Literature Review
2.4 Theoretical Model
2.4.3 Convective based weld pool model
The numerical model that takes into account fluid flow is more close to the real welding process. Though the small characteristic length in microwelding limits the liquid flow to some extend yet convection is still an important mechanism of heat transfer in weld pool. Although a few literatures have come up to study the heat transfer and fluid flow in micro joining, till it is in the premature stage and needs to be investigated.Convective flow of liquid metal within weld pool is the most important factor to influence the pool geometry, change in pool shape, composition and the aspect ratio. The shape and size of weld pool are decided by the nature of circulation of liquid metal that are driven by electromagnetic, surface tension gradient and buoyancy forces. An extensive review of the physical processes prevalent in fusion weld pool was studied by Debroy and David [1995].According to the authors, the convective flow in weld pool is driven by surface tension, buoyancy and when electric current is used, electromagnetic forces. Aerodynamic drag forces of the plasma jet might also be contributed to the convective flow in the weld pool. Buoyancy effects originate from the spatial variation of the liquid-metal density, mainly because of temperature variation, and, to a lesser extent, from local composition variations. Electromagnetic effect is a consequence of the interaction between the divergent current path in the weld pool and the magnetic field that it generates. This effect is important in arc and electron-beam welding, especially when a large electric current passes through the weld pool. In arc welding, a high velocity plasma stream impinges on the weld pool. The friction of the impinging jet on the weld pool surface can cause significant fluid motion. The spatial gradient of surface tension results in a driving force, referred to Marangoni stress, along the top surface of the weld pool. The spatial variation of the surface tension at weld-pool surface may arise owing to variations of both temperature and composition [He et al., 2004]. Frequently the main driving force for convection is the spatial gradient of surface tension at the top surface of the weld pool from its center to the periphery. For such a situation, the Marangoni stress can be expressed as [DebRoy and David, 1995]:
48 dy
.dT dT
d
(2.12)
where τ is the shear stress due to temperature gradient, γ is the interfacial tension, T is the temperature, and y is the distance along the surface from the axis of the heat source. The nature of liquid convection in weld pool and the shape of the weld pool due to different driving forces are schematically shown in Fig. 2.8. Due to the variations of temperature and composition, the temperature coefficient of surface tension may be positive or negative as shown in Figs 2.8(b) – (c) and the shape of the weld pool is influenced subsequently.
Fig. 2.8 Various driving forces and resulted liquid convection in weld pool (a) electromagnetic force, (b) and (c) surface tension force, (d) buoyancy force, and (e) arc plasma force [Schauer et
al., 1978].
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Though, the dynamics of molten pool is an important phenomenon in a sophisticated weld pool model, very few have attempted to simulate velocity field and their differential effects on the formation of weld pool in laser microwelding process. An excellent literature review on thermal modeling of laser welding was performed by Mackwood and Crafer [2005]. However, to what extend the flow dynamics influences the formation of weld pool in microjoining is still not understood due to difficulty in experimental observation of the same. Hence, the flow dynamics is generally analysed by numerical models that solved the conservation of mass, momentum, and energy in the molten region. Rohde et al. [2010] performed numerical simulation of microjoining using the finite-volume method which is based on the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm.A transient three dimensional model to study heat transfer and fluid flow during laser spot micro welding of a 304 stainless steel was stimulated by He et al.
[2005]. It is seen during most of the welding time Peclet number was greater than unity which showed the importance of convection in heat transfer analysis. Brockmann et al. [2001]
developed a model to study the temperature field induced by laser on moving thin foils. Effects of evaporation, melting and solidification of sheet material is taken into account. Convective and radiation cooling, nonlinear effects connected with temperature dependencies of material properties are included into the model. In order to include the Marangoni effect into the model, the heat conductivity of melted metal to solid metal is increased several times. He et al. [2004]
studied the composition change of stainless steel during micro joining with short laser pulse.
Using the computed temperature fields, vaporization rates of various alloying elements resulting from both concentration and pressure driven transport of vapours and the resultant composition change of the alloy were calculated. The vaporization took place mainly from a small region near the centre of the beam-work piece interaction zone, where the temperatures were very high.
