Easy teaching of numerical simulation of welding with COMSOL

Transcription

1 Easy teaching of numerical simulation of welding with COMSOL I. Tomashchuk* 1, P. Sallamand 1, J.-P. Chateau-Cornu 1 Laboratoire Interdiscilinaire Carnot de Bourgogne UMR CNRS 633, Université de Bourgogne Franche-Comté, 1 rue de la Fonderie, 71 Le Creusot, France Laboratoire Interdiscilinaire Carnot de Bourgogne UMR CNRS 633, Université de Bourgogne Franche-Comté, Institut Maray-Maison de la Métallurgie, 64 rue de Sully, 1 Dijon, France * iryna.tomashchuk@u-bourgogne.fr Abstract The initiation in numerical modeling of welding with COMSOL Multihysics is roosed to the nd year students of the Professional Master Program «Processes, Controls, Metallic Materials: Nuclear Industry» (PCM) of University of Burgundy, France since 16 within the module «Simulation of welding hysics». This training follows transversal aims such as easy comrehension of the influence of oerational arameters on weld roerties, learning different kinds of hysical henomena of welding and getting handson exerience in creation of multihysical models. We hoe that this course will romote the culture of multihysical modeling amongst young secialists in the manufacturing of metallic arts and structures, in articular for the nuclear industry. Introduction The oularization of numerical simulation methods for arehending the roblems of materials rocessing, and in articular the quality of welding, in industry as well as in research, makes it necessary to create sufficient baggage of knowledge for new generations of secialists in materials science. In this light, COMSOL Multihysics reresents an interesting edagogical tool that allows recreating and understanding the rinciles of relatively comlex models without imortant rior background in rogramming and numerical methods. Practical works in simulation of welding with COMSOL Multihysics have been roosed to the nd year students of the Professional Master Program «Processes, Controls, Metallic Materials: Nuclear Industry» (PCM) of University of Burgundy, France created in 15, which is a unique rofessional training dedicated to the metallurgy in France [1]. The module «Simulation of welding hysics». This training follows three transversal aims: 1. hands-on exerience of creation, solving and ost-rocessing of multihysical models;. better understanding of coexistent hysical henomena of welding and their synergetic effect; 3. easy comrehension of the influence of oerational arameters and materials roerties on resulting weld. These ractical works are comosed by four sessions of 3 hours each, dedicated to the creation of models of increasing comlexity: 1. comarison of time-deendent and quasi-steady formulations of welding roblem in Heat Transfer module;. erforming the arametrical studies of inut arameters (material roerties, welding velocity etc.) influence on melted zone dimensions; 3. simulation of several convection forces and the analysis of their synergetic effect on melted zone dimensions and temerature (strong couling between CFD and Heat Transfer modules); 4. modeling of elements transort in the melted zone (strong couling between CFD, Heat Transfer and Diluted Elements Transort modules). Theoretical content and ste-by-ste descrition of models creation along with efficient ost-rocessing tis are rovided in form of richly illustrated workbook of 4 ages. The students work in a air and are evaluated basing on the reorts that contain a short descrition of modeling stes and a vast discussion dedicated to the understanding of simulated henomena and their imact on calculated thermal, velocity or comosition fields as well as to the associated numerical challenges (effect of mesh size, stabilization, solving of convergence roblems). The calculations are erformed with edagogical license of Calculation Center of University of Burgundy. For the reason of limited work time, the validation of the models by comarison with exerimental results is not treated; however, it can be erformed in case of more extended works such as individual research roject for obtaining Master s degree. This ractical course is associated with 1-hour exlanation of theoretical setu of each roosed model and receded by 4 h of lectures on numerical simulation of welding given by two academicals and one invited RD secialist. The following aragrahs will resume the content and main outcome of the roosed models.

