Koji Hirano
email: hirano.koji@nsc.co.jp

Remy Fabbro

Possible explanations for different surface quality in laser cutting with 1 m and 10 m beams

Keywords: laser cutting, striations, hydrodynamic instability

In laser cutting of thick steel sheets, quality difference is observed between cut surfaces obtained with 1 m and 10 m laser beams. This paper investigates physical mechanisms for this interesting and important problem of the wavelength dependence. First, striation generation process is described, based on a 3D structure of melt flow on a kerf front, which was revealed for the first time by our recent experimental observations. Two fundamental processes are suggested to explain the difference in the cut surface quality: destabilization of the melt flow in the central part of the kerf front and downward displacement of discrete melt accumulations along the side parts of the front. Then each of the processes is analyzed using a simplified analytical model. The results show that in both processes, different angular dependence of the absorptivity of the laser beam can result in the quality difference. Finally we propose use of radial polarization to improve the quality with the 1 m wavelength.

I. Introduction

Recent progress of high power and high brightness lasers has enabled high throughput and low cost operation in a number of laser material processing applications in industries.

Meanwhile, laser cutting of thick-section steel with inert gas, one of the important applications, has so far failed to benefit from this advantage. The problem concerns striations which are created on cut surfaces during laser cutting process. For thickness typically over ~ 4 mm, roughness of cut surfaces obtained with a fiber or disc laser ( L ~ 1 m) is higher than that achieved with a conventional CO 2 laser ( L = 10.6 m). [START_REF] Wandera | Cutting of stainless steel with fiber and disk laser[END_REF][START_REF] Himmer | High brightness lasers in cutting applications[END_REF][START_REF] Hilton | Cutting Stainless Steel with Disc and CO 2 Lasers[END_REF][START_REF] Scintilla | A comparative study on fusion cutting with disk and CO2 lasers[END_REF] For example, Scintilla et al. [START_REF] Scintilla | A comparative study on fusion cutting with disk and CO2 lasers[END_REF] compared laser cutting of steel with disc and CO 2 lasers using almost the same laser beam diameter and gas condition. For thicknesses of 5 mm and 8 mm, cut surface quality obtained with a disc laser was worse than the one obtained with a CO 2 laser. Considering that the operating conditions were nearly the same, it seems reasonable to infer that the quality difference is attributed to the influence of the laser wavelength on the absorption process and more particularly, the Fresnel absorption.

Whereas wavelength dependence of the Fresnel absorption law has been related to difference in achievable thickness, [START_REF] Mahrle | Theoretical aspects of fibre laser cutting[END_REF] very few investigations have been made on the mechanism of the difference in the cut surface quality. Poprawe and co-workers observed ripple formations on the kerf front with a 1 m beam but not with a 10 m beam, [START_REF] Poprawe | Hydrodynamics of material removal by melt expulsion: Perspectives of laser cutting and drilling[END_REF][START_REF] Vossen | Optimization of Partial Differential Equations for Minimizing the Roughness of Laser Cutting Surfaces[END_REF] which they claim is the cause of the quality difference. This correlation between the ripples on the front and the striations on the sides is not so clear; striations appear even in the case of CO 2 laser cutting where the ripple formations were not observed. Petring et al. [START_REF] Petring | The relevance of brightness for high power laser cutting and welding[END_REF] has proposed another point of view that multireflections, which occur within the kerf in laser cutting with a 1 m beam, can destabilize lower part of kerf sides. According to experimental results, however, the degradation of the surface roughness in the case of a 1 m beam starts at 1 ~ 2 mm below the top surface, [START_REF] Wandera | Cutting of stainless steel with fiber and disk laser[END_REF][START_REF] Himmer | High brightness lasers in cutting applications[END_REF][START_REF] Hilton | Cutting Stainless Steel with Disc and CO 2 Lasers[END_REF][START_REF] Scintilla | A comparative study on fusion cutting with disk and CO2 lasers[END_REF] where the laser beam absorption from multi-reflected components is not supposed to be important.

Consequently, multi-reflections cannot be the main mechanism.

One of the problems which have hindered a proper understanding of this phenomenon is that, before discussing details of the wavelength effect, we have not understood properly the mechanism of the striation generation process itself. The situation has been changed, however, by direct experimental observations of the process. Yudin and co-workers observed hydrodynamics on kerf sides during laser cutting of Rose's alloy [START_REF] Yudin | Visualization of events inside kerfs during laser cutting of fusible metal[END_REF] and mild steel [START_REF] Grigory | Visualization and modeling of combustion effects at laser cutting of mild steel with oxygen[END_REF] by visualization through a glass plate. They confirmed that striations are developed by intermittent downward displacement of melt accumulations along kerf sides. In order to clarify the origin of this intermittent generation of melt accumulations, we observed melt flow dynamics from above the kerf front in laser cutting of steel. [START_REF] Hirano | Experimental investigation of hydrodynamics of melt layer during laser cutting of steel[END_REF] The results indicated an important role of surface tension, which tends to hold melt accumulations at the top of the kerf side counteracting to assist gas force. Another important phenomenon was found in an intermediate velocity range: melt flow in central part of the kerf front is continuous whereas flow in side parts is discontinuous, and it is this unstable side flow that leads to striation generation. This result indicates the importance of distinction between central and side flows when one considers the influence of the melt flow stability on the striation generation.

The object of this paper is to discuss theoretical aspects of the quality difference observed between the two wavelengths in thick section laser cutting of steel. In the following, we first describe striation generation process suggested from our recent experimental observations, and then discuss possible mechanisms of the quality difference.

II. Mechanism of striation generation

Figure 1 schematically shows melt flow on a kerf front and striation generation process. We pay attention to the three-dimensional structure of the melt flow on the kerf front, considering the results of our experimental observation, [START_REF] Hirano | Experimental investigation of hydrodynamics of melt layer during laser cutting of steel[END_REF] which revealed the importance of the distinction of the flows in the central and side parts. This point is contrasted with the existing models (for example, Refs. 6 and 7), where only processes in the central plane of cutting were described.

First of all, it should be noted that, it is the discontinuity of the resolidification process on the kerf side that leads to striations, as was already pointed out by Yudin and Kovalev. [START_REF] Yudin | Visualization of events inside kerfs during laser cutting of fusible metal[END_REF] In the top part of the kerf, the discontinuity comes from discrete melt accumulations (MAs hereafter) that are generated periodically and displaced downwards along the kerf sides. Our observation showed that the MAs are created one by one along an arc EQ in Fig. 1 of MAs, and so on. When cutting velocity V c is increased, for instance, a increases and thus the interception is more likely to occur. Now let us consider the regime of thick section cutting with a 1 m laser beam, which is the main interest of the present study. In this regime, the central part of the front is expected to be discontinuous, because a is so small. We experimentally investigated the stability of the central part using a 1 m disc laser beam [START_REF] Hirano | Experimental observation of hydrodynamics of melt layer and striation generation during laser cutting of steel[END_REF] and the results showed that, when a < 13 degrees, humps appear in the central part. (Throughout this paper, the term hump is used for a MA that appears in the central part of the kerf front in order to distinguish the one from a MA in the side part, which is called as such.) In general, the maximum value of a can be estimated from (d/h) (h: thickness of specimen, d: laser beam diameter). [START_REF] Mahrle | Theoretical aspects of fibre laser cutting[END_REF] For a typical condition of thick section cutting (h ≥ 4 mm, d ~ 200 m), one obtains a ≲ 3 degrees. The angle is so small that the central part is likely to be unstable. This regime of humps for thick section cutting was reported also in Ref. 6.

The humps in the central part can affect striations, since melt flow on the whole kerf front is discontinuous and the humps in the central part can disturb downward movement of MAs on the side through interaction caused by surface tension and can end up in the increase of surface roughness on the kerf sides. This kind of interaction between the central and side flows was observed in our experiments for a low velocity range (V < 2 m/min). [START_REF] Hirano | Experimental investigation of hydrodynamics of melt layer during laser cutting of steel[END_REF] Then what is the reason of the quality difference between the 1 m and 10 m wavelengths?

The above discussion leads us to propose two fundamental processes: the destabilization of the melt flow in the central part, which can disturb the process of downward displacement of MAs and the downward displacement itself, which directly results in striation generation. Each of these two processes is examined in the following. Although there are many parameters that can alter the characteristics of the two processes, we focus on the influences of different wavelengths to clarify the principal mechanism that leads to the quality difference.

III. Stability of melt flow in the central part of the kerf front

First we consider the wavelength dependence of the stability of the melt flow in the central part of the kerf front. The interest of the problem is not limited to the quality problem related to cutting applications. For example, in keyhole laser welding, it is well known that more spatters are generated with a 1 m laser beam than with a 10 m beam. This may be caused by strong metal vapor jet which is emitted from humps on the keyhole front wall.

In spite of its importance, the wavelength dependence of the stability of a cut front or a keyhole front has been scarcely investigated. Koch et al. compared evolutions of keyholes for the two wavelengths with a numerical simulation. [START_REF] Koch | Laser deep penetration welding simulation based on a wavelength dependent absorption model[END_REF] The keyhole front was found to be stable for a 10 m beam but unstable for a 1 m beam, by changing only the input data of the Fresnel absorption formula. In these simulations, however, constant values of 0.1 and 0.4 were added to the absorption formula for 1 m and 10 m beams, respectively. The validity of this operation is not obvious. Poprawe and co-workers mathematically analyzed the melt film stability. [START_REF] Poprawe | Hydrodynamics of material removal by melt expulsion: Perspectives of laser cutting and drilling[END_REF][START_REF] Vossen | Optimization of Partial Differential Equations for Minimizing the Roughness of Laser Cutting Surfaces[END_REF] They found a parameter that measures the degree of the stability. According to the parameter, the system is more stable as       sin sin   A becomes small. Here A is the absorptivity, which depends on the local inclination angle a of the front. Using the Fresnel absorption formulae, however, it is easy to show that this derivative term is larger for the 10 m wavelength than for the 1 m in the range of a < 3 degrees, which applies to thick section cutting. It appears that the proposed stability parameter does not correctly represent the wavelength dependence experimentally observed.

