A Physical Model For Microstructural Predictions In Multi-Pass Welding Of Seamless Pipes

Transcription

1 A Physical Model For Microstructural Predictions In Multi-Pass Welding Of Seamless Pipes P.E. Di Nunzio*, M.C. Cesile*, E. Anelli*, A. Poli** *Centro Sviluppo Materiali S.p.A., Via di Castel Romano , Rome - Italy **Dalmine S.p.A. - Tenaris Group - Piazza Caduti 6 Luglio 1944, Dalmine (BG) - Italy Abstract A thermal-microstructural model for multi-pass welding has been developed to estimate the hardness maps in girth welds of seamless pipes. Analytical equations have been used to describe the thermal evolution and a series of physical models have been applied to evaluate grain growth during austenitization, taking also into account the inhibition effect of microalloying precipitates, and phase transformation. Empirical relationships to predict the hardness after each pass have been taken from the literature together with the evaluation of the fraction of high-c martensite formed in infracritical reheating. The model has been validated through specific laboratory experiments as well as industrial welding trials, showing good prediction capabilities. The hardness results have also been compared with the Yurioka s empirical approach. The main advantage of the present approach is the high flexibility and the possibility to obtain maps of the microstructural state to be further processed to estimate the fracture toughness behaviour of the joint. The model requires few input data. First of all, the chemical composition of the steel and the volume fraction of the microstructural constituents in the as-q&t base metal must be given. Then, the welding parameters of the pass sequence (preheat temperature, velocity, nominal heat input, process efficiency) must be supplied together with the co-ordinates of each pass centre according to the bevel shape. The latter could be also deduced a posteriori from the macrograph of the joint after sectioning and etching. Finally, the number of nodes of the grid and the position of the grid origin have to be defined. In fig. 1 the reference system and a schematic example of the calculation grid extended on the whole thickness are shown. Introduction Aim of the model is the prediction of the final hardness of the heat affected zone (HAZ) in multi-pass arc welded joints to optimize the design of seamless quenched & tempered (Q&T) linepipes with respect to the required field weldability. The model has been specialized for low-c ( mass% C) steels microalloyed with V, V+Nb, V+Nb+Ti and for pipes with the wall thickness in the range from 8 to 40 mm. A wide range of heat input (from 0.6 to 4.5 kj/mm) has been also considered in order to cover the most common welding techniques. A through-thickness mapping approach has been adopted. The steel hardness is evaluated over a set of points arranged on a fine grid with typical lattice spacing of 0.2 mm. The final result is a map of hardness and volume fraction of the main microstructural constituents deriving from the decomposition of austenite. The map, generally extended over the whole wall thickness and over the most significant regions, may include part of the fusion zone, the HAZ, and part of the base metal. The final goal is to have an estimate of the local brittle zones and, possibly, of the fracture toughness behaviour of the joint. Fig. 1 Schematic representation of the reference system used for defining the calculation grid and the pass sequence. Structure of the model The overall model is composed by many sub-models, each describing an elementary process. The main modules are the following: i) a thermal model based on analytical expressions for calculating the temperature evolution as a function of time during the welding process; ii) a physical model of austenite grain growth taking into account the effect of a time-dependent inhibition by second phase particles of Ti/Nb/V carbonitrides; iii) a simplified physical model for dissolution/coarsening of carbonitrides;

2 Fig. 2 Flow diagram of the model for passes involving complete austenitization and phase transformation. vi) iv) a physical model for predicting the volume fraction of different microstructural constituents deriving from the decomposition of austenite during cooling; v) an empirical model for estimating the hardness of the ascooled steel just after the current pass; an empirical model for estimating the tempering effect on the hardness due to reheating of the transformed microstructure in subsequent pass; vii) an empirical model for estimating the amount of high-c martensite formed during infracritical reheating and the resulting hardness. They will be described in more detail in the following sections. In figs. 2 