2 Practical work 1 (PW1): main rinciles of heat-transfer simulation in welding During the first ractical work, the students discover the interface of COMSOL Multihysics and Heat Transfer module and go through the stes of setu, solving and ost-rocessing of heat equation based models. 3D model with simlest Gaussian heat source alied to the to limit of the geometry is used (Q surf). Two aroaches to the reresentation of the welding rocess are comared: 1. quasi-steady aroach where the heat source itself does not include velocity term, but the dislacement of the welded late is taken in account through the convective term of heat equation given in stationary form [] (x +y ) -.5 R P Q surf = ex R C V T kt. time-deendent aroach with moving heat source and zero convective field in heat transfer equation: (x + yvt ) -.5 R P Q surf = ex R T C C T kt t where - efficiency coefficient, R heat source radius, P laser ower, - material density, C heat caacity, k thermal conductivity, V welding seed, T temerature, t time. The choice of limit conditions for two cases is discussed. In the first lace, the thermohysical roerties of materials from Materials Library are considered (AISI34L stainless steel). The influence of mesh size on the recision of calculated thermal field is demonstrated by the series of calculation with more and more thin domain mesh. In the ost-rocessing art, the students are invited to comare melted zone shaes and thermal gradients roduced by two models, that aear to be very close when steady regime is attained by time-deendent model (Figure 1). The students learn to roduce animations, extract melted zone (MZ) length and volume. Practical work (PW): role of materials roerties and arametric studies The second ractical work is dedicated to various arametric studies in quasi-steady 3D model: the influence of materials roerties on melted zone dimension (by comarison of different materials from Materials Library) the influence of the quality of introduced material data (constant values, functions of temerature, taking in account latent heat of fusion) the influence of welding seed on melted zone dimensions. In the first lace, the students are invited to comare the shae and the dimensions of the melted zones roduced by the same welding condition (fixed ower and velocity) on different metallic materials and correlate them with melting temeratures T m and thermal diffusivities (Table 1). Table 1. Melted zone widths roduced on cm thick lates with Gauss heat source with P = 1 kw, Ø = 1 cm, =.7 and V =.5 m/min. Material Tm (K) (m²/s) MZ width (mm) AISI 34L 1673* Ti Al Cu Sn *solidus temerature Next, the calculation of thermal field on 16 MnNiMo 5 steel is erformed: with constant roerties, with roerties as function of temerature and latent heat of fusion taken into account through equivalent heat caacity aroach [3]: t = 6 s Figure 1. The comarison of 1673 K (solidus of 34L) isotherm for time-deendent and quasi-steady models of heat source.

3 C C T L m e T Tm T T where C(T) heat caacity as function of temerature, L m latent heat of fusion, T m melting temerature, T smoothing range. The dimensions of melted zone and thermal history along the joint line are comared (Figure ) to highlight the imortance of correct data for accurate simulation of melted zone length and cooling temeratures. T (K) Constant roerties Proerties f(t) Width (mm) Figure. The dimensions of melted zone and thermal history at the to of the joint line comared for constant and temerature-deendent material roerties. Figure 3. The effect of welding seed on melted zone dimensions of 16MND5, P = 1 kw, Ø = 1 cm, =.7 and V =.5 m/min. Length (mm) Constant roerties Proerties f(t) y (m) Finally, the arametric study of the influence of welding seed on melted zone dimensions is erformed (Figure 3). It can be noticed that the melted zone length is more sensible to the welding seed than melted zone width. Practical work 3 (PW3): convective forces in welding Previously considered heat transfer models do not rovide a correct descrition of thermal field within the melted zone because of neglecting of convective forces that strongly influence the melt temeratures, which remains unrealistic (1 K) in urely thermal models. In two next ractical works, the students learn to introduce to the D model two convective forces that are common for all fusionwelding methods: natural convection through Boussinesq aroximation [4] F g ( T T ) m A where F A Archimedes force, g gravity constant, - thermal exansion coefficient; Marangoni convection created by the variation of surface tension with temerature [5] : T) ( T T ) ( m M m where - surface tension temerature coefficient. In these models, melted metal is reresented as Newtonian liquid undergoing laminar flows. The strong couling between the heat and Navier-Stokes equations is alied, because from one side density and viscosity are temerature-deendent functions and from other side heat equation contains, in contrary to the revious models, comlete velocity field U(u,v): UT kt C U U I U U U T F where - relative ressure, I identity tensor, - dynamic viscosity. The equivalent viscosity aroach is used, where very high value caable to suress any velocity field is alied to the solid art of domain: = solid + (liquid-solid). flchs(t-tm, T), where flchs() a smoothed Heaviside function with a continuous second derivative without overshoot. This model reresents the simlified case when the defocused laser beam is alied on the surface of metallic material with high thermal conductivity, and the thermal equilibrium is attained, which means the melted zone does not evolve with time. The students observe the evolution of velocity fields (Figure 4) and maximal melt temeratures (Table ) along with melted zone dimensions and the direction of the flows. A

4 This study hels better understand the influence of the absolute value and the sign of on the resulting shaes of the melted zones. The students create in the first lace steady heat transfer model and note maximal temerature and dimensions of the melted zone roduced by defocused laser beam on the metal late. Next, the natural convection is activated, and its imact on heat transfer is evaluated. It can be seen that quite slow velocity field created by natural convection does not affect the temerature and the dimensions of the melt. Then the Marangoni convection is activated. For given conditions, it results in maximal melt velocity of about 1 m/s. Negative sign of results in melt convection from the hot center to the erihery of the melted zone, that reduces maximal temerature (-4 K) and roduces larger and less dee melted zone. Positive sign of inverses the direction of the flows : colder liquid comes from the erihery of the melt to its center, and hot liquid descends at the bottom of the melt, which results in slightly hotter, more rofound and less large melted zone. U (m/s) U (m/s) Table. The effect of different convective forces on melting of metal late with defocused laser (P = 1 kw, Ø =. cm). Calculation T max (K) Width (mm) Height (mm) Umax (m/s) Heat transfer only Natural convection Marangoni effect, = N/m/K Marangoni effect, = N/m/K Practical work 4 (PW4): simulating the elements transort in multimaterial welding The last model contains trile multihysics with timedeendent study (Figure 5): heat transfer roduced by a ulsed defocused laser, calculated during and after the ulse: x ulse -.5 a P R Q surf = ex t t R where a absortion coefficient, t ulse ulse duration of.15 s. develoment and attenuation of natural and Marangoni convection in the melt; the mixing of to layer of Ni with base material steel according to Fick law c U c = D c t where c is the mass fraction of Ni and the diffusion coefficient of Ni in liquid steel D is given by the equation of Stokes-Einstein [6]: k T D = T Tm 6 rni where r Ni the atomic radius of Ni. U (m/s) Figure 5. Trile multihysics scheme. (c) Figure 4. Velocity field (m/s) : natural convection only, natural convection and Marangoni effect with = N/m/K, (c) natural convection and Marangoni effect with = N/m/K. The D geometry of the model reresents the crosssection of 34L steel late (8 wt Ni) with 5 µm thick ure nickel layer. In such model, the local roerties of materials should deend at once on the temerature and on the local mass fraction c of Ni. For simlification, the additivity rule is alied for calculation of local material roerties A i in form:

