Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process

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Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process Jie Xia, Hui Jin∗ Jiangsu Key Laboratory of Engineering Mechanics, & Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, School of Civil Engineering, Southeast University, Nanjing 210096, China

a r t i c l e

i n f o

Article history: Received 6 April 2017 Revised 9 July 2017 Accepted 28 August 2017 Available online xxx Keywords: Welding simulation Coupling thermal–metallurgical analysis Heat transfer Phase transformation Latent heat Finite element analysis

a b s t r a c t Welding is a significant joining technology in engineering construction. In addition to the effect of residual stress on joining quality, an obstacle in welding analysis is the complex phenomena, including phase transformation, thermal cycle and microstructure kinetics. The influence is manifested by microstructural development, defect formation and metallurgy transformation in the weld region. For the further knowledge of phase transformation behavior in the welding process, a simulation procedure of coupling thermo-metallurgical is elaborated by utilizing finite element theory. Heat transfer analysis and solid-state transformation in the welding process are implemented in the developed welding simulation model. The Koistinen–Marburger model and Leblond phase evaluation model are employed in the established user subroutine tool to consider the continuous heating transformation and continuous cooling transformation. The utilization of this method makes it possible to more precisely highlight the phase transformation behavior law in the welding region since the thermal cycle in welding process is essentially different from the general heat treatment process. The thermal cycle and cooling rate are taken into account to predict the metallurgical transformation behavior and phase fraction. Transformation latent heat is implemented in the proposed procedure for the thermal–metallurgical coupling analysis in welding. The calculated results are compared with some experimental data and results from standard software. The proposed coupling analysis simulation model is validated by the good agreement between the simulated and experimental results. © 2017 Published by Elsevier Ltd.

1. Introduction As a modern technique to joint of material, welding is commonly applied in various industries. It is an interaction process of thermal, mechanical and metallurgical behavior. Complex phenomena, such as solidification, microstructural evolution and defect formation, have great influence on the quality of welded joints. Temperature gradients and phase transformation in the solid state contribute to the changes in the thermal-physical and mechanical properties of the material in the fusion zone (FZ) and heataffected zone (HAZ) [1]. The formation of bainite, ferrite, pearlite and martensite microstructures at various cooling rates may influence the microstructural development and material properties. Experimental research and prediction of phase transformation are challenging for the large requirements of time and financial resource.

∗

Corresponding author. E-mail addresses: [email protected] (J. Xia), [email protected] (H. Jin).

The application of numerical methods has contributed to the development of computational welding mechanics [2]. The phase diagram and thermal cycle in welding are integrated to explain the microstructural evolution law and mechanical properties in welds [1]. Deng and Murakawa [3] investigated the residual stress profiles in butt-welded 9Cr-1Mo steel pipes considering the effect of the volume change and yield strength change due to the martensite transformation. Lee and Chang [4] predicted the axial and hoop residual stresses in carbon steel pipe weld joints incorporating the effect of the martensite transformation in the solid state. Based on the JMAK kinetics of diffusional transformation model and established elastic-plastic constitutive model considering the volume change and transformation-induced plasticity due to solid-phase transformation, Song et al. [5] presented the residual stresses and distortion of TA15 titanium alloy welding. The effect of the phase transformation on the mechanical behavior in laser metal power deposition was studied by Fang et al. [6]. The residual stresses in flash-butt joints of U71Mn rail steel were studied by Ma et al. [7], but only the austenite-pearlite and austenite-martensite transformations were employed in the cooling transformation analysis. The parameters of the phase transformation kinetics models are

