The corresponding slow surfaces are indicated in Fig. The slow surfaces intersect at the stable quasi-steady point. As a result of quantitative analysis of the ODE-system 2. For a Gaussian distribution this value is of the order of unity. An Inverse Problem A control problem relevant to contour cutting or during the start of a cut can be posed. Using the reduced equations of motion 2. An inverse problem can be formulated R as follows. The result for this deviation is shown in Fig.
Asymptotic analysis of the quasi-steady solution 2. The ansatz 2. Inserting the ansatz 2. Owing to time scale separation as shown in Fig. The intersection of the xz-plane and the cutting front gives a curve referred to as the ceiling line, or centre line of the cutting front. In particular, the arc length can change faster than the cutting speed resulting in U-shaped ripples evolving at the cut surface. Therefore the axial dynamics of the melting front are determined predominantly by spatially one-dimensional heat conduction in the feed-direction [32, 33]. The position where the surface temperature reaches the melting point is called the leading edge of the cutting front.
The cut evolves at the leading edge. In general, thermal boundary layers are singular perturbations of the heat conduction equation and are therefore hard to analyse by numerical methods. Detail at the corner of the cut. The intensity is considered to be constant and no ripple formation occurs. The trace of the laser beam axis is indicated as a dashed line.
Numerical simulation Fig. Deviations from the ideal shape of the cut kerf are limited by the extent of the thermal boundary layers. The results indicate that at the start of the cut and near the corner, deviations of the boundary layer thickness from the ideal values are present, which can be calculated in detail by taking into account the local curvature.
The onset of evaporation at the irradiated metal surface is a further example of a sequel-process.
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These variables are time-dependent parameters of the spatial distributions of the velocity and the temperature in the melt. The dynamics on shorter time scales governing relaxation to the equilibrium distributions can be described by spectral methods. The cutting problem is extended by the dynamical system for the motion of the melting front 2.
Inserting the time dependent characteristic parameters into the ansatz for the spatial distribution allows the reconstruction of the three-dimensional representation of the movement in phase space. Two examples, namely the formation of ripples and adherent dross, will be used to demonstrate that the analysis in phase space — spanned by integral quantities — is more transparent than the interpretation of spatially three dimensional results from direct numerical integration.
The formation of ripples is a characteristic dynamical feature of the cutting process. Processing domains related to cut quality. Quality classes introduced by Arata  for oxygen cutting a are applicable to fusion cutting b, c. The maximum cutting speeds dotted are limited by material thickness and laser power.
The subsequent heat transport — convection in the axial direction — leads to an additional and delayed motion of the melting front by a heat wave 2. As a result, the ripple frequency is doubled. Introduction of quality classes by Arata  is applicable to fusion cutting Fig. Three main processing domains in fusion cutting Fig. If the capillary forces become 2 Simulation of Laser Cutting 45 Fig. The tendency to the formation of dross is estimated from the solution Fig. The dross shows a circular shape and adheres on one side of the cutting kerf. The interpretation for low values of the Weber number is that the CCD-image shows an asymmetric position of the single melt thread Fig.
With the onset of the evaporation pressure the CCD-image shows a symmetric splitting of the melt thread and dross at both sides of the kerf appears, referred to as dross of kind 2. Finally the maximum cutting speed achievable Fig. The equations of motion 2. Equations 2. The cutting process can evolve periodically using modulated laser power. The capillary forces become dominant for low cutting speeds and for cw operation. Low cutting speeds are encountered in contour cutting and therefore a reliable control strategy is of interest.
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From the results about the capillary forces Fig. The modulation parameters, namely pulse duration and the duty cycle, can be chosen such that only one wave of ejected melt is produced during each laser pulse. Using these constraints, the parameters for the pulse mode operation, namely pulse duration and duty cycle, are determined. Figure 2. The CCD-images show that the melt thread remains at the centre of the cutting front as for cw-cutting and parameters corresponding to quality class III in Fig.