In the present study, the stability of the kerf front is investigated with a simple analytical model, which was used in the past for investigations of keyhole front profiles during laser welding. [START_REF] Matsunawa | The simulation of front keyhole wall dynamics during laser welding[END_REF][START_REF] Kaplan | A model of deep penetration laser welding based on calculation of the keyhole profile[END_REF][START_REF] Fabbro | Keyhole modeling during laser welding[END_REF][START_REF] Fabbro | Dynamical description of keyhole in deep penetration laser welding[END_REF] We analyze the kerf front in the central plane of cutting, which is shown in Fig. expressed by displacement of nodes that connect the chains. In the frame attached to the laser beam, displacement velocity of a chain is written as

2(a). The front is represented by a set of chains and the dynamics of the front profile is

A B C D A' C' a eq a BC a a  a a  h d (a) (b) I L I L V C V p n a V B a A B' C D' a eq J a AB A B C D A' C' a eq a BC a a  a a  h d (a) (b) I L I L V C V p n a V B a A B' C D'
p c chain V V V   . ( 1
)
Here c

V is the cutting speed and p V is the local processing velocity that is expressed by

       n A kI V L p sin   , ( 2
)
where  n is the normal unit vector of the chain (The subscript adenotes the inclination angle of the chain.), I L is the laser beam intensity and k is a linear constant, [START_REF] Fabbro | Keyhole modeling during laser welding[END_REF][START_REF] Fabbro | Dynamical description of keyhole in deep penetration laser welding[END_REF] which is determined from the energy balance. In fact, if we assume that the surface temperature of the kerf front is equal to the melting temperature T m , it is easily shown from an energy balance equation that k -1

≈ C p (T m -T 0 ) + L m within the present 2D approximation (: density, C p : heat capacity, T 0 : ambient temperature, L m : latent heat of melting). Using Eqs. ( 1) and ( 2), the velocity V chain , which is defined as the component of chain V normal to the chain, is calculated as

     F kI V n V V L c chain chain     cos , (3)
where the function F is defined as

       sin A F  , (4)
for the ease of formulation. By setting V chain = 0, the angle a eq in the stationary condition is determined:

  L c eq eq kI V A    tan . ( 5
)
Please note that this is a general equilibrium equation for a moving surface subjected to various combinations of I L and V c . For example, this equation can also be applied to a keyhole front wall during welding process [START_REF] Fabbro | Keyhole modeling during laser welding[END_REF][START_REF] Fabbro | Dynamical description of keyhole in deep penetration laser welding[END_REF] with slight modification of the coefficient k. Since A(a)tana increases monotonously with a, a eq is uniquely determined from Eq. ( 5) for a given combination of I L and V c . For simplicity, we assume that the laser intensity is constant at I L , and consequently kerf front is straight with a constant a eq . As shown in Eq. ( 5), a eq increases with V c . As far as the maximum value of a eq is concerned, it can be estimated independently from Eq.

(5), geometrically by (d/h), which is typically smaller than 3 degrees for thick section cutting.

The following discussion assumes a constant value of a eq (< 3 degrees). Now let us discuss the stability of the kerf front profile. As shown in Fig. 2(a), we consider a small perturbation that displaces the node B to the left (= to the opposite direction of eq n ) from

the straight line corresponding to a eq . The two chains AB and BC, which are assumed to have the same length, are tilted by (a eq -a) and (a eq + a), respectively. The velocity component of the node B perpendicular to the straight line AC can be evaluated from the average of the velocities of the two chains AB and BC, which are calculated in the same way as Eqs. ( 1) and

(2):

                        eq L eq c L eq eq L eq c eq L c eq L c B F kI V F F kI F F kI V n n F kI V n n F kI V V eq eq eq eq eq                                       cos 2 cos cos 2 cos 2 1 2 2 2 . (6)
In order to obtain the final expression, we have neglected terms of the forth order of (a) [START_REF] Scintilla | A comparative study on fusion cutting with disk and CO2 lasers[END_REF] and higher. According to Eqs. ( 3)-( 5), the second term in the right hand side of Eq. ( 6) is zero.

Defining another function S:

          F F S     2 2 , (7)
one obtains

  2 2      eq L B S kI V . ( 8
)
As will be shown in the following, S(ais the key parameter that governs destabilization and it determines a type of unstable modes that can appear. This "stability" function S(a) is shown in Fig. 3 for the two wavelengths of 1.06 m and 10.6 m. For this calculation, the complex refractive indices of iron at T = T m were taken from Ref. 18 and these values are shown in Table 1. The random polarization was assumed in the calculation. The stability function S(a) takes a positive value at a= 0. It decreases with a and passes zero at some angle. We call this angle a 0 that satisfies S(a  ) = 0. a 0 is 1.4 degrees for 10.6 m and 5.2 degrees for 1.06 m. For aa 0 , S(a) stays negative for both wavelengths.

Table 1 The complex refractive indices (n + ik) used in the calculation of the stability function S(a) [START_REF] Dausinger | Energy Coupling Efficiency In Laser Surface Treatment[END_REF] Wavelength n k 1.06 m (a eq a 0 ). The equation (8) shows that 0  B V in this case. Therefore, once the node B is displaced to the left, it gains velocity to the In this case (a < 0), the perturbation is suppressed.

When the node B is displaced to the left, the perturbation can be amplified more and more. To see this point, let us continue the same discussion as above for the two sets of sub-chains BD-DC, and AJ-JB. First, we consider the case where D and J are both on the straight segments BC and AB, respectively. The velocity component V D0 of the node D normal to the segment BC is written as

  BC L BC c D F kI V V     cos 0 . ( 9
)
Since

eq BC    , one obtains 0 0  D V from the relation       BC BC eq eq L c A A kI V     tan tan  
. The velocity component V J0 of the node J along AB n at the same moment is found to be positive, since eq AB    . This difference of the sign between V D0 and V J0 represents initiation of downward transport of the perturbation of ABC  Now let us consider a small perturbation of a 1 added to the segment BC. Then the velocity component V D normal to the segment BC is modified as

            0 2 1 1 1 2 2 1 1 1 D BC L BC L c BC L c D V S kI n n F kI V n n F kI V V BC BC BC BC                       D V V
. Therefore, once the point D is displaced by a small amount of distance to the left from the straight segment BC, the point can travel to the left faster than V D0 . This makes the section BDC more bended with the segment DC more inclined.

Therefore, the initial small perturbation of ABC, can be amplified while transported downwards.

There appears a region like DC, where the local a becomes higher and higher. This process of bending continues as far as S(a> 0, until the local angle a reaches a 0 (S(a 0 ) = 0). After this moment, there will only be the downward transport of the perturbation without further In summary, the above discussion shows that, whatever the initial equilibrium inclination angle a eq is, the kerf profile is inherently unstable (except the case where a eq is exactly equal to a 0 ). When a eq a 0 ,   0  eq S  and the concave mode as in Fig. 2(a) develops with the increase of a. On the other hand, when a eq a 0 ,   0  eq S  and the convex mode is amplified with the decrease of a (Fig. 2(b)). For both cases, the development of the perturbation is terminated when the local abecomes equal to a 0 . It might be surprising that the kerf front is only stable when local a is exactly equal to a 0 . It seems that this result is caused partly by simplifications used in this model. For example, consideration of surface tension will add a damping effect against the perturbations and should enlarge a stable region of a around a 0 .

In spite of the simplified assumptions, our model allows us to discuss the interesting point of the wavelength dependence of the stability of the kerf profile as follows. We focus on the low a eq condition for thick section cutting (typically when a eq < 3 degrees).

(i) The case of 10 m

In the case of 10.6 m, S(a) changes its sign at a  1.4 degrees. According to the above discussion, when a eq < 1.4 degrees, S(a) > 0, so the concave mode develops. There appears a region where a > a eq , but the increase of the local a stops at a  1.4 degrees. When 1.4 < a eq < 3 degrees, on the other hand, S(a) < 0. The convex mode appears in this case and the development ceases if the local a is decreased to the same value of 1.4 degrees. In any case, the difference of the angle between a  and a eq is small, and thus the corresponding perturbation along the kerf front is small and cannot grow so large.

(ii) The case of 1 m For 1.06 m, S(a) becomes zero at a  5.2 degrees and is always positive for a eq < 3 degrees. The concave mode appears and this continues to develop until the local areaches a  .

Because of the larger value of a  , the profile is perturbed much more strongly than the case of 10.6 m. This is considered to be the fundamental reason why the front profile in the case of the 1 m wavelength tends to be less stable than 10 m. It can be added here that a  is about the half of the Brewster angle for each wavelength, so the stability is closely related to wavelength dependence of the Brewster angle.

Although the present model predicts that the local inclination angle can be stagnated at 5.2 degrees for 1 m, more perturbed profiles with much larger acan be observed experimentally.

The proper description of this successive development after 5.2 degrees is left for a future work, but it seems possible that the initial perturbation developed up to 5.2 degrees can trigger larger deformation of the profile. Once a so-called shelf or step, where a is locally very high, comes out, strong drilling occurs on the shelf due to higher absorbed intensity. This localized drilling transports the shelf downwards. In the case of welding, strong metal vapor jet emitted from the shelf can destabilize melt pool dynamics. For the striation generation process in laser cutting, localized melt on the shelf, which we call a hump, can disturb the dynamics of the downward displacement of MAs along the kerf sides.

A closer look at the above analysis shows that the perturbation is amplified due to the fact that bending is favorable in terms of energy efficiency. That is, when the straight line AC in Fig. 2(a) is bended, averaged absorptivity for the laser beam section A'C' increases. It is interesting to note that for 1 m this effect can also be observed in a larger scale, in the energy efficiency of the whole cutting process. Let us consider the absorptivity for a model profile for the hump regime shown in Fig. 4(b). The profile is composed of vertical walls and inclined parts of shelves. The laser beam is then irradiated only on the shelves, where local inclination angle ais much larger than a eq . According to the angular dependence of the absorptivity for 1 m shown in Fig. 4(a), the absorptivity always increases when ais increased from a eq that is situated in the range of a eq < 3 degrees. Consequently, when the unstable hump regime is established from the destabilization effect discussed above in the case of 1 m, the averaged absorptivity can be raised, compared with the case of straight profile with a constant inclination angle a eq . In fact, the increase of the effective absorptivity has already been suggested experimentally: Wandera et al. [START_REF] Wandera | Laser power requirement for cutting thicksection steel and effects of processing parameters on mild steel cut quality[END_REF] reported that less laser power is required to cut 10 mm thick stainless steel with a fiber laser than with a CO 2 laser for the same cutting velocity. Scintilla et al. [START_REF] Scintilla | A comparative study on fusion cutting with disk and CO2 lasers[END_REF][START_REF] Scintilla | Primary Losses In Disk And CO 2 Laser Beam Inert Gas Fusion Cutting[END_REF] investigated the maximum cutting speed to cut samples of different thicknesses for the two wavelengths, and confirmed that the maximum cutting speed reached by a disc laser is higher than a CO 2 laser even for 8 mm thick steel. Also one must note that the averaged values of a eq for these thicknesses (10 mm, 8 mm) are so small that A(a eq ) for the averaged angle a eq is higher for CO 2 laser (see Fig. 4(a)).

