Numerical Investigation of the Effect of Some

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[1]. Several operating parameters involved in a laser cutting operation. ... Karim Kheloufi and El Hachemi Amara / Physics Procedia 39 ( 2012 ) 872 – 880. 873.
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Physics Procedia 39 (2012) 872 – 880

LANE 2012

Numerical Investigation of the Effect of Some Parameters on Temperature Field and Kerf Width in Laser Cutting Process Karim Kheloufi , El Hachemi Amara Laser Material Processing Team, Center of Development of Advanced Technologies (CDTA), B.P17, Baba Hassen, 16303 Alger

Abstract A transient numerical model is developed to study the temperature field and the kerf shape during laser cutting process. The Fresnel absorption model is used to handle the absorption of the incident wave by the surface of the liquid metal and the enthalpy-porosity technique is employed to account for the latent heat during melting and solidification of the material. The VOF method is used to track the evolution of the shape of the kerf. Physical phenomena occurring at the liquid/gas interface, including friction force and pressure force exerted by the gas jet and the heat absorbed by the surface, are incorporated into the governing equations as source terms. Temperature and velocity distribution, and kerf shape are investigated. © 2012 2011 Published Published by by Elsevier Elsevier B.V. Ltd. Selection © Selection and/or and/or review review under under responsibility responsibility of of Bayerisches Bayerisches Laserzentrum Laserzentrum GmbH GmbH Keywords: Laser cutting; Fresnel absorption; numerical simulation; surface tracking

1. Introduction In the process of laser cutting, the laser beam focused on the surface of the part causes the rapid heating of the material until the fusion. Molten metal is then ejected by using a gas jet of high pressure [1]. Several operating parameters involved in a laser cutting operation. Some parameters are related to the laser source, the other material considered and the gas jet used. These parameters have a direct influence on the final quality of the cut. For the previous research, most of the results were derived from preassumed geometrical kerf shapes [2,3]. This work focuses on modeling the cutting process by the VOF method taking into account the Fresnel absorption of the incident wave. It is obvious that the energy absorbed by the surface of the liquid metal depends on the shape of the kerf (angle), hence the need to

* Corresponding author. Tel.: +21-351040; fax: +21-351039. E-mail address: [email protected]

1875-3892 © 2012 Published by Elsevier B.V. Selection and/or review under responsibility of Bayerisches Laserzentrum GmbH doi:10.1016/j.phpro.2012.10.112

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calculate absorptivity at each grid cell on the L/G surface. The impact of the gas jet on surface of the kerf and the absorbed laser intensity will be taken into account in the Navier-Stokes and energy equations by the VOF function. 2. Mathematical model 2.1. Assumptions The present numerical model is base on the fellowing simplification/assumption: (1)Only single absorption of the beam is considered (repeated reflection and absorption are ignored). (2)The gas jet flow is not modeled. (3)The metal in the solid and liquid states is isotropic and has constant properties. (4)Chemical reactions that occur in the case of oxygen driven cutting are ignored. 2.2. Governing equations In the case of multi-phase fluids and based on the above-listed assumptions ,the basic transport phenomena of energy, mass, momentum, and free surface can be expressed for Newtonian, incompressible, and laminar flow by the following governing equations: Energy equation: This problem requires application of a heat flux to the changing surface of cutting front. The approach proposed in [4] to model heat transfer at the volume fraction interface is used. In this approach, the heat flux q (W/m2) applied to the interface is treated as an equivalent volumetric heat source S (W/m3) added to the energy equation: S=q. F , where F denote the volume fraction of the material in a computational cell. Since the gradient of the VOF variable F is nonzero only in the cells adjacent to the free surface, the source is applied only to the interface. The energy equation based on the enthalpy method and continuum formulation is given by[5]:

t

H

vH

k T

(1)

S

By dividing the total enthalpy H into the sensible enthalpy heat h and latent heat content H [6,7] H=h+ H, where h=c p .T and H=f liq .L, the energy conservation equation in enthalpy–porosity technique, written in terms of temperature is described as follows: cp

T t

v T

k T

H t

v

H

I abs

F

(2)

Continuity and momentum equations: The momentum transfer from the assist gas flow to the melt is carried out by means of two mechanisms, one due to the pressure gradient of the flow and the other consisting of shear stress due to viscous friction [8,9]. In this study it is assumed that the pressure gradient inside the kerf is a constant quantity, and the pressure gradient force acting on the film surface at any .Ug2.(z/L), and the magnitude of the gas friction force is depth z inside the kerf is: Fp=(p1given by: the pressure at any depth inside the kerf, Ug is the gas the gas viscosity.The pressure force acts in the normal direction (Oz) and the friction force acts in the tangential direction of the free

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surface and is incorporated into the momentum equation as a source term by multiplying with the gradient of the VOF function F.The continuity and momentum equation are given by: v c

(3)

0 v t

v

v

p

v

K

v

g T

T

Fp

F ez z

F friction

(4)

sF

In the above equation s denotes the gradient in the tangent plane.The mushy zone is treated as a porous medium in momentum equations. A sink is added to the momentum equation (third terme in equ…) to extinguish velocities in the solid region. The permeability term K, is related to the liquid volume fraction by the Carman– Koseny equation [10]. VOF: Conservation of F is expressed as [11]: F v T