The corrections to the spatially integrated equations of motion are found by applying a spectral method, which can be applied in a similar way to more detailed formulations of the problem. We assume that the gas pressure along the surface is constant. The results agree very well and the error introduced by the integral approximation can be determined using spectral methods. Both methods are suitable to evaluate numerical calculations. The equation of motion 2. The mass balance 2. Density gradient of a supersonic gas jet.
The positions of two Mach discs are indicated white arrows. As result, the numerical scheme can be used to reproduce the limiting case of a viscous boundary layer. The wave pattern within the jet consists of shock and expansion waves as well as Mach discs Fig. For free expansion of the jet, the shock and expansion waves have an almost linear spatial shape and the contact discontinuity is curved. Across the contact discontinuity the gas density as well as the velocity component in the tangential direction changes discontinuously while pressure and the normal component of the velocity are continuous.
The shape of the contact discontinuity depends on the nozzle parameters and thus is a free surface within the ambient gas. The 2 Simulation of Laser Cutting 55 Fig. Expansion waves arise during the transition from the converging shock wave to the contact discontinuity. Agreement between Schlieren photography and simulation is striking Fig. An additional oblique shock is formed between body and nozzle when the gas jet impinges on a rigid body.
As a consequence the aligned part of the jet is related to the driving forces for melt acceleration along the rigid body, i. Pressure and tangential velocity component along the edge related to Fig. The range of jet alignment also depends on the nozzle position and parameters as well as on the body shape; the driving forces can therefore be adjusted by a proper choice of nozzle position and parameters.
Simulation therefore shows that the instantaneous density changes even in the lower part of the kerf are much stronger than expected from Schlieren photography. The pressure gradient changes its sign and the velocity component tangential to the wall is slowed down considerably. The parameters for design and alignment of a conical-cylindrical nozzle with respect to the cut kerf.
A larger nozzle pressure pK leads to an increase of the separation depth ds. This behaviour can be observed in trepanning, where a drill hole is widened by performing a trim cut along the circular wall. The pressure gradient as well as the gas velocity are directed dominantly in the axial direction. There are no shocks at the cut surfaces and even the pressure and velocity vary smoothly along the cutting front and the cut surfaces. In general, the spatial changes of gas pressure p along the cutting front change by an order of magnitude.
As a rule of thumb, for a typical situation in cutting the pressure 2 Simulation of Laser Cutting 61 Fig. Simulation of the three dimensional problem including the compressible Navier-Stokes equations. The maximum value of the pressure gradient located near the upper edge of the front is up to ten times larger, but the extent of this region of high pressure gradient is limited to a few hundred microns, as shown in Fig.
As is well known from experimental evidence, the simulation also shows that it is advantageous to use a conical nozzle design in cutting instead of the Laval or Laval-Venturi design. Variations along the front are pronounced for the pressure gradient pz , while the axial component vz of the gas velocity changes only slightly. Dross Formation Depending on Gas Pressure Discussion of the onset of dross formation is carried out with respect to cutting speed v0 and sheet thickness d Fig. Pressure gradient pz solid and gas velocity vz dashed depending on the displacement Vx between nozzle axis and front.
As a result, the simulation reproduces the experimental results for the onset of evaporation and droplet formation as functions of the cutting speed v0 and sheet thickness d Fig. The processing domain III for determination for a cut free of dross. Dross of kind 1 domain II: droplet formation, gray, insert a and kind 2.
CCD-images of the thermal emission from the cutting front. One crucial step towards a cutting machine having more autonomous properties consists of extending knowledge about the processing domains and including a larger set of the processing parameters. References 1. Phys Rev Lett 85 23 : —7 2. Sov J Quant Electr — 3. Nemchinsky VA Dross formation and heat transfer during plasma arc cutting. J Phys D: Appl Phys — 4. Applied Physics A — 6. Phys Fluids A 1: — 9. Phys Fluids A — J Fluid Mech — Rev Mod Phys — Archive of Applied Mechanics 81—90 Z angew Math Phys — Phys Rev Lett — Trends and Applications of Pure Mathematics to Mechanics.