Finally it should be noted that there is another mechanism for the generation of humps. As discussed in Refs. 11 and 21, when a eq is small, humps are generated periodically from the surface due to combined effect of surface tension and thermal instability. Obviously this mechanism does not depend on the wavelength. Another important difference is that, according to this mechanism, humps are generated only from the surface, whereas humps can emerge anywhere on the kerf front in the case of the destabilization of the front profile discussed above.

IV. Downward displacement of melt accumulations along kerf sides

Let us discuss the influence of the laser beam wavelength on the dynamics of the downward displacement of MAs along kerf sides and on the roughness of striations. As discussed in Ref.

11, the surface roughness is created after the displacement of MAs, which are generated periodically at the top part of the kerf side. The striation wavelength , which corresponds to the width of each of the MAs along the cutting direction, is determined from a balance between force exerted by assist gas and surface tension that retains the accumulations. The downward displacement is almost vertical and the MAs continue to receive laser energy during their downward displacement. Each MA transfers a part of this energy to the solid part. As a result, local melting of the solid part in the contact area creates a stripe of striations.

In thick section cutting, inclination angle of kerf sides is very small, generally less than the angle a eq of the front. For such a small angle, the absorptivity of the laser beam on the MAs along the sides is higher for 10 m than for 1 m (see Fig. 4(a)). The MAs in the case of CO  laser are thus expected to have higher temperature and consequently lower viscosity. Resultant higher displacement velocity of MAs may reduce the total energy consumed for the local melting during the period of the downward displacement and thus leads to lower surface roughness. This aspect of the temperature dependence of the melt ejection has been pointed out in the past, but the regime of discrete MAs on the kerf side has never been considered. In the following, we examine this rather complex problem with a simplified analytical model and discuss the impact of the temperature of MAs on the final quality of surface roughness.

The model that is investigated is shown in Fig. 5. For simplicity we assume that the stationary condition is reached. A MA slides down along the kerf side wall with a constant velocity u. It receives laser intensity and transfers a part of the energy to the solid part. As a result, the solid part is eroded by the depth of R z . The prediction of R z is the final goal of this analysis. The MA is assumed to be a deformed droplet, whose characteristic width, thickness and length are given by ,  and l, respectively. The width  corresponds to the striation wavelength, and  represents thickness of the MA at the surface, which is also related to the force balance between the surface tension and assist gas. According to our observation, [START_REF] Hirano | Experimental investigation of hydrodynamics of melt layer during laser cutting of steel[END_REF] it seems reasonable to assume that  and  are constant. We regard the problem as 2D, reducing the dimension along . The length l of MA increases during the downward displacement, since gradual melting of solid part provides additional volume to MA. Modeling of this complex hydrodynamics is beyond the scope of this work, however, and we assume a constant value of l.

First let us describe the temperature field in the solid part. Before the passage of a MA, the solid part is already pre-heated by heat conduction from the traveling laser beam and the surface temperature reaches T m , the melting temperature. The initial temperature field inside the solid has the penetration depth y, which is approximated by y ≈ r k (Pe/2) -0.7 (r k : kerf radius, Pe:

Peclet number(= r k V C /)), [START_REF] Hirano | Experimental investigation of hydrodynamics of melt layer during laser cutting of steel[END_REF] where the y axis is taken perpendicularly to the solid-liquid interface. The temperature field is approximated by a linear distribution as the bold line in Fig. 6. The first equation comes from the heat flux boundary condition at the surface of the MA:

  2 sin    m L T T K A I   , ( 11
)
where I L is the laser intensity,  is the inclination angle of the MA's surface, and K is the heat conductivity. Please note that the increase of the absorbed intensity in the left hand side results in the temperature increase of the MA. The second equation concerns the Stefan condition along the solid-liquid interface.

w f m q v L T T K      2 , ( 12
)
where v is the velocity of the melting front into the solid part, and q w is the heat flux lost into the solid. Considering that the melting front advances by R z during the solid-liquid interaction over the distance l, v can be expressed as

t R v z   , ( 13
)
where t ≈ (l/u) is the interaction time.

The heat flux q w is determined from the temperature gradient in the solid part. The bold line in Fig. 6 is the approximate temperature distribution along the line x = x 0 shown in Fig. 5, which corresponds to the moment when the MA arrives. During the interaction time t with the MA, heat flux from the MA penetrates into the solid and the solid-liquid interface moves into the solid part by R z . Considering that the penetration depth of temperature diffusion can be approximated with ~(t) 1/2 , the temperature field after t, along the line x = x 0 -l in Fig. 5, can be approximated as the dotted line in Fig. 6. Please note that the temperature field outside the thickness ~(t) 1/2 is not modified in this approximation. One can then calculate the heat flux q w at the solid-liquid interface from the temperature gradient:

    y T T K l u R y T T K t R dy dT K q m z m z R y w z             0 0 1 1 1 1   . ( 14
)
q w is increased by the factor (1-R z (u/l) 1/2 ) -1 , compared with the heat flux (≈ K(T m -T 0 )/y) before the arrival of the MA. When the interaction time t is smaller, that is, when the length l of the MA is shorter or the velocity u is larger, q w becomes larger. From Eqs. ( 12) and ( 13), one can see that v and R z become smaller, which means that the melting is restrained.

Finally we consider kinetics of the MA from a force balance equation. As already mentioned, higher T leads to lower viscosity  and higher u. In order to estimate the order of u under the shear stress applied on the surface of MA from assist gas, we refer to a result of an experimental study on droplets sliding down along an inclined surface. [START_REF] Podgorski | Corners, Cusps, and Pearls in Running Drops[END_REF] In this study, a rather general law was found: Ca ~ A m Bo, where A m (≈ 0.005 ± 0.002) is a constant, Ca = u/ is the capillary number and Bo = gsinV 2/3 /is the Bond number (: surface tension coefficient;

inclination angle of the surface; V: volume of the droplet). Replacing the force term (Vgsin) with  g (l), which represents the shear force by assist-gas in our case, we obtain

  l A u g m  . ( 15
)
It can be mentioned here that dimensionally Eq. ( 15) is equivalent to the well-known Newton type viscous friction stress that works on the liquid-solid surface, although in the present case, the droplet slips on the solid surface with the velocity u. The temperature dependence of the viscosity  is expressed by the Arrhenius law:

       RT E a exp 0   , ( 16
)
where E a and R are the activation energy and the gas constant, respectively. 11), ( 12) and ( 15) are rewritten as

With non-dimensional parameters

  z k R l L r L L , ,    , C V u u   ,     0 T T T T T m m     ,   C m p L V T T C I I 0     , m a RT E   , Eqs. (
         T Pe A I 2 sin , ( 17
) 7 . 0 2 1 1 2                        Pe l u R Pe l u R St Pe T z z  , ( 18
)                               k C m g m r V A T T l u    1 exp , ( 19
)
where

         m a m RT E exp 0   (20)
is the viscosity at the melting temperature. The non-dimensional parameter b  (A m  g r k / m V c ) is about 2.5 ± 1, if we take the values of  g  500 Pa,  m ≈ 5 x 10 -3 (Pa•s), V c = 20 (mm/s), r k = 100 (m) and A m ≈ 0.005 ± 0.002. Finally we obtain

            T T l b u 1 exp  . (21)
  m a RT E   is about 3 for steel.

Figure 7 shows the dependencies of R z ' and u' on T' calculated from Eqs. ( 18) and ( 21) with ' = 0.1, l' = 1.0 and b = 2.5. The curves are shown also for b = 1.5 and 3.5 to see the influence from the variation of A m . It is confirmed that these curves have the same tendency as the case of b = 2.5, so we discuss only this case in the following. When T'< 0.23 (T < 2.2 x 10 3 K), R z ' increases with the increase of T'. In this temperature region, u' does not increase strongly with T', whereas the heat flux through the solid-liquid interface does increases with T'. This increment of the heat flux is consumed to melt more volume per unit time, which is proportional to (u'R z '), and thus R z ' is increased. As u' and R z ' increase, however, the heat conduction loss to the solid part (the second term in the right hand side of Eq. ( 18)) begins to grow up and the heat flux that can be used to melt the solid is decreased. Consequently R z ' takes the maximum at T'= 0.23. After this point, R z ' decreases with T' mainly due to the reduction of the viscosity with the increase of T'. For this temperature region, the present simplified model predicts that R z decreases with T', and this can explain the worse quality of cut surfaces obtained with a 1 m beam.

Considering striking difference observed between 1 m and 10 m, however, it seems that the difference predicted by this model is underestimated. Moreover, in reality, the roughness might decrease with the increase of temperature also in the range of T'< 0.23. One way to improve the present model is to take into account the evolution of the geometry of the MA and its effect on the kinetics of the MA. This point will be investigated in a future work.

V. Summary and conclusion

In order to clarify the mechanisms of the quality difference observed in laser cutting of thick section steel with 1 m and 10 m laser beams, we investigated the wavelength dependence of the two fundamental processes.

