Modelling of CO2 laser welding of magnesium alloys

Modelling of CO2 laser welding of magnesium alloys

ARTICLE IN PRESS Optics & Laser Technology 40 (2008) 581–588 www.elsevier.com/locate/optlastec Review Modelling of CO2 laser welding of magnesium a...

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ARTICLE IN PRESS

Optics & Laser Technology 40 (2008) 581–588 www.elsevier.com/locate/optlastec

Review

Modelling of CO2 laser welding of magnesium alloys Kamel Abderrazaka,, Wacef Ben Salemb, Hatem Mhiria, Georges Lepalecc, Michel Autricc a

Unite´ de Thermique et Environnement, Ecole Nationale d’Inge´nieurs de Monastir, route de Ouardanine, 5000 Monastir, Tunisie b Laboratoire de Ge´nie Me´canique, Ecole Nationale d’Inge´nieurs de Monastir, route de Ouardanine, 5000 Monastir, Tunisie c Institut de Me´canique de Marseille, 60, rue Joliot-Curie, Technopoˆle de Chaˆteau-Gombert, 13453 Marseille cedex 13, France Received 4 May 2007; received in revised form 1 October 2007; accepted 10 October 2007

Abstract Laser welding is an important joining process for magnesium alloys. These materials are being increasingly used in different applications such as in aerospace, aircraft, automotive, electronics, etc. To date, carbon dioxide (CO2) neodymium-doped yttrium aluminum garnet (Nd:YAG) and the high power diode laser have been extensively used to investigate the weldability of magnesium alloys. The present work describes an analytical thermal model for the weldability of magnesium alloys (WE43) using an industrial (CO2) laser source. The main target of the project is to present to the industrial community a simple and rapid tool for the determination of the penetration depth and the bead width as a function of both the incident laser power and welding speed. The proposed model is based on the Davis thermal approach, largely considered for the characterization of the average radius of the liquid zone, aiming at predicting the joint shape. Moreover, since during the welding process considered in this study, a protecting gas is used to avoid joint oxidation, both thermal convection and radiation phenomena in the welding area have been estimated and introduced in our model for a better characterization of the welding process. The obtained results have been compared to the experimental ones and a satisfactory correlation has been observed, indicating the reliability of the model developed in this study. r 2007 Elsevier Ltd. All rights reserved. Keywords: Laser welding; Magnesium alloys; Thermal modelling

Contents 1. 2.

3. 4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem modelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Position of the problem and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Analytical approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Magnesium alloys have different interesting specific characteristics, including the best strength/weight ratio Corresponding author. Tel.: +216 733 48773; fax: +216 735 00514.

E-mail address: [email protected] (K. Abderrazak). 0030-3992/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2007.10.003

581 582 582 583 584 585 588 588

among all commercial alloys [1]. These materials classes have both high thermal conductivity and high damping capacity. These material properties improve the heat transfer during the welding process as well as their impact resistance. Moreover, magnesium alloys have a low density and are completely recyclable. These distinctive physical, mechanical, and thermal properties have encouraged

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Nomenclature as cps cpl cpg d D Hf Hv P Pa Ps Pl Pg T0 Tf Tv V

coefficient of diffusion, m2 s1 specific heat of solid at constant pressure, J kg1 K1 specific heat of liquid at constant pressure, J kg1 K1 specific heat of gas at constant pressure, J kg1 K1 capillary diameter, mm bead width, mm latent heat of fusion, J kg1 latent heat of evaporation, J kg1 laser power, kW absorptive power, kW absorptive power by solid metal, kW absorptive power by liquid metal, kW absorptive power by gas metal, kW initial metal temperature, K fusion temperature, K evaporation temperature, K welding speed, cm min1

