Analysis of grain grow th in hybrid weld HAZ based on the coupled thermo-fluid model

Zhang Zhuanzhuan and Wu Chuansong张转转，武传松*



Analysis of grain grow th in hybrid weld HAZ based on the coupled thermo-fluid model

Zhang Zhuanzhuan and Wu Chuansong
张转转，武传松*

Accurate calculation of thermal cycles isa prerequisite tomodel grain growth in the heat-affected zone（HAZ）.To improve the computation precision of thermal field and HAZ geometry，a coupled model of heat transfer and fluid flow is developed for laser+GMAW-P hybrid welding of TCS stainless steel.Utilizing computed temperature fields from the coupled model，the evolution of grain structure in the HAZ of TCS stainless steel in hybrid welding is numerically simulated by using a three dimensional Monte Carlo model.Simulation results show thatmore accurate HAZ grain structure can be obtained based on the coupled model of fluid flow and heat transfer，and the computed grain size distribution agrees well with the corresponding experimental results.

grain growth，HAZ，hybrid welding，numerical analysis

0　Introduction

TCS stainless steel，made by Chinese steel companies，is a new type of ferritic stainless steel used inmanufacturing railway wagons［1］.However，rapid grain growth will occur in heat-affected zone（HAZ）when TCS stainless steel iswelded，which results in large deterioration in plasticity and toughness.This would seriously reduce the mechanical property of weld joints under the dynamic load，and even hardly satisfies the application requirements［2］.Thus，awelding processwith high energy density should be used to reduce HAZ width and the grain size in HAZ of TCS steel welds.Various kinds of traditional welding processes cannot completely meet the quality requirement of welding TCS stainless steel［1，3］.As an advanced welding process，laser+pulsed gasmetal arc hybrid welding，combining advantages of laser welding and pulsed gasmetal arc welding（GMAW-P），is characterized with high welding speed，low heat input，narrow HAZ，deep weld penetration and high process stability［4］. Thus，it has significant potential to solve the challenging problems of welding TCS stainless steel.But it is still uncertain of the influence mechanism of hybrid heat source on dimension of HAZ and grain growth in HAZ.

Until now，considerable researches have been carried out on numerical simulation of the grain growth in HAZ by using the Monte Carlo（MC）model in combination with thermal analysis［5-8］.However，these investigationsmostly focus on the HAZmicrostructure of titanium alloys and austenite steels under typical welding process，such as GTAW.Although Zhang et al.［9］has given comprehensive experimental and theoretical investigations to understand the grain growth in HAZ of TCS stainless steel during the laser+GMAW-P hybrid welding，the temperature field used to predict the grain growth was calculated from the solution of the heat conduction equation that could result in the important deficiency in the numerical analysis of HAZ grain structure［5］.In order to improve the accuracy of the numerical computation of HAZ microstructure for hybrid welding of TCS stainless steel，it is essential to develop the HAZmicrostructure model based on the thermofluid model，i.e.，the temperature profiles should be determined by a coupled model of fluid flow and heat transfer.

In this study，a 3D coupled model of heat transferand fluid flow is firstly developed for laser+GMAW-P hybrid welding of TCS stainless steel to acquiremore accurate temperature field.Base on themore accurately calculated HAZgeometry and thermal cycles，the MCmethod is used to conduct the analysis of the grain growth in hybrid weld HAZ of TCS stainless steel.At last，the validity of the numericalmodel is confirmed by comparing the simulation resultswith the corresponding experimental data.

1　Coupled thermo-fluid model

1.1Conservation equations

The fluid flow and heat transfer in hybrid welding of TCS stainless steel aremodeled by using the continuum equations of energy，momentum and mass conservation，which are given as follows［说10-11］：

Energy conservation：

Momentum conservation：

Mass conservation：

Fig.1 Physicalmodel of hybrid welding process

1.2Boundary conditions

The calculation domain is depicted in Fig.1，and the corresponding boundary conditions are expressed as follows：

On the top surface of the workpiece

where⇀n is the normal unit vector to top surface，q（r）is

tathe heat input from the arc，qcon，qradare heat loss fromconvection and radiation respectively，V⇀tis the velocity vectorof top surface，tx，

tyare tangential unit vectors of

top surface parallel to the xz and yz plane，respectively，∂γ/∂T is the temperature gradient of surface tension，σis the Stefan-Boltzmann constant，αcris the heat transfer coefficient，T0is the ambient temperature.

Keyhole surface

where Tevpis the boiling temperature.This represents that the keyhole surface is at the boiling temperature.

Inlet and outlet

where u0is the welding velocity that represents themovement of the workpiece relative to the hybrid heat source.

Other surfaces

1.3Heat source model

In laser+GMAW-P hybrid welding，heat input comes from laser beam，arc heat and droplet heat content. To reflect the characteristics of each heat source，a combined volumetric heat source model was proposed in this paper to take into account the heating effect for the energy equation.The temperature of keyhole surface is set to the evaporation temperature that means the temperature of keyhole ismaintained at the boiling point by balancing laser beam energy with the heat absorbed by workpiece and the evaporation heat loss.A Gaussian density function is used to dealwith the heat input from the arc and a hemispheroid with uniformly distributed heat density represents the droplet enthalpy，and they are given as follows：

whereηis the arc efficiency，U and I are the effective arc voltage and welding current，rais the heat distribution parameter，rwis thewire radius，ρwis the density of the electrode wire，uwis the wire feeding speed，rdis the droplet radius，fdis the drop generation rate，Hvis the average heat content of the weld pool，and Hdris the droplet heat content.