Furthermore, the alloying element vaporization was most pronounced toward the end of the pulse. Fig.2.9 shows the computed three-dimensional temperature and velocity fields for a typical linear Nd:YAG laser microweld of 304 stainless [He et al., 2005]. Since the temperature coefficient of surface tension dγ/dT is negative, the molten metal flows from the middle to the periphery of the liquid pool. As a result, the convection aids in the transport of heat in the weld pool. The calculated maximum temperature and liquid velocity along the y direction in the weld pool are 2119 K and 440 mm/s, respectively. Compared with large welds, smaller weld pool size for laser microwelding restricts the liquid velocities, but convection still remains an important
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mechanism of heat transfer [He et al., 2005; Bag and De., 2010]. There is little evidence to experimentally measure liquid flow velocity within weld pool. Pitscheneder et al. [1997]
attempted to experimentally measure the flow velocity in laser welding of thick material.
However, in microwelding there does not exists any such attempt in current literature and these may be because of complexity of the rapid process itself and of small scale component size. It is also evident that the presence of surface active elements in parent material has great influence in the formation of weld pool shape [Pitscheneder et al., 1996; Bag and De, 2010] and these phenomena is still unclear in the microjoining process.
Fig. 2.9 Calculated temperature and velocity fields in three dimensions in a 304 stainless steel sample. Laser power: 100 W, beam radius: 100 mm, and welding speed: 1 mm/s [He et al.,
2005].
Not much work has come up yet in the field of theoretical modeling of micro plasma arc welding. Tam et.al [1989] studied the process of mechanized plasma arc butt welding of thin gauge mild steel sheets. McKellit[1990] developed a mathematical model to predict the velocity, temperature and electromagnetic fields inside an inductively coupled plasma torch, as well as the motion and thermal histories of particle injected into the torch. Keanini [1993] presented a three dimensional finite element model of the plasma arc welding process. The model allows calculation of three dimensional flow and temperature fields, and solid phase temperature distribution. The flow in vertical cross sections is dominated by a large jet driven vortex, competition between surface tension and jet shear produces a stagnation region near the top of the pool. Flow in horizontal planes is largely determined by the plate‟s motion and buoyancy is a secondary driving force within the plasma arc weld pool. Xu et.al [2009] developed a model to TH-1698_11610311
simulate the electromagnetic phenomena and flow field in low current micro plasma arc welding process.
Together with the aforementioned literature on microjoining, various authors developed integrated models in order to keep a complete vision of the welding problems [Sudnik et al., 1996; Ye and Chen, 2002].But most of the all of the models mainly focused on the study on the steel materials or aluminum alloys. Not much investigation was found to predict the weld profile of the laser weld for titanium alloy. With the special materials properties, the weld geometry of titanium alloys appears difference characters with other materials. A thorough investigation of flow in the weld pool can meet the needs for exactly controlling the profile of the weld, which is very important for the titanium alloy products of various industries. Rai et al. [2008] calculated and compared the temperature fields, thermal cycles, weld geometry, and fluid flow of laser and electron beam welded joints of Ti6Al4V and stainless steels. The fusion zone size in Ti6Al4V alloy was larger than that of the 21Cr6Ni9Mn stainless steel during both the electron beam and laser beam welding. In the EBW of both the alloys, there were significant velocities of liquid metal along the keyhole wall driven by the Marangoni convection. In contrast, during LBW, the velocities along the keyhole wall were negligible. A comprehensive fluid flow model is developed to simulate the geometric profile of the laser beam welding of titanium alloys [Du et al., 2004]. The result confirmed that the momentum interpolation system with under-relaxation parameter based on non-staggered grid technology can effectively eliminate the pressure oscillations. The calculated results showed that the molten pool becomes shorter and wider with the Marangoni effect. It also indicated that the metal flow is the main reason for forming the typical “hourglass” cross-section profile.
A comparison between computed weld dimensions using both conduction heat transfer and transport phenomena based model in laser spot welding was carried out by Bag and De [2010] to relate the relative importance of both the model as depicted in Fig. 2.10. It is demonstrated that the conduction model predicts weld geometry well in case of small geometry (low on-time) and material having low weight percent of sulfur whereas the transport phenomena based heat transfer and fluid flow model predicts bigger weld pool (high on-time) better. Also, the conduction based model fails to predict the weld geometry for the material having considerable amount of surface active elements (0.015 wt % of sulfur). Thus, it can be accepted
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that for thin plate welding especially below 0.5 mm conduction mode with a suitable heat source would be preferable. Moreover Ti6Al4V has no content of sulphur. Thus, conduction mode heat transfer model with a suitable heat source would be better for simulation of weld pool of Ti6Al4V.
Fig. 2.10 Comparison of weld geometry prediction between conduction model and transport phenomena based heat transfer and fluid flow model in spot welding [Bag and De, 2010].