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Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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only temperature-dependent. Based on the previous kinetics of diffusional and diffusionless transformation models, some types of structural steel were applied in welding simulations to analyze the residual stress and distortion [8–10]. The research works on welding analysis mentioned above were performed based on the kinetics of metallurgy transformation during heat treatment process. In order to obtain the expected mechanical properties of the materials, the specimen must undergo specific heat treatment processes, such as tempering, quenching, and laser hardening. The microstructural development law is closely related to the applied heat treatment technology; therefore, some mathematical kinetics models of phase transformation as mentioned above have been proposed to describe diffusional and diffusionless transformation law. These models were used to predict the phase fraction and mechanical properties of material undergoing heat treatment by numerical methods [11–13]. Eser et al. [11] predicted the relaxation of internal stress during tempering of AISI H13 tool steel and explicitly considered the evolution of microstructure by finite element (FE) methods. In addition, different tempering conditions can be taken into account in the analysis of stresses relaxation at the macroscopic scale. The effects of prior austenite deformation in the hot-press forming process were investigated by Bok et al. [14]. The influences of boron and austenite deformation on the transformation behavior were described by modified kinetics equations. The numerical research progress on the metallurgy phenomena in the area of heat treatment process has contributed to the development of welding metallurgy analysis. However, the types of transformation behavior mentioned above were predefined by kinetics of mathematical models according to the way of heat treatment. For example, the austenite to martensite transformation can be defined by the Koistinen– Marburger (KM) model. The components of the microstructure were also presupposed in the above analysis. The continuous cooling transformation (CCT) diagram for heat treating steel can also be useful for the analysis of welding metallurgy. However, some fundamental differences between welding and heat treatment must be considered [1]. The peak temperature in welding is much higher than that in heat treating. The former can approach 1500 °C in the HAZ. For welding, the heating rate is very high and the retention time above A3 is very short, but the inverse is true for heat treatment. The non-uniform temperature field in the FZ and HAZ leads to different temperature gradients and cooling rates, which influence the transformation behavior and microstructural development. It is difficult to predefine the phase transformation law and ensure which phase types are formed in transformation in a non-uniform field, because the thermal and metallurgical phenomena are closely dependent on the welding parameters adopted in welding (e.g. heat input, welding speed and welding sequence). Therefore, the thermal and metallurgical behavior during welding are definitely different from those in heat treatment. Simplified kinetics models of diffusional or diffusionless transformation cannot precisely elaborate the complex transformation phenomena and microstructural development in welding. Professional heat treatment software can be used to simulate the thermal–metallurgical-mechanical behavior in welding. Heinze et al. [15] analyzed the influence of heat input on the mechanical deformation of welded structures by utilizing SYSWELD. The formation of welding residual stresses and distortions is inevitably influenced by phase transformation and microstructural development law. Caron and Heinze et al. [16,17] studied the effect of the phase and transformation law on weld-induced residual stress and distortion. However, the user cannot fully access the implemented methods and does not know how the process is performed in that standard software. Furthermore, it is impossible to model some materials if their transformation laws have not been imple-

mented in the standard software. According to the CCT diagram for EH36 steel, Han et al. [18] calibrated the parameters of the Leblond model [19] to predict the metallurgical transformation behavior and the phase fraction in welding. Piekarska et al. [20] proposed an analytical method to predict the phase fraction in the welding of S355 steel. The transformation behavior was defined as a function of the cooling rates. However, the effect of the transformation latent heat was ignored in the subsequent coupling analysis above. In the present study, a FE simulation procedure is proposed to model the thermal–metallurgical coupling phenomena of welding by using ABAQUS software. The Leblond model is implemented in a developed user subroutine “LEBM” by FORTRAN language to predict the transformation behavior of S355J2 steel in welding. Based on the non-uniform temperature field and the cooling rates in the FZ and HAZ in welding process, the proposed method can more precisely predict the thermal cycle, phase components and fraction corresponding to the applied welding parameters. The transformation latent heat is taken into account for the coupling analysis, and it contributes to the greater accuracy of the simulated results of the thermal cycles in welding. The established procedure is applied to a S355J2 steel sample. The coincidence between the simulated and experimental results confirms the applicability of this simulation tool. 2. Mathematical and numerical models 2.1. Heat transfer analysis In welding process, heat transfer analysis is of importance due to its dominant effect on mechanical and metallurgical behavior. Higher welding speeds and lower rates of heat transfer in materials result in a severe temperature gradient on the front side of the weld pool and a smooth temperature gradient on the rear side. Modeling the heat distribution in weld pool is essential to the analysis of temperature field in welding. In this study, the double-ellipsoidal heat source model proposed by Goldak [21] is used to model the geometry sharp of the weld pool and the distribution of heat source. The heat source is distributed in a Gaussian manner to compensate the changes in the weld pool area caused by differing thermal conductivity. The mathematical models of the power density distribution inside the front and rear quadrant of the ellipsoidal heat source can be expressed by the following equations [21]:

q(x, y, z, t ) =

√ 6 3ff

π 3/2 a21 c



exp −

3(x + vt )2 3y2 3z 2 − 2 − 2 2 b c a1



  √ 3(x + vt )2 3y2 3z 2 6 3 fr  q(x, y, z, t ) = 3/2 2 exp − − 2 − 2 b c π a2 c a22