1.4 Numerical simulation

Due to the symmetry with respect to the weld center line，half of the workpiece was selected as the computational domain，which was of a size of75mm in length，20 mm in width and 6 mm in height.A non-uniform structured mesh system was adopted with finer grids near the heat source and coarser ones far away from it.To perform the analysis of the thermal process in hybrid welding of TCS steel，the commercial CFD solver Fluent was employed to solve the governing equations and their boundary conditions.

The study case is with following test conditions：the average values of arc voltage and current are 20.3 V and 114 A；thewire diameter is1.2mm；laser power is2 kW；the welding speed is0.8m/min.During the hybrid welding experiments，the laser is leading and normally acts on the workpiece，the arc is tilted backwards by 30°relative to the laser head，and the separation distance between laser focal pointand arc electrode is 2mm.

2　Grain growthmodel for hybrid weld HAZ of TCS steel

Based on the calculated HAZ shape and size and thermal cycles，three dimensional Monte Carlo method isemployed to develop the HAZ grain growth model for hybrid welding of TCS stainless steel，and the evolution of grain structure in hybrid weld HAZ of TCS stainless steel is numerically simulated.Detailed description of themodel can be referred to literature［9］.The dimension of the solution domain used in MC simulation is 0.7 mm×4.6 mm×5.0mm in consideration of hybrid weld HAZ geometry and computing time，and it is discretized into uniform grid with grid spacing of 10μm.The grid spacing is set to the actual initialmean grain size.The total number of the grain orientations used in the present calculation is taken to be 65 since the grain growth exponent becomes almost independent of it［12］.

3　Simulation results

Fig.2 demonstrates the three-dimensional temperature field and fluid flow in weld poolwith a keyhole.It can be seen that the temperature contours in hybrid welding are compressed in front of the weld pool and spread out at the rear of it.Besides，the fluid flow field is clearly displayed.At the top surface near the keyhole wall，the flow is outward to the weld pool edge，and then to the weld pool rear，and finally is reversed toward to the keyhole.In the region below the top surface the molten metal flows downward along the keyhole wall，and then towards the weld pool rear and boundary.

Fig.2 Three dimensional tem perature field of TCS stainless steel in hybrid welding

Fig.3 shows the simulated finalmicrostructure of the hybrid weld HAZ for TCS steel.As expected，the grain size is coarser at the site near the fusion line.Largest grain size is observed in the region slightly below the top surface.Furthermore，it can be seen that grain growth near the top surface of the HAZ ismuch more significant than that near the bottom of weld pool.The grain size is dependent on the thermal history，and the temperature near the top surface is higher than at the bottom of the weldment due to the feature of heating action in hybrid welding.

Fig.3 3D map of grain structure of HAZ

The accurate numerical simulation of HAZ grain structure requires a temperature field with high calculation accuracy.Therefore，the more accurate thermal cycles and HAZ shape and size calculated by the coupled model are applied to the numerical analysis of the grain growth in hybrid weld HAZ of TCS stainless steel，and it is compared with the corresponding experimental data and the simulation results based on the pure thermal conduction model in Fig.4.It can be observed that the 2D map of grain structure distribution and the widths of the coarse grained HAZ（CGHAZ）in Fig.4b are in better agreement with the experimental ones，but the location of the widest CGHAZ near the point P in Fig.4c is closer to the top surface than that around the point m.Besides，the mean grain size and CGHAZ width below the point P are smaller compared with the experiment results.These results indicate that more accurate HAZ grain structure can be ob-tained if the coupled model of fluid flow and heat transfer is employed.

To verify the predicted results，the variation of the mean grain size with distance from the fusion line along line AB is plotted in Fig.5.The predicted mean grain sizes based on the data calculated by two different models are compared with themeasurements.Although the calculated results for two differentmodels bothmatch the experimental data，those based on the coupled model of fluid flow and heat transfer are in better agreement with the measured ones，especially in the transition zone between the CGHAZ and the fine grain region.

Fig.4 Com parison between experim entally measured and simulated HAZ Microstructure

Fig.5 Com parison between experim ental data and predicted mean grain size based on two different thermalmodels

4　Conclusions

A three-dimensionalmodel is established to simulate the heat transfer and fluid flow in laser+GMAW-P hybrid welding of TCS stainless steel.The temperature field，thermal cycles and HAZ geometry are calculated.On the base of the calculated HAZ shape and size and thermal cycles，three dimensional Monte Carlo approach is used to develop the HAZ grain growth model for hybrid welding of TCS stainless steel，and the evolution of grain structure in hybrid weld HAZ of TCS stainless steel is numerically simulated.Simulation results show that microstructure features of coarse and fine grain region in HAZ based on the heat and fluid flow model are much closer to the experimental ones in contrastwith the predicted results based on the pure heat conduction model.

Acknow ledgement

The authors are grateful to the financial support for this project from Shandong Province Natural Science Foundation（ZR2014EL025）and the Open Research Fund of Provincial Key Lab of Advanced Welding Technology at Jiangsu University of Science and Technology.

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*Zhang Zhuanzhuan，School of Construction Machinery，Shandong Jiaotong University，Jinan，250023. Wu Chuansong，MOE Key Laboratory for Liquid-Solid Structural Evolution and Materials Processing，and Institute of Materials Joining，Shandong University，Jinan，250061. Wu Chuansong，Corresponding author，E-mail：wucs@sdu.edu.cn