On the calculation of the free surface temperature of gas-tungsten-arc weld pools from first principles: Part II. modeling the weld pool and comparison with experiments

By combining a mathematical model of the welding arc and of the weld pool, calculations are presented to describe the free surface temperature of weld pools for spot welding operations. The novel aspects of the treatment include the calculation of the heat and current fluxes falling on the free weld pool surface from first principles, a realistic allowance for heat losses due to vaporization, and a realistic allowance for the temperature dependence of the surface tension. The most important finding reported in this article is that the free surface temperature of weld pools appears to be limited by Marangoni convection, rather than heat losses due to vaporiza-tion. Furthermore, it was found that once thermocapillary flow can produce high enough surface velocities (>25 cm/s), the precise nature of the relationship between temperature and surface tension will become less important.     

Mathematical modeling of three-dimensional heat and fluid flow in a moving gas metal arc weld pool

Mathematical models capable of accurate prediction of the weld bead and weld pool geometry in gas metal arc (GMA) welding processes would be valuable for rapid development of welding procedures and empirical equations for control algorithms in automated welding applications. This article introduces a three-dimensional (3-D) model for heat and fluid flow in a moving GMA weld pool. The model takes the mass, momentum, and heat transfer of filler metal droplets into consideration and quantitatively analyzes their effects on the weld bead shape and weld pool geometry. The algorithm for calculating the weld reinforcement and weld pool surface deformation has been proved to be effective. Difficulties associated with the irregular shape of the weld bead and weld pool surface have been successfully overcome by adopting a boundary-fitted nonorthogonal coordinate system. It is found that the size and profile of the weld pool are strongly influenced by the volume of molten wire, impact of droplets, and heat content of droplets. Good agreement is demonstrated between predicted weld dimensions and experimently measured ones for bead-on-plate GMA welds on mild steel plate.     

A unified numerical modeling of stationary tungsten-inert-gas welding process

In order to clarify the formative mechanism of weld penetration in an arc welding process, the development of a numerical model of the process is quite useful for understanding quantitative values of the balances of mass, energy, and force in the welding phenomena because there is still lack of experimentally understanding of the quantitative values of them because of the existence of complicated interactive phenomena between the arc plasma and the weld pool. The present article is focused on a stationary tungsten-inert-gas (TIG) welding process for simplification, but the whole region of TIG arc welding, namely, tungsten cathode, arc plasma, workpiece, and weld pool is treated in a unified numerical model, taking into account the close interaction between the arc plasma and the weld pool. Calculations in a steady state are made for stationary TIG welding in an argon atmosphere at a current of 150 A. The anode is assumed to be a stainless steel, SUS304, with its negative temperature coefficient of surface tension. The two-dimensional distributions of temperature and velocity in the whole region of TIG welding process are predicted. The weld-penetration geometry is also predicted. Furthermore, quantitative values of the energy balance for the various plasma and electrode regions are given. The predicted temperatures of the arc plasma and the tungsten-cathode surface are in good agreement with the experiments. There is also approximate agreement of the weld shape with experiment, although there is a difference between the calculated and experimental volumes of the weld. The calculated convective flow in the weld pool is mainly dominated by the drag force of the cathode jet and the Marangoni force as compared with the other two driving forces, namely, the buoyancy force and the electromagnetic force.     

Prediction of weld pool and reinforcement dimensions of GMA welds using a finite-element model

Mathematical models of the gas metal arc (GMA) welding process may be used to study the influence of various welding parameters on weld dimensions, to assist in the development of welding procedures, and to aid in the generation of process control algorithms for automated applications. In this work, a three-dimensional (3-D), steady-state thermal model of the GMA welding process has been formulated for a moving coordinate framework and solved using the finite-element method. The model includes temperature-dependent material properties, a new finite-element formulation for the inclusion of latent heat of fusion, a Gaussian distribution of heat flux from the arc, plus the effects of mass convection into the weld pool from the melted filler wire. The influence of weld pool convection on the pool shape was approximated using anisotropically enhanced thermal conductivity for the liquid phase. Weld bead width and reinforcement height were predicted using a unique iterative technique developed for this purpose. In this paper, the numerical model is shown to be capable of predicting GMA weld dimensions for individual welds, including those with finger penetration. Also, good agreement is demonstrated between predicted weld dimensions and experimentally derived relations that describe the effects of process variables and their influence on average weld dimensions for bead-onplate GMA welds on steel plate. E. PARDO, formerly Postdoctoral Fellow, Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1,     

Fluid flow and weld penetration in stationary arc welds

Weld pool fluid flow can affect the penetration of the resultant weld significantly. In this work, the computer simulation of weld pool fluid flow and its effect on weld penetration was carried out. Steady-state, 2-dimensional heat and fluid flow in stationary arc welds were computed, with three driving forces for fluid flow being considered: the buoyancy force, the electromagnetic force, and the surface tension gradient at the weld pool surface. The computer model developed agreed well with available analytical solutions and was consistent with weld convection phenomena experimentally observed by previous investigators and the authors. The relative importance of the influence of the three driving forces on fluid flow and weld penetration was evaluated, and the role of surface active agents was discussed. The effects of the thermal expansion coefficient of the liquid metal, the current density distribution in the workpiece, and the surface tension temperature coefficient of the liquid metal on weld pool fluid flow were demonstrated. Meanwhile, a new approach to free boundary problems involving simultaneous heat and fluid flow was developed, and the effort of computation was reduced significantly.     

