to a level below 2 ppm shortly after welding. However, Fig. 11 (d) shows that the concentration at this position is predicted to increase to nearly 2.5 ppm at seconds. A level of 2 ppm corresponds approximately to the critical limit for cold cracking [2]. In contrast, in the case of post weld heating the hydrogen concentration has dropped more than an order of magnitude in all log points at seconds, far below this critical limit.

17 Fig. 7: Computed hydrogen concentration in traps (ppm) after respectively 500, 1000, 2000, 4000, 5500, 7000, 10000, and seconds.

18 Fig. 8: Computed hydrogen concentration in lattice (ppm) after seconds. Fig. 9: Computed hydrogen concentration in traps (ppm) after and seconds in the case of interpass and post weld heating. C B A Fig. 10: Position of log points referred to in following time plots.

19 Hydrogen in lattice (ppm) Point A Point B Point C Point A heating Point B heating Point C heating Hydrogen in lattice (ppm) heating Point A heating Point B heating Point C heating Point A Point B Point C Hydrogen in lattice (ppm) Hydrogen in traps (ppm) Time (s) (a) Point A Point B Point C Point A heating Point B heating Point C heating Hydrogen in traps (ppm) Time (s) (b) Point A Point B Point C Point A heating Point B heating Point C heating Temperature ( C) Time (s) (c) Point A Point B Point C Point A heating Point B heating Point C heating Temperature ( C) Time (s) (d) Point A Point B Point C Point A heating Point B heating Point C heating Time (s) (e) Time (s) (f) Fig. 11: Computed evolution in log points shown in Fig 9 of: (a) and (b) hydrogen concentration in the lattice, (c) and (d) hydrogen concentration in traps and (e) and (f) the temperature.

20 STRESS ANALYSES In Fig. 12 it is shown a comparison of axial, hoop and mean stress fields at the end of the 2D and the 3D simulation, as well as from the 2D analysis with high axial restraint. There are strong local variations in the stress values, and some of these are not captured by the spatial resolution in the shown 3D mesh cross section. Nevertheless, the 2D and 3D results are generally in good correspondence. The axial stress is predicted to be compressive at the outer surface and tensile at the inner surface with peak values close to the root bead. High compressive stresses are seen in the coarse grained HAZ due to an assumption of a delayed transformation from austenite. A band of tensile stresses are found in regions close to the transformed zone generated by the different weld passes. The hoop stress component is in general more tensile than the axial component. A high axial restraint leads to significantly higher axial stresses. In the regions of stress localization, the stress increase is even higher than what is in general observed in the results. A comparison of the development of the hoop and the axial stress components in the 2D and the 3D analyses in log point A is shown in Fig. 13. The figure reveals that although the stresses are in quite good agreement at the end, large discrepancies occur during the simulations of the welding process. It is not possible to explain these differences in a simple manner. A difference in the root pass fusion line can be a reason for the differences seen for the first weld passes. There is a differences in how 2D and 3D domains responds to thermal gradients in the radial direction. In the graph to the right showing the results during the 5th weld pass it is seen that a strong peak is computed for the axial stress in the 2D simulation, probably due to a more rapid expansion of the metal closer to the weld bead. This peak is much less pronounced in the 3D analyses. In the plot the 3D peak appear later as the heat source has to travel some distance before reaching the cross section containing the log point. In the 3D simulation, the cold metal ahead of the weld pool appear to restrain the thermal expansion leading to more compressive axial strains than in the 2D simulation. Moreover, gradients in the results fields are large, and a single point may not provide representative values for a large area. As the residual stresses are strongly connected to the local phase transformation, one should in general be careful when results are compared. In Fig. 14 is shown the predicted fraction of martensite at the end of the simulation together with contour lines showing different levels of original base metal ferrite defining the extent of the heat affected zone. There are large variations of phase compositions over short distances. It is also questionable if such high concentrations of martensite could be found in a real weld for this X70 steel. Better modelling of the tempering of the HAZ during multipass welding as well as a recalibration of transformation parameters for large austenitic grain sizes should be considered.