5 Ni steel Ai = A ( T) c A ( T) 1 c. i i The calculation time is chosen big enough to witness the whole melting and solidification rocess (which means, the evolution of solidus line is also estimated with the additivity rule), along with dissolution and mixing of Ni in the melted zone. The students are invited to exress the variation of melted zone comosition with time and to estimate the influence of value on final comosition. For the ositive value of (Figure 6), the rogressive dilution of ure nickel in stainless steel is more raid than in case of negative (Figure 7), because of deeer weld enetration, and it also results in lower content of Ni in the final melted zone. Discussion The gradual increase in comlexity allows the students to start with simle heat-transfer models and quickly rogress u to double and trile multihysics cases. Because of the limited time, the calculations remain simlified: quasi-steady aroaches (PW 1, and 3) or D geometry (PW 3 and 4) are alied where ossible. In actual form, the module is missing thermomechanical simulation that can be included, for examle, in the second ractical work that does not contain new theoretical information. During 3 h session, about h are sent on model building and trouble shooting and 1 h on solving and ost-rocessing..6 s.6 s.1 s.1 s.15 s.15 s (c).9 mm 56 wt Ni (c) 4 mm 64 wt Ni 1.5 mm 1 mm.4 s.4 s (d) (d) Figure 6. Comosition field (wt Ni) and velocity field (arrows) roduced by natural convection and Marangoni effect with = N/m/K. Figure 7. Comosition field (wt Ni) and velocity field (arrows) roduced by natural convection and Marangoni effect with = N/m/K.

6 The analysis of average marks over the last three years (Figure 8.a) shows that that multiysical models (PW 3 and 4) aear more difficult. This is true for both trouble shooting and interretation of the results. Paradoxically, the general average note slowly diminishes in site of continuous ugrade of ste-byste manual, and standard deviation does not exceed (Figure 8.b). However, all students areciate the user-friendliness of COMSOL Multihysics comared to other FEM software used in materials science and all of them could validate the module by obtaining average mark suerior to 1 of.several students decided to use COMSOL Multihysics for the scientific calculations associated with master internshi, and for one student it was imosed References 1. htt://blog.u-bourgogne.fr/master-cm/. I.Bendaoud, S. Matteï, E. Cicala, I. Tomashchuk, H. Andrzejewski, P. Sallamand, A. Mathieu, F. Bouchaud, The numerical simulation of heat transfer during a hybrid laser MIG welding using equivalent heat source aroach, Otics & Laser Technology,56, (14). 3. C. Bonacina, G. Comini, A. Fassano, M Primicerio, Numerical solution of hase-change roblems, Int. J. Heat Mass Transfer, 16, (1973). 4. H. Eisazadeh, D. J. Haines, M. Torabizadeh, Effects of gravity on mechanical roerties of GTA welded joints, Journal of Materials Processing Technology, 14, (14). 5. W. Dong, S. Lu, D. Li, Y. Li, GTAW liquid ool convections and the weld shae variations under helium gas shielding, International Journal of Heat and Mass Transfer, 54, (11). 6. C. R. Wilke, Pin Chang, Correlation of diffusion coefficients in dilute solutions, AIChE Jounal, 1, 64-7 (1955) No of ractical work Acknowledgements The authors acknowledge the contribution of the students of Master Program PCM/University of Burgundy, France: Florent Gabard graduated in 16, Gwendoline Colin graduated in 17 and Bastien Ravry graduated in Figure 8. The average marks obtained in last three years for each ractical work, for each year. Conclusions The use of COMSOL Multihysics within recently created Master Program «Processes, Controls, Metallic Materials: Nuclear Industry» (PCM) of University of Burgundy allowed to easily arehend the main rinciles of henomenological simulation of welding rocess within rather short ractical module of 1 h. The gradual increase in comlexity allows the students to start with simle heat-transfer models and quickly rogress u to double and trile multihysics cases.