and 3 a block diagram illustrating the main calculation flow is shown. A typical calculation sequence for a generic grid point can be synthetically described as follows. The thermal cycles for all passes are calculated. Then, the pass at which the last complete austenitization occurs is found. The thermal profile of the austenitizing stage is used to evaluate the austenite grain size from which the phase transformation takes place during cooling. The phase transformation during cooling is computed even when the point undergoes only a melting pass and no further complete austenitization. In this case, a coarse AGS is imposed to simulate the solidification structure. Subsequently, the volume fractions of the microstructural constituents (ferrite, pearlite, Widmanstätten ferrite, bainite and martensite) formed from the austenite decomposition are calculated depending on the cooling time between 800 and 500 C, τ 85. A first estimate of the hardness just after the pass can now be performed. Next passes can have different effects on the microstructure, depending on the peak temperatures, T P, of the thermal profiles. If all the following cycles have T P <Ac 1, then the original microstructure experiences a tempering treatment which reduces its hardness. On the other hand, the occurrence of a T P between the critical temperatures of the steel, Ac 1 and Ac 3, implies that a partial reaustenitization of the microstructure occurs. Consequently, some high-c martensite (MA) islands are formed after the subsequent cooling, due to the carbon enrichment of the austenite regions. From experimental evidences, the maximum attainable volume fraction of high-c martensite is generally less than 15%. Remaining passes, if any, can produce tempering of MA or even form it again, depending on the specific thermal cycles. After the last pass, the overall tempering effect is estimated according to a critical tempering parameter. The final hardness is calculated taking also into account the presence of tempered or not tempered MA. Thermal Model The thermal evolution during each pass is calculated by means of the analytical pseudo-steady state solution of the Fourier equation of heat flux [1]. In the adopted thick plate 3D formulation, a point source in an anisotropic semi-infinite

3 Fig. 3 Flow diagram of the model for passes involving partial or no phase transformations. medium with surfaces impermeable to heat is assumed. Constant thermal properties of the steel are also used. The equation has the form: T - T 0 = η W 0 1 2π λ R exp - v (R+x) (1) 2a where T 0 is preheat temperature, W 0 the nominal power, η the efficiency factor, a the thermal diffusivity, v the welding velocity and λ the thermal conductivity. circumference, the y-axis is parallel to the pipe length and the z-axis is parallel to the pipe thickness. In Eq. (1), the source position along the welding axis is x whereas R is the distance between the source and the grid point (fig. 4). If the source moves with a constant speed and the origin of its motion is placed at x=x 0, its current position is given by: Then, the distance R=R(t) is calculated as: x = x 0 - vt (2) R(t) = (x 0 - vt) 2 + y 2 P + z2 P (3) where y P and z P are the horizontal and vertical distances of the measuring point from the x axis, respectively. The equation does not depend on the plate thickness. Fig. 4 Definition of the grid point (P) and source (S) position in the thick plate 3D equation The reference system is oriented with the x-axis parallel to the motion of the heat source along the pipe Austenite Grain Growth Model A discrete analytical model is used, which is based on interactions between grain pairs [2] and where the local grain boundary curvature is used instead of the mean grain curvature [3]. It calculates the average grain size and the grain size distribution as a function of time during any non-isothermal

4 process. The effect of a time-dependent inhibition due to coarsening or dissolution of second phase particles is also taken into account. If, for a given pass, the peak temperature on the grid point is above Ac 3, a complete transformation with an initial austenite grain size (AGS) of 2 µm is assumed. Then, the grain growth occurring during the fast thermal peak is calculated down to the start of the austenite decomposition, at a conventional temperature equal to Ae 1. Calibration of this physical model is accomplished by a proper choice of the specific energy and mobility of grain boundaries within a limited range of values. In particular, a temperature dependent relationship for mobility has been used, related to the self-diffusion coefficient of iron [4]. Particle Dissolution and Coarsening Model In the microalloyed steels