One of the first approaches in the literature related to the heat distribution and flow during welding was a theoretical model developed by Rosenthal (1941). This author made a number of simplifying assumptions to allow solution of a theoretical model for the heat transfer during arc welding:
As a primary approximation, the physical properties of the material would remain constant with temperature;
The heat flow in a workpiece of long length was considered steady, or quasi-stationary;
The heat source was regarded as a point source;
The heat losses through the surface to atmosphere were ignored. This assumption was supported by experiments which showed that thermal conduction is much greater than heat transmission through the surface;
The heat created by resistance heating in the filler wire, and latent heat of fusion were not considered;
No convection in the weld pool was considered.
145 Using mathematical derivation and the assumptions above, Rosenthal (1941) obtained the two-dimensional state equation to describe the heat flow during welding of thin plates of infinite width:
𝑇 − 𝑇0 =2𝜋𝑘𝑄𝑝 exp −𝜆𝑣𝑥 K0 λvr g (3.1)
Where,
T = temperature;
T0 = temperature of workpiece before welding;
Qp =heat transferred from the heat source to the workpiece;
k = Thermal conductivity of the workpiece;
λ = Thermal diffusivity of the workpiece;
v = welding speed;
K0 = Bessel function of second kind and zero order, for each value of λvr, using tables of Bessel function;
r = radius of a circle drawn around the heat source;
g = thickness of the plate x= distance
The analytical solution obtained by Rosenthal (1941) for the three-dimensional heat flow problem, considering a semi-infinite workpiece, was defined by the Equation 3.2, as follows:
𝑇 − 𝑇0 =2𝜋𝑘𝑄𝑝 exp −𝜆𝑣𝑥 exp −𝜆𝑣𝑅
R (3.2)
Where R was considered the radial distance from the origin, calculated from the expression 𝑎2+ 𝑏2+ 𝑐2.
Rosenthal (1941) considered that in cases where the thickness becomes small enough, the heat losses through the surface to the surrounding atmosphere should be taken into account, and for that he suggests a modification factor into the Bessel function. Some experimental analysis reported by his work (Rosenthal 1941) shows that for thicknesses of 10 mm or above heat losses might be entirely overlooked. He estimated that less than 20%
of the total arc energy is consumed in heating the solid part of the electrode and heat losses associated with vaporization, radiation, etc were roughly estimated to be 15% for small electrodes, hence approximately 65% the total energy was assumed to be delivered to the workpiece.
Some of the effects analysed in his work showed that for the same welding conditions wider heat affected zones can be found for thin workpieces than for the thicker material. This implies a less pronounced gradient of temperatures. The material properties shape and structural design, arc current, welding speed and preheating were also referred to as conditions that could affect the isotherms determined by his theoretical approach.
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Eagar and Tsai (1983) described the work by Christensen et al. (1965) on a dimensionless version of the Rosenthal model, applied to different materials under a wider range of heat inputs. This study indicated a good agreement with Rosenthal solution for the actual bead geometry.
Glickstein (1976) analysed ionization potential of the gases during welding to show that metal vaporization can modify the thermal and electrical properties of the arc. Temperature measurements using 100A GTAW with 2mm gap were carried out and temperatures of 11000K near the cathode and 8000K near the anode were observed. Friedman and Glickstein (1976) developed an analytical model to characterize the thermal cycle in GTAW and predict the effect of process parameters on weld bead shape and depth of penetration.
In parallel, the finite element method was applied to predict the welding transient thermal cycle considering a stationary GTAW heat source to weld moderately thick plates. Good agreement between modelling results and thermocouple measurement were found by the authors, but the depth of penetration was not predicted by this model. The authors concluded that heat transfer exclusively by conduction is inadequate to characterize the depth of penetration and bead width.
The work of Essers and Walter (1981) focussed on heat transfer and penetration mechanisms with GMAW and plasma-GMAW and demonstrated that the heat associated with the transfer of metal droplets influences the total cross-sectional area of weld penetration and the impact of the drops on the liquid metal weld pool influences the depth of penetration. The analysis of the physical phenomena in GMAW (electrode positive mode) was also performed by Waszink and Van Den Heuvel (1982) in order to understand how the welding parameters affect the generation and flow of heat in the filler wire. They found out that melting rate is governed by the Joule heating and heat flow developed from the surface of the filler wire through the liquid tip, while the drop of temperature is determined by the heat generated at the surface of the filler wire. The authors analysed the heat flow mechanism considering globular and spray transfer modes, and the transition region was also considered. Oreper et al. (1983) considered that electromagnetic and surface tension forces have a major effect on the heat flow.
Nunes (1983) modified the analytical model developed by Rosenthal considering phase changes and the heat flow mechanisms in the weld pool. Although this complex model opened new perspectives for the understanding of heat flow and transfer in arc welding, the model was limited to a fixed position (i.e. without movement). Eagar and Tsai (1983) considering the solutions of Rosenthal and Christensen, and pointed out the scatter observed in Christensen’s work. They showed that the point source solution did not provide any information in respect to the shape of the weld pool. Reporting the work of Linnert (1967), they mentioned the importance of including the weld pool shape in heat flow models because of the wide variations in welding behaviour associated with heat sources.