First we analyzed the destabilization of the melt flow in the central part of the kerf front, which can disturb the dynamics of displacement of MAs (melt accumulations). It is concluded that when the stability function S(a eq ) is positive (negative) the concave (convex) mode of perturbation appears and develops. For both modes, the growth of the perturbations stops when the local inclination angle reaches a 0 , which satisfies S(a 0 ) = 0. In the case of thick section cutting (a eq < 3 degrees), the stopping angle a 0 for 1 m (5.2 degrees) is far away from the mean angle a eq of the cutting front, whereas a 0 for 10 m (1.4 degrees) is very close to the operating range of a eq . This explains why the cutting front for a 1 m laser beam is perturbed much more strongly than that for a 10 m beam.

Then we investigated the dynamics of downward displacement of MAs along kerf sides, which is more directly related to the development of striations. Using a simple analytical model, it was shown that an increase of the absorbed intensity on the MAs can increase their temperature and decrease the surface roughness. This result indicates that the lower absorptivity for very small inclination angle of the kerf sides can be the reason for the worse quality obtained for thick section cutting with a 1 m laser beam.

From these considerations, we finally propose that a possible solution to improve the quality for 1 m is to utilize lasers with the radial polarization. The absorptivity on the kerf side can be increased because the radial polarization works as the favorable p-polarization on the side. To the best of our knowledge, the interest of the use of the radial polarization on the cut surface quality has never been pointed out, while relevant theoretical discussions have focused on improvement of capacity of the cutting process in terms of cut thickness or cutting velocity. [START_REF] Niziev | Influence of beam polarization on laser cutting efficiency[END_REF][START_REF] Zaitsev | Numerical analysis of the effect of the TEM 00 radiation mode polarization on the cut shape in laser cutting of thick metal sheets[END_REF] Please note that the cutting capacity is determined mainly by the absorptivity on the central part of the kerf front and not by the absorptivity on the side, which is the present interest.

Experimentally, for CO 2 laser cutting of steel, it has already been reported that the surface roughness can be improved with the use of radial polarization compared to the ordinary circular polarization. [START_REF] Ahmed | Radially polarized high-power lasers[END_REF] For the 1 m wavelength, the problem of the destabilization of the central flow may not be completely solved with the radial polarization, because the stoppingangle a 0 is still kept high at 4.8 degrees even for the absorption of the p-polarization. Nevertheless, it is the dynamics of MAs that is directly related to the final surface roughness. Therefore, with the radial polarization, a better absorption of the laser beam on kerf sides should improve the quality to some extent. The authors are willing to see the experimental verifications in near future.

FIG. 1 .

 1 FIG. 1. Schematic of the striation generation process. (MA: Melt accumulation, CF: Central flow, LB: laser beam)

FIG. 2 .

 2 FIG. 2. The 2D model of kerf front profiles. Evolution of the profile depends on the sign of the stability function S(a) (see Eq.(7)), where a is the local inclination angle of the front. (a) When S(a) > 0, a concave mode can develop: the node B moves to the left from the line AC, and then the node D to the left from the line BC. (b) When S(a) < 0, an inversed convex mode develops as from the line AC to AB'C and then to AB'D'C.

  First let us consider the case where   0  eq S 

FIG. 3 .

 3 FIG.3. The angular dependences of the stability function S(a) (defined by Eq. (7)) for the two wavelengths of 1.06 m and 10.6 m.

  a 0 ). The same discussion as above leads us to conclude that the perturbation to the right as AB'C in Fig. 2(b) increases, since the velocity component V B' of the point B' along eq n is positive. The segment B'C tends to be bended further as B'D'C in Fig. 2 (b). The local inclination angle aof the segment D'C becomes smaller than a eq The growth of the perturbation thus decreases the local aand it stops when areachesa  .

FIG. 4 .

 4 FIG. 4. (a)The angular dependences of the absorptivity A(a) for the two wavelengths of 1.06 m and 10.6 m at T = T m .[START_REF] Dausinger | Energy Coupling Efficiency In Laser Surface Treatment[END_REF] (b) A model kerf profile in the case of the regime of humps. 

FIG. 5 .

 5 FIG.5. The 2D model of the striation generation process. The solid part is melted due to heat transfer from the melt accumulation (MA) sliding down along the kerf side wall.

FIG. 6 .

 6 FIG.6. Temperature field inside the solid. 

5 FIG. 7 .

 57 FIG. 7. Calculated R z ' and u' as a function of T' for different values of b.

Acknowledgements

The authors would like to thank L. Limat (Paris Diderot University), M.V. Troshin (Tomsk Polytechnic University), P. Yudin (Khristianovich Institute of Theoretical and Applied Mechanics) and K. Sugioka (Tohoku University) for useful discussion and advice.


E Le Guen

R Fabbro
email: remy.fabbro@gmail.com

M Carin

F Coste

P Le Masson

Analysis of hybrid Nd:Yag laser-MAG arc welding processes

Keywords: Hybrid, Laser, Arc, welding, 3D modelling, melt pool depression, high speed video camera PACS Numbers: 42.62.b, 81.20.Vj Greek symbols  mass density, kg.m -3  coefficient

In the hybrid laser-arc welding process, a laser beam and an electric arc are coupled in order to combine the advantages of both processes: high welding speed, low thermal load and high depth penetration thanks to the laser; less demanding on joint preparation/fit-up, typical of arc welding. So the hybrid laser-MIG/MAG (Metal Inert or Active Gas) arc welding has very interesting properties: the improvement of productivity results in higher welding speeds, thicker welded materials, joint fit-up allowance, better stability of molten pool, and improvement of joint metallurgical quality. The understanding of the main relevant involved physical processes are therefore necessary if one wants for example elaborate adequate simulations of this process. Also, for an efficient use of this process, it is necessary to precisely understand the complex physical phenomena that govern this welding technique. This paper investigates the analysis of the effect of the main operating parameters for the laser alone, MAG alone and hybrid Laser/MAG welding processes. The use of a high speed video camera allows us to precisely characterize the melt pool 3-D geometry such as the measurements of its depression and its length and the phenomena occurring inside the melt pool through keyholemelt pool-droplet interaction. These experimental results will form a database that is used for the validation of a three-dimensional thermal model of hybrid welding process for a rather wide range of operating parameters where the 3-D geometry of the melt pool is taken into account.

Nomenclature

C

Lagrange multiplier f frequency, Hz g gravity, m.s - welding speed, m.s -1 V d droplet speed, m.s -1 V w filler wire speed, m.s -1

Introduction

Hybrid welding, which combines the techniques of laser welding and arc welding, was originally invented for combined laser-TIG (Tungsten Inert Gas) welding [START_REF] Steen | Arc augmented laser welding[END_REF]. During hybrid welding, the laser beam creates a vapour capillary, the keyhole, where the beam energy is deposited throughout the work piece depth which enables a deep penetration welding effect. The feeding wire is melted by the electric arc created between the MIG/MAG-wire and the work piece. Both the arc and the keyhole create a plasma, thus producing a highly complex physical situation. As two techniques are combined, the number of process parameters is rather large and therefore difficult to optimize in order to achieve the desired weld. A general review and a complete bibliography of hybrid processes can be obtained in the paper of Bagger and Olsen [START_REF] Bagger | Review of laser hybrid welding[END_REF].

Once the mutual interaction between the two energy sources is optimized, the combination of the two processes opens large areas of applications and increases its capabilities : the arc welding process, characterized by relatively lower power density and wider process zone, gives a wide bead, thus enhancing the joint's root bridging ability and enlarging the manufacturing tolerances for joint preparation. The laser beam process, characterized by higher localized power density, leads to a deeper penetration. Thus in hybrid GMA (Gas Metal Arc)-laser beam welding, a wide and deep bead is achieved with higher welding speeds compared with the GMAW (Gas Metal Arc Welding) process by its own. As a result, the industrialization of that process become now a real objective, which can be facilitated for example, by the development of more efficient hybrid head [START_REF] Petring | Recent progress and innovative solutions for laser-arc hybrid welding[END_REF], and/or by a rather complete mastering of the process based on its basic understandings.

Deep penetration allows the welding of rather thick materials even at high welding speeds allowing filling of unavoidable gaps of the joints, with possible improved metallurgical properties and controlled geometry of the weld seam [START_REF] Bagger | Review of laser hybrid welding[END_REF][START_REF] Ono | Development of Laser-arc Hybrid Welding[END_REF]. It is known that the strength of a weld seam is defined by many parameters. Its geometry is one of these crucial parameters that have to be controlled or even optimized if one wants to minimize the effect of induced stress field generated during loading cycles of these welds. Similarly the metallurgical properties of these welds are also depending of the thermal cycles induced by the involved heat sources, the arc and the laser, which are used during this process [START_REF] Gao | Microstructure characteristics of laser-MIG hybrid welded mild steel[END_REF]. So far, most of the hybrid laser-MIG/MAG welding research is focusing on how to effectively combine a laser welding process with an arc welding process together by experimental methods. These studies have the objective to analyse the influence of various operating parameters on the weld joint shapes. It has been shown that the bead width is mainly controlled by the arc power and consequently the mode of transfer whereas laser power influences the penetration [START_REF] Gao | Microstructure characteristics of laser-MIG hybrid welded mild steel[END_REF][START_REF] El Rayes | The Influence of Various Hybrid Welding Parameters on Bead Geometry Welding Research[END_REF][START_REF] Campana | The influence of arc transfer mode in hybrid laser-MIG welding[END_REF]. The distance between the arc and the laser as well as the laser beam focal position are also key factors that affect the penetration depth and bead shape [START_REF] El Rayes | The Influence of Various Hybrid Welding Parameters on Bead Geometry Welding Research[END_REF][START_REF] Casalino | Statistical analysis of MIG-laser CO2 hybrid welding of Al-Mg alloy[END_REF][START_REF] Song | Overlap welding of magnesium AZ31B sheets using laser-arc hybrid process[END_REF][START_REF] Kim | Position welding using disk laser-GMA hybrid welding[END_REF]. In general a distance between the two sources smaller than 5 mm is recommended. Kah [START_REF] Kah | The effect of the relative location of laser beam with arc in different hybrid welding processes[END_REF] discussed the choice of the arc-torch direction and the distance between laser and arc. This decision should be made case by case and depends on various parameters like laser beam properties available, the material, arc source parameters, the function of filler wire (to improve metallurgy, to fill up air gap or form weld bead). The weld penetration is deeper when smaller inclinations for MIG torch are used. Casalino has observed deeper penetration using a 45° angle rather than 60° in MIG-laser CO2 hybrid welding of Al-Mg alloy. The stability and efficiency of the laserarc process are influenced by the shielding gas. Tani et al. recommend a 30 up to 40% helium content in hybrid CO2 laser-GMAW welding of AISI 304 stainless steel [START_REF] Tani | The influence of shielding gas in hybrid laser-MIG welding[END_REF]. A pulsed/spray transfer mode should be preferred in order to achieve a stable and repeatable process [START_REF] El Rayes | The Influence of Various Hybrid Welding Parameters on Bead Geometry Welding Research[END_REF]. Other authors have also studied the hybrid laser-arc welding of dissimilar metals [START_REF] Thomy | Hybrid laser-arc welding of dissimilar metals In Hybrid laser-arc welding[END_REF] and the hybrid welding of aluminum [START_REF] Thomy | Effect of process parameters on joint properties in laser-MIG hybrid welding of aluminium to steel Lasers in Manufacturing[END_REF].