Fluid flow and weld penetration in stationary arc welds

Weld pool fluid flow can affect the penetration of the resultant weld significantly. In this work, the computer simulation of weld pool fluid flow and its effect on weld penetration was carried out. Steady-state, 2-dimensional heat and fluid flow in stationary arc welds were computed, with three driving forces for fluid flow being considered: the buoyancy force, the electromagnetic force, and the surface tension gradient at the weld pool surface. The computer model developed agreed well with available analytical solutions and was consistent with weld convection phenomena experimentally observed by previous investigators and the authors. The relative importance of the influence of the three driving forces on fluid flow and weld penetration was evaluated, and the role of surface active agents was discussed. The effects of the thermal expansion coefficient of the liquid metal, the current density distribution in the workpiece, and the surface tension temperature coefficient of the liquid metal on weld pool fluid flow were demonstrated. Meanwhile, a new approach to free boundary problems involving simultaneous heat and fluid flow was developed, and the effort of computation was reduced significantly.     

Three-dimensional transient model for arc welding process

A direct computer simulation technique, discrete element analysis (DEA), was utilized in the development of a transient multidimensional (2-D and 3-D) mathematical model for investi-gating coupled conduction and convection heat transfer problems associated with stationary and moving arc welding processes. The mathematical formulation considers buoyancy, electro-magnetic, and surface tension driving forces in the solution of the overall heat transfer conditions in the specimen. Furthermore, the formulation of the model allows realistic consideration of the geometrical variations in the workpiece. The model treats the -weld pool surface as a truly deformable free surface, allowing for the prediction of the weld surface deformations such as the “weld crown.≓ A marked element formulation was employed to monitor the transient de-velopment of the weld pool as determined by the latent heat considerations and the calculated velocities in the weld pool. The model was utilized to simulate the heat and fluid flows in the weld pool that occur during stationary (spot) and moving (linear) gas tungsten-arc welding. Also, the present analysis considers a simple rectangular specimen and a geometrically complex specimen to demonstrate the capability of the model to simulate realistic 3-D arc welding prob-lems. The results of the present investigation clearly demonstrate the significant influence of the heat and fluid flows and the specimen geometry on the development of the weld. Comparison of the predicted and the experimentally observed fusion zone and heat-affected zone (HAZ) geometries indicate good agreement.     

表面活性元素硫对焊接熔池中流体流动方式和熔池深宽比的影响

综述了近20年国内、外有关特定焊接条件下,硫含量对熔池中流体流动方式和熔池深度影响方面的研究状况。表面活性元素硫主要是通过改变熔池中流体的流动方式来影响熔池的形状和尺寸。表面张力温度系数是熔池表面温度和活性元素硫含量的函数,表面张力不仅仅与硫含量有关,而且还与熔池表面温度关系密切。硫含量并不是获得最好的焊接熔池深宽比的唯一因素,而是硫含量、焊接电流、电弧移动速度、焊接能量以及能量密度的共同作用影响了熔池中流体的流动方式和熔池深宽比。     

The study of surface-active element oxygen on flow patterns and penetration in A-TIG welding

A three-dimensional mathematical model was developed to simulate the flow patterns and temperature distributions in a moving A-TIG weld pool of 304 stainless steels with different oxygen content using PHOENICS software. It is shown that the surface-active element, oxygen, is important, because it affects the weld shape by changing the flow patterns in the weld pool. The weld bead penetration and the depth/width ratio increase first sharply and then remain nearly a constant with increasing oxygen content. Depending upon the oxygen contents, three, one, or two vortexes that have different positions, strength, and directions may be found in the weld pool. Oxygen can cause significant changes in the weld shape by varying the sign of the surface tension coefficient. The situation with the maximum surface tension moves from the edge to the center with increasing oxygen content. As oxygen content exceeds a critical value, a positive surface tension coefficient dominates the flow patterns. The vortexes with opposite directions caused by positive surface tension coefficient can efficiently transfer the thermal energy from the arc, creating a deep weld pool. The critical oxygen content increases with the increase of the welding current.     