manufacturers to introduce such alloys basically in vehicle and plane industry. Magnesium alloy welding requires high energy density and shielding gases that effectively protect the metal from the oxygen action. For this kind of materials, different welding techniques have been discussed in the literature [2–5]. The tungsten-arc inert gas (TIG), metal-arc inert gas (MIG), plasma arc, electron, laser, friction, adhesive, explosion, stud, ultrasonic, and spot welding are the essence of these techniques. Basically, the TIG and MIG processes are frequently used. However, results reported by Marya et al. [6] indicated that these two welding processes have such limitations as low welding speed, large heat affected zone (HAZ) and fusion zone (FZ), high shrinkages, variations in microstructures and properties, evaporative loss of alloying elements, high residual stress, and distortion of arc-welded joints [7,8]. Consequently, the laser welding can be considered as the most reliable technique for the welding of the magnesium alloys. This technique consists of using either the Nd:YAG or the CO2 sources. The Nd:YAG laser light (l=1.06 mm) has a much higher absorption degree than CO2-laser light (l=10.6 mm) due to the higher absorption degree of short wave light. Their power ranges from 1 to 50 kW and its fluctuations can be about 10%. The most commonly used CO2 laser consists of a mixture of CO2 with nitrogen and noble gases. Between the two energy levels of nitrogen, there is nearly the same energy gap as between the two vibration modes of CO2. A discharge in nitrogen fills the vibration levels of CO2 molecules which results in a laser emission [9]. In this study, an analytical thermal model for the CO2-laser welding of the magnesium alloy WE43 has been

Greek symbols a d ls ll rs rl rg

power lost fraction, % penetration depth, mm solid thermal conductivity, W m1 K1 liquid thermal conductivity, W m1 K1 solid metal density, kg m3 liquid metal density, kg m3 gas metal density, kg m3

Indices s l g v f a 0

solid liquid gas vapor fluid absorptive initial

developed. Generally speaking, laser welding is optimized relying on several parameters such as laser power, laser beam characteristics, welding speed, focal position, shielding gas flow, physical, and metallurgical properties of materials. Hence, elucidating and providing the industrial community with a fast tool for studying the effect of both the power laser beam and the speed welding source on the penetration depth, the capillary size, and the bead width in the workpiece was among the priorities of this analysis. In the suggested model, thermal losses due to both radiation and convection phenomena taking place during the welding process have been considered for a better characterization of this process. 2. Problem modelling 2.1. Model description During the laser welding process, three different heat transfer phenomena take place, as illustrated in Fig. 1. These are the conduction, convection, and radiation phenomena. These phenomena are usually accompanied by the buildup of the capillary of ionized metal vapor (keyhole) that can be observed when the intensity of the laser beam is higher than 106 W cm2 [9]. For these laser densities, the energy accumulated by the base material cannot be evacuated by conduction only. Therefore, such energy creates a hydrostatic balance between the pressure inside cavity and the pressures generated by the molten pool. The beam is absorbed on the totality penetration depth and loses its energy gradually. At the bottom of the capillary, it is too weak and does not ensure the formation

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Flux Laser Base metal Fusion zone Plasma

Radiation Convection

Conduction

Fig. 1. The thermal phenomena in the welding process.

Laser beam x D Capillary (plasma)

V Molten zone

d 0

y

δ

Fig. 2. The geometry of welding zone.

of plasma any more: the penetration is stabilized. As a matter of fact, the plasma plays a role of interface between the beam and the target: it retransmits the stored energy in the form of ultraviolet and visible radiations which are absorbed better by metallic materials. As a result, the beam–matter coupling is improved. In front of the capillary progression, molten metal solid runs out around this one, releasing the passage to the plasma column; it cools, then in the back and forms the weld bead [6]. To provide a better characterization and prediction of the laser welding process, the size and the shape of this capillary area should be known. In the current work, the capillary (also called plasma) process was supposed to take place throughout the base material thickness, in a cylindrical form, as usually considered in the literature [10] (Fig. 2). In this figure, d and D illustrate, respectively, the diameter of the cylinder at which the capillary process has taken place and the diameter of the molten area (width of the weld line). 2.2. Position of the problem and assumptions The model suggested in this study results from a heat balance in the immediate vicinity of the welded joint. This