F

(5)

0

0 F 1 with the extreme values occurring in void and fluid elements, respectively, and the intermediate values occurring in free surface elements. The VOF variable F should be updated at each time step to re-obtain the cells with F 0 , i.e., free surface of the cutting kerf. In the aforementioned equations, is density, v is the velocity vector, p is the pressure, the dynamical viscosity of liquid phase, F the volume fraction of fluid occupying each computational cell, T is temperature, k heat conductivity, c p the specific heat, K the permeability coefficient dependent on the material microstructure, buoyancy coefficient, g gravity acceleration, f liq the fraction of the liquid metal which assumed to vary linearly with temperature [10] and L latent heat of fusion of the material. I abs is the absorbed intensity of the laser beam by the kerf surface and will be described further in the next subsection. 3. Laser power absorbed by the cutting front The molten metal surface of the kerf is regarded as specular in this paper, and it is reasonable to adopt the Fresnel reflection model [12] for the material’s laser absorption rate. The intensity of the absorbed laser radiation can be formulated as [13]: I abs

(6)

A I x, y cos

A is the absorption coefficient, I the intensity of the incident laser beam, and the angle of incidence. In this study, the radiation intensity is described by the Gaussian distribution, which corresponds to the TEM 00 mode [6]. In this case the intensity of the laser beam is given by [14, 15]: I x, y

2P R02

exp

2r 2

(7)

R02

Here P is the radiation power, R 0 is the radius of the focused laser beam , and r

x2

y2 .

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Fig. 1. (a) relationship between angle of incidence and the normal vector; (b) computational domain and physical model

In the case of circularly or un-polarized laser radiation , the reflectivity R Ave can be estimated as the average value of the reflectivities of parallel and perpendicularly polarized radiation [15], R P and R S according to: R

RP

RP

R Ave

RS

(8)

2

n cos

12

n cos

2

1

m cos

2

m cos

2

, and RS

n cos

2

m2

n cos

2

m2

(9)

where n the refractive index, and m the extinction coefficient. The averaged absorptivity A is given by: A 1 R Ave

1

RP

RS

(10)

2

It should be mentioned that accurate values of the normal vector on each point of the interface is essential for incorporating the absorbed intensity of the incident beam. In VOF method, the normal vector N on the interface can be expressed in terms of the gradient of F: N Nx, N y , Nz

F

F

x

, F

y

, F

z

(11)

The value of the angle of incidence varies with the cutting depth due to the curved shape of the cutting front. Its value is given by (see Fig 1.a): cos

1

Nz N

(12)

4. Parameters used in the simulation Since the transient cutting kerf evolution, heat transfer and fluid flow behaviour in laser cutting are solved coupled, the time step will be very small (typically around 10-8 s) in the simulation. The commercial code Fluent 6.3 CFD, to which several modules were appended (User Defined Functions UDF) was used to accomplish the simulation. The calculation domain is illustrated in figure 1.b,

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including the substrate and part of the gas region (gas phase). The computational domain contains all three phases, solid, liquid, and gas. The governing equations are solved in the reference attached to the laser beam. Material properties and appropriate calculation arrangement (moving material) were made in different phases. In order to make the calculation tractable, small physical size of the specimens, 4mm × 5mm × 1.5mm is employed in the simulation and a uniform cell grid mesh was used. The physical properties used in the simulation corresponding to that for mild steel [14].The optical properties n and m (refractive and extinctive indexes) are function of wavelength and different temperature-dependent material properties ([16,17]). Values used in this paper are for liquid iron and correspond to the wavelengths of CO 2 [18].The parameters adopted in the simulation are: laser power: 2 KW, cutting velocity: 12-50 mm/s, gas velocity: 100 mm/s, laser beam radius: 0.5 mm. 5. Results and discussion The predicted 3D temperature field and kerf formation evolution during the cutting process is illustrated in Figure 2.a-b and c. The figures are sequential snapshots of the cutting process of the whole geometry for a cutting time from 2 to 65 ms and cutting speed U cut =50mm/s. Because of the high-power laser, the process quickly melts the material, and approximately, only 20 ms is needed to achieve full melting of all the thickness of the material. In order to track the dynamics of heating and kerf formation during the process, the results of the present model will be presented in only half of the domain.

Fig. 2. 3D thermal field (a) t=2. 10-3 s; (b) t= 2. 10-2 s; (c) t=5.6 10-2 s

5.1. Heating stage Figure 3 shows the temperature field during the heating stage of the edge of the sheet at three instants t=0, t=2.10-3, and t=4.5 10-3s. W note that for the firts millisecond, the laser heat up the sheet through all its thickness with relatively low temperature (T=520 K at t=2 10-3s). As the sheet moves, and du to the heat flow in the solid by conduction, the temperature of the top surface of the materials start to increase to reach (T=1370 K à t=4.5 10-3 , see Fig 3.c). 5.2. Melting and kerf formation The melting of the material start at the top surface (t=18 ms, T=1900 K). During this stage the temperature variation are very important (see Fig. 4.b). Once the melt film cover the whole thickness a stable cutting kerf is formed. The total laser power absorbed by the workpiece increases after the cutting front is formed and a constant melting front is maintained. The peak temperature in the molten film at t=0.021s is around 2080 K. As it continues, the peak molten pool temperature drops to around 2150 K.