(1)

(2)

where, a1 , a2 , b, and c are the size parameters that determine the geometric shape of the heat source model. The values of the size parameters can be selected based on the geometric size of weld pool in practice. The power of the heat source  can be expressed by the following equation:

 = η ·U ·I

(3)

in which, η is the arc efficiency, U is the arc voltage and I is the welding current. The temperature boundary conditions describe the heat loss due to convection and radiation between the surface and ambient temperature. In this study, a combined temperature-dependent convection coefficient αh (W · m−2 · K −1 ) is employed in the welding analysis. The equation can be expressed as [22]:



αh =

0.0668 · T 0.213 · T − 82.1

0 < T < 500 T > 500

(4)

Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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model of the transformation. The equilibrium phase components and proportions should be determined by kinetics in consideration of multi-phase transformation behavior, transformation direction, cooling conditions, temperature and time. 2.2.2. Model of transformation during the heating period Phase transformation to austenite occurs during the heating process. Since the rapid heating rate used in welding, this transformation may appear at higher temperature (Ac1 and Ac3 ) than the corresponding equilibrium temperature (A1 and A3 ). In this study, the phase fraction during the heating process in each step is calculated by using a modified Koistinen–Marburger model [23]:



F (T , t ) = 1 − exp k

Ts − T Ts − T f



(5)

in which, F (T , t ) is the volume fraction that is defined as a function of temperature T and t . T s and T f are the start and finish temperatures of the austenite transformation.

Fig. 1. Transformation diagram related to the heating and cooling processes.

where, T is the current temperature at the Gauss point in the FE welding simulation model. 2.2. Kinetics of phase transformation 2.2.1. Welding metallurgy phenomena Fig. 1 depicted the main phase transformation law in the solid state appear in heat treatment process of metal material. Metallurgical transformation generally includes diffusional and diffusionless transformation. Diffusional transformation is accompanied by changes of chemical compositions from the parent phase to a new phase. Atoms need to experience relatively longer distance movement for new phase development, such as ferrite and pearlitic transformation. Just like the martensitic transformation, diffusionless transformation changes the crystal structure but not the composition of the parent phase. Some mathematical models have been proposed to predict the transformation law in heat treatment by some equations, such as the Avrami equations and Koistinen– Marburger [23] model. A CCT diagram reflects the phase evolution law of a material with a specific chemical composition. The diagram provides some parameters of the metallurgical behavior during the cooling process. The phase component is a function of the temperature, time and cooling rate. It is the basis of heat treatment of a material to the designer. As shown in Fig. 1, transformation behavior may appear in both the heating and cooling periods, and the new phase components may be significantly different due to the influence of the cooling rate on the transformation behavior. The metallurgical transformation law in material heat treatment process has contributed to the progress of welding metallurgy analysis. Some differences between welding and heat treating are fundamental and worthy of attention. Different microstructural development may appear in the HAZ, which is characterized by non-uniform thermal cycles and cooling rates. No phase transformation occurs far from the weld pool since the temperature is too low. In addition, welding metallurgical behavior is more complex than that of heat treating. It is not merely a unique transformation between the parent phase and a new phase. Several transformations may occur due to the co-existence of multiple phases in the HAZ. Therefore, it is imprecise to presume specified transformation behavior in welding metallurgy by a general kinetic

2.2.3. Phase transformation during the cooling period The phase transformation in the solid state during the cooling period determines the finial microstructural and mechanical properties of the material in the FZ and HAZ. It is of significance to understand the phase evolution and thermal mechanical behavior of welded joints because heat of transformation influences both the temperature field and the stress field. In this study, transformation phenomena in the welding are modeled by kinetics of Leblond model [19] to precisely predict multi-phases transformations. This model enables the relationship of the phase fraction, transformation rate, cooling rate and temperature to be specified. The mathematical model for phase transformation j → i can be expressed by the following equation [19]:





p˙ i T , T˙ , t =

ji pi,eq ( T ) − pi ( T , t )

τ ji (T )