Computational modeling of stationary gastungsten-arc weld pools and comparison to stainless steel 304 experimental results

A systematic study was carried out to verify the predictions of a transient multidimensional computational model by comparing the numerical results with the results of an experimental study. The welding parameters were chosen such that the predictions of the model could be correlated with the results of an earlier experimental investigation of the weld pool surface temperatures during spot gas-tungsten-arc (GTA) welding of Type 304 stainless steel (SS). This study represents the first time that such a comprehensive attempt has been made to experimentally verify the predictions of a numerical study of weld pool fluid flow and heat flow. The computational model considers buoyancy and electromagnetic and surface tension forces in the solution of convective heat transfer in the weld pool. In addition, the model treats the weld pool surface as a truly deformable surface. Theoretical predictions of the weld pool surface temperature distributions, the cross-sectional weld pool size and shape, and the weld pool surface topology were compared with corresponding experimental measurements. Comparison of the theoretically predicted and the experimentally obtained surface temperature profiles indicated agreement within ±8 pct for the best theoretical models. The predicted surface profiles were found to agree within ±20 pct on dome height and ±8 pct on weld pool diameter for the best theoretical models. The predicted weld cross-sectional profiles were overlaid on macrographs of the actual weld cross sections, and they were found to agree very well for the best theoretical models.     

A New Model for Keyhole Mode Laser Welding Using FLUENT

Evolution of the free surface at gas?Cliquid interface during keyhole mode welding is complex and its calculation is computationally expensive. Similarly, models based on only heat conduction without considering vapour cavity and liquid convection around it, are computationally efficient but are not effective in defining the weld pool shape especially for low conducting material like steel. In the present study a useful yet computationally efficient model has been presented for keyhole mode laser welding using commercial software FLUENT. Here instead of evolving the free surface of keyhole in a rigorous way, various possible steady keyhole shapes are assumed partially based on literature evidence and subsequently their dimensions are calculated by an overall heat balance. The estimated keyhole profile is then mapped into the thermo-fluid framework of FLUENT and steady computational fluid dynamics calculations is carried out around the keyhole that is considered rigid wall at boiling temperature. Next, an optimized keyhole shape is identified by comparing the predicted fusion lines with the experimental weld fusion lines reported in literature. Finally, using this optimized keyhole shape independent predictions are made for two materials of widely different thermal conductivities, like steel and aluminum, under different operating conditions. In all cases the results of the present simulation is found to in close agreement with experimental data and even better than the model predictions reported in literature. The present model emerges as a simple yet effective model for predicting the weld bead profile encompassing wide range of materials under different operating conditions.     

双电弧集成冷丝复合焊中冷丝位置对焊接过程的影响

搭建了双电弧集成冷丝复合焊接系统,研究了冷丝不同位置对焊接过程的影响机理,其中包括冷丝作用位置对其加热熔化作用及表面成形的影响。实验结果表明:冷丝从两引导焊丝正前方送入时,熔池前端对冷丝的加热熔化作用不充分,冷丝末端会顶触熔池底部,随着冷丝的持续送进和母材的向后移动,某一时刻冷丝回弹,焊丝末端的熔滴弹出落在母材表面形成大颗粒飞溅。当冷丝从侧面送入时,熔池一侧的温度较低,影响熔池金属的流动,导致最终的焊缝成形不对称分布。当冷丝从两引导焊丝正后方送入熔池时,冷丝始终插入熔池中,焊接过程稳定,是理想的冷丝作用位置。此外,随着冷丝送丝速度的增加,两种脉冲电流模式（同相和反相）下,熔敷率均随之增加,且相差不大。同相脉冲电流下电弧对冷丝的加热熔化作用最强烈,反相脉冲电流下次之,直流模式下最弱。      

Computer simulation of convection in moving arc weld pools

Computer simulation for three-dimensional convection in moving arc weld pools was described, with three distinct driving forces for flow considered — the electromagnetic force, the buoyancy force, and the surface tension gradient on the pool surface. Formulation of the electromagnetic force in the weld pool was presented. The calculated and experimentally observed fusion boundaries were compared. The arc efficiency and spatial distributions of the current density and power density used in the calculations were based on experimentally measured results, in order to verify the model. The effects of the electromagnetic and surface tension forces were discussed.     