Karim Kheloufi and El Hachemi Amara / Physics Procedia 39 (2012) 872 – 880

Fig. 3. Thermal field during the heating stage (U cut =50 mm/s). (a) t=0 s; (b) t=2 10-3 s; (c) t=4.5 10-3 s

Fig. 4. Thermal field during the melting and kerg formation stage (U cut =50 mm/s). (a) t=1.8 10-2 s; (b) t=2.1 10-2 s; (c) t=5.6 10-2 s

5.3. Effect of laser cutting on temperature field and kerf shape Figure 5 show the thermal field in the cut front for cutting speed U cut =12 and 50 mm/s. It is observed that at low cutting speeds the cut front is almost vertical. In this case only the peripheral part of the beam interacts with the sheet surface. At high speed the cut front geometry becomes curved with high surface temperatures. The increase in the cutting speed has two effects: (1) The molten material cannot flow out of the cut zone quickly enough to allow the cut front to remain vertical. Thus, there will be a horizontal lag between the top and bottom of the cut front. (2)The change in inclination of the cut front increases, therefore, the proportion of the beam which interacts with the cut front increases. Therefore the efficiency of the cutting process increases with increase in cutting speed because a higher proportion of the absorbed laser power will be used for melting the kerf volume than is lost to the substrate metal through heat conduction from the cutting zone.

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Fig. 5. (a) thermal field and temperature variation along kerf projection on the cutting direction. (a) U cut =12mm/s; (b) U cut =50mm/s

Figure 6 represents the velocity profile of the liquid metal in the molten layer. These values of velocities correspond to the liquid surface (the maximal velocity).As seen in figure 6, the kerf wall is formed with a thin molten liquid layer due to massive expulsion of liquid metal.

Fig. 6. Velocity magnitude in the liquid film. (a) U cut =12mm/s; (b) U cut =50mm/s

In the figure 7 a. and b. are plotted the variations of the velocity in the liquid film (at the surface) along the depth z. It is noted that an increase in speed has only a minor effect on maximal value of the melt velocity at the exite kerf (the velocity of ejected material): U melt =0.998 m/s for U cut = 12mm/s and U melt =1.020 m/s for U cut = 50mm/s.

Karim Kheloufi and El Hachemi Amara / Physics Procedia 39 (2012) 872 – 880

Fig. 7. Variation of the velocity magnitude along the depth od the cutting kerf. (a) U cut =12mm/s; (b) U cut =50mm/s

However, it is remarked that for low cutting velocity the metal is accelerated along all the depth of material, while for high velocity cutting we observe an accelerating stage then the melt kept almost a constant velocity along the rest of the thickness. 6. Conclusion A 3D model for laser melt cutting process has been presented, which considered multiphysical phenomena such as Fresnel absorption, heat transfer, fluid flow, melting, and solidification. The numerical model was built to deal with different phases (gas, liquid, solid, and mushy zone) in the calculation domain. A derived heat source term which considers the rate at which the heat is absorbed by the cutting front surface, was incorporated into the energy equation. The forces of the gas jet acting on the cutting front surface were embedded in the momentum equation. Different stages during the cutting process are identified and the effect of cutting speed on the formed kerf is discussed. In the future, more detailed discussions for the effects of different parameters such as gas jet velocity, beam polarization, and material thickness will be investigated. References [1]

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[12] Kovalev, O. B.; Orishich, A. M. Theory of Metal Surface Destruction under the Action of Laser Radiation, Doklady Physics, Vol. 49, No. 3, 2004, pp. 175–178. [13] Kovalev, O. B.; Zaitsev,A. V. Journal of Applied Mechanics and Technical Physics, Vol. 46, No. 1, pp. 9–13, 2005. [14] Ahmadi, B. Torkamany, M. J.; Jaleh, B. and Sabaghzadeh, J. Theoretical Comparison of Oxygen Assisted Cutting by CO2 and Yb:YAG Fiber Lasers. CHINESE JOURNAL OF PHYSICS VOL. 47, NO. 4. [15] Zaitsev, A.V.; Kovalev, O.B.; Orishich, A.M.; Fomin, V.M. Numerical analysis of the effect of the TEMQO radiation mode polarisation on the cut shape in laser cutting of thick metal sheets, Quantum Electronics 35(2) 200-204 (2005). [16] Petring, D. Anwendungsorientierte Modellierung des Laserstrahlschneidens zur rechnergestützten Prozessoptimierung.PhD Thesis, RWTH Aachen, Germany, Shaker Verlag, 1995. [17] Beyer, E. Schweißen mit Laser, 1995 (Springer, Berlin, Heidelberg). [18] Mahrle, A.; Beyer, E. Theoretical aspects of fibre laser cutting. J. Phys. D, Appl. Phys., 2009, 42, 9.