 

f ji T˙

(6)

where, pi is the fraction of phase i, which depends on temperaji ture T and time t . pi,eq is the equilibrium proportion of the phase in the j → i transformation. τ ji is a metallurgical parameter representing the time of the j → i transformation. f ji (T˙ ) is a parameter obtained from the CCT diagram that is dependent on the cooling rate. Based on the relationship of transformation between two phases, the kinetic model of phase transformation was generalized for the case of n phases by Leblond and Devaux [19]:





p˙ i T , T˙ , t = −

n 

Ai j in which

j=i

n 

pi = 1

pi ≥ 0

(7)

1

where, Ai j is the algebraic proportion of phase i, which is transformed into phase jper unit of time. Ai j > 0 indicates the transformation i → j; Ai j < 0 indicates the transformation j → i; and Ai j = −A ji , which can be calculated by the following equations:

⎧ (ki j (T ) pi − li j (T ) p j ) fi j (T˙ ) ⎪ ⎪ ⎪ ⎪ i f ki j (T ) pi − li j (T ) p j > 0 i → j transf. ⎪ ⎪ ⎪ ⎪ ⎪ ⎨−(k ji (T ) p j − l ji (T ) pi ) f ji (T˙ ) Ai j i f k ji (T ) p j − l ji (T ) pi > 0 j → i transf. ⎪ ⎪ ⎪ 0 i f ki j ( T ) pi − li j ( T ) p j ≤ 0 ⎪ ⎪ ⎪ ⎪ and k ji (T ) p j − l ji (T ) pi ≤ 0 ⎪ ⎪ ⎩

(8)

no transformation between phases i and j

The metallurgy parameters ki j and l i j were defined in Ref. [19] as below:

ki j =

j pij,eq (T )

τ i j (T )

li j =

j 1 − pij,eq (T )

τ i j (T )

(9)

Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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Fig. 2. Thermal–metallurgical coupling analysis diagrams by ABAQUS software.

The model proposed by Leblond and Devaux [19] in Eqs. (6)–(9) determines the relationships among the phase fraction, temperature, time, phase proportion and cooling rate. The metallurgical parameters of the model are obtained from the CCT diagram of the applied material. Eq. (7) can be solved using the four-order Runge– Kutta method for ordinary differential equations to obtain the evolution of each phase. The mathematical models were implemented in ABAQUS software to predict the phase evolution in welding simulation. The proposed procedure enables analysis of the coupling thermal–metallurgical phenomena in welding and provides more accurate knowledge about the welding process. 3. Simulation technology implemented in ABAQUS The rapid development of numerical methods has allowed to computational welding mechanics to reach a stage where it can solve a number of problems in engineering. The application of FE methods and commercial software has aided the progress of welding analysis. In this paper, an analysis procedure for the coupling thermal–metallurgical phenomena is developed by using ABAQUS software and its user subroutines contained in the software. The subroutines were implemented by FORTRAN language and were linked to ABAQUS software. The overall procedure for the coupling analysis diagram is presented in Fig. 2. For the analysis of heat transfer in welding, user subroutines “DFLUX” and “FILM” were employed to model the heat source load and temperature-dependent boundary conditions. Doubleellipsoidal heat source model was defined by the “DFLUX” subroutine in order to simulate the geometry shape of the weld pool, which is of great importance to the prediction of temperature fields in welding. In addition, the heat loss due to convection and radiation was taken into account in the simulation. Therefore, a

temperature-dependent heat transfer coefficient was defined by the “FILM” subroutine in order to consider the heat loss from the surface of the welded structure. User subroutine “USDFLD” defined field variables at the Gauss integral point. Most material properties at the Gauss integral point can be defined as functions of temperature or other field variables. The phase field variables can be given by f ield (k ) =F k (k= 1, 2, 3, 4 ), where F k represents the phase fraction. The material properties at the Gauss point can be calculated by using the mixture rule at each increment. The material proper ties at point i at time t can be obtained by pi,t = k Fk pi,t,k (T ). In this case, the temperature-dependent material properties were defined in the welding analysis. The phase proportions at each increment were obtained based on the results of transformation analysis by the developed “LEBM” user subroutine. Internal heat generation is accompanied with the phase transformation. User subroutine “HETVAL” was used to model the effect of the transformation latent heat. The heat power can be defined by this equation:

q˙ =

 k

Hk

F k ρ t k

(10)

in which, F k denotes the fraction increment of phase k, and H k (J/kg) is the enthalpy of phase k. The kinetics models of phase transformation Eqs. (5)–(9) were implemented in the developed user subroutine “LEBM”, which was linked to ABAQUS software. The metallurgical transformation analysis at each Gauss point was conducted in this module to predict the proportion of each phase according to the temperature field and cooling rate. The metallurgy parameters of the model were obtained from CCT diagram of S355J2 steel in this paper. There-

Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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Fig. 3. Simulated FE model.