It should be mentioned that most of these works are essentially based on macrograph analysis. However observations of the melt pool hydrodynamics using high speed video camera in the visible range for the melt pool surface analysis [START_REF] Fabbro | Analysis of the various melt pool hydrodynamic regimes observed during CW Nd-YAG deep penetration laser welding[END_REF][START_REF] Norman | Monitoring undercut, blowouts and root sagging during laser beam welding[END_REF] or by X-ray radiography [START_REF] Katayama | Collaboration of physical and metallurgical viewpoints for understanding and process development of laser welding[END_REF] for the internal melt pool behaviour give very interesting insights on the physical phenomena and help in understanding the complex interaction between the many parameters involved in this process.

A numerical approach of the hybrid welding was given by Zhou [START_REF] Zhou | Modeling of transport phenomena in hybrid laser-MIG keyhole welding[END_REF] and Wouters [START_REF] Wouters | Hybrid Laser-MIG welding: an investigation of geometrical considerations[END_REF]. GMA welding process alone has also been previously studied by using a 3-D heat and fluid flow model of melt pool [START_REF] Ushio | Mathematical modelling of three-dimensional heat and fluid flow in a moving gas metal arc weld pool Metall[END_REF]. We will use a similar approach for our hybrid welding description. Cho [START_REF] Cho | Three-Dimensional analysis of molten pool in GMA-laser hybrid welding[END_REF] presents a whole modelling of hybrid welding where he uses the VOF method to track the movement of free surfaces. The Navier-Stokes equation, heat and species conservation are solved for melt pool description. For the behaviour of the capillary, surface tension and recoil pressure are taken into account. The effects of multiple reflections on the walls of the capillary function of time are also taken into account in calculating the melt flow. However this work was only numerical, no comparison with the resulting experimental is presented.

In a first part of this paper, we will present the different experimental results we obtained on the study of hybrid welding, mainly by an extensive use of a high speed video camera that allowed a better understanding of the phenomena induced during laser, MAG and hybrid laser-MAG processes. These new experimental results complete some previous experimental results and give a complete set of data that must be taken into account and reproduced in the corresponding simulations. The numerical approach will be described in the second part of this paper with corresponding results. We use a numerical modelling of hybrid laser-GMA welding in order to reproduce the 3-D geometry of the weld reinforcement observed at the top and the melt pool surface depression observed under the arc.

Our final goal here is to define a numerical tool that is rather easy to run and enough precise in order to reproduce these geometrical observations that appear to be decisive for a correct determination of the induced thermal field, once the main operating parameters are defined. These simulations should allow us to determine in a second step the thermal cycles induced inside the material for estimating the resulting metallurgical transformations. So these simulations that are validated with a set of experimental observations will be discussed in the last part of this paper and will allow us to define the corresponding parameters related to arc and laser energy deposition and resulting applied pressures at the melt pool surface. Experiments were carried out with a CW Nd:Yag 4006D TRUMPF Laser, with a maximum power of 4 kW. The laser beam was delivered through a 600 µm optical fibre. The welding head images the exit of the optical fibre by using a collimating and focusing lens that generates a focal spot of 600 µm diameter. The focal spot intensity distribution, which was analysed by using a PROMETEC beam analyser, can be considered as uniform.

Experimental set-up

The arc torch is a DIGI WAVE 400 model from SAFT PRO (Air Liquide Welding France). It delivers up to 400 A current for different configurations of control of current and tension of the arc. Welding current and arc voltage traces were recorded via a transient recorder. Arcal21 shielding gas flowing at 20 L/min was used (92% Ar and 8% of CO2). Of course, it is possible to vary all the geometric parameters of the torch such as the position and the wire angle with the vertical laser beam (see figure 1). The dynamics of the melt pool was analysed with a CMOS high speed camera (PHOTRON IMAGER FASTCAM APX RS 3000) with a maximum frame rate of 100 kHz. However, 10 kHz was sufficient for these configurations. Lateral observations of the melt pool geometry were realized by locating this camera on the side, perpendicularly to the welding displacement, with the optical axis of the camera at an angle of 45° with the vertical of the incident laser beam (see figure 2).

The work piece studied here consists in a steel S355 plate of 20 mm thick (S355 composition 1.1% Mn, 0.003% Si, 0.014% P, 0.004% S, 0.03% Cu, 0.076% C and 0.005% N). Fusion lines were carried with a G4 Si1 filler wire of 1.2 mm diameter (1.5% Mn, 1% Si 0.1% C). After welding, cross sections of the weld beads were ground, polished and etched according to the standard procedures. All these sections were cut midway from the welded specimen. The bead dimensions corresponding to each welding parameter were measured using a stereo microscope. Partial penetration welds were made using the following operating parameters:  Maximum incident laser power was 4 kW.  Welding speed was progressively increased from 0.5 m/min to few m/min until the visual aspect of weld seam was irregular.  Wire speed (from 2 m/min to 12 m/min) and current and voltage were imposed by the synergy of welding machine (figure 3). One must recall that this synergy (U-I relation as a function of wire speed) does not depend of the welding speed.  Arc torch inclination of 30° from the vertical laser beam was fixed.  Laser beam was positioned behind the MAG torch.  Distance between filler wire (MAG) and laser beam was set to 2 mm. diameter wire, shielding gas: 92% Ar -8% CO2).

Experimental observations

Metal transfer modes

It is well known that the wire transfer mode is determined by the heat input and the used shielding gas.

In our case, the short-circuiting transfer occurs between 100 to 200 A, the globular mode between 200 to 250 A and the spray mode from 250 to 400 A. The observations using fast video camera confirm the 3 metal transfer modes according to the used current (figure 4).

Geometry

Examples of typical cross sections of weld seams for laser, MAG and Hybrid conditions are shown in Figure 5. Moreover, Figure 6 shows the corresponding views of the melt pool observed using the high speed video camera. Because of the rather low welding speeds used here (typically less than 5 m/min) the cross section of a weld with the laser alone shows the well-known nail head shape and the surface melt pool shows the characteristic humps observed around the keyhole rim for these welding conditions.

These effects result of the induced melt flow that is dragged upwards along the keyhole wall by the friction forces due to vapour expansion out of the keyhole [START_REF] Fabbro | Basic processes in deep penetration laser welding[END_REF]. MAG cross section shows the characteristic height seam reinforcement, with a penetration depth that is much lower than in a laser case.

The weld bead shows a rather complex structure where the depressed zone, resulting from the impingement of the droplets flow and the arc pressure area (bright zone), is followed by the weld reinforcement that is melted along a rather large distance. Finally for the hybrid process, one can observe a greater keyhole penetration compared to the laser alone and the geometry of the reinforcement similar to the one obtained with the MAG process alone.

In that case the keyhole aperture is located inside the melt pool surface just behind the arc centreline in agreement with the arc trailing position. Measurements carried out on macrographs (figure 7) show that the penetration depth is greater in hybrid process than in MAG process. More precisely, the penetration depth ranges from 2 to 10 mm in hybrid and from 1 to 7 mm in MAG. The weld pool length is also longer in hybrid process than in MAG process. It varies from 14 to 43 mm in hybrid process compared to 10 to 38 mm in MAG.

Beside, the melt pool width is larger in MAG process than in hybrid process. In MAG, the width ranges from 2.5 to 15.5 mm, whereas in hybrid, it varies from 2.5 to 12.5 mm. As expected, the width and penetration depth decrease when the welding speed increases, and the three characteristic melt pool dimensions (width, length and deep penetration) increase when the wire feeding rate increases. The weld pool length does not seem to vary with the welding speed.

Another point concerns the bead surface reinforcement S reinf defined by the feeding wire, which should depend on the filler wire speed V w , its wire radius r w and the welding speed U 0 with the following relation:

U 0 S reinf = V w r 2 w (1)
In fact, one observe that the average difference between the calculated (equation 1) and the measured value of the reinforcement is about 13% and 19% for MAG alone and hybrid laser-MAG respectively. The experimental bead surface reinforcements are always larger than the calculated one and this difference is larger for the hybrid process than for the MAG one. This difference can be explained by the presence of reinforcement that is always observed even during laser welding alone, although there is no material addition in that case. The origin of this reinforcement is likely the effect of the obvious macroscopic deformation of the welded part resulting from the depth gradient of energy deposition inside the material. This effect is particularly important in case of the hybrid process, because of the difference of level and location of the energy input between the two processes (at the surface for MAG compared to surface and volume for the hybrid process).