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area was supposed to be divided into three main zones, i.e. the capillary, the liquid, and solid zones (Fig. 2). Basically, the capillary zone, usually called the plasma zone, is directly influenced by the incidental beam and is supposed to have a cylindrical form of diameter d. The plasma temperature is considered to be uniform in this work and is about 13,000 K [10]. The liquid zone contains the metal in fusion, whose temperature is the arithmetic mean of the vapor and fusion temperatures. The diameter D of this molten zone is supposed to be a cylindrical form, representing the weld width after processing. In this zone, it has been considered that the influence of convective movement was neglected. The solid part, which constitutes all the plate remainder, is subjected to a linear source of heat and having a temperature equal to the metal base. It is well known that during the welding process, part of the laser energy could be evacuated from the workpiece by both convection and radiation phenomena. Generally, these phenomena are not considered in the two analytical models suggested in the literature for better characterization of the welding process. In this study and in order to quantify these energy losses, a computational fluid dynamics software FLUENT was used. The software is composed of the preprocessor GAMBIT, solver, and postprocessor. GAMBIT is used to set the geometry, the mesh, and the boundary types of a 3D computational domain, and, FLUENT running allows one to obtain the numerical solution of the flow equations by finite volume discretization. An implicit scheme is used, and the standard k–epsilon model that solves a modeled transport equation for the turbulent viscosity can be suitable for solution convergence. Basically, different simulations were conducted to estimate the relationship between the incident laser energy and the amount of losses. Such an estimation has been based on the experimental device used by Dhahri et al. [11] (Fig. 3). In this figure, the shielding gas (argon+helium) comes from the nozzle with specific characteristics: pressure ¼ 4 bar and flow ¼ 60 l/min. The plasma area was supposed to have a temperature equal to 13,000 K, as proposed by Wang [10]. On the other hand, the melting temperature of 1380 K was chosen for the melting zone. The energy losses were calculated in the flow form crossing a virtual cylinder containing the control volume of the problem. For a better estimation of these losses, a considerable radius of this cylindrical shape has been considered. For accurate result, a dense triangular grid close to the welding zone where the temperature gradients are important was adopted (Fig. 4). An example of the obtained results is shown in Figs. 5 and 6. The result obtained in these figures is for an incident laser beam of power 2000 W. Fig. 5 shows the contours of static temperature at the level of the welding. As can be seen the temperature varies from the keyhole to the base material. Fig. 6 of the contours of velocity shows that the welding zone is well covered by the protection gas, and that the impacting jet increases considerably the losses by convection on the level of the welding zone. The result of

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and for liquid metal part   pD2 . V ðD  dÞd þ 8

38mm

Field

(2)

As indicated in the previous section, the energy balance of the base material exposed to the incidental laser beam is

Nozzle Exit of the nozzle

P ¼ Pa þ ðPlost by convection þ Plost by radiation Þ,

(3)

with Pa ¼ Pg þ Pl þ Ps ¼ aP.

30mm 14mm

The power transmitted to the capillary is

Plate

z

Pg ¼ V dd½½rs cps ðT f  T 0 Þ þ H f rs  þ ½rl cpl ðT v  T f Þ þ H v rl  þ ½rg cpg ðT plasma  T v Þ

y x

Thermal loose Plate

Moreover, the power evacuated in the base material by conduction is evaluated by supposing that this material is subject to a linear heat source of diameter D, at a temperature equal to the melting one, i.e. Tf. This problem has an analytical solution which is [12]

Fig. 3. Configuration of the problem.

Ps ¼

Z X

Grid FLUENT 6.0 (3d, dp, segregated, spe2, ske)

Fig. 4. The grid density at the level of welding zone.

2pls T v d  . 8as Ln 1:78Vd

(7)

Therefore, the equation giving the laser power according to various welding parameters is 3 2 3 2 rs cps ðT f  T 0 Þ þ H f rs 7 6 7 7 6 V dd6 4 þrl cpl ðT v  T f Þ þ H v rl 5 7 6 7 6 þr c ðT  T Þ v plasma g pg 7 6 7 6   2 7  6 7 6 þV ðD  dÞd þ pD 1 7. 6 P¼ 8 7 1a 6 7 6  7 6 T  T v f 7 6  rs cps ðT f  T 0 Þ þ H f rs þ rl cpl 7 6 2 7 6 7 6 2pls T v d 5 4 þ Lnð8as =1:78VdÞ

simulation using the 3D commercial software FLUENT gives estimated power losses around 20%.