Table 1 Chemical components of S355J2 steel (wt. %) [24]. Steel

C

Si

Mn

P

S

Cr

Mo

Ni

Cu

S355J2

0.18

0.55

1.6

0.03

0.03

0.1

0.08

0.3

0.4

fore, the ordinary differential equations should be solved by the fourth-order Runge–Kutta method to obtain the phase fraction at each increment. The calculated phase proportion is a timely dependent on the temperature field and cooling rate formed in welding process. The welded joint of S355J2 steel plate was investigated in this study to verify the proposed procedure of analysis. As Fig. 2 shows, the fraction of each phase was calculated from the metallurgical analysis module in “LEBM”. The results were delivered to the ABAQUS solver for the coupling thermal– metallurgical analysis in welding. 4. FE simulation model Coupling thermal–metallurgical analysis for welded joints of S355J2 steel plate was performed to validate the numerical modeling procedure proposed in this paper. The predicted thermal cycles and phase transformation behavior were compared with experimental data and results from standard software in the literatures [15–17] because the same type of welded joint was discussed in these papers for different conclusions. The geometric structure of the FE model is given in Fig. 3. As the figure shows that a fine mesh was employed in region of the FZ, HAZ and their vicinity, because a severe temperature gradient and mechanical behavior differences are present in this area. While a coarse mesh was applied for other area of the base plate due to the relatively lower effect of the thermal cycle in the welding process. The established mesh model satisfied the requirements for precision and efficiency in calculation as much as possible. The plate dimensions for the welding simulation model were 300 mm length, 200 mm width and 5 mm thickness as depicted in this figure. The detailed geometry of the welding joint, with 60° angle of V-groove shape, is presented in Fig. 3(a). A single-pass complete-penetration gas metal arc weld (GMAW) was conducted in the welding simulation in accordance with DIN EN ISO 14,341. In addition, the welding conditions were a 261 A welding current, a 30.4 V average arc voltage and a 0.4 m/min travel speed. S355J2 structural steel was applied for welding metallurgy analysis. The chemical components of this material, according to the codes in Europe [24], are listed in Table 1. The yield stress is

Fig. 4. Continuous cooling transformation diagram of S355J2 structural steel (A: austenite, F: ferrite, P: pearlite, B: bainite, M: martensite).

355 MPa, and the thermal and mechanical properties of the material were detailed in cited reference [25], such as specific heat, conductivity, elasticity modulus and density. Temperature-dependent material properties were defined in the welding simulation. The CCT diagram of S355J2 steel, implemented in SYSWELD, provided the metallurgical transformation law in heat treating [26]. The metallurgical parameters for the Leblond model were obtained from CCT diagram of S355J2 steel to predict the phase transformation behavior in the cooling process. The CCT diagram was rebuilt by the Leblond model to reflect the relationships among the phase fraction, temperature, cooling time and cooling conditions in transformation law as much as possible (Fig. 4). Fig. 4 shows the phase evolution law of S355J2 steel under different cooling conditions. The main products of the phase transformation are ferrite, pearlite, bainite, and martensite, and the transformation process is strongly dependent on the cooling conditions, which determine the new phase. Greater proportions of ferrite and pearlite may appear at higher cooling rate, and more martensite is produced under the lower cooling condition. The phase transformation law of S355J2 steel depicted in Fig. 4 was implemented in the metallurgy analysis subroutine. The phase fraction of S355J2 steel can be calculated in procedure by

Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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Fig. 5. Thermal cycles at different locations on the surface of the simulated model.