Springer-Verlag, New York 29—48 Eggers J Tropfenbildung. Phys Bl — Springer, Berlin, 43—54 Multiphase Science and Technology 9: — Rose JW Condensation heat transfer. Heat and Mass Transfer, Springer — Rose JW Accurate approximate equations for intensive sub-sonic evaporation. Int J Heat and Mass Transfer — Journal of Statistical Physics 3 : — SpringerVerlag, New York Chaos 5: — Oxford University Press, Oxford Pitman, Boston Springer Verlag Quart Appl Math — Springer Verlag, Berlin, — Int J Heat Mass Transfer 40 12 : — Cambridge University Press, Cambridge J Comp Phys 2—22 Numer Math — Zenger C Sparse grids.
Trans JWRI 8 2 : 15—26 J High Temp Soc 5: 2 Olsen FO Cutting with polarized laser beams. DVS-Berichte Springer, London Vicanek M, Simon G Momentum and heat transfer from an inert gas jet to the melt in laser cutting. J Phys D: Appl Phys — Shachrai A Application of high power lasers in manufacturing. Annals of the CIRP 2 Schulz W, Becker D On laser fusion cutting: a closed formulation of the process. Group, Coburg, — Olsen FO Fundamental mechanisms of cutting front formation in laser cutting. Proc SPIE — Kaplan AFH An analytical model of metal cutting with a laser beam.
J Appl Phys 79 5 : — J Phys D: Appl Phys 12—16 Corrosion Science —52 Meisenbach, Bamberg — Adv Quantum Chem 1: 15 J Atmos Science Kluwer, Dodrecht Cambridge Univ Press, Cambridge J Fluid Mech 8: — Modelling Simul Mater Sci Eng — Meisenbach Verlag, Bamberg, — Deep penetration laser welding relies on the evaporation of material by a high power laser beam in order to drill a vapour capillary, usually referred to as a keyhole.
During continuous welding the keyhole is kept open by the pressure in the vapour which evaporates continuously from its wall; the pressure acts continuously against the surface tension pressure that favours contraction. For some of them mathematical models and calculation results will be presented, complementing a comprehensive survey that was published earlier .
Notation employed in this chapter is given in Table 3. The heat so generated drives the thermodynamics of the welding process.
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In deep penetration laser welding absorption is a highly complex mechanism  composed of contributions from the direct absorption of the laser beam at the keyhole wall the main governing mechanism , absorption during multiple scattering, absorption in the metal plasma and absorption at the top surface of the work piece. The amount of absorbed energy is most simply expressed as the product of the incident laser beam power multiplied by an overall absorptance.
For more accurate study of heat conduction, however, the spatial and temporal distribution of the absorbed laser beam power across the keyhole wall surface is also of importance. Models in which a point and a line source of heat are superimposed , or several point sources are superimposed , take this into account. Other models implicitly calculate the distribution of the absorbed power , as will be described below.
In particular, the absorptivity of a material at any location is determined by its optical constants n and k that are functions of the material, the laser wavelength, the temperature, and the angle of incidence. Moreover, the surface topography and chemistry usually in the form of oxides alter the local absorptance [7, 8]. As a result of the singularity at the origin, these solutions are inaccurate close to the heat source. A numerical integral has to be evaluated, but in contrast to the moving point source the beam radius is taken into account, giving solutions that are quite accurate even close to the laser beam.
The method has proved to be very powerful. In particular, it was demonstrated that approximating higher order modes by a Gaussian beam can under certain circumstances cause fundamental errors. Model of superposition of moving point sources of heat and resulting isotherms: a melting and evaporation isotherm, b evaporation isotherm dependent on the number of sources employed. Figure 3. Twin-sided simultaneous welding with two nail-head shapes is shown in Fig. Calculated shape of the melt pool and keyhole based on superposition of moving point sources of heat: a low power W , not welded through, b moderate power W , not welded through, c high power W , welded through, d welded through, widening at the top, e widening at top and bottom e.