The work of Eagar and Tsai (1983) was performed in order to analyse the temperature
147 distribution using a Gaussian travelling heat source model. This dimensionless solution included two variables to describe the heat source, the width of the heat source and the intensity or magnitude of the input energy. These two parameters were cited as varying markedly for different materials and welding processes. The study of those authors provided the first estimation of weld pool geometry based on an empirical model of heat transfer. Although this model improved previous solutions considering the transient temperature distribution, it does not accurately predict the depth of penetration, partly due to the assumption of semi-infinite thickness.
Kou and Le (1984) developed the first computer models to study the heat flow on pipe welding using autogenous GTAW. Their 3D steady-state model of the heat flow during pipe seam welding agreed well with the thermal cycles and fusion boundary measured experimentally, while a 3D transient state for girth welding agreed reasonably well, for the conditions of constant current and heat input studied.
Lancaster (1984) introduced the plot in Figure 3.1. It compares the power densities of the different welding processes considered and respective physical mechanisms occurring. This represented a clear understanding of the phenomena that are occurring during heat transfer.
Figure 3.1 – Power density for different welding processes (Lancaster 1984).
Gilckstein and Friedman (1984) used developments in computer science to launch new approaches in the study of heat flow during welding. New models analysing both fluid flow and heat transfer mechanisms together were developed. Kou and Wang (1986) built for the first time a 3D mathematical model to describe the heat flow and convection motion in the weld pools. The model included the effect of the buoyancy, electromagnetic and surface tension forces. Finite thickness workpieces were modelled, allowing partially and fully
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penetrated welds. Tsao and Wu (1988) improved the model of Kou and Wang (1986) for applications with GMAW. They added to the forces the energy exchange between the weld pool and the molten metal droplets during spray transfer. These research works were based on the heat input, and showed for the first time that is essential to know precisely the value of process efficiency for the welding process and conditions considered.
Zacharia et al. (1988 a) (1988 b) developed a 3D model where melt deformation during molten pools, particularly important in autogenous and non-autogenous GTA welding, was considered. Their simulation considered the weld pool under motion, with melting at the leading edge of the pool and weld solidification at the trailing edge. This model is a more realistic solution, when compared with the work carried on by Kou and Wang (Kou and Wang 1986).
Meanwhile, other models were developed to study the heat transfer in other welding processes, such as resistance spot welding (Han, et al. 1989) (Y.-S. E. Kim 1990).
Choo et al. (Choo, Szekely and Westhoff 1990) considered the earlier cited role of the forces interacting in the convection phenomena in the weld pools, and the shear stress exerted by the gas on the molten pool surface was also considered. They modelled high current arcs, characterized by deformed weld pools, and where interfacial regions are significantly important. Agreement with experimental results, considering flat and deformed weld pools, was found by those authors. However, when significant deformations occurred due to high heat and current flux, the model failed, suggesting that Gaussian heat flux distribution did not cover this situation. They also concluded that deformed free surfaces might result in a complex weld pool circulation outline.
Advances in the understanding of the physics beyond heat transfer have been considered by Eagar (1990) in respect to the plasma atmosphere and variations between helium and argon arcs. This author reported that the effect of helium and argon in melting and heat transfer is explained by the variation of thermal conductivity of those gases. In monatomic gases such as helium and argon, thermal conductivity is controlled by the mass diffusivity of the atoms, proportional to the inverse of square root of the atomic mass. The physical mechanisms involved were also described, such as the effect of gas mixtures on anode voltage drop, electrical current distribution, arc temperature, and radiation. Other gas mixtures can also have a significant variation in the role on thermal processes, when reactive components are present. The model developed by Kim et al. (1991) to understand the effect of electrode heat transfer in GMAW provided advances in information about the metal transfer using estimated time scales for drop formation and detachment. They analysed electron condensation on the surface of the electrode, modelling the thermal energy generated, and demonstrated that it is a major factor influencing the heat flow through the electrode.
Following the previous studies of Kim et al. (1991), Vilarinho et al. (2005) developed an experimental modelling study for the temperature and voltage drop along the electrode
149 during GMAW. They pointed out that those parameters can dramatically affect the prediction of process efficiency during the electrode melting and heat flow through the electrode tip. The model accounted for material properties, temperature field and voltage drop. However, when globular transfer was identified the experimental results did not agree with the model; they considered that droplet geometry between plasma and electrode should be further evaluated. It should be noted that the process efficiency is an important factor in many of the actual models available, but there is no general agreement on the process efficiency to use, and assumed values are often adopted.