Melt pool depression

Figure 8 shows an enlarged view of the depressed zone below the arc during MAG processing. One can clearly see that under the arc centreline the melt pool surface is depressed below the initial work piece surface by more than three millimetres. The level of this depression depends on the intensity of the arc current and begins to become significant for currents above 150 A. This depression results from the arc pressure due to the induced hydrodynamic gas flow and of course of the impingement of melt droplets. It is clear that thermal field induced inside the work piece by the arc from this depressed surface has to be very different from the one obtained if the arc is deposited on a flat surface. The characterization of this depression is therefore very important for its comparison with corresponding simulations. The evolution of the depression "h" along the welding direction, in the symmetry plane of the weld seam, can be very easily determined from the video images by taking into account the video perspective and the inclination angle of the camera axis with the solid surface of the sample by using the simple relation h = h'/cos(45°), where h' is the projected value of the depression measured on the recorded image plane (see an example on figure 8). The uncertainty in the measurement of the depression h' is ± 0.2 mm. This uncertainty is obtained by making several measurements of depression on the same video. An error of ± 0.2 mm on the measurement of depression leads a numerical error on the maximum arc pressure of only ± 50 Pa. Figure 9 shows the variation of these maximum obtained depressions, as a function of the welding speed U0, for different wire feeding rates. One must also add that the depressions determined by this method are in good agreement with those observed directly on the work piece after welding, at the end of the weld seam. One can easily understand that the depression increases for higher wire feeding rates, due to higher arc current, and for lower welding speeds U0, due to resulting larger melt pool widths. It is important to note that this rather high value of the induced depression is typically half of the final obtained melt pool penetration; therefore the effect of surface depression must be taken into account for a correct simulation of the experimental melt pool geometries. We also note that the hybrid depressions are slightly larger than the depressions obtained with MAG alone.

Droplets pressure measurements

In the spray mode, which is the main metal transfer mode of our experiments, the droplets impinging at rather high velocity the melt pool surface must have also a non-negligible contribution to the melt pool surface depression. If one considers that m d is the mean mass of a droplet, V d its velocity, and R d its mean radius (about 0.4 mm), the resulting pressure P d obtained during an impact of droplets emitted with a frequency  is given by:

2 d d d d R V m P    (2)
In equation 2, we have considered that there is no spreading of the droplet during its impact onto the surface. These different parameters can be easily measured from video movies. Figure 10 (a to c) shows respectively the droplet velocity, droplet frequency and the resulting induced pressure (given by equation 2) for hybrid process, as a function of the welding speed and for different wire feeding rates. As there is some acceleration of the droplet due to the drag force of the plasma flow, the droplet velocity reported on figure 10-a is an average velocity along its trajectory. As the wire feeding rate increases, it is expected that the droplet velocity and the frequency of detachment increase (as shown by the experimental tendency). There is no clear effect of the welding speed and the frequency of detachment  which varies in the range from about 400 to 1000 Hz (Figure 10-b). These values of frequencies are in good agreement with previous values observed by Valensi [23]. He studied the influence of oxygen in the shielding gas on the droplet frequency. For a wire with high content of silicium, as in our case, this frequency increases from 0 to 750 Hz when the oxygen level decreases from 70 to 0% and is equal to 700 Hz at 8% oxygen as in our study. Measurements of size, velocity and frequency of the droplets are also in agreement with the work of Lin [START_REF] Lin | Metal transfer measurements in gas metal arc welding[END_REF]. Indeed, droplet diameters were found around 2-3 mm in globular and 1 mm in spray. The droplet frequency increases from 50 to 500 Hz when the wire speed (or arc intensity) increases from 7 to 12 m/min for a wire diameter of 0.9 mm. The droplet velocity in this work increases by 0.5 to 1.4 m/s when the current increases from 160 to 150 A for a wire diameter of 1.2 mm. pressure (given by equation 1), as a function of the wire feeding rates.

The induced droplet pressure varies from 2 to 8 kPa; as expected, it increases with the wire feeding rate that controls the arc current. These pressures are in agreement with the results of Xu [START_REF] Xu | Numerical analysis of weld pool geometry in globular-transfer gas metal arc welding Front[END_REF] which predicts zero droplet pressure at low intensity (low wire feeding rate) and pressures up to 5 kPa for the high intensity. Even in taking into account some increase of the impact diameter due to local spreading during the impact, it appears that these values are not negligible compared to arc pressure that we will determine in § 4.2. Therefore, the droplet impact must be taken into account as a very local contribution of pressure on the melt pool surface. This impact induces a localized penetration that can be observed, at high wire feeding rates, by a pronounced penetration on some macrographs or deep deformation of melt pool surface observed on videos (see section 4.2.1.).

Melt pool surface speed

From video movies, one can see that these melt pools have complex hydrodynamic flows. For estimating the importance of convection and conduction processes inside these flows for the energy transport, it would be necessary to determine the fluid flow field. This will dictate the necessity of taking into account, the complete description of the hydrodynamic flow field in the simulations. In order to estimate the magnitude of fluid speed at the melt pool surface, tracer particles were deposited on the sample surface before welding. During melting, these tracers follow the fluid motion. It is then possible to track the motion of particles from the video sequences and deduce fluid velocities by assuming that the particles faithfully follow the fluid dynamics. Different tracers were tested, and it appeared that small silica grains (about 0.1 mm in diameter) had the best behaviour for MAG and hybrid processes and could be easily followed on the video movies. Figure 12 shows typical tracers velocities observed at the centre of the melt pool behind the arc, along the transition from the arc depression to the weld reinforcement. It is at this position that the surface speed appears to be maximum; then, behind that zone, the surface flow is redirected towards the edges of the melt pool with a vortex-like structure (see arrows in figure 11-a). This effect is rather similar for hybrid and MAG process. The measurements show that the fluid speed increases with wire feeding rate. This speed is quite constant with the welding speed and is slightly greater in hybrid than in MAG at low currents. The presence of the keyhole modifies the local fluid motion since the fluid has to flow around the keyhole. In addition, the vapour ejected from the keyhole modifies the dynamics fluid motion [START_REF] Fabbro | Analysis of the various melt pool hydrodynamic regimes observed during CW Nd-YAG deep penetration laser welding[END_REF]. The magnitude of maximum surface velocities results to be rather high, in the range 0.5 -1 m/s, and so correspondingly the Peclet number (Pe) that can be estimated as Pe ~ 200-300. This would indicate that the convective transfer of energy is not negligible compared to the conductive process. However, these velocities are measured at the surface of the melt pool, and may largely overestimate the real internal flow speed.

Figure 12.

Tracer speed as a function of welding speed for different wire feeding rates for hybrid and MAG processes at a typical welding speed of 1 m/min.

Analysis of melt pool geometry along the welding direction

The 3-D shape of the melt pool inside the work piece, during the process is also an interesting parameter for modelling comparisons. Analysis of longitudinal sections is more sensitive, in order to determine the contour of the melt pool, which is not normally visible due to the continuity of the melt pool in the solidified zone. For an estimation of the longitudinal shape of the melt zone, we use a small amount of contrast material, which is different from the S355 base material and filler wire, which is inserted perpendicularly to the work piece. This contrast material is introduced before welding, as a wire inside a hole drilled perpendicularly to the work piece, on the symmetry plane of the weld seam (see figure 13). If its diameter is small enough, it does not disturb the melt pool hydrodynamics; this point is verified through the width and length weld bead measurements. When the melt pool reached the contrast material, it is assumed that the contrast material is redistributed very quickly throughout the available volume of liquid before its solidification. Then chemical etching can be adapted to reveal the contour, as can be seen in longitudinal sections (Figure 14).Different contrast materials and wire diameters have been tested and it appears that a copper alloy (Cu-10% Al) wire with a diameter of 1 mm, give the best results. However, this technique has some limitations; it can be used only for configurations with rather low MAG filler wire rates; for high power MAG, and so correspondingly high filler wire inputs, the contrast with the copper alloy wire is not sufficient. Nevertheless, when this technique can be applied, interesting melt pool longitudinal internal profiles can be obtained (see figure 14). They will be discussed and compared with corresponding simulations in paragraph 4.2. As expected, for MAG process, the internal melt pool has a shape of a rather flat bowl (figure 14-a). But in case of hybrid process (figure 14-b), this shape is modified by the localized melt flow occurring around the deeply penetrating keyhole.

Numerical simulation

3D thermal numerical model

In order to analyze these experimental observations by using simulations, one must take into account the addition of the filler wire and the observed depression resulting of the arc pressure and the momentum of the droplets flow previously described experimentally. It necessitates describing more precisely the interaction zone and it is also intended to estimate the weld reinforcement and root drop out for joints with a gap. Despite the rather high value of the characteristic Peclet number inside the melt pool we have previously determined in §3.4, the melt pool hydrodynamics was not taken into account in these simulations. This is of course a great simplification for these simulations and we will For the description of the laser keyhole welding alone and also for describing the laser interaction for the hybrid process, we used a previous analysis of Lankalapalli et al. [START_REF] Lin | Metal transfer measurements in gas metal arc welding[END_REF] where they consider that the keyhole is a vertical cylinder with a uniform temperature along its wall that is slightly above the evaporation temperature of the material involved. Because of the rather low welding speeds used here for these hybrid welding conditions, we know that the keyhole is almost vertical [START_REF] Fabbro | Analysis of the various melt pool hydrodynamic regimes observed during CW Nd-YAG deep penetration laser welding[END_REF]. However, concerning the hypothesis of the keyhole wall temperature close to the evaporation temperature of the material, we know, since the study of Semak and Matsunawa [START_REF] Semak | The role of recoil pressure in energy balance during laser materials processing[END_REF], that this hypothesis is not necessarily verified during laser welding. But nevertheless we have used it, because of its simplified consequences in terms of modelling and its ability to easily reproduce the geometry of the longitudinal and transverse weld seam (Fig. 15). Based on experimental observations, the keyhole diameter corresponds to the focal spot diameter (0.6 mm). The depth of the keyhole can then be defined when the integrated heat flux through the entire keyhole walls surface corresponds to the total absorbed laser power. An analytical description can also be used for that determination [START_REF] Lankalapalli | A model for estimation penetration depth of laser welding processes[END_REF].

