MODELLING & SIMULATION OF LASER MATERIAL PROCESSING: PREDICTING MELT POOL GEOMETRY AND TEMPERATURE DISTRIBUTION

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1 Proceeding of International Conference MS 07, India, December 3-5, MODELLING & SIMULATION OF LASER MATERIAL PROCESSING: PREDICTING MELT POOL GEOMETRY AND TEMPERATURE DISTRIBUTION M. A Sheikh Laser Processing Research Centre, School of Mechanical, Aerospace & Civil Engineering, The University of Manchester, Manchester, M60 1QD, UK m.sheikh@manchester.ac.uk Abstract This paper presents the enhanced thermal conductivity approach for modelling of laser melting processes. Here, Finite Volume Method (FVM) has been used to simulate the transient effects of a moving laser beam in the melting of mild steel (EN- 43A). Experimental melt pool geometry has been compared with CFD model and enhanced thermal conductivity model. Key words Enhanced Thermal Conductivity Approach, Finite Volume Method, Laser Material Processing, Melt Pool Geometry. M I. INTRODUCTION any laser manufacturing processes involve laser melting of material e.g. selective laser melting, welding, brazing, soldering, glazing, surface alloying, cladding etc. Modelling of these processes is extremely important for controlling these processes by predicting the melt pool geometry, thermal gradients, cooling rate, microstructure, and stress distribution etc. However, modelling of processes involving laser melting is not straightforward due to Marangoni and buoyancy convection within the melt pool. It is well established that heat transfer in melt pool is influenced more by fluid flow than by heat conduction [1]. Fluid flow within the melt pool is dominated by thermocapillary or Marangoni forces and hence conduction based models are not able to accurately predict the laser melting process, particularly in metals [1]. Thus any modelling attempt to investigate the effects of beam geometries on laser melting of metals should take into account melt pool convection due to thermo-capillary and buoyancy forces. Detailed CFD models are therefore required to accurately predict the melt pool geometry and temperature distribution. CFD modelling of melting processes require considerable expertise and computational resources. CFD models are also prone to errors due to uncertainties in the values of surface tension co-efficient and viscosity of material in the fluid state [2]. Model agreement can be improved by adjusting the values of surface tension coefficient and viscosity but to reach the correct figure, a sizeable computational effort is required. To simplify and speed up the modelling process, many researchers have used the enhanced thermal conductivity approach to account for melt pool convection. Here, instead of solving the intricate Navier-Stokes equations, only the energy equation is solved by enhancing the thermal conductivity beyond the melting temperature, to predict the melt pool geometry and temperature distribution. This approach has been used in the past for modelling laser cladding, laser welding [3-5] etc. However, researchers have used the values of enhanced thermal conductivity from literature which range from 2 times the original values to 420 times [3-5]. Due to this large bandwidth it is difficult to pick an accurate value from the available literature. Moreover, even if careful selection is made by looking at the materials and processing conditions, it is not known whether it would give the desired matching between the experimental and the predicted melt pool profile and temperature distribution. Thus there is a need to study the enhanced thermal conductivity approach and see its effectiveness.

2 Proceeding of International Conference MS 07, India, December 3-5, This paper presents an analysis of the enhanced thermal conductivity approach for modelling laser melting processes. A finite volume model is constructed using a commercial software FLUENT to simulate the transient effects of a moving beam for laser melting of mild steel (EN-43A). Melt pool convection induced due to the Marangoni and buoyancy forces is taken into account in the CFD model, whereas enhanced thermal conductivity approach is used for the conduction model. Experimental melt pool geometry is compared with the CFD model and the enhanced thermal conductivity model to demonstrate the effectiveness of enhanced thermal conductivity approach. II. FINITE VOLUME MODEL A 3D finite-volume model, based on the Reynolds Averaged Navier Stokes Equations and the Enthalpy-Porosity technique was set-up in FLUENT for modelling of the laser melting process. The laser beam was input as surface heat flux. An area sector approach [6] was used to simulate the moving laser beam instead of a moving wall approach. Necessary subroutines were added to handle the spatially varying heat flux to simulate the moving laser beam. For the normal heat transfer and enhanced thermal conductivity approach same model was used but only the energy equation was solved. In the enhanced thermal conductivity model, thermal condcutivity values were enhanced by three to four times their original values. The enhancement in thermal conductivity k is defined by (1) as: k = α k (1) where k is the normal thermal conductivity value at the corresponding temeprature and α is the enhancement factor which is defined as: 1 if T< Tliquidus & T α = multiplying factor if T > T liquidus solidus where T liquidus is the temperature at which solid formation begins and T solidus is the temperature at which full solidification occurs. Energy conservation equation for the complete single domain in enthalpy-porosity technique is written in terms of enthalpy and temperature, as in (2), [7]: t r ( ρh) +.( ρυh) =. ( k T) + S% (2) where H is enthalpy, ρ is density, υ r is the fluid velocity and S % is the surface heat source. For enahnced thermal conductivity model k is replaced by k in (2). Enthalpy of material is computed as the sum of sensible enthalpy (h) and latent heat ( H), as in (3). H = h+ H (3) where T = ref + Tref h h C dt h ref p = Reference enthalpy T ref = Reference temperature C p = Specific heat at constant pressure Latent heat content ( H) can be written in terms of latent heat of the material, as in (4) [7]: H = β L (4) where β is the liquid fraction, which is defined as: 0 if T< Tsolidus T Tsolidus β = if Tsolidus <Τ < T Tliquidus Tsolidus 1 if T > Tliquidus liquidus Thermocapillary or Marangoni convection is treated as shear stress applied at wall. Shear stress applied at the wall is given by (5), [7]: dσ τ = st (5) dt where τ is the shear stress, dσ dt is the surface tension gradient with respect to temperature and T is the surface s gradient. Shear stress given by (5) is then applied to momentum equations. The governing equations are finally solved simultaneously using a segregated solver and employing SIMPLE algorithm to obtain temperature and velocity fields. Because of the complexity of the model simplifying assumptions have been made which are:

3 Proceeding of International Conference MS 07, India, December 3-5, Liquid metal flow within the melt pool is Newtonian, incompressible and laminar. 2. As the power density is low and there is no external gas pressure, the free surface is assumed planar. Similar laser processes involving melting, have been modelled in the past with the assumption of planar free surface with reasonable accuracy. 3. Radiation effects are neglected maximum surface temperature was recorded. Figure 1 shows the schematic arrangement of experimental set-up. A circular laser beam with a diameter of 3.34 mm was used for the model. The power distribution of fiber optic coupled high power diode laser was close to top-hat; therefore a uniform power distribution was used in the model. The power density was set at 5.5kW/cm 2 and the processing of a single surface track length of 20 mm was modelled. The scanning speed of laser was set at 5 mm/s. The material used was bright drawn mild steel EN-43A ( wt % C, wt % Si, wt% Mn, wt %S, wt % P), as supplied (average hardness of 220 HV). The size of the work piece was (mm 3 ). The ambient temperature was set at 20 C. Temperature dependent material properties were used for the model [8, 9]. III. EXPERIMENTAL SET-UP The laser source used was a 1.5 kw fiber coupled high power diode laser (LDL ) operating in the range of nm, with a top hat (approximately uniform) power distribution and a circular laser spot. The sample was sand blasted to improve the absorptivity of the laser beam. Ocean Optics SD 2000 fibre optic spectrometer was used to measure the reflectivity of the investigated material (EN-43A) at the abovementioned laser wavelengths. It was found to be between % at room temperature. A CNC table was used to move the material under the laser beam, and the table velocity was set at 5 mm/sec. The input power was adjusted according to the material absorptivity and fiber coupling in order to maintain the power density at 5.5kW/cm 2. A single colour Impac Pyrometer, requiring input of material emissivity, was used for temperature measurement in this study. The upper limit of pyrometer was 2000 C (2273 K) while the lower limit was 250 C (523 K). The temperature sensitivity at the lower limit was poor. Emissivity of material increases significantly close to melting temperature due to changing surface conditions and oxidation. Emissivity of molten mild steel of 0.50 (taken from literature) was therefore supplied as input to the pyrometer for accurate measurement of surface temperature. The temperatures recorded by the pyrometer below the melting temperature were therefore inaccurate and were not considered; only Fig 1. Schematic representation of the experimental set-up IV. RESULTS & DISCUSSION To analyse the effects of enhanced thermal conductivity approach for predicting the melt pool geometry and the temperature distribution, a comprehensive post-processing analysis was carried out on all the four models (i.e. CFD, heat transfer and two enhanced thermal conductivity models). The global co-ordinate system for the model was in the middle and on the top of the work-piece. Three orthogonal paths were created namely Along ( path along the scanning direction), Cross-sec and Depth for the purpose of analysis. A liquidus line has been superimposed on all the graphs to quickly see the temeprature distribution above the melting temeprature. the melt zone. Some of the results have also been compared with the experimental results. Fig 2 shows the temperature distribution on the Along path. Melt pool length can be estimated by looking at the temperature distribution above the liquidus line. It can be seen that the melt pool length predicted by all the four models is approximately similar. The maximum temperature predicted by the normal heat transfer model (Circle HT 1) is 2615 K, whereas the maximum temperature predicted by the CFD model (Circle conv) is 1946 K which is much closer to the experimentally measured temperature of 1992 K. The enhanced thermal conductivity models predict a temperature in between the CFD and the heat transfer model. The maximum temperature predicted by the four times model is 2069 K, which is less than the maximum temperature predicted by the three times model (i.e K) is mainly due to the increased heat diffusion above the liquidus temperature. Although the maximum temperature predicted by the enhanced thermal conductivity models is less than the normal heat transfer model, nevertheless the temperature profile