Further to their previous model, Choo and Szekely (1992) researched the vaporization kinetics and surface temperature, including Langmuir vaporization and gas phase in the model developed. They found out that heat losses due to vaporization do not play a major role in limiting the temperature at the free surface of weld pools. The results suggested a thermocapilarity motion effect controls the temperature at the free surface of the weld pools. The model also pointed out that relationships between temperature and surface tension and also other parameters controlling temperature distribution at the free surface play a significant role in the behaviour of the weld pool. These authors also analyse the role of turbulence in the weld pool for GTAW (Choo and Szekely 1994). This research study demonstrated that the postulate of laminar flow in weld pool might is incorrect when penetration depth is greater than 1 mm. Following the results of their modelling, they considered that the flow in weld pools is probably turbulent or at least transitional.
A model considering the electrode extension during GMAW in short circuit mode of transfer was developed by Quinn et al. (1994). It is well established that arc stability, metal transfer mode and deposition ratio are affected by the electrode extension (or arc length) (American Welding Society 2007). Further to this study, Kim and Na (1995) analysed the effect of the contact tip to the workpiece distance (CTWD) on weld pool and shape of GMAW using 3D modelling of heat transfer and fluid flow, considering the convection forces and the effect of molten electrode drop. CTWD has a significant effect on the weld pool and shape geometry, which also depends on arc length and arc current.
The effect of thermal properties and process efficiency on the transient temperatures during welding was analysed by Little and Kamtekar (1998). The main focus of this work was on thermal conductivity and process efficiency. Thermal conductivity has a major impact on the peak temperatures obtained; higher values of this parameter create lower peak temperatures near the weld bead and higher peak temperatures in areas away from the bead. Process efficiency also can affect results, and apparently is more critical for high heat input values, where process efficiency could be smaller.
Nguyen et al. (1999) developed an analytical solution for the transient temperature field of a semi-infinite workpiece subjected to a double ellipsoidal power density travelling heat source. Experimental results well matched with the model developed in the prediction of geometrical aspects, such as the weld pool width and depth. Nguyen et al. (2004 b)
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reporting the limitation of their previous model to semi-finite plates (Nguyen, Ohta, et al.
1999), and developed another analytical solution applied to finite thick plates, considering the double ellipsoidal heat source. The results published show an agreement with experimental data assessed by them, suggesting the application to thermal stress analysis, residual stress and microstructure modelling of multipass welds.
3D numerical study for the heat transfer and fluid flow in a moving GMAW process was extended by Jaidi and Dutta (2001). They launched for the first time a model combining the electrode transfer analysis with the weld pool heat transfer and fluid flow. They added that energy and momentum of the droplets have to be considered when filler metal addictions are present. The authors modelled the Lorentz force field using the Maxwell equations and simulated the heat transfer and fluid flow in the weld pool using a pressure based finite volume method, where melting and solidification could be included. The model presented is also able to reveal the typical “finger penetration” sometimes present in GMAW. However, quantitative considerations are not fully accurate, and there are uncertainties associated with different welding aspects, such as process efficiency, molten droplet behaviour, surface tension coefficients, high temperature metal properties variation, etc.
A 3D string heat source model to simulate the thermal process in GMAW using a new transient solution of heat transfer was developed by Wang et al. (2005). Agreement with experimental results was obtained for GMAW.
Camilleri et al. (2004) applied infrared thermography to measure transient temperature fields generated during arc welding. Using theoretical and analytical approaches they created a finite element method to describe the variations of temperature observed within welding in different positions and time. Thermography has shown good advantages in the analysis of the temperature profile in complex and large scale plates. However, this method is limited to a thin scale plates and simple geometries, which the thermal camera can monitor.
More recently, Goncalves et al. (2006) used inverse techniques to estimate heat source, thermal efficiency and melting efficiency in GTAW. The physical model included the variation of thermal properties with temperature, phase change, and heat losses, which they considered necessary to characterize melting and process efficiency for each instant of the welding. Goyal et al. (2009) researched thermal behaviour and geometry of weld pools in pulsed GMAW using analytical modelling. Their model is able to predict penetration and width of fusion in the parent material and consequently the geometry of the weld pool.
However, they consider that accuracy is ± 10% and some limitations have been observed, which suggest that some physical aspects should be considered in order to improve precision.
The study of temperature distribution and thermal cycles associated with the heat source has been considered for a long time. Process efficiency represents a fundamental parameter
151 to include in the thermal models where arc energy should be corrected from the heat losses present during welding. Recently, other authors (Karkhin, et al. 2003) have developed an analytical solution bases on Green’s equation to understand the effect of latent heat on process efficiency. Karhin et al. (2003) considered the problem of the heat flow, including the latent heat factor, which account with the heat associated with the phase transformations during welding. Although that study did not account for different physical phenomenon defined earlier, such as the convection phenomenon, agreement was established for experimental results in the prediction of process efficiency parameter.
The science of heat flow in arc welding has been considerably discussed over the last one hundred years. Relationships between heat and fluid flow have been established and modelling is nowadays often applied to reduce time and support experimental work.
However, new advances have been performed in arc welding technology in particular associated with the control of metal transfer mechanisms and the reduction of heat input.
In addition, the development of thermal models to explain the heat flow, residual stresses and metallurgical features should include an accurate measurement of process efficiency, considering the heat losses during an arc welding process.