For the arc and hybrid description, the high speed video movies have shown the shape of the interaction zone: a depression of the melt pool under the arc followed by weld reinforcement due to the filler wire. In that case, the weld pool surface is not flat and its final shape must satisfy an equilibrium condition between surface tension, hydrostatic pressure and arc pressure. Ushio and Wu [START_REF] Ushio | Mathematical modelling of three-dimensional heat and fluid flow in a moving gas metal arc weld pool Metall[END_REF] have already proposed a solution for solving this problem taking into account these constraints, on the basis of an approach that minimizes the total energy of the melt pool, by adding the constraints that the melt pool has a constant volume and the weld reinforcement geometry is equal to the filler wire mass flow. This total energy of the melt pool taken into account concerns the variation of surface energy with a corresponding change of its area, the total potential energy inside the gravitational field, and the work performed during that change of area by the arc pressure and droplets flow momentum. The resulting equation describing the height of the surface profile (x, y) is given by equation ( 3) where x and y correspond respectively to longitudinal (or welding) and transverse direction, in the laser beam frame:

C P g surf y x yy x xy y x xx y                                2 / 3 2 2 2 2 ) 1 ( ) 1 ( 2 ) 1 ( (3)
           2 1 2 2 max 2 ) ( exp ) , ( r
y x P y x P surf (4)
where  is the surface tension,  the mass density, g the gravity, P surf (x,y) the applied pressure distribution at the melt pool surface, where P max is the maximum pressure with a characteristic radius r 1 For the sake of simplicity, we have combined in equation ( 4) the effect of arc and droplets. The index x and y are the respective derivative of profile (x, y) with x and y variables. C is a Lagrange Multiplier adjusted by the mass conservation constraint of the feeding wire that defines the transverse profile shape (x, y) of the solidified weld seam that must fulfil the following equation:

   dy z r w ) ( U V 0 0 w 2   (5)
where r w and V w are the wire radius and feeding speed, U 0 the welding speed and z 0 the height of the initial work piece flat surface.

            2 0 2 2 2 0 2 ) ( exp 2 ) , ( r
y x r I U y x surf   (6)
Equation 6 defines the heat flux  surf (x, y) deposited by the MAG on the melt pool surface. The arc efficiency of the process  and the characteristic radius r 0 are adjusted in order to reproduce the experimental results concerning the melt pool geometry (width, depth). A Gaussian distribution was chosen to describe the arc power. This kind of distribution is widely used in the literature [START_REF] Ushio | Mathematical modelling of three-dimensional heat and fluid flow in a moving gas metal arc weld pool Metall[END_REF][START_REF] Kim | Modeling of temperature field and solidified surface profile during gas-metal arc fillet welding[END_REF][START_REF] Zhang | Heat and fluid flow in complex joints during gas metal arc welding-Part I: Numerical model of fillet welding[END_REF][START_REF] Cao | Three-Dimensional Simulation of Transient GMA Weld Pool with Free Surface Supplement to the Welding journal[END_REF][START_REF] Kumar | Heat Transfer and Fluid Flow during Gas-Metal-Arc Fillet Welding for Various[END_REF]. However, Xu [START_REF] Xu | Three-dimensional modeling of arc plasma and metal transfer in gas metal arc welding[END_REF] recently highlighted that the heat distribution is far from being symmetrical. He directly calculated the physical processes inside the plasma arc and showed that the arc pressure and energy distribution are not Gaussian. Indeed, the distribution is altered by the effect of droplet detachment. In our study, as we do not take into account the description of the arc plasma and the interaction of droplets with the melt pool, a simplified Gaussian distribution for the power deposition flux was chosen. Arc pressure distribution defined by the equation 4 and the maximum pressure are adjusted in order to reproduce the melt pool depression determined experimentally from high speed video movies. More detailed description concerning the heat equation and the algorithm used for solving the complete set of equations by using the Comsol software [33] will be given in a companion paper [START_REF] Guen | 3D heat transfer model of hybrid laser Nd:Yag-MAG welding of S355 steel and experimental validation[END_REF].

Results and discussion

Using the previous procedure, we have simulated 28 experimental tests: 4 tests concerned laser alone, 12 the MAG alone and 12 the hybrid process. These experiments concerned only fusion lines, however, we found that these configurations are similar to assemblies with a gap of less than 200 microns width. For these experimental tests, the welding speed and the filler wire rate were the main parameters that have been varied. Only four unknown parameters of equations 4 and 6 (P max , , r 0 and modified thermal conductivity) have been determined by comparison with experimental data given by weld seam cross section and melt pool (geometry and depression) analysis. In the following sections, we will discuss the methodology used for deriving these parameters and the physical mechanisms that can inferred from these analysis.

Arc efficiency and intensity distribution; Heat conductivity modification.

Figure 15 shows the comparisons between experimental and numerical results concerning the weld seam cross section, for the 3 processes. Generally, a rather good agreement is obtained between numerical and experimental cross sections. However, these comparisons show some limits of our approach: Indeed, in the case of MAG welding, at high filler wire speed (11 m/min) and low welding speed (0.4 m/min), the observed complex geometry, similar to that observed in hybrid welding and probably resulting of very localized intense droplets impingement, cannot be correctly reproduced using this purely conductive model. However, the model reproduces a wide operating range corresponding to the configurations currently used in industry. It is important to note that another parameter, the liquid thermal conductivity, had to be modified in order to correctly reproduce the melt pool length (see figure 16). In fact, this liquid heat conductivity had to be increased by a factor K, depending on the experimental conditions that point out some physical processes occurring inside the melt pool. For example, in order to reproduce the melt pool length in MAG alone process (otherwise it was twice longer), the factor K had to be set to about 3. This isotropic increase of liquid thermal conductivity has the effect of homogenizing the temperature field that is what would be expected by a hydrodynamic flow inside the melt pool, which is not taken into account here. Moreover, this increased liquid thermal conductivity has also the effect of reducing the maximum surface temperature to a level near the evaporation temperature of the material. Otherwise, for these input surface intensities, and welding speeds, the obtained temperatures would have been much higher, which is not physically possible. For similar approach in the case of the laser process alone, an anisotropic conductivity in the welding direction has to be introduced. This conductivity in the welding x-direction had to be multiplied by a typical factor K of 5 to 6 compared to the transverse one in order to reproduce the experimental weld pool length . Without this increase, the simulated weld pool was much shorter compared to experimental one. The high value of this anisotropic K used here, reflects probably the strong flow field obtained in laser welding compared to MAG conditions. Finally for hybrid welding, the K factor used had to be varied from 3 (this increase being in that case isotropic) for high filler wire rates (corresponding to large melt pools) to an anisotropic K of about 5-6, at low filler wire rates, when the arc power was less important. This K variation is consistent with the expected evolution of the hydrodynamic melt pool flow as a function of the operating parameters. An example of longitudinal melt pool shape for the hybrid welding case is shown in Figure 16. The melt flow localized around the penetrating keyhole below the melt pool generated by the arc is not correctly reproduced because only the thermal field is simulated here, without taking into account the hydrodynamics of melt pool. Table 1 shows a summary of thermal conductivity modifications with the various welding configurations.

It is also important to add that during this procedure of identification of these unknown parameters, we have observed that the determination of the couple of unknown parameters such as the arc efficiency  and the radius r 0 of power deposition cannot be unique if one only analyzes a weld seam cross section.

It is only when the melt pool length is also considered that a unique determination of the couple ( and r 0 ) is possible. The arc efficiencies  determined by using these simulations have been reported in figure 17-a as a function of welding speed for different filler wire speeds. We recall that the efficiency we defined here corresponds to the fraction of arc power UI that is used for reproducing the observed geometry of melt pool and final weld seam cross section. For these simulations, the only loss mechanisms used were the standard losses from convective exchange with ambient air and from grey body emissivity. One can see that this arc efficiency is quite not depending of the welding speed but it increases from 30% in spray regime (high arc power, about 8-10 kW) to 70 % in short-circuit regime (low arc power, about 3-4 kW). The high efficiency for short-circuit regimes can be easily understood. For high arc current regime (spray mode), radiation losses from the arc is a possible reason for such reduced efficiency. This tendency was also observed in TIG welding by Niles & Jackson [START_REF] Niles | Weld thermal efficiency of the GTAW Process Welding[END_REF]. Their measurements have indicated that the arc efficiency decreased from 60 to 30% when the intensity increased from 125 to 225 A. We may also add that evaporation losses were not taken into account here. At high arc current it is experimentally observed a high level of evaporation from the melt pool surface due the high resulting surface temperature. Moreover, considerable spattering was observed for these high arc current regimes. The precise estimation of these evaporation losses is difficult because the level of re-condensation of ejected metallic vapours occurring at atmospheric pressure is not known. If one uses the evaporation rate given by the Langmuir law [START_REF] Dushman | Scientific Foundations of Vacuum Technique 2[END_REF][START_REF] Debroy | Physical processes in fusion welding[END_REF], we observe that losses are largely overestimated and cannot be included at this level. DebRoy [START_REF] Debroy | Physical processes in fusion welding[END_REF] has pointed out that this law can be used for evaporation rates at low pressure environment when no significant re-condensation occurs. His experiments indicate that evaporation rates in usual welding conditions would be 5 to 10 times lower than those predicted by the Langmuir law. So, for these reasons, we did not take into account these evaporation mechanisms in the simulations, because of these too large uncertainties on these mechanisms. One must also add that even if evaporation losses are efficient for reducing surface temperature to levels near evaporation temperature, they were not able to reproduce experimental melt pool lengths, as the increased liquid heat conductivity did, with similar effect on surface temperature. The radius r0 used in equation 6 for characterizing the profile of deposited arc power has been reported in figure 17-b. As expected, this radius increases with the arc current, and as for arc efficiency, this parameter is not sensitive to the welding speed. 4.2.2. Laser efficiency. Figure 17-d shows the laser power that must be used in the simulations in order to reproduce the experimentally obtained keyhole depths, as the function of the operating parameters. There is a singular point at V w = 11 m/min and U 0 = 1 m/min, which is not consistent with the other results that show a general tendency of an increase of the useful laser power with the welding speed. In fact, for MAG welding alone, at high filler wire speeds and low welding speed, we have already seen on figure 15 a similar deviation, with a rather deep penetration already observed. So for corresponding hybrid welding conditions, a crude analysis considering that this observed deep penetration results only from the laser keyhole is not correct and thus this point has to be discarded. As the incident laser power was set to 4 kW, one can see that maximum necessary useful fraction reaches about 75 % and in spite of some dispertion of the data, it is clear that the laser efficiency decreases when the welding speed decreases. This behaviour has already been analysed for laser welding alone [START_REF] Fabbro | Basic processes in deep penetration laser welding[END_REF]. In fact this result can be explained if one considers that low welding velocities induce deep keyholes, with large depth/diameter ratios, so the keyhole geometry becomes unstable due to Rayleigh-Taylor instability [START_REF] Fabbro | Basic processes in deep penetration laser welding[END_REF]. As a consequence of these internal fluctuating closures, the keyhole is non-stationary and so a stationary thermal model is not appropriate for this description: as the resulting penetration depth is limited by this instability, the corresponding laser power necessary for reproducing this penetration depth is of course reduced. As this behaviour becomes dominant at low welding speeds, the effective laser efficiency can be much lower than the usual 80 to 90% observed laser efficiency resulting from the geometrical trapping of laser beam inside the keyhole. So the laser efficiency is a rather sensitive function of the welding speed, particularly in case of hybrid welding where the keyhole can be easily perturbed by the rather large surrounding melt pool generated by the arc.