Reprinted from , copyright with permission from Old City Publishing. Steady State 2D-Heat Conduction from a Moving Cylinder at Constant Temperature Another powerful analytical solution is the moving cylinder the keyhole cross section , where the surface of a cylinder is set at a constant temperature; this 76 Alexander Kaplan might be the evaporation temperature in the case of a keyhole. More sophisticated is the assumption of a moving ellipse  instead of a cylinder, providing an additional geometrical parameter of freedom.
For an ellipse that is strongly elongated in the lateral direction, Fig. Reprinted from , copyright with permission from Institute of Physics Publishing Ltd. Conservation of energy for quasi-steady state conditions requires equivalent heat losses at the boundaries. For analytical modelling very few solutions can take this phase transformation discontinuity into account. A generally applicable method that, however, has to be checked case by case with regard to accuracy and thus applicability, is an enthalpy transformation.
The boundary problem is expressed in terms of enthalpy h instead of temperature T , i.
It is easier to handle phase transformations at the surface, e. For oscillating conditions powerful techniques for the solution of the heat conduction equation have been developed [13, 19], particularly by expanding the steady state solutions of moving sources of heat to allow for oscillating conditions. Reprinted from , copyright with permission from Elsevier. Instead it focuses on dynamic behaviour, particularly the stability of oscillations. In the calculation each ring 82 Alexander Kaplan Fig. Calculated radius, rm and rv , of the surface melting and evaporation domains as a function of time for two laser pulse energies EL.
From the various calculated results in , one for AuNi-coated copper is shown in Fig. For two laser beam pulse energies the melting radius at the surface is plotted as a function of time. For higher beam energies, the evaporation temperature will be reached and the development of the evaporation domain radius assuming no changes in shape of the surface is also shown.
The analysis allows detailed study of the absorptance as a function of space and time. Correspondingly, beyond the melting threshold the melting radius grows rapidly, making the process highly sensitive to disturbances. This was recognised as a source of unreliability and a serious industrial problem; it was possible to study it and performance was successfully improved by lowering the sensitivity of the surface conditions that in turn lower the absorptance. The impact of small absorbing pollutions hot spots and the threshold to keyhole formation can be explained, for example.
The cross section achieved during the process, which is often a design goal, is a projection of the three-dimensional interface, e. Moreover, the temperature gradients at the interface determine the metallurgical structure. Mass Balance of a Welding Joint Figure 3. An increasing of the average gap width, as seen in Fig. In contrast, the addition 84 Alexander Kaplan Fig. The cross sectional area added by wire feeding depends on the process.
For the most common case of cw-laser welding heat conduction leads to quasi-steady state conditions relative to the laser beam. For pw-laser welding, and in particular for single pulse laser welding, the conditions are highly transient and even more complex. One example, namely the keyhole collapse  during single spot laser keyhole welding that often ends in the formation of a pore, is described in Chapter 7.
Spatter ejection during drilling of the keyhole is also typical, as the transient conditions are not in balance, in contrast to cw-laser welding, and often lead to a considerable excess of evaporation recoil forces that accelerate the melt. Pulsed conditions also take place during laser hybrid welding where periodically drops detach from the feeding wire that move towards the melt and interact with it.
Uncontrolled violent melt motion and drop ejection behind the keyhole. The driving force for this acceleration is the evaporation recoil pressure at the front of the keyhole, controlled by the incident laser beam power and by the local keyhole wall angle.
As a regulating mechanism, the more the upstream melt tries to push the keyhole front wall forward, the more strongly is the laser beam locally absorbed; the keyhole wall reacts by evaporation and through the resulting ablation recoil pressure. High velocities are therefore required in these regions to maintain the mass balance.
At lower speed the melt pool becomes wider. For a larger keyhole a very narrow channel can result where a high pressure develops in order to drive the melt around the keyhole, to ensure conservation of mass. The high speed generated can lead to phenomena such as surface waves, undercuts with central peaks mechanism E in Fig.