21 (a) (b) (c) (d) (e) (f) (g) (h) (i) Fig. 12: Residual stresses from welding computed in 2D (left), 3D (centre) and 2D with high axial restraint (right): (a) -(c) axial stress, (d) -(f) hoop stress and (g)-(i) mean stress Stress (MPa) Hoop stress 2D Axial stress 2D Hoop stress 3D Axial stress 3D Time (s) Stress (MPa) Hoop stress 2D -600 Axial stress 2D -800 Hoop stress 3D Axial stress 3D Time (s) Fig. 13: Evolution of the axial and the hoop stress components from both the 2D and the 3D analyses computed in the log point A shown in Fig. 10.

22 Fig. 14: Contour plot of fraction martensite with iso-lines of fraction (base metal) ferrite. FRACTURE MECHANICS Results from the hydrogen diffusion analysis are shown in Fig. 15 and 16. During the 24 minutes with only residual stresses, the hydrogen distribution reached almost a steady state. The final load of 606 MPa held for 24 minutes did not influence the concentration values significantly. At the surface, the root bead notch and cold lap crack had normalized hydrogen concentrations of and respectively for the low restraint case. For the high restraint case, the same locations had concentration values of and respectively. Stress values for each element are imported to the gauss points of the element using a user subroutine. In this case, reduced integration linear elements with one gauss point were used, thus the stresses from WELDSIMS were interpolated to the coordinates of the gauss point for each element. ABAQUS performs stress equilibrium iterations when importing stresses as initial conditions, and depending on the mesh size in the welding simulations and the fracture simulations, the stresses may be redistributed slightly. Another cause of redistribution is that information on plastic strains, hardening, and yield stress are not imported to the mechanical analyses. In the low restraint case, imported stresses were lower than the yield stress for the HAZ material, thus there was limited redistribution due to plastic flow in the equilibrium iterations. The high restraint case had equivalent stresses (850 MPa) exceeding the yield stress, but only limited redistribution took place. Significant stress redistribution took place when importing stresses to the models containing cohesive zone elements. This is shown for the root area in Fig. 17, where it can be seen that peak axial stresses near the cold lap are reduced by 30% after equilibrium iterations. The likely cause of this is that residual stresses are not imported to the cohesive elements. During equilibrium iterations, the cohesive elements deform and give a stress response to the neighbouring continuum elements as shown before in Fig. 4. The equilibrium iteration algorithm does not have the ability to adjust traction values in the cohesive elements directly, thus the surrounding elements are unloaded as the crack faces are deformed.

23 The low-restraint case led to failure of the first cohesive element in the cold lap crack at an axial load level of 364 Mpa, while the same element failed at 320 Mpa for the highrestraint case. The final deformation and axial stresses are shown in Fig. 18. Cohesive element failure is identified from a characteristic drop in traction stresses, seen in Fig. 19. After stress import and equilibrium iterations (step time 1), the traction stresses are 363 MPa and 516 MPa for the low- and high-restraint case respectively. A further comparison of the two simulations is shown in Fig. 20, where the traction stress for the same element is plotted versus global axial stress. Fig. 15: Final normalized hydrogen concentration in the low restraint case (left) and in the high restraint load case (right). Fig. 16: Detail view of normalized hydrogen concentration values near the two crack locations (low-restraint case).

24 (a) (b) (c) Fig. 17: Axial stresses for the low restraint case prior to loading. Imported stresses are shown in (a) and (c), while the balanced stresses after equilibrium iterations are shown in (b) and (d). (d) Fig. 18: Comparison of the final load level at failure for the low restraint case (left) and high restraint case (right).