Arc pressure determination.

The induced pressure applied at the melt pool surface is given by equation 4 by defining the two parameters P max and r 1 . In fact, unlike to the determination of the arc power parameters, it is not possible to show the uniqueness of the couple (P max , r 1 ) using only the maximum depression measurement, because several couples (P max , r 1 ) can give the same maximum depression, but with significantly different profiles. So again in order to simplify the analysis by minimizing the number of parameters to determine, we have chosen to use the radius of pressure distribution r 1 that is equal to the radius distribution r 0 . Thus, the maximum pressure has been adjusted to obtain the maximum observed depression.

The arc pressure evolution for hybrid conditions is reported in figure 17-c. The uncertainty on the arc pressure of about 100 Pa, results from the accuracy on depression measurements which is about 0.3 mm. The maximum pressure P max (equation 4) clearly increases from the short circuit regime with pressures about 800 Pa to the spray regime with pressures about 2300 Pa. We have also observed that pressures for hybrid conditions are about 30 % higher than for MAG process. These results can be d c understood if one considers that the arc pressure is directly related to the arc current. Finally, one can notice that these pressures determined by this indirect method, are in agreement with those determined by Lin and Eager [START_REF] Lin | Pressures produced by gas tungsten arcs[END_REF].

Summary of the experimental results and corresponding numerical parameters

The large amount of the experimental data presented in section 3, and the corresponding analysis of determined parameters for reproducing them by using our numerical approach, discussed in section 4, has allowed us to obtain rather precise analytical expressions of these different parameters as a function of the 2 main operating parameters that were used in these experiments, which are the welding speed U 0 and the arc power P arc (P arc is defined by giving the filler wire speed V w used, and the corresponding arc synergy defined on figure 3). These analytical expressions have been obtained by determining a best fit of a polynomial expression of the 3 rd degree with the variables U 0 and P arc , with the corresponding results. We used the following functions: Y(U 0 , P arc ) = a 1 U 0 3 + a 2 U 0 2 P arc +a 3 U 0 2 +a 4 U 0 P arc 2 +a 5 U 0 P arc +a 6 U 0 +a 7 P arc 3 +a 8 P arc 2 +a 9 P arc +a 10 [START_REF] Campana | The influence of arc transfer mode in hybrid laser-MIG welding[END_REF] where the constants a 1 to a 10 are given in tables 2 and 3 for the different data. The mean accuracy of this polynomial fit with the corresponding results, given in the last column in these two tables, is rather correct. These determinations are valid on our range of the operating parameters used: from 0.4 to 4 m/min for the welding speed U 0 , and from 2 to 11 kW for the arc power P arc . These analytical functions are very useful because for any set of operating parameters U 0 and P arc given in the previous validity range, one can obtain with the Table 2 the corresponding experimental geometrical parameters of the resulting melt pool, and with the Table 3, the numerical parameters necessary to use in order to reproduce this melt pool with our simulations.

Parameter :

a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 a 10 (%)

Melt pool width (mm) -0,16 0,07 1,5 0,0017 -0,51 -4,23 -0,0024 -0,01 1,41 5, 37 11 Penetration depth (mm) 0 0 0,14 0 -0,078 -1,45 0 -0,0079 0,52 5,65 7

Weld seam height (mm) -0,2 -0,0091 0,31 -0,0032 0,064 -1,47 0,0044 -0,06 0,36 Arc radius (mm) -0,019 -0,004 0,1708 -0,0011 0,05 -0,65 -0,0033 0,5 -0,14 Table 3: For hybrid conditions, polynomial expressions for the parameters used in the numerical simulations, (U 0 is expressed in m/min and P arc in kW).

Conclusion

A set of experimental observations has been realized for a wide range of the main operating parameters concerning the hybrid laser-MAG process. The main geometrical characteristics of the melt pools have been determined and we have seen the importance of melt pool depressions as a result of applied pressure at the surface of the melt pool due to arc interaction. By using numerical simulations, we have reproduced the final cross section of the weld seams and the 3-D shapes of these melt pools. For the last point, we have shown the interest of increasing the liquid thermal heat conductivity in order to simulate heat hydrodynamic flow inside the melt pool. This procedure has allowed us to determine the corresponding parameters related to arc and laser energy deposition and also the resulting applied pressures at the melt pool surface, as a function of the used operating parameters. This approach can be applied to an industrial configuration (with a groove, or for full penetration). This paper presents encouraging results concerning the modelling of the hybrid laser-MIG/MAG process obtained by using rather simple approaches and hypothesis that allowed us to reproduce realistic melt pool geometries.

Future work

With these simulations, we should be able now to estimate any temperature profile inside the work piece. Future experiments will concern direct measurements of temperature profiles (by using embedded thermocouples or thermal camera) in order to validate the temperature profiles predicted by these simulations and to estimate the corresponding metallurgical transformations. New steps of this program should also consist in describing hydrodynamic flow of the melt pool and thermocapillary effects, for studying their consequences on geometry and energy transport inside the melt pool order to reproduce the melt pool in MAG welding for extreme configurations (high wire speed and low welding speed). This much more complex task should be possible by using the same Comsol software.

Figure 1 .

 1 Figure 1. Scheme of hybrid laser -MIG/MAG process.

Figure 2 .

 2 Figure 2. Schematic representation of the high speed camera disposition.

Figure 3 .

 3 Figure 3. Voltage and current synergy obtained with the parameters of our study (S355 steel, 1.2 mm diameter wire, shielding gas: 92% Ar -8% CO2).

Figure 4 .

 4 Figure 4. Metal transfer in MAG process: a -short-circuiting (Vw = 3 m/min), b -globular (Vw = 6 m/min), c -spray (Vw = 11 m/min).

Figure 5 .

 5 Figure 5. Weld bead obtained for: (a) Laser alone : Welding speed 1 m/min, Laser power 4 kW (b) MAG alone : Welding speed 1 m/min , Wire speed 5m/min, current 200 A, voltage 17.6 V. (c) Hybrid Laser-MAG : Welding speed 1 m/min, Laser power 4 kW, wire speed 5m/min, current 200 A, voltage 17.6 V.

Figure 6 .

 6 Figure 6. Examples of images extracted from high speed video movies: (a) Laser alone : Welding speed 1 m/min, Laser power 4 kW. (b) MAG alone : welding speed 1 m/min , wire speed 5 m/min, current 200 A, voltage 17.6 V. (c) Hybrid Laser-MAG : Welding speed 1 m/min, Laser power 4 kW, wire speed 5m/min, current 200 A, voltage 17.6 V.

Figure 7 .

 7 Figure 7. Width, penetration and length of the melt pool obtained with hybrid Laser-MAG (a-b-c) and MAG alone (d-e-f) as a function of welding speed, for different wire speeds.

Figure 8 .

 8 Figure 8. Visualization of depression below the arc for MAG process (Incident arc power UI=8kW). The dotted line shows the symmetry line of the weld seam located on the flat surface of the sample and the continuous line shows the profile of the depressed zone. Dimension h' is the projection of the real depression on the observation plane, which is perpendicular to the video camera axis.

Figure 9 .

 9 Figure 9. Maximum surface depression below the solid surface for MAG and Hybrid processes, as a function of welding speed for different wire feeding rates V w (Hybrid parameters: P laser : 4 kW, wire diameter : 1.2 mm, distance wire/beam: 2 mm).

Figure 10 .

 10 Figure 10. For Hybrid laser-MAG process, (a) droplet velocity, frequency (b) and (c) inducedpressure (given by equation 1), as a function of the wire feeding rates.

Figure 11 (Figure 11 .

 1111 Figure 11. (a and b): Two images extracted from a video sequence showing the displacement of a tracer (indicated by an arrow) between a time interval of 2ms (MAG process: Welding speed U 0 : 2 m/min; Wire speed V w : 9 m/min).General trend of the melt flow surface is also indicated by curved arrows on figure 11-a.

Figure 13 :

 13 Figure 13: Scheme using the tracer implant inside the work piece.

Figure 14 .

 14 Figure 14. Longitudinal macrographs obtained with copper/aluminium alloy contrast material. The dotted line shows the melt pool boundary. Vertical white bar shows the initial position of the contrast wire. a-MAG alone (U 0 = 0,8 m/min, V w = 5 m/min). b-Hybrid laser/MAG (P laser = 4kW, U 0 = 1 m/min, V w = 5 m/min, wire/laser beam distance: 2 mm).

  .2 that the use of a modified thermal conductivity inside the melt pool allows us to correctly reproduce its size.

Figure 15 .

 15 Figure 15. Comparison between measured and calculated cross section weld seam for MAG, laser and hybrid processes.

Figure 16 .

 16 Figure 16. Comparison of experimental and calculated longitudinal weld pool shape for: MAG alone: welding speed: 1 m/min, wire speed: 9 m/min, current: 200 A, voltage: 17.6 V Hybrid Laser-MAG: Welding speed: 1 m/min, Laser power: 4 kW, wire speed: 5m/min, current: 200 A, voltage: 17.6 V, distance wire/beam 2 mm.

Figure 17 .

 17 Figure 17. Parameters used in the simulation to reproduce the weld pool characteristics determined from macrographs and melt pool length measured using videos: arc efficiency (a), arc power radius (b), arc pressure (c) and laser power (d), obtained with hybrid Laser-MAG for different wire speeds.

Table 1 .

 1 Summary of liquid thermal conductivity adjustments used for the various configurations

Table 2 :

 2 For hybrid welding conditions, polynomial expressions for several experimental geometrical melt pool parameters (U 0 is expressed in m/min and P arc in kW).

	2,07	12

Acknowledgments:

This study has been realized in the frame of the project "HYPROSOUD" that was financed by the French National A. N. R.