The high speed is a result of steep pressure gradients in the melt that in turn are caused by evaporation at the keyhole front. The evaporating keyhole front has a self-regulating mechanism for continuously redirecting the upstream melt laterally around the keyhole. The resulting speed of the melt at the centreline of the melt and along the keyhole boundary is plotted in Fig. Various simulations with somewhat differing results can be found in the literature for this boundary value problem.
For a circular keyhole and low speed, Fig. For high welding speed, see Fig. This kind of eddy due to the fact that welding speed eddies become advancing spirals supports heat conduction radially away from the keyhole, thus widening the weld pool and making it more shallow.
This mechanism may be one of the origins for the often typical nail shape or wine glass shape of the weld. Marangoni convection is a complex but important phenomenon which is always present and often dominant during laser welding. The wall more or less reacts to the developing vapour 90 Alexander Kaplan pressure that keeps the keyhole open against surface tension contraction. The rear keyhole wall is the boundary to the weld pool at the rear side, where the melt extension is much larger compared to the thin region in front of and beside the keyhole. Moreover, surface waves directed backwards into the melt pool can be generated.
It is characterised by the regular development of large drops on the melt pool; see mechanism D in Fig. These periodically resolidify at the top weld surface, thus leading to an unacceptable weld quality. In particular, strong acceleration of the melt under a blind keyhole followed by subsequent stagnation far behind the keyhole was observed at high welding speed with the aid of high speed imaging.
Moreover, in contrast to or in combination with drops at the surface formed by humping, channels can form between the resolidifying drop and the lateral boundaries of the weld. In the weld seam they appear as cavities or severe undercuts. It usually has a shape convergence towards the centreline, as in Fig.
This phenomenon results in undercuts at the sides and a peak in the centre of the weld, as can be observed in the weld seam cross section. Stagnation and redirection at the lower boundaries of the melt pool occurs, as shown for mechanism F in Fig. Consequently, the melt can either be accelerated to the top or bottom. The latter often leads to root drop out as illustrated by mechanism G in Fig. It is caused by ablation pressure augmented by the gravitational force. Again, momentum imparted by incident drops during hybrid welding can also support the mechanism.
The evolution of root drop-out together with surface lowering and wire addition has already been described in Section 3. Mathematical modelling and simulation as well as high speed imaging are suitable methods for improved understanding and control of these phenomena; such understanding is important since these phenomena often determine the resulting weld quality.
Kapadia P, Dowden J Review of mathematical models of deep penetration laser welding. Lasers in Engineering 3 3—4 : — 2. Adam Hilger, Bristol UK 4. J Phys D: Appl Phys — 5. J Phys D: Appl Phys — 6. Lasers in Engineering 7 3—4 : — 7. Appl Surf Sci — 8. J Appl Phys 11 : — 9.
Rosenthal D The theory of moving sources of heat and its application to metal treatments. Trans ASME — Oxford Clarendon, Oxford J Appl Phys 48 9 : — Appl Phys Lett 70 2 : — Simon G, Gratzke U, Kroos J Analysis of heat conduction in deep penetration welding with a time-modulated laser beam. J Phys D: Appl Phys 30 8 : — Kaplan AFH Semi-analytical modeling of the process interaction zone. Kaplan AFH Modelling the absorption variation during pulsed laser heating.
Appl Surf Sci 3—4 : — Dowden J, Kapadia P Oscillations of a weld pool formed by melting through a thin work piece. Lasers in Engineering 8 4 : — Otto A, Geiger M From basic research to industrial applications — new developments for laser welding, Proc. Welding Journal 73 2 : 25s—31s Several aspects of the properties of the keyhole and its relationship to the weld pool in laser keyhole welding are considered. The aspect of most immediate importance is the exchange of energy between the laser beam itself and the molten material of the weld pool.