25 Separation (mm) Cold lap Root bead Step time Normal traction (MPa) Cold lap Root bead Step time Fig. 19: Plot of separation and normal traction for the cohesive element closest to the stress concentrations (low restraint case). The first step is the equilibrium iteration where the imported residual stresses are introduced. Axial loading is applied in the second step and the simulation stops when the first cohesive element fails Normal traction (MPa) High restraint Low restraint Axial stress (MPa) Fig. 20: Plot of axial loading vs. normal traction for the two restraint cases. The failure occurs at approximately the same traction stress, although the low restraint case fails at a higher axial load. CONCLUSIONS A model has been presented that accounts for how diffusion of hydrogen in steel welds is influenced by the temperature and stress field, phase transformations and the trapping phenomenon. The possibilities of the model has been demonstrated in a case study involving multipass girth welding of a pipe. Mechanisms that lead to an enhanced concentration of hydrogen in the HAZ have been identified. Including a lot of coupled phenomena makes the model very complex and challenging to use. Another problem is a lack of methods to measure local hydrogen concentration that could verify such a model. There are also uncertainties in the modelling from lack of accurate material data for different steel alloys. Nevertheless, the model represents a framework that can employ trapping parameters found in electrochemical permeation experiments, and their effect on the hydrogen concentration in welds can be assessed. Additional experiments on the studied X70 steel in

26 e.g. fine grained HAZ and tempered HAZ material would be of interest in order to better cover the material conditions that are present in a multipass weld. Residual stresses computed in 2D axisymmetric simulation correspond well with 3D results, but dissimilarities in the stress field development indicate that a 2D approximation is not always appropriate for simulating of girth welding. Fracture mechanics simulations were performed using the residual stress fields and hydrogen concentration levels obtained from the welding simulations. Cohesive elements were placed at two locations in the model; near a root bead and at an assumed lack of fusion. The constitutive model of the cohesive elements is based on a polynomial tractionseparation law that can describe the reduction in fracture toughness due to presence of hydrogen. Two load cases were simulated; one with high restraint (equivalent to e.g. a repair weld) and one low restraint comparable to normal pipe manufacturing conditions. The lowrestraint case led to failure in the cold lap crack at an axial load level of 364 MPa, while the same element failed at 320 MPa for the high-restraint case. No cold-cracking occurred due to the residual stresses; however, during the equilibrium iteration of the imported residual stresses, the cohesive elements caused significant stress redistribution and artificial lowering of the stresses at the points of interest. Further work is required on the user element subroutine to allow for interaction with the equilibrium iteration algorithm in ABAQUS. ACKNOWLEDGEMENT The present work was financed by the Research Council of Norway (Petromaks project /S60), Statoil, Technip and EFD Induction and performed within the DEEPIT project (DEEPIT). REFERENCES [1] N. WOODWARD: Developments in diverless subsea welding, Welding Journal, Vol. 85, No. 10, pp 35-38, [2] P. WONGPAYA, T. BOELLINGHAUS and G. LOTHONGKUM: Numerical simulation of hydrogen removal heat treatment procedures in high strength steel welds, Mathematical Modelling of Weld Phenomena 8, Verlag der Technischen Universität Graz, Austria, 2007, pp , [3] P. WONGPANYA, TH. BOELLINGHAUS and G. LOTHONGKUM: Evaluation of Heat Treatment Procedures for Hydrogen Assisted Cold Cracking Avoidance in S 1100 QL Steel Root Weld, Welding in the World, Vol. 52, pp , [4] R.A ORIANI: The diffusion and trapping of hydrogen in steel, Acta Metallurgica, Vol. 18, No. 1, pp , [5] A. H. M. KROM, R. W. J. KOERS and A. BAKKER: Hydrogen transport near a blunting crack tip, Journal of the Mechanics and Physics of Solids, Vol. 47, pp , [6] K. TAKAYAMA, R. MATSUMOTO, S. TAKETOMI and N. MIYAZAKI: Hydrogen diffusion analyses of a cracked steel pipe under internal pressure, International Journal of Hydrogen Energy, Vol. 36, pp , 2011.