considered in the present study, carbonitrides of Ti, Nb and V are formed after the industrial Q&T final treatment of the pipe. Generally speaking, their solubility is higher in austenite than in ferrite. Therefore, only those passes where a complete austenitization occurs can affect the precipitate population and are considered. A simplified model of diffusion-controlled particle dissolution and coarsening in austenite has been developed which considers the pure compounds TiN, NbC and VC only, each one as an ideally pure phase, neglecting the possible formation of mixed carbonitrides. Starting from a known initial average particle size of precipitates, the model predicts the evolution of the average diameter and volume fraction during the thermal cycle of the welding pass. The thermodynamic solubility of the phases as well as the surface energy between austenite matrix and precipitate must be given as input data. If the actual precipitate fraction is close to the equilibrium value, particle coarsening occurs by Ostwald ripening. The evolution of the average particle radius is calculated by integration of the Lifshitz-Slyozov-Wagner (LSW) equation [5,6]: <r>(t+ t) = (<r>(t) - k LSW t) 1/3 (4) where k LSW is a factor depending on the interface energy, diffusion coefficient of the microalloying element etc.. Otherwise, particles dissolve or grow from supersaturated solution with a rate given by the following relationship [7]: d<r>/dt = k A [M(t) - M eq (<r>,t)] r m /(<r> (r m - <r>)) (5) where M(t) is the current concentration of the microalloying element in solid solution, M eq (<r>,t) is the equilibrium solubility accounting for the capillarity effect, r m is the radius of the influence sphere defined in the Asimow theory, and k A is a factor including interface energy, diffusion coefficient and other constants. The drag force on grain boundaries is evaluated according to the Zener criterion [8] as: Z = k Z f v /<r> (6) where k Z is a calibration factor and f v the overall precipitate fraction. Contributions from different phases are added together and a minimum inhibition level is always imposed, also for C-Mn steel without microalloying in order to take into account the presence of AlN particles. A calibration of this model together with that for grain growth has been carried out on a series of short isothermal treatments on steels with various microalloying combinations. Austenite Decomposition Model A physical model based on nucleation and growth mechanisms [9,10], has been used to predict the austenite transformation kinetics after an isothermal or generic continuous cooling profile. The model takes into account the steel composition, the initial AGS and the possible residual strain in austenite. It computes the microstructure in terms of volume fractions of allotriomorphic ferrite, Widmanstätten ferrite, pearlite, bainite and martensite. The formation of the microstructural constituents is computed on the basis of thermodynamic stability criteria. Nucleation of ferrite is assumed to be heterogeneous at the austenite grain boundaries. Following the coherent pillbox model for the description of the nucleus shape, the nucleation rate is computed according to the classical nucleation theory as a function of the active austenite grain boundary surface. The parabolic growth constant for describing the ferrite diffusion-controlled growth kinetics is evaluated according to Zener [11] as a function of temperature from the mole fractions of carbon at the α/γ interface, taking also into account small additions of alloying elements. Pearlite and bainite are described in a similar way considering the available austenite grain boundary surface. Only for Widmanstätten ferrite, nucleation is assumed to be homogeneous within the austenite grains. The fraction of martensite is evaluated from the empirical relationship by Koistinen and Marburger [12] and on the basis of Gibbs free energy evaluations. The model has been originally calibrated on low-c steels (plain C-Mn and Nb-microalloyed) by a slight adjustment of the maximum density of active nucleation sites on the austenite grain boundaries. It has required a limited further tuning, mainly concerning the growth rate of bainite and Widmanstätten ferrite, to reproduce the microstructures found in the specific experiments carried out to simulate welding cycles where the phase transformation can take place from a coarse AGS. Hardness Models Two empirical models from the literature have been used to calculate the hardness of the weld starting from the predicted microstructure after cooling. They were originally developed for low and medium-c steels (C= mass%) with a total alloy content (Mn+Cr+Ni+Mo) less than 5 mass%.