Many mechanisms are involved, but the two considered here are the process of direct absorption at the keyhole wall Fresnel absorption and the two-stage process of absorption of energy by inverse bremsstrahlung into the ionised vapour that forms in the case of the longer-wavelength lasers such as the CO2 laser, followed by thermal conduction to the wall. Consideration is given to the role of the Knudsen layer at the boundary. A simple model of the interaction of the vapour with the molten material in the weld pool is proposed which can be used to investigate their interaction.
Order of magnitude estimates suggest that it is far from simple but that some simplifying approximations are possible. The relative geometry of the work piece, laser and keyhole during laser keyhole welding, and the transfer processes involved. It is either re-radiated or else passed by thermal conduction in the vapour to the keyhole wall. For a CW CO2 laser this fraction can be substantial, but is much less when the wavelength is shorter.
This transfer process is illustrated in Fig. If time dependence is ignored, the main equations and the reasons for them can be found in  and in a form extended to variation along the keyhole in  and . The quasi-neutrality approximation can then be used. Equations 4. The vapour itself is strongly conductive at these temperatures. The results obtained so far must be combined with the equation of heat conduction 1. Mass is not conserved along the length of the keyhole because of John Dowden ablation at the keyhole wall.
Sometimes the pressure can be regarded as not varying greatly from the average local value. Equation 4.
Since molecules immediately adjacent to the boundary cannot have a component of velocity relative to it that is directed towards it, there is an adjustment layer with a thickness of a few mean free paths before equilibrium is reached. The region is known as the Knudsen layer.
The distribution of velocities immediately adjacent to the wall is usually assumed to be half-Maxwellian, an assumption which is well supported by observation. In laser processing consideration of the Knudsen layer can be important since strong vaporisation can occur on, for example, the keyhole wall in laser keyhole welding.
The gas near the wall is not in translational equilibrium, which is reached in a few mean free paths as a result of particle collisions.
Ablation Through the Knudsen Layer At the boundary between the liquid and vapour phases the material of the work piece crossing it experiences an intense phase change. The result is that a Knudsen layer forms in the vapour in which the transition from a non-equilibrium velocity distribution at the surface of the liquid region, to a local Maxwell-Boltzmann distribution some few mean free paths above the metal surface occurs.
See for example —. Knight  has shown that the following discontinuity relationships hold. Figure 4. The normal components of gas velocity are related by the condition of conservation of mass, 1. Conditions inside a keyhole, however, are not those of a vacuum, and Finke et al. The same notation is used as in Fig. The results are not straightforward, but the arguments in favour of 1.
The same may not be true, though, when condensation occurs. When there is no phase change at the boundary, the formal position is that 1. The theory so far has been derived for a solid boundary at rest, but the same ideas apply if the boundary were liquid and in motion, provided the slip velocity is understood to be relative to the tangential velocity of the boundary.
Related to 4. In particular, it is likely that the no-slip condition 1. The subject was analysed in detail by Stratton  and was applied in the case of p-polarised light to laser cutting by Schulz et al. It is assumed that the 4 Laser Keyhole Welding: The Vapour Phase light is absorbed by the classical Fresnel formulae and the light beam couples to the metal electron gas.
This absorbs some of the intensity by Joule heating. A CO2 laser with a wavelength of This simple electromagnetic model for absorption at a metal surface is often used at the wavelength of a CO2 laser; at that wavelength a simple model of electromagnetic interaction involving resistive dissipation is probably adequate. At shorter wavelengths, though, the model becomes less satisfactory; neither does it allow for surface impurities.
Power absorbed per unit depth at the keyhole wall for iron vapour as c a function of power at the given cross-section of the keyhole. When substituted in 4. It is worth note that the speed of sound in unionised iron vapour at this temperature is nearly three times that for air at room temperature. At the CO2 wavelength, an order of magnitude calculation suggests that the dominant term is the second on the left, with the convection terms on the right playing a relatively minor role. Reference  pp — gives the solution of this equation; Fig. The lower branch is an unstable alternative solution.