Table 2 Latent heat of phase transformation [27]. Phase transformation

x104 (J/kg)

Austenite to ferrite-pearlite Austenite to bainite Austenite to martensite

8–9 11 11

the Leblond mathematical model, which considers the combined effect of temperature and cooling time. The analysis of heat transfer in the welding simulation is of significance due to its dominant effect on the microstructural and mechanical fields. The internal heat generation caused by phase transformation affects the temperature distribution in welding. The consideration of the phase transformation latent heat improves the prediction of the thermal cycle in the welding analysis. The enthalpy of each phase in the transformation is detailed in Table 2 and was applied in the coupling analysis to calculate the internal heat generation. 5. Results and discussion 5.1. Results of the thermal cycle analysis The simulation results of the non-uniform temperature field in welding are discussed in this section. Since the thermal cycle load leads to complex phenomena in the microstructural development and mechanical behavior, heat transfer analysis is fundamental in analysis of welding metallurgy. The conclusions are primarily presented here for the transient thermal cycle associated with the welding of S355J2 steel plate joints. Fig. 5 exhibits the comparison of the thermal cycles at different locations on the surface of the weld region. The temperature history on the top surface of the plate is displayed in Fig. 5(a). The curves show the thermal cycles at locations which are 8.4 mm, 9.0 mm and 9.5 mm from the weld centerline. For the bottom surface, the selected positions are 4.1 mm, 5.4 mm and 7.3 mm from the weld centerline, as shown in Fig. 5(b). It can be observed that the maximum temperature is obtained while the weld heat source is closest to the selected locations, and the peak temperature decreases with the increasing distance from the weld centerline. The conclusions of the thermal cycles reflect the non-uniform temperature field results from the transient thermal process in welding.

The effects of the weld thermal process are mainly observed in the FZ and HAZ. Therefore, the conclusion can be deduced that base material in the region far from the weld pool shows almost no changes since the influence of the temperature is weak. The relevant experimental work was reported in the literature [15]. Its measurement data are superimposed in Fig. 5 with mark symbols to validate the simulation. It can be seen that the overall trends between the simulated results and the experimental data coincide well. The agreement verified the conclusions of the welding simulation in this case. In addition, the measurement data of the peak temperature at specific locations were detailed in Ref. [15]. The simulated results at selected positions close to the measured points in the cited paper are listed in Table 3. The average time to cool from 850 °C to 700 °C was calculated as representative of t 8/5 in this case. The comparison in the table shows good agreement between the peak temperature in the simulated model and the experimental work. The temperature cooling time is close to the cited results from related research. Since the mesh size applied in the model and the severe temperature gradients in this area, there is some disagreement in the results for the bottom surface of the plate. The size parameters of the heat source model may require further consideration to obtain more accurate predictions in the temperature field. However, the overall results coincide with the cited results, which demonstrates that established welding simulation model is reasonable. As the figure (Fig. 5) shows that different locations are subjected to thermal cycle loads in welding with different peak temperatures and cooling times. Full austenite transformation may occur while the peak temperature is higher than Ac3 . No transformation occurs when the peak temperature is lower than Ac1 . In addition, partial transformation may be observed at temperatures between the threshold temperatures. It can be deduced that nonuniform phase evolution may arise in the FZ and HAZ of weld joints due to the influence of the peak temperature and cooling time in welding. 5.2. Prediction analysis of the phase transformation As mentioned above, the phase evolution laws vary significantly during the heating and cooling processes due to the influence of the temperature and cooling time. Metallurgical phenomena are complex due to the non-uniform transient thermal process in welding. The numerical analysis of welding metallurgy is

Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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Table 3 Comparison of the calculated results and measured thermal cycles. selected location

distance from the weld centerline (mm) simulated/measured [15]

peak temperature (°C) simulated/measured [15]

t8/5 (s) calculated/cited [15]

top of plate

8.44 9.01 9.58 4.15 5.42 7.31

941 953 889 795 844 765 1521 1159 1311 1007 1060 937

31.3 31.4 37.8 42.4 37.5 32.9

bottom of plate

8.4 8.9 9.1 3.9 4.9 6.8

32 36 39 30 30 30

Fig. 6. Simulated phase fraction of bainite at plate midsection.