(8) As previously discussed, the melting zone has a circular shape. According to Davis et al. [13], the diameter of this zone is translated by the following equation:

2.3. Analytical approach Consider now a geometric simplified form of the welding zone in Fig. 7, the elementary volume considered are translated as follows: for gas metal V dd

ð5Þ

and the power transmitted to the liquid zone can be estimated by   pD2 Pl ¼ V ðD  dÞd þ 8   Tv  Tf  rs cps ðT f  T 0 Þ þ H f rs þ rl cpl . ð6Þ 2

Keyhole andmelting zone

Y

(4)

(1)



8as V  exp



ls ðT f  T 0 ÞLnðdV =8as Þ  0:5772ll ðT v  T f Þ ls ðT f  T 0 Þ þ ll ðT v  T f Þ

 .

ð9Þ

ARTICLE IN PRESS K. Abderrazak et al. / Optics & Laser Technology 40 (2008) 581–588 7.00e+03 6.66e+03 6.33e+03 5.99e+03 5.66e+03 5.32e+03 4.99e+03 4.65e+03 4.32e+03 3.98e+03 3.65e+03 3.31e+03 2.98e+03 2.64e+03 2.31e+03 1.97e+03 1.64e+03 1.30e+03 9.67e+02 6.31e+02 2.96e+02

Y

585

X

Z

Contours of Static Temperature (k) FLUENT 6.0 (3d, dp, segregated, spe2, ske) Fig. 5. The contours of static temperature at the level of the welding.

6.77e+02 6.43e+02 6.10e+02 5.76e+02 5.42e+02 5.08e+02 4.74e+02 4.40e+02 4.06e+02 3.72e+02 3.39e+02 3.05e+02 2.71e+02 2.37e+02 2.03e+02 1.69e+02 1.35e+02 1.02e+02 6.77e+01 3.39e+01 0.00e+00

Y Z

X

Contours of Velocity Magnitude (m/s) FLUENT 6.0 (3d, dp, segregated, spe2, ske) Fig. 6. The contours of velocity.

3. Results and discussion In the first step, emphasis was given to the fraction of the incidental power transmitted in the plasma (Pg), in the liquid (Pl) and in the solid (Ps), using Eqs. (5)–(7). This estimation was determined for different welding speeds (Fig. 8). A comparison between the analytical results obtained in this study and the experimental one of Dhahri et al. [11,14] will be done (Table 1). These experimental results have been obtained for the WE43 alloys using 2 kW CO2 laser welding. The main characteristics of these alloys are summarized in Table 2.

Fig. 9 shows the results of the analytical model on the effect of the welding speed on the bead width for different capillary diameters. These results indicate that the bead width decreases as the welding speed increases. The experimental results confirm this tendency. However, according to the model suggested, the decrease seems to be nonlinear, particularly at a very low welding speed. The results shown in Fig. 9 also indicate that the Dhahri experimental results are obtained for capillary diameters ranging between 0.5 and 0.6 mm. This is an expected finding that predicts the size of the capillary zone for the laser power used. Thence, experimental tests should be

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3

D

• experimental values - model

V Bead width (mm)

2.5

δ

2 d= 0.7 mm d= 0.6 mm

1.5

d

d= 0.5 mm d = 0.4 mm

Fig. 7. A simplified form of welding zone.

1

0

100

0.8 Pg Pl Ps Pg Pl Ps

0.7

0.5

700

800

δ = 4mm

10

0.4

9

0.3

8

0.2 0.1 0

300 400 500 600 Welding speed (cm/min)

Fig. 9. Effect of welding speed on bead width of cast WE43 alloy joints, P ¼ 2 kW.

0

100

200 300 400 Welding speed (cm/min)

500

600

Fig. 8. Fraction of the incidental power transmitted in plasma (Pg), in the liquid (Pl), and in the solid (Ps).

