Computation and validation of weld pool dimensions and temperature profiles for gamma TiAl

Previous research by the authors has shown that the welding current has a strong effect on the weld properties and microstructures of gamma TiAl. This article presents the results of experimentally measured and theoretically predicted temperature profiles of gas tungsten arc (GTA) welded gamma TiAl for welding currents of 75 and 100 A. The GTA welding model used in this study accounts for the fluid flow in the weld pool as well as conductive, convective, and phase change heat transfer processes in the solid, liquid, and mushy regions of a metal. The computed temperature fields predicted that as the welding current is increased, the maximum temperature reached in the weld pool also increases. Experimental validation of the computed temperature fields was determined by placing thermocouples at three locations on the specimen, to record the temperatures during welding using computer-based data acquisition hardware and software. The agreement between theoretical predictions and measurements was reasonably good, which provided a direct validation of the model. This article is based on a presentation made in the symposium entitled “Fundamentals of Structural Intermetallics,” presented at the 2002 TMS Annual Meeting, February 21–27, 2002, in Seattle, Washington, under the auspices of the ASM and TMS Joint Committee on Mechanical Behavior of Materials.     

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.     

Mass Transfer and Weld Appearance of 316L Stainless Steel Covered Electrode During Shielded Metal Arc Welding

The mass transfer and the weld appearance of 316L stainless steel covered electrodes during shielded metal arc welding were investigated. According to the experimental measurements on the deposited metal and the observations on the welding process, the mass transfer coefficient of the nickel was found to be in the range of 88.09 to 99.41 pct, while those of molybdenum, chromium, manganese, and silicon are in the ranges of 84.60 to 92.51 pct, 71.59 to 77.64 pct, 20.88 to 30.15 pct, and 6.72 to 10.47 pct, respectively. Some relationships between the mass transfer and the flux coating ingredient/welding current were established. The formability properties of the weld, including the spreadability, spattering, slag detachability, and oxidation tint on the weld surface, were also discussed based on the tested data and the observations.     

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.     

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,     

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.     

Effect of Welding Speed on Gas Metal Arc Weld Pool in Commercially Pure Aluminum: Theoretically and Experimentally

Temperature and velocity fields, and weld pool geometry during gas metal arc welding (GMAW) of commercially pure aluminum were predicted by solving equations of conservation of mass, energy and momentum in a three-dimensional transient model. Influence of welding speed was studied. In order to validate the model, welding experiments were conducted under the similar conditions. The calculated geometry of the weld pool were in good agreement with the corresponding experimental results. It was found that an increase in the welding speed results in a decrease peak temperature and maximum velocity in the weld pool, weld pool dimensions and width of the heat-affected zone (HAZ). Dimensionless analyses were employed to understand the importance of heat transfer by convection and the roles of various driving forces in the weld pool. According to dimensionless analyses droplet driving force strongly affected fluid flow in the weld pool.     

On the calculation of the free surface temperature of gas-tungsten-arc weld pools from first principles: Part I. modeling the welding arc

A mathematical formulation has been developed and computed results are presented describing the temperature profiles in gas tungsten arc welding (GTAW) arcs and, hence, the net heat flux from the welding arc to the weld pool. The formulation consists of the statement of Maxwell's equations, coupled to the Navier-Stokes equations and the differential thermal energy balance equation. The theoretical predictions for the heat flux to the workpiece are in good agreement with experimental measurements — for long arcs. The results of this work provide a fundamental basis for predicting the behavior of arc welding systems from first principles.     

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.     

Modeling of laser keyhole welding: Part II. simulation of keyhole evolution,velocity, temperature profile,and experimental verification

This article presents the simulation results of a three-dimensional mathematical model using the level set method for laser-keyhole welding. The details of the model are presented in Part I.^[4] The effects of keyhole formation on the liquid melt pool and, in turn, on the weld bead are investigated in detail. The influence of process parameters, such as laser power and scanning speed is analyzed. This simulation shows very interesting features in the weld pool, such as intrinsic instability of keyholes, role of recoil pressure, and effect of beam scanning. For verification purposes, visualization experiments have been performed to measure melt-pool geometry and surface velocity. The theoretical predictions show a reasonable agreement with the experimental observations.     