5 The first one applies to continuous cooling, the second one estimates the hardness after a tempering treatment. In the present case, the cooling after austenitization is considered equivalent to a constant cooling with a rate calculated from the thermal profile in the temperature range from 800 to 500 C. On the other hand, the subsequent subcritical or infracritical reheating is assimilated to short tempering treatments. In the following approach, the hardness of a calculated microstructure is estimated as a weighted average of the pure constituents based on their volume fractions: FP F%+P% HV = HV + HV 100 B B% + HV 100 M M%+MA% 100 where, F%, P%, B%, M% and MA% are the percentages of Ferrite, Pearlite, Bainite, Martensite and High-C Martensite, respectively. For continuous cooling, the quantities HV M, HV B and HV FP, obtained empirically as a function of the steel chemical composition and cooling rate (v r ) in K/h, are expressed as follows [13,14]: HV FP = C+53 Si+30 Mn+12.6 Ni+7 Cr+19 Mo (7) +(10-19 Si+4 Ni+8 Cr+130 V) log 10 (v r ) (8a) HV B = C+330 Si+153 Mn+65 Ni+144 Cr+191 Mo +(89+53 C-55 Si-22 Mn-10 Ni-20 Cr-33 Mo) log 10 (v r ) (8b) HV M = C+27 Si+11 Mn+8 Ni+16 Cr +21 log 10 (v r ) (8c) with standard deviations σ FP =6.4 HV, σ B =10.5 HV and σ M =13.0 HV, respectively. For describing tempering, an equivalence parameter, P T (K), relating times and temperature of the treatments is used. It is defined according to the following relationship [15,16,17]: P T = -1 1 R - ln(t T T H T ) T where T T is the tempering temperature (K), t T the tempering time (h), H T the activation energy, which is independent on the carbon content and as-cooled microstructure ( H T =419±21 kj mol -1 ), and R the gas constant. (9) If the tempering parameter P T exceeds a critical value P cr, a fast decrease in hardness occurs. Bainite and martensite only are involved in this process. The critical tempering parameter is computed as: 1000 P cr = C Mo V (10) To evaluate the hardness of martensite and bainite after tempering, the following expressions are used: HV T B = C-349 Si-64 Mn-6 Ni-186 Cr -458 Mo-857 V ( C+336 Si+79 Mn P T +16 Ni+196 Cr+498 Mo+1094 V) (11a) HV T M = C-368 Si+15 Mn+37 Ni +17 Cr-335 Mo-2235 V ( C+321 Si P T -21 Mn-35 Ni-11 Cr+352 Mo+2345 V) (11b) with standard deviations σ=9 HV and σ=10 HV, respectively. The final average hardness is calculated according to Eq. (7) where HV B and HV M are replaced with HV T B and HV T M, respectively assuming that the hardness of mixed ferrite-pearlite microstructures is not significantly affected by tempering. Infracritical Reheating Model Islands of high-c martensite (also known as Martensite-Austenite, MA, constituent) are formed when the structure undergoes a partial transformation. In the heating stage carbon-enriched austenite is formed which, on cooling, transforms into high-c martensite. The latter is responsible for the formation of brittle zones in the weld. Therefore the prediction of its formation is very important in modelling multi-pass welding. An empirical model has been used to estimate the fraction of. the hard phase MA formed in the infracritical region [18]. It is based on a set of regression equations obtained from an extensive experimental activity. The relative ratio between the formed MA fraction (MA%) and the maximum allowable fraction (MA% max ) is calculated by a m-th degree polynomial MA% m = MA% a i θ i (12) max i=0 where a i are constant coefficients and θ is the reduced peak temperature defined with respect to the critical transformation temperatures of the steel as: θ = T P - Ac 1 Ac 3 - Ac 1 (13)

6 and MA% max is given by a linear function of the chemical composition. Experimentally it is found that the amount of MA in the steels of interest reaches a maximum value ranging from 10 to 15%. The ratio MA%/MA% max, when plotted versus the reduced temperature, shows a peak increasing up to about θ=0.3 and then decreasing. Validation After a separate validation, the sub-models have been linked together to build up an integrated computer program for hardness prediction. The check of the overall model has been carried out on single points by comparing the calculations with experimental hardness values from thermal cycles simulated by a dilatometer and from real multi-pass welds of seamless pipes. A first set of tests has been carried out on three highstrength steels previously studied [19] whose chemical composition is listed in Table 1. Thermal cycles of a welding process were reproduced with a dilatometer by imposing a rapid heating followed by a short holding in the austenite range and a continuous cooling. Details of the treatments are reported in Table 2 together with the resulting hardness values from measurements and calculations. It can be observed that the predictions are in good agreement with the experiments within an average error of about ±20 Vickers. Table 1 Chemical composition (mass %) of the steels used in tests of the model by dilatometric cycles. Code C Mn Si Mo Ni Cu Ti Nb < <0.005 <0.005 S <0.03 <0.03 <0.03 < ISP < Table 2 Processing conditions and hardness results of the tests of the model by dilatometric cycles. Code Heating Time (s) Holding T ( C) Soaking Time (s) CR (K/s) HV exp. HV calc S ISP Secondly, welding treatments in the most critical positions, namely those in the HAZ near the root and the cap pass, have been simulated taking into account the effect of reheating due to further passes. Experimental data on the