27 [7] H. G. FJÆR, J. LIU, M. M'HAMDI and D. LINDHOLM: On the use of residual stresses from welding simulations in failure assessment analyses for steel structures, Mathematical Modelling of Weld Phenomena 8, Verlag der Technischen Universität Graz, Austria, pp , [8] H. G FJÆR, R AUNE, M. M HAMDI and O. M. AKSELSEN: Modelling the development of stresses during single and multipass welding of a ferritic steel in an instrumented restraint cracking test, Modelling of Casting, Welding, and Advanced Solidification Processes - XII, TMS, USA, pp , [9] W. A. JOHNSON and R. F. MEHL: Reaction kinetics in processes of nucleation and growth, Trans. AIME, Vol. 135, pp , [10] Z. ZHANG, D. DELAGNES and G. BERNHART: Microstructure evolution of hot-work tool steels during tempering and definition of a kinetic law based on hardness measurements, Materials Science and Engineering A, Vol. 380, pp , [11] L. B. LEBLOND and J. DEVAUX. A New Kinetic Model for Anisothermal Metallurgical Transformations in Steels Including Effect of Austenite Grain Size, Acta metall, Vol. 32, pp , [12] T. RETI, Z. FRIED, and I. FELDE. Computer simulation of steel quenching process using a multiphase transformation model. Computational Materials Science, Vol. 22, pp , [13] I. ANDERSEN and Ø. GRONG: Analytical Modelling of Grain Growth in Metals and Alloys in Presence of Growing and Dissolving Precipitates-I. Normal Grain Growth, Acta Materialia, Vol. 43, pp , [14] K. BANERJEE, M. MILITZER, M. PEREZ and X. WANG: Nonisothermal Austenite Grain Growth Kinetics in a Microalloyed X80 Linepipe Steel, Metallurgical and Materials Transactions A, Vol. 41, pp , [15] V. OLDEN, R. JOHNSEN and C. THAULOW: Modelling of hydrogen diffusion and hydrogen induced cracking in supermartensittic and duplex stainless steel, Materials & Design, Vol. 29, pp , [16] A. H. M. KROM and A. D. BAKKER: Hydrogen trapping models in steel, Metallurgical and Materials Transactions B, Vol. 31B, pp , [17] O. C. ZIENKIEWICZ, R. L. TAYLOR and J.Z. ZHU: The Finite Element Method: Its Basis and Fundamentals 6th Edition, Chapter , Elsevier, [18] R. CORTÉS, A. VALIENTE, J. RUIZ, L. CABALLERO and J. TORIBIO: Finite-element modeling of stress-assisted hydrogen diffusion in 316l stainless steel, Materials Science, Vol. 33, No. 4, pp , [19] H. FOSTERVOLL, J.O. BERGE, N. WOODWARD AND R. AUNE: Remotely controlled hyperbaric welding of subsea pipelines, Proceedings from Pipeline Technology Conference 2011, April 4-5. Hannover Messe, Germany, [20] M. I. ONSØIEN, M. MHAMDI and A. MO: A CCT Diagram for an Offshore Pipeline Steel of X70 Type, The Welding Journal, Vol. 88, No. 1, pp. 1-6, [21] M. SKJELLERUDSVEEN, O. M. AKSELSEN, V. OLDEN, R. JOHNSEN and A. SMIRNOVA: Effect of Microstructure and Temperature on Hydrogen Diffusion and Trapping in X70 grade Pipeline Steel and its Weldments, Proc EUROCORR Conference, Moscow, Paper No 9184, [22] T. BOELLINGHAUS, H. HOFFMEISTER and A. DANGELEIT: A scatterband for hydrogen diffusion coefficients in micro-alloyed and low carbon structural steels, Welding in the World, Vol. 35, No. 2, pp , [23] C. SAN MARCHI, B.P. SOMERDAY and S.L. ROBINSON: Permeability, solubility and diffusivity of hydrogen isotopes in stainless steels at high gas pressures, International Journal of Hydrogen Energy, Vol. 32 pp , 2007.