4 Proceeding of International Conference MS 07, India, December 3-5, remains similar to the normal heat transfer model. transfer model and the enhanced thermal conductivity models) remains the same. The only effect of increased thermal conductivity is that it clips the maximum surface temperature due to the increased heat diffusion. Thus it can be said that the enhanced thermal conductivity model is not able accurately to predict the melt pool depth. Fig 2. Temp vs distance on the Along path Fig 3 shows the temperature distribution on the Cross-sec path. Melt pool width can be estimated by examining the temperature distribution above the liquidus line. It can be seen that the melt pool width predicted by all the models is approximately similar. Fig 4. Temp vs distance on the Depth path Fig 5 compares the experimental melt pool profile and the cross-sectional melt pool profiles predicted by the CFD, heat transfer, and enhanced thermal conductivity models. It can be seen that the experimental pool profile is flatter and is in better agreement with the CFD model. The melt pool profile predicted by the normal heat transfer model and the enhanced thermal conductivity models is having a meniscus profile. Accurate prediction of melt pool profile is very important as the solidification microstructure would exist within the melt pool. Moreover the orientation of solidification microstructure is dictated by the melt pool profile. Thus if the predicted melt pool profile is not accurate the predicted orientation of the solidification microstructure will also be inaccurate. Fig 3. Temp vs distance on the Cross-sec path From Figures 2 and 3, it can be suggested that if the enhanced thermal conductivity value is further increased, the maximum surface temperature will approach that predicted by the experiments and the CFD model. Fig 4 shows the temperature distribution on the Depth path. Melt pool depth can be estimated by looking at the temperature distribution above the liquidus line. Unlike the Along and the Cross-sec paths, the melt pool depth predicted by the CFD model and the heat transfer models is significantly different. The melt pool depth predicted by the heat transfer and the enhanced thermal conductivity models is approximately five times higher as predicted by the fluid flow model (Table 1). This shows that increasing the thermal conductivity does not change the melt pool depth. This is mainly due to the energy balance. The melt pool volume predicted by the heat transfer models (.i.e. the normal heat Fig 5. Comparison of melt pool profiles

5 Proceeding of International Conference MS 07, India, December 3-5, Model Max Temp (K) Width (mm) Depth (mm) Experiment Results CFD Model Heat Transfer Model Enhanced thermal Conductivity model 3 Enhanced thermal Conductivity model Table 1. Comparison of experimental and modelling results V. CONCLUSIONS Modelling of laser manufacturing processes involving laser melting is extremely important for controlling and optimising these processes. However, modelling of these processes is not straightforward due to Marangoni and buoyancy convection within the melt pool. Detailed CFD models are required to accurately predict the melt-pool geometry and temperature distribution. CFD modelling of melting processes require greater user expertise and longer computational times. To simplify and speed up the modelling process, many researchers have used the enhanced thermal conductivity approach to account for melt pool convection. Instead of solving the intricate Navier-Stokes equations, only the energy equation is solved by enhancing the thermal conductivity beyond the melting temperature, to predict the melt pool geometry and temperature distribution. However, researchers have used the values of enhanced thermal conductivity from the available literature without any validation. Moreover, it is not esatblished whether the enhanced thermal conductivity is able to accurately predict the melt pool geometry and temperature distribution. The work presented in this paper has investigated the enahnced thermal conductivity approach to artificially simulate the fluid flow within the melt pool. A CFD model, a normal heat transfer model, and two enhanced thermal conductivity models have been developed using finite volume method. REFERENCES [1] Mills, K. C., Keene, B. J., Brooks, R. F., and Shirali, A., 1998, "Marangoni Effects in Welding," in The Royal Society, pp [2] Eustathopoulos, N., Dervet, B., and Ricci, E., 1998, "Temperature Coefficient of Surface Tension for Pure Liquid Metals," Journal of Crystal Growth, vol. 191, pp [3] Toyserkani, E., Khajepour, A., and Corbin, S., 2004, "3-D Finite Element Modeling of Laser Cladding by Powder Injection: Effects of Pulse Shaping on the Process," Optics and Laser in Engineering, vol. 41, pp [4] Zhang, W., Kim, C.-H., and DebRoy, T., 2004, "Heat and Fluid Flow in Complex Joints During Gas Metal Arc Welding-Part Ii: Application to Fillet Welding of Mild Steel," Journal of Applied Physics, vol. 95, pp [5] Kim, C.-H., Zhang, W., and DebRoy, T., 2003, "Modeling of Temperature and Solidified Surface Profile During Gas- Metal Arc Fillet Welding," Journal of Applied Physics, vol. 94, pp [6] Safdar, S., Li, L., Sheikh, M. A., and Schmidt, M. J., 2006, "A Thermal History Analysis of Surface Heating of Mild Steel with Different Laser Beam Geometries," Journal of Mechanical Engineering Science, IMechE Part C, vol. 220, pp [7] Fluent, "Users Guide," vol. Vol 1,2 &3, pp [8] Beranger, G., Henry, G., and Sanz, G., The Book of Steel, Intercept Limited, [9] Kumar, A., Zhang, W., and DebRoy, T., 2005, "Improving Reliability of Modelling Heat and Fluid Flow in Complex Gas Metal Arc Fillet Welds-Part I: An Engineering Physics Model," Journal of Physics D:Applied Physics, vol. 38, pp It has been found that the enhanced thermal conductivity approach gives reasonable results on the work-piece surface. However, it is not able to accurately predict the melt pool depth and melt pool profile, which are of significant importance for any process involving laser melting.