Penetration depth (mm)

Power fraction (%)

0.6

δ = 2mm

200

7 6 5 4 3 2 1 100

Table 1 Experimental results for width of the cord D ¼ 2.5 mm [11,14] P (kW)

Vs (cm min1)

d (mm)

2 2 2 1 2 3

300 400 600 200 200 200

2.1 2.1 2 1.3 4 4.75

Table 2 Properties of WE43 magnesium alloy at its melting point [15] Properties

Values

Density (kg m3) Specific heat at constant pressure (J kg1 K1) Thermal conductivity (W m1 K1) Fusion temperature (K) Evaporation temperature (K) Latent heat of evaporation (J kg1) Latent heat of fusion (J kg1)

1590 1340 146 913 1380 5,260,000 362,000

2 kW 3.5 kW

200

300 400 500 600 Welding speed (cm /min)

700

800

Fig. 10. Effect of welding speed on penetration depth of cast WE43 alloy joints.

conducted for confirmation and is therefore under consideration. The effect of the welding speed on the penetration depth is illustrated in Fig. 10. For the different laser powers considered in this case, a good correlation between the analytical and experimental results was observed, especially in the low laser power case. These results, together with those translated in Fig. 9, show that the analytical model presented in this study can be considered as a reliable tool for rapid determination of the different welding parameters during processing. In the following, the theoretical results will be presented in a condensed form (abacus) to be consulted by the industrial community for the selection of the optimum welding conditions versus the bead width (Figs. 11, 12), the workpiece thickness (Figs. 13, 14), and the thermal conductivity of the considered material (Fig. 15). On the use of the abacus, we considered: Case one: (point A, Fig. 11). In this case, the penetration depth is equal to 1 mm. With laser conditions (2 kW laser

ARTICLE IN PRESS K. Abderrazak et al. / Optics & Laser Technology 40 (2008) 581–588 Welding speed (cm/min) 600

3

587

Welding speed (cm/min)

500

400

600 500

8

300

400

3mm

2.5

7

300

2.5mm

4mm

OA

200

1.5mm

1.5

1mm D=0.5mm

1

100

Laser power (kW)

Laser power (kW)

6 2mm

2

200

3.5mm 3mm

5

2.5mm

4

2mm

3

100

1.5mm δ=1mm

2 0.5

1 0 0.1

0.15

0.2

0.25 0.3 0.35 Linear energy (kJ/cm)

0.4

0.45

0

0.5

Fig. 11. Abacus showing the bead width as a function of laser power and welding speed, with penetration depth d ¼ 1 mm.

0

0.2

0.4

0.6

600 500

8

400

3

4mm

7

400

300

o experimental values (Table 2)

200

2.5 2

5

300

1.5 1

D = 0.5mm

200 3

Laser power (kW)

Laser power (kW)

2

3.5mm

6

4

1.8

Welding speed (cm/min)

500

7 6

1.6

Fig. 13. Abacus showing the penetration depth as a function of laser power and welding speed, with bead width D ¼ 2 mm.

Welding speed (cm/min) 600

0.8 1 1.2 1.4 Linear energy (kJ/cm)

3mm

5

2.5mm 2mm

4

o δ =1mm

2

2

0.4

0.5

0.6 0.7 0.8 Linear energy (kJ/cm)

0.9

0

1

Fig. 12. Abacus showing the bead width as a function of laser power and welding speed, with penetration depth d ¼ 3 mm.

power and a welding speed of 600 cm/min), the result was a bead width equal to 2 mm. This abacus is available only for a welding process of sheet thickness less than 1 mm. Case two: (point B, Fig. 14). It has been considered that the bead width is about 2.5 mm, a case that we can be conditioned with the width of the workpiece (Felled weld operation). With laser conditions (1 kW laser power and a 200 cm/min welding speed), the result was a penetration depth of 1 mm. In this case, there is a possibility to choose between several sheet thicknesses for a welding with full penetration. Fig. 15 shows the influence of the thermal conductivity variation on the penetration depth. If the welding depths remain relatively close when the welding speed is low, the variations reached for the strong values are rather important. Thus, a 2.5 kW laser power is sufficient to

o

o

1

o

o

0.4

0.6

oB

0

0.2

0.8 1 1.2 1.4 Linear energy (kJ/cm)

1.6

1.8

2

Fig. 14. Abacus showing the penetration depth as a function of laser power and welding speed, with bead width D ¼ 2.5 mm. Welding speed (cm/min) 600 500

5

400

300

200 220 Wm-1K-1 -1 -1

4.5 p=3mm

4 Laser power (kW)

1 0.3

100

100

1.5mm

3

167 Wm K 140 Wm-1K-1

3.5 3 2.5

p=2mm

100

2 1.5

p=1mm

1 0.5 0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Linear energy (kJ/cm)

Fig. 15. Influence of the solid thermal conductivity variation.