The order of magnitude of the right hand side of the equation is then 6. At lower temperatures, of the order of 5 kK at atmospheric pressure, the ratio of the convective term to the absorption term rises dramatically and is very high at the boiling temperature. If the velocity scale W0 is taken as the magnitude of the exit velocity at either end of the keyhole, a solution for T independent of z is then possible. The solid line in Fig. From 4. Furthermore, for a conical blind keyhole the average temperature over the whole keyhole is then predicted to be of the order of 13 kK.
For lasers with higher fundamental frequencies much less energy is absorbed by inverse bremsstrahlung resulting in a much lower temperature on the axis and on average over the whole keyhole. A consequence is that the radial ablation velocity increasingly tends to suppress absorption by inverse Bresstrahlung when progressively higher wavelengths are used. Included in Fig. At higher levels of convection no solution is possible and the plasma is extinguished.
The same is generally true of longitudinal convection. Some estimates for the maximum viscosity of ionised gases. Table 4. A maximum value is reached as indicated in the table followed by a fairly rapid fall to a value under 0. For example, consider the Reynolds Number in the melt pool; it is possible to estimate its order of magnitude. Graphs of the degree of ionisation, the Prandtl number and the Reynolds number as functions of temperature at atmospheric pressure are shown in Figs.
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Uworkpiece indicates the direction of translation of the work piece relative to the laser beam. The reason for this lies in the molten region, not the keyhole itself. The Reynolds number close to the keyhole wall based on the same length scale and velocity is very high, with a value at the level associated with fully developed turbulence. In consequence, a strongly turbulent motion is to be expected near the keyhole wall in the liquid region though not in the vapour.
As a result, it seems likely that the welding region for a blind keyhole can be divided schematically into regions as in Fig. In order to avoid highly pressurized zinc vapor caused weld defects like spatters and blowholes, either the zinc coating should be removed before the steel melts or the vaporized zinc needs to be vented out properly during the welding process.
The most direct way of accomplishing this is to mitigate the presence of high pressure zinc vapor during the welding process. In order to achieve this goal several techniques are proposed which will be described in the following sections of this chapter. Ribic et al. A lower welding speed will generate an enlarged weld pool that will require a longer solidification time. An experimental work is presented to show that the effect of zinc vapor on the quality of a weld in a zero-gap lap joint configuration may be successfully mitigated.
A fiber laser of 4 kW in power with a focused spot of 0. Pure argon with a flow rate of 30 standard cubic feet per hour SCFH was employed as side shielding gas to suppress the laser-induced plasma and to protect the molten material against corrosion. The base material used in this work was galvanized high strength dual phase DP steel DP, whose nominal chemical composition is listed in Table 2 Burns, The coupons of galvanized DP steel sheets were 1.
The top and bottom views of the weld obtained under a laser power of 2. A high-speed CCD camera with a frame rate of fps combined with a green laser with a band pass filter wavelength of nm as the illumination source were used for real time monitoring of the dynamic behavior of the molten pool under different laser welding conditions.
The weld pool formed under a relatively low welding speed was larger and relatively stable see Fig. On the other hand, the molten pool acquired under a higher welding speed shows sever fluctuation, and the high pressured zinc vapor generated at the faying surface jetted into the molten pool causing blowholes see Fig. However, if the welding speed is exceedingly low, the sagging may be generated, which also reduces joint strength. A higher failure load was acquired under a lower welding speed. The trapped zinc vapor may result in pores inside the joints which could decrease the failure load with respect to the joints acquired under the same welding conditions but without zinc at the faying surface see Fig.
Top and bottom views of the weld obtained under a laser power of 2. The dynamic behavior of the molten pool acquired under different welding parameters: a laser power of 1. The failure load for tensile shear testing of the DP lap joints acquired under different welding speeds and with the laser power of 2.
In order to improve the production efficiency, the automotive industry requires a welding technique that can join of overlapped galvanized high strength steels successfully under a higher working speed. As discussed previously, if the zinc coating is removed before the steel starts to melt, a much higher welding speed can be achieved. Therefore, a two-pass laser welding process that is capable of successfully joining galvanized steel sheets in a zero-gap lap joint configuration is presented.