Table 4 Comparison of calculated final phase fraction and cited results of S355J2 steel while t8/5 = 28 s. CCT diagram

Ferrite + pearlite (%)

bainite (%)

martensite (%)

Simulated Sysweld[ 16 ] Gleeble[ 16 ]

6.04 0.2 6.7

93.96 96 91

0.0 3.4 2.3

presented in this section for the precise prediction of the phase fraction. Based on the CCT diagram of S355J2 steel implemented in the proposed procedure, the phase transformation behavior was analyzed by a numerical welding model subjected to the applied welding parameters, such as welding sequence, travel speed, and arc current. The result concludes that the majority phase in the FZ and HAZ is bainite (Fig. 6). The phase percentage is greater than 93%, while the calculated result from SYSWELD indicates 96.3% for bainite in this area [16]. As the figure shows that similar metallurgical behavior occurs in the FZ and its vicinity because of the major phase proportion in this area. In addition, the length of the HAZ is approximately 10 mm. The predicted result agrees with the conclusions from the standard software in Ref. [16], which further confirms the reasonability of the proposed procedure in this paper. It can be seen from the figure that the proportion of bainite in the HAZ decreases with respect to the distance from the weld centerline. In addition, no phase transformation occurs outside of the HAZ region for the weak temperature effect. Partial phase transformations were observed in the transition region. A proportion of the parent phase was transformed into austenite in heating, and then decomposed to martensite, bainite, ferrite or pearlite during cooling. The complicated distribution of new phases reflected the microstructural evolution law in welding because of the non-uniform temperature field and cooling time. This result is also confirmed by a number of previous experimental works on material microstructure in the HAZ. The developed procedure is therefore applicable to the numerical analysis of welding metallurgy.

Fig. 7. Phase transformation history while t8/5 = 28s (A: austenite, F: ferrite, P: pearlite, B: bainite, M: martensite). Table 5 Comparison of calculated final phase fraction and other results of CCT diagram of S355J2 while t8/5 = 5 s. CCT diagram

Ferrite + pearlite (%)

bainite (%)

martensite (%)

Simulated Sysweld[ 17 ]

0.0 0.0

47.3 47

52.7 53

Further discussion of the simulated results is detailed in Table 4 to verify the method . According to the developed subroutine “LEBM”, the new phase fraction can be calculated under any cooling conditions. The major phase is martensite while the cooling rate is higher than 150 K/s. And bainite is predicted to start forming at cooling rates less than 150 K/s. Ferrite-Pearlite is predicted for cooling rates lower than 11 K/s. A detailed comparison of the simulated data and results from the standard software is presented in Table 4. The cited results were detailed in Ref. [16] and were obtained by SYSWELD and the Gleeble weld thermal simulator. For a cooling time t8/5 = 28 s, the simulated results showed 93.96% bainite and 6.04% ferrite and pearlite. The SYSWELD database predicted 96% bainite, 0.2% ferrite and pearlite, and 3.4% martensite. The Gleeble data prodicts 91% bainite, 6.7% ferrite and pearlite, and 2.3% martensite. The comparison in Table 4 shows that the simulated data is agreement with the results from the standard software for the phase prediction of S355J2 steel. Based on the established the CCT diagram of S355J2 steel and the Leblond model, a program was developed to predict the kinetics of the phase transformation history under specific cooling conditions. Fig. 7 shows the phase evolution history for a cooling time of t8/5 = 28 s as mentioned above. For a cooling time of t8/5 = 5 s, the transformation behavior from austenite to new phases is depicted in Fig. 8. The new phase is 47.3% bainite and 53.7% martensite. The results from SYSWELD for S355J2 steel are provided in Table 5 to compare with the simulated data.

Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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Fig. 8. Phase transformation history while t8/5 = 5s (A: austenite, F: ferrite, P: pearlite, B: bainite, M: martensite).

for better understanding of the coupling thermal–metallurgical behavior. To improve the efficiency of the calculation, a smaller numerical model was employed here. The geometric size of the FE model is 100 mm × 50 mm × 5 mm. The thermal cycle at location where 5.98 mm away from the weld centerline is presented in Fig. 9. The solid curve represents the temperature history at the selected location considering the influence of the transformation latent heat. The dashed curve represents the performance of the thermal cycle at the same position while the latent heat of the phase transformation is omitted from simulation model. It can be deduced that the transformation latent heat results in the differential temperature field in the welding simulation. The consideration of latent heat contributes to the prediction of the temperature distribution in welding. Fig. 10 displayed the phase distributions of bainite and ferritepearlite. The major phase in the FZ and HAZ is bainite. As a parent phase, the ferrite-pearlite in the FZ and HAZ decreases due to the metallurgical transformation in this area. Although the geometric size of the FE model is changed, the phase transformation distribution does not change significantly because the same welding parameters were applied in this case. The phase prediction agrees with the above results. It can be observed that the impact of the latent heat of metallurgical transformation in the solid state on the temperature field is measurable. Since the dominant effect of the temperature field on the metallurgical and mechanical behavior, it is important to consider the latent heat of the phase transformation in the heat transfer analysis in welding. The procedure proposed in this paper contributes to the analysis of coupling thermal–metallurgical phenomena. It is fundamental to the comprehensive understanding of welding joints. 6. Conclusions