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obtain a 2 mm depth, when the welding speed is 600 cm/min and that the thermal conductivity is 140 W m1 K1, whereas a 3 kW laser power is necessary when the conductivity is 220 W m1 K1, due to the fact that the heat lost by conduction is higher. 4. Conclusions In the present study, an analytical model has been proposed to predict different welding parameters during processing. The following conclusions could be drawn from the work:





 



The industrial and scientific community has been provided with a simple and rapid tool for the determination of the penetration depth and the bead width as a function of both the incident laser power and the welding speed. A relatively satisfactory agreement between the model and the experiment could be obtained. It can even be improved if one manages to have the material thermophysical characteristics relative to the temperature. The results make it possible to prevent the characteristics of the welding zone and give an estimation of the capillary diameter. Both thermal convection and radiation phenomena in the welding area have been estimated and have not been neglected. They were estimated to be about 20% of the laser power. The specific reason for the choice of magnesium alloys is that it is one of the particular materials, thanks to their light weight and good mechanical properties. Laser welding will be an important joining technique for magnesium alloys with their increasing applications in aerospace, aircraft, automotive, electronics, and other industries. However this model is available for other materials, the thermophysical characteristics for the corresponding material just being changed.

References [1] Mordike BL, Ebert T. Magnesium: properties–applications–potential. Mater Sci Eng A 2001;302:37–45. [2] Haferkamp H, Burmester I, Niemeyer M, Doege E, Droder K. Innovative production technologies for magnesium light-weight construction laser beam welding and sheet metal forming. In: Proceedings of the 30th international symposium on automotive technology and automation, Florence, Italy, 1997. [3] Westengen H. Magnesium die casting: from ingots to automotive parts. Light Metal Age 2000;58:44–52. [4] Busk RS. Magnesium products design. New York: Marcel Dekker; 1987. [5] Avedesian MM, Baker H. Magnesium and magnesium alloys. ASM Specialty Handbook; 1999. [6] Marya V, Edwards G, Marya S, Olson DL. Fundamentals in the fusion welding of magnesium and its alloys. In: Proceedings of the seventh JWS international symposium, 2001. [7] Haferkamp H, Bach FrW, Burmester I, Kreutzburg K, Niemeyer M. Nd:YAG laser beam welding of magnesium constructions. In: Proceedings of the third international magnesium conference, Manchester, UK, 1996. [8] Haferkamp H, Von Alvensleben M, Goede M, Niemeyer J. Fatigue strength of laser beam welded magnesium alloys. In: Proceedings of the 32nd international symposium on automotive technology and automation (ISATA) on advances in automotive and transportation technology and practice for the 21st century, Vienna, Austria, 1999. [9] Sprow EE. The laser-welding spectrum: what it has to offer you. Tool Prod 1988;54:556–63. [10] Hai-Xing W, Chen X. Three-dimensional modeling of the laserinduced plasma plume characteristics in laser welding. J Phys Appl Phys 2003;36:628–39. [11] Dhahri M, Masse JE, Mathieu JF, Barreau G, Autric M. Laser weldability of WE43 magnesium alloy for aeronautic industry. In: Proceedings of the third laser assisted net shape engineering conference, LANE 3, Erlangen, 2001. [12] Sayegh G. Technical and economical aspects of integrating, handling and exploiting high power laser beams in industrial welding systems. In: Proceedings of the meeting on high power CO2 laser systems and applications, 1988, p. 172–8. [13] Davis M, Kapadia P, Dowden J. Modelling the fluid flow in laser beam welding. Welding J 1986;17:167–74. [14] Dhahri M, Masse JE, Mathieu JF, Barreau G, Autric M. Laser welding of AZ91 and WE43 magnesium alloys for automotive and aerospace industries. Adv Eng Mater 2001;3:504–7. [15] Ocana JL, Lavin A, Dhahri M, Autric M. Numerical modelling of CO2 laser welding of magnesium alloys. In: Proceedings of the conference on cutting and joining of new materials, 2001, p. 311–22.