The defocused laser beam shown in Fig. The laser power was set at its maximum value of 4. The preheating parameters, like the defocused position of the laser beam and the laser scanning speed, are critical in achieving a final weld quality. The schematic view of the two-pass welding process: a laser preheating, b laser welding, and c geometrically defined width of zinc coating treated during preheating and welding.
As the defocused off-set distance increased, the defocused laser beam spot became larger, and the laser energy distribution was dispersed. A defocused off-set distance combined with a lower scanning speed generated too much energy that penetrated the top sheet resulting in spatters and permanent defects which could not be mitigated by the following laser welding pass see Fig. A longer defocused off-set distance combined with a higher scanning speed could not vaporize a sufficient amount of zinc coating; the remaining zinc coating at the contact interface caused weld defects see Fig.
Thus, only for the optimized laser defocused off-set distance and the scanning speed, will a reasonable width of the zinc coating be vaporized see Fig. The optimized preheating parameters that allowed a sound weld are shown in Fig. The schematic view of the preheating process: a molten pool penetrates the interface, b narrow vaporized zinc coating area, and c optimized width of the vaporized zinc coating area.
Experimentally determined combinations of defocused off-set distance and scanning speed that result in a good weld quality. The zinc coatings far from the preheated zones at the top and bottom sheets are not affected see Figs. Preheated surface of the top steel sheet obtained with a laser power of 4.
During the laser preheating pass, the defocused laser beam burns the zinc at the top surface, and melts and partially vaporizes the zinc coatings at the interface of the two overlapped steel sheets, and improves the absorption of the laser beam which results in the formation of a stable keyhole through which any zinc vapor formed at the interface will be vented out Yang et al.
The tensile shear test was carried out in order to determine the mechanical strength of the welded joints obtained by the two-pass laser welding procedure. The experimental results demonstrated that the two-pass welded joints were broken in the HAZ of the bottom steel sheet. One of the tensile shear results is shown in Fig. The tensile shear test for the welded coupons without a zinc coating at the interface was also performed. In order to use the data as a reference, the welded coupons without a zinc coating at the interface had a average failure load value of The reason for this difference in results is explained by the fact that the preheating process increased the laser beam absorption of the coupons, which contributed to a stronger wider partially penetrated weld joint.
Preheated surface of the bottom steel sheet obtained with a laser power of 4. Based on the experimental study performed, it was found that the stability of the laser welding process was sensitive to the clamping conditions. A relatively loose clamp condition resulted in a better weld than a very tight clamp condition. The gap ahead of the weld pool is the key to performing the laser welding of galvanized steel in a lap joint configuration successfully.
Moeckel et al. The Fraunhofer Institute developed a pressure wheel system which could control the roller clamping force that allows for the controlling of the gap at the faying surface Fraunhofer Institute website. The laser welding of galvanized steels for a lap joint configuration with a pressure wheel control system is shown in Fig. Laser welding of galvanized steel for a lap joint configuration with a pressure wheel control system. The feasibility of welding galvanized steel sheets in a lap joint configuration by controlling the pressure wheel force during the fiber laser welding process is discussed.
Offers updated and expanded coverage of the numerical and analytical approaches to laser materials processing techniques including a new chapter on glass cutting Places emphasis on the underlying physical causes of observed phenomena Gives readers an understanding of the strengths and limitations of core numerical and analytical models Includes an introduction to meta-modelling, an interactive tool which can be used as a means of obtaining fast, reliable models see more benefits. Buy eBook. Buy Hardcover. Buy Softcover. FAQ Policy. About this book The revised edition of this important reference volume presents an expanded overview of the analytical and numerical approaches employed when exploring and developing modern laser materials processing techniques.
Show all. Glass Cutting Pages Schulz, Wolfgang. Laser Forming Pages Pretorius, Thomas.