Fig. 9. Temperature history under the influence of latent heat at select location (distance from the weld centerline is 5.98 mm).

5.3. Effect of latent heat The internal heat generation is accompanied with the process of phase transformation in welding. The effect of the transformation latent heat on the temperature field is discussed in this section

In this study, a coupling thermal–metallurgical analysis procedure by FE software and its included user subroutines, such as “DFLUX”, “FILM”, “USDFLD” and “HETVAL”, is proposed. Metallurgical analysis code source “LEBM” was developed according the Leblond model and the CCT diagram of S355J2 steel. The applied method is verified by simulation model of the welding process of a plate joint. The methods is reasonable and applicable for the analysis of welding metallurgy. Since some fundamental differences between the welding process and heat treating, the proposed procedure contributes to the progress of welding metallurgy analysis. The developed method predicts the proportion of each possible new phase in welding. It

Fig. 10. The phase distribution while the latent heat is taken into consideration.

Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011

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is unnecessary to predefine a specific transformation law based on the kinetics model and temperature. The phase evolution behavior is prior unknown and changes with the applied welding parameters in proposed method. Each possible phase fraction can be predicted according to the current temperature and cooling conditions appeared in welding. A numerical plate welding joint was studied using the proposed method in this paper. The simulated results were compared with the related experimental work and the data from standard software to verify the applied method. Unlike the general heat treatment, a non-uniform temperature field and phase transformation phenomena were predicted in the welding area, especially in the FZ and HAZ. The components and proportions of the new phases are different respectively in the HAZ. The conclusions provide more comprehensive knowledge about the microstructural behavior of material in the HAZ. The latent heat of the phase transformation was implemented in the developed method to perform the coupling thermal– metallurgical analysis. The influence of the internal heat of the phase transformation is considerable and should be included in the analysis to obtain more accurate predictions of the temperature field in welding. Acknowledgments The research was supported by National Natural Science Foundation of China (51578137, 51438002, 51108075), Open Research Fund Program of Jiangsu Key Laboratory of Engineering Mechanics (LEM16A10) and A Project Funded by the Priority Academic Program Development of the Jiangsu Higher Education Institutions, (CE02-1/2-0×) and A Science and Technology Project of Ministry of Housing and Urban-Rural Development (2010-K2-7). References [1] Kou S. Welding metallurgy. New Jersey: John Wiley & Sons, Inc.; 2003. p. 393–5. [2] Lindgren LE. Numerical modeling of welding. Comput Methods Appl Mech Eng 2006;195 6710–36. [3] Deng D, Murakawa H. Prediction of welding residual stress in multi-pass buttwelded modified 9Cr–1Mo steel pipe considering phase transformation effects. Comput Mater Sci 2006;37 209–19. [4] Lee C, Chang K. Prediction of residual stresses in high strength carbon steel pipe weld considering solid-state phase transformation effects. Comput Struct 2011;89 256–65. [5] Song KJ, Wei YH, Dong ZB, Ma R, Zhan XH, Zheng WJ, et al. Constitutive model coupled with mechanical effect of volume change and transformation induced plasticity during solid phase transformation for TA15 alloy welding. Appl Math Model 2015;39 2064–80. [6] Fang JX, Dong SY, Wang YJ, Xu BS, Zhang ZH, Xia D, et al. The effects of solidstate phase transformation upon stress evolution in laser metal powder deposition. Mater Des 2015;87 807–14.

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Please cite this article as: J. Xia, H. Jin, Numerical modeling of coupling thermal–metallurgical transformation phenomena of structural steel in the welding process, Advances in Engineering Software (2017), http://dx.doi.org/10.1016/j.advengsoft.2017.08.011