Marangoni convection in weld pool in CO<Subscript>2</Subscript>-Ar-shielded gas thermal arc welding

Small CO₂ additions of 0.092 to 10 vol pct to the Ar shielding gas dramatically change the weld shape and penetration from a shallow flat-bottomed shape, to a deep cylindrical shape, to a shallow concave-bottomed shape, and back to the shallow flat-bottomed shape again with increasing CO₂ additions in gas thermal arc (GTA) welding of a SUS304 plate. Oxygen from the decomposition of CO₂ transfers and becomes an active solute element in the weld pool and reverses the Marangoni convection mode. An inward Marangoni convection in the weld pool occurs when the oxygen content in the weld pool is over 80 ppm. Lower than 80 ppm, flow will change to the outward direction. An oxide layer forms on the weld pool in the welding process. The heavy oxide layer on the liquid-pool surface will inhibit the inward fluid flow under it and also affects the oxygen transfer to the liquid pool. A model is proposed to illustrate the interaction between the CO₂ gas and the molten pool in the welding process.     

Modeling of the effects of surface-active elements on flow patterns and weld penetration

A mathematical model was developed to calculate the transient temperature and velocity distributions in a stationary gas tungsten arc (GTA) weld pool of 304 stainless steels with different sulfur concentrations. A parametric study showed that, depending upon the sulfur concentration, one, two, or three vortexes may be found in the weld pool. These vortexes are caused by the interaction between the electromagnetic force and surface tension, which is a function of temperature and sulfur concentration, and have a significant effect on weld penetration. For given welding conditions, a minimum threshold sulfur concentration is required to create a single, clockwise vortex for deep penetration. When two metals with different sulfur concentrations are welded together, the weld-pool shape is skewed toward the metal with a lower sulfur content. Detailed physical insights on complicated fluid-flow phenomena and the resulting weld-pool penetration were obtained, based on the surface tension-temperature-sulfur concentration relationships.     

Liquid Metal Pool Behavior during the Vacuum Arc Remelting of INCONEL 718

Non-steady-state ensemble arc behavior has been observed during the Vacuum Arc Remelting (VAR) of 508-mm-diameter ingots of INCONEL 718. The liquid metal flow in the melt pool of a 508-mm ingot during VAR has been simulated under two alternative sets of conditions: (1) a steady-state axisymmetrical arc distribution, as has been typically used in modeling work previously; and (b) a transient asymmetrical arc distribution. Due to the computational requirements, neither mass flux nor solidification were modeled; instead, the pool shape was fixed from measurements from a 508-mm-diameter ingot, and a constant pool wall temperature of 1609 K was used. The transient simulation assumed a localized Gaussian arc whose effective center was located at a distance of 0.1 m from the ingot centerline; this simulation rotated clockwise around the centerline with a period of 36 seconds. The steady-state model was simulated with axisymmetrical distributions of current and power input to the pool top surface calculated by time averaging the transient current and power inputs. The standard k-ε solver of ANSYS CFX 5.6 software was used for both simulations. The transient model results suggest that 5 seconds of asymmetrical arc behavior is enough to change the pool from steady state to transient and that, after 30 seconds, the flow is almost fully developed (at least to the accuracy of the model) and dominated by the Lorentz force. Aspects of the model results agree with key features of the melt pool observed during VAR.     

Effects of surface active elements on weld pool fluid flow and weld penetration in gas metal arc welding

This article presents a mathematical model simulating the effects of surface tension (Maragoni effect) on weld pool fluid flow and weld penetration in spot gas metal arc welding (GMAW). Filler droplets driven by gravity, electromagnetic force, and plasma arc drag force, carrying mass, thermal energy, and momentum, periodically impinge onto the weld pool. Complicated fluid flow in the weld pool is influenced by the droplet impinging momentum, electromagnetic force, and natural convection due to temperature and concentration gradients, and by surface tension, which is a function of both temperature and concentration of a surface active element (sulfur in the present study). Although the droplet impinging momentum creates a complex fluid flow near the weld pool surface, the momentum is damped out by an “up-and-down” fluid motion. A numerical study has shown that, depending upon the droplet’s sulfur content, which is different from that in the base metal, an inward or outward surface flow of the weld pool may be created, leading to deep or shallow weld penetration. In other words, it is primarily the Marangoni effect that contributes to weld penetration in spot GMAW.     

Computational modeling of laser welding of Cu-Ni dissimilar couple

A three-dimensional transient model to solve heat transfer, fluid flow, and species conservation during laser welding of dissimilar metals is presented. The model is based on a control volume formulation with an enthalpy-porosity technique to handle phase change and a mixture model to simulate mixing of molten metals. Weld pool development, solidified weld pool shape, and composition profiles are presented for both stationary as well as continuous laser welding in conduction mode. Salient features of a dissimilar Cu-Ni weld are summarized and thermal transport arguments are employed to successfully explain the observations. It is found that the weld pool shape becomes asymmetric even when the heat source is symmetrically applied on the two metals forming the couple. It is also observed that convection plays an important role in the development of weld pool shape and composition profiles. As the weld pool develops, the side melting first (nickel) is found to experience more convection and better mixing. Results from the case studies of computation are compared with corresponding experimental observations, showing good qualitative agreement between the two.