source positions were taken from the metallographic sections of the welded joint after sectioning, mechanical polishing and chemical etching. Vickers hardness measurements were carried out in the HAZ at a distance from the fusion line ranging between 0.5 and 1.5 mm and at a distance of 1.5 mm from the lower and upper pipe surfaces, for root and cap pass, respectively. Pipes of Ti, Ti+V and Ti+Nb+V microalloyed steels with wall thickness in the range 11 to 26 mm have been considered with a wide range of carbon content and different microalloying combinations to better verify the model. A list of the chemical composition of the steels is reported in Table 3. Table 3 Chemical composition (mass %) of the steels used in the single-point validation of the model. Code C Mn Si Mo Ti Nb V TA < TA < CRC < H H The calculation results are compared with experimental hardness in fig. 5. The dotted lines define the region with an error of ±20 HV with respect to the exact match. It can be observed that the model predictions are satisfactory in the whole experimental hardness range from about 170 to 280 HV and that the error bars are representative of the standard deviation of the scatter, as expected on the basis of the empirical correlation in Eqs. (8) and (11). Fig. 5 HV calc TA1 TA2 CRC H96 H HV exp Comparison between experimental hardness values and the model predictions in the single-point tests. Examples of Application In this section, a sensitivity analysis of the model is presented and an example of simulation of a real multi-pass weld is described to show some of the possible applications. Firstly, a single submerged metal arc weld (SMAW) on the steel H96 in Table 3 simulating a single pass has been calculated with the following base parameters: 220 C preheat, 0.30 and 2.38 kj/mm heat input, mm/min welding speed and 0.8 welding efficiency. The effect of the steel carbon content and of the heat input on the hardness have been put in evidence. A distance of 0.2 mm from the fusion line has been assumed and maintained as a constant geometric parameter even when the size of the fusion zone changed as a function of

7 the heat input. Being the cap pass equivalent to a single-pass weld without any post-weld treatment or tempering effects due to further passes, the results have been compared with the empirical hardness model by Yurioka [20]. The results are shown in fig. 6 and fig. 7 for the carbon content and the heat 30 mm is presented. The steel composition (mass%) was: C, 1.08 Mn, 0.25 Si, 0.13 Cr, Ni, 0.10 Mo, 0.12 Cu, Ti<0.005, Nb, V, Al, S and N. On the U-shaped joint 13 passes were carried out, Vickers Hardness model Yurioka heat input = 0.3 kj/mm heat input = 2.38 kj/mm Carbon content (mass%) Fig. 6 Calculated effect of carbon content on the hardness of a single-pass weld and comparison with the empirical model by Yurioka. input, respectively. The present model gives results slightly higher than the empirical equations by Yurioka, with differences generally below 20 Vickers. The trends are substantially equivalent. It Vickers Hardness Fig model Yurioka Heat Input (kj/mm) Calculated effect of heat input on the hardness of a single-pass weld and comparison with the empirical model by Yurioka. can be clearly observed from fig. 7 that low values of heat input ( kj/mm), typical of root passes, produce hard structures that require further heat treatment from the subsequent passes. On the other hand, cap passes for which post-weld heat treatments are not required, should be performed with a heat input higher than about 0.8 kj/mm in order to obtain a hardness lower than about 250 Vickers. As second example, a multi-pass pulsed gas metal arc weld (PGMAW) on a X65 grade pipe with wall thickness of Fig.8 Macrostructure of the multi-pass PGMAW welding. all centred on the welding axis z, including a root and a hot pass, 8 fill passes, a strip and a cap pass. The macrostructure of the joint, after polishing and etching, is shown in fig. 8. Calculations have been performed adopting the values of current, voltage, welding velocity and preheat temperature reported in the welding technical report. The efficiency of each pass was defined according to the usual criteria for multi-pass welds and welding technique [1]. A square grid extended over the whole wall thickness of the pipe with a spacing of 0.2 mm has been used for calculation. In order to avoid numerical errors due to the singularity of Eq. (1) for points located exactly on the source, an y-offset of the grid equal to 1 mm has been introduced. The correctness of the chosen parameters has been verified by mapping the highest peak temperatures for each point and classifying the macrostructure as follows: Weld Metal: T Peak > T Liq Heat Affected Zone: Ac 1 < T Peak < T Liq Base Metal: T Peak < Ac 1 In the HAZ also the infracritically reheated points have been included. The thermal-macrostructural map is reported in fig. 9. In fig. 10 the map of the final hardness at the end of the process is shown as a typical output example of the model. The correspondence between the experimental and the predicted macrostructure is good. The critical points of the weld where hardness is greater than 240 HV clearly appear in the map. The lines superimposed to the map are the same reported in fig. 9 to better define the relationship between hardness and the macrostructural regions. It can be observed that the hardness peaks in the HAZ are located mainly in the regions close to the root pass.