Fluid velocities in induction melting furnaces: Part I. Theory and laboratory experiments

Fluid flow in an induction furnace due to electromagnetic stirring forces is predicted theoretically from furnace design parameters by the simultaneous solution of the Maxwell and Navier Stokes equations. Streamline plots and velocity profiles are obtained and compared with surface velocities measured experimentally. The measurements were made on a mercury pool stirred inductively by a Tocco 30 kW 3 kHz induction melting unit. The agreement between the experimental measurements and theoretical predictions was good considering that no curve fitting by manipulation of adjustable parameters was involved. It is believed that such a model would be of value in the design and development of induction furnaces.     

Analytical,numerical, and experimental analysis of inverse macrosegregation during upward unidirectional solidification of Al-Cu alloys

The present work focuses on the influence of alloy solute content, melt superheat, and metal/mold heat transfer on inverse segregation during upward solidification of Al-Cu alloys. The experimental segregation profiles of Al 4.5 wt pct Cu, 6.2 wt pct Cu, and 8.1 wt pct Cu alloys are compared with theoretical predictions furnished by analytical and numerical models, with transient h _i profiles being determined in each experiment. The analytical model is based on an analytical heat-transfer model coupled with the classical local solute redistribution equation proposed by Flemings and Nereo. The numerical model is that proposed by Voller, with some changes introduced to take into account different thermophysical properties for the liquid and solid phases, time variable metal/mold interface heat-transfer coefficient, and a variable space grid to assure the accuracy of results without raising the number of nodes. It was observed that the numerical predictions generally conform with the experimental segregation measurements and that the predicted analytical segregation, despite its simplicity, also compares favorably with the experimental scatter except for high melt superheat.     

Mathematical modeling of microsegregation in binary metallic alloys

A mathematical model was developed to calculate microsegregation in binary metallic alloys. This model utilized the mathematical techniques of the method of lines combined with invariant imbedding (MOL/II) to solve the problem of combined heat and mass transfer during and after solidification. Model predictions were compared to experimental measurements in the Al-Cu system and to other microsegregation models. The MOL/II model predicted nonequilibrium second-phase contents within ±3 pct at low and intermediate cooling rates, when dendrite-arm coarsening was included in the model. It also was able to reproduce concentration profiles reasonably well. The analytical models commonly used (equilibrium cooling, Scheil equation, Brody/ Flemings model, Clyne/Kurz model, Solari/Biloni model, and Basaran equation) in micro-segregation calculations were shown to be considerably less accurate than the numerical models (MOL/II and the Ogilvy/Kirkwood model). Formerly Graduate Research Assistant, The University of Michigan     

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.     

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.     

Effect of evaporation and temperature-dependent material properties on weld pool development

This paper evaluates the effect of weld pool evaporation and thermophysical properties on the development of the weld pool. An existing computational model was modified to include vaporization and temperature-dependent thermophysical properties. Transient, convective heat transfer during gas tungsten arc (GTA) welding with and without vaporization effects and variable properties was studied. The present analysis differs from earlier studies that assumed no vaporization and constant values for all of the physical properties throughout the range of temperature of interest. The results indicate that consideration of weld pool vaporization effects and variable physical properties produce significantly different weld model predictions. The calculated results are consistent with previously published experimental findings.     

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.     

A model for the silicon-manganese deoxidation of steel weld metals

From an analytical and theoretical study of flat and out-of-position gas metal arc (GMA) C-Mn steel welds containing varying additions of silicon and manganese, we conclude that the buoyancy effect (flotation obeying Stokes’ law) does not play a significant role in the separation of oxide inclusions during weld metal deoxidation. Consequently, the separation rate of the particles is controlled solely by the fluid flow pattern in the weld pool. A proposed two-step model for the weld metal deoxidation reactions suggests that inclusions formed in the hot, turbulent-flow region of the weld pool are rapidly brought to the upper surface behind the arc because of the high-velocity flow fields set up within the liquid metal. In contrast, those formed in the cooler, less-turbulent flow regions of the weld pool are to a large extent trapped in the weld metal as finely dispersed particles as a result of inadequate melt stirring. The boundary between “hot” and “cold” parts for possible inclusion removal is not well defined, but depends on the applied welding parameters, flux, and shielding gas composition. As a result of the intricate mechanism of inclusion separation, the final weld metal oxygen content depends on complex interactions among the following three main factors: (1) the operational conditions applied, (2) the total amount of silicon and manganese present, and (3) the resulting manganeseto-silicon ratio. The combined effect of the latter two contributions has been included in a new deoxidation parameter, ([pct Si][pct Mn])^−0.25. The small, negative exponent in the deoxidation parameter indicates that control of the weld metal oxygen concentrations through additions of silicon and manganese is limited and that choice of operational conditions in many instances is the primary factor in determining the final degree of deoxidation to be achieved.