8 z (mm) Base Metal HAZ Weld Metal MA (%) y = 4 mm y (mm) Fig.9 Calculated thermal map of the peak temperature locating the different macrostructural regions. z (mm) y (mm) Beside hardness, also maps of the volume fraction of microstructural constituents can be obtained. For example, a trough-thickness profile of the volume fraction of the untempered MA constituent is shown in fig. 11 to illustrate the capabilities of the model. The points where MA is formed are those where infracritical reheating cycles occurred. Summary and Conclusions Fig.10 Calculated hardness map of the joint. Welding of steel is surely one of the most complex processes to be quantitatively described in materials science. This is due to the fact that many different phenomena are involved, from thermal flow to a wide variety of metallurgical transformation processes. In the present approach, although a Root z (mm) Cap Fig.11 Calculated profile of the untempered MA constituent in the joint at 4 mm from the weld axis. number of approximations was necessary to estimate some of the quantities and some empirical approaches were used instead of physical models, good predictive capabilities have been obtained. In addition, the very flexible structure allows to evaluate hardness and microstructures both on selected single points, e.g. for a detailed comparison of the calculations with experimental hardness determinations, and on grids, to obtain maps of hardness and volume fraction of microstructural constituents. The latter aspect represents the first step for a possible improvement of the model in order to estimate the extension of local brittle zones and the fracture toughness of the joint. A very careful analysis of the correlation between microstructure and fracture is required together with a critical examination of the typical scale lengths involved in these processes. References [1] Ø. Grong, Metallurgical Modelling of Welding, The Institute of Materials, London [2] P.E. Di Nunzio, Acta Mater. 49, (2001). [3] P.E. Di Nunzio, submitted to Metall. Mater. Trans. [4] M. Militzer, A. Giumelli, E.B. Hawbolt, T.R. Meadowcroft, Metall. Mater. Trans. A 27A, (1996). [5] I.M. Lifshitz, V.V. Slyozov, J. Phys. Chem. Solids 19, (1961). [6] C. Wagner, Z. Elektrochem , 581 (1961). [7] R. Asimow, Acta Metall. 11, 72-3 (1963). [8] C. Zener, private communication to C.S. Smith, Trans. Am. Inst. Min. Engrs. 175, 11 (1957). [9] E. Anelli, S. Amato, P.E. Di Nunzio, ECSC Contract No. 7210/EA-418, Final Report EUR IT (1998). [10] E. Anelli, P.E. Di Nunzio, Proc. 4-th European Conference on Advanced Materials and Processes (EUROMAT), September, 1995, Padua/Venice, Italy, vol. IV, p [11] C. Zener, J. Appl. Phys. 20 (1949) 950.

9 [12] D.P. Koistinen, R.E. Marburger, Acta Metall. 7, (1959). [13] R. Blondeau, Ph. Maynier, J. Dollet, Mem. Sci. Rev. Métall. 70, (1973). [14] J. Brisson, R. Blondeau, Ph. Maynier, J. Dollet, Mem. Sci. Rev. Métall. 72, (1975). [15] G. Pont, Ph. Maynier, J. Dollet, P.Bastien, Mem. Sci. Rev. Métall. 67, (1970). [16] A. Ponsot, Ph. Maynier, J. Common, P. Bastien, Rev. de Métall. 68, (1971). [17] R. Blondeau, Ph. Maynier, J. Dollet, Mem. Sci. Rev. Métall. 73, (1976). [18] D. Kaplan, Multipass Welding in ECSC Contract 7210-PR/245, Technical Report No. 3, (2002). [19] E. Anelli, D. Colleluori, ECSC Contract No EC/406, Final Report EUR EN (2000). [20] N. Yurioka, M. Okumura, T. Kasuya, H.J.U. Cotton, Metal Construction 19, 217R (1987).