- Email: [email protected]
Laser induced heating of coated carbon steel sheets: Consideration of melting and Marangoni flow
Optics & Laser Technology 47 (2013) 47–55
Contents lists available at SciVerse ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Laser induced heating of coated carbon steel sheets: Consideration of melting and Marangoni flow S.Z. Shuja, B.S. Yilbas n ME Department, KFUPM Box 1913, Dhahran 31261, Saudi Arabia
a r t i c l e i n f o
abstract
Article history: Received 2 February 2012 Received in revised form 19 July 2012 Accepted 25 July 2012 Available online 12 October 2012
Laser induced melting of coated carbon steel workpiece is simulated. The coating materials include tungsten carbide, alumina, and boron are incorporated in the simulations. The coating thickness is kept constant at 7.5 mm in the analysis. The enthalpy porosity method is used to account for the phase change in the irradiated region. The study is extended to include the influence of laser intensity transverse mode pattern (b) on the resulting melting characteristics. It is found that peak temperature predicted at the surface is higher for alumina and boron coatings than that of tungsten carbide coating. The influence of the laser intensity transverse mode pattern on the melting characteristics is considerable. Surface temperature predicted agrees with the thermocouple data. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Laser Melting Marangoni flow
1. Introduction Laser controlled melting is widely used in surface treatment of engineering materials. Lasers provide precision of operation, fast processing, and low cost. In laser surface treatment of metals, in general, repetitive pulses are used and the size of the melt depends on the duty cycle of repetitive pulses, laser pulse intensity distribution at the workpiece surface, and the properties of the substrate material. The use of controlled melting is to form homogeneous and fine structures at the surface. Depending on the surface condition prior to laser treatment, homogeneous and fine structures can be formed. Carbides and Ceramics layers/ coatings on the metallic substrate surfaces can be treated by a laser to generate fine structures in the surface region of the metallic substrates. However, thermal response of the surface to the laser heating pulse changes for different coating materials. Consequently, investigation into effect of laser pulse parameters on laser induced melt formation in the coating layer becomes fruitful. Considerable research studies were carried out to examine laser heating and melt formation at the surface. Phase change and conduction heating in relation to laser drilling were examined by Zang and Faghri [1]. The location of the solid-liquid interface was obtained through solving energy equation at the interface and findings revealed that heat conduction reduced the melt layer thickness. A model study on characteristics of molten pool during laser processing was carried out by Yang et al. [2]. The Marangoni
n
Corresponding author. Tel.: þ966 3 860 4481; fax: þ966 3 860 2949. E-mail address: [email protected] (B.S. Yilbas).
0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2012.07.029
effect was incorporated in the model used to predict flow field in the melt pool. Numerical modeling of laser induced melting and re-solidification in metals were investigated by Chung and Das [3]. They derived relations for the time corresponding to the melting initiation and the melt depth. The analytical model for the evaluation of the melt geometry in laser cutting process was introduced by Tani et al. [4]. They proposed the relation between the dross attachment and the melt flow in the kerf. The comparison of volumetric and surface heat sources in relation to laser melting of ceramic surfaces was carried oute by Li et al. [5]. The findings revealed that the model study incorporating the volumetric heat source was more accurate than that incorporating the surface heat source for the melt size predictions. Melting and resolidification of a subcooled metal powder particle subjected to a nanosecond laser heating pulse were studied by Konrad et al. [6]. They used an integral approximation method to locate the solid–liquid interface during the melting and solidification process. The solid-liquid phase change under pulse heating was investigated by Krishnan et al. [7]. The coupled effect of pulse width and natural convection in the melt pool was found to have a profound effect on the overall melting behavior. The influence of non-conventional laser beam geometries during laser melting of metallic materials was examined by Saftar et al. [8]. They presented temperature distribution, melt pool geometry, flow velocity, and heating/cooling rates after incorporating the Marangoni effect in the melt pool. Laser induced heating and melting due to laser irradiation onto solid surface were investigated by Shen et al. [9]. They indicated the presence of temperature gradient discontinuity across the solid–melt interface and conduction heat transfer into solid limited the melt pool size in the laser irradiated region. Yilbas and Mansoor [10] and Shuja
48
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Nomenclature a Amush cp H h href ht Io k L Lh r rf Sx Sh So
Gaussian parameter ðmÞ Mushy zone constant Specific heat capacity J=kg K Total enthalpy ðJÞ Enthalpy J=kg K Reference enthalpy J=kg 2 Heat transfer coefficient W=m K 2 Laser peak power intensity W=m Thermal conductivity W=m K Coating thickness ðmÞ Latent heat of melting J=kg Radial distance ðmÞ Reflection coefficient Momentum sink per unit mass flow rate m=s Phase source term per unit mass flow related rate m=s Source term W=m3
et al. [11] investigated the phase change due to laser heating pulses. Although they incorporated the Marangoni flow in the resulting melt pool, laser processing of coating layer located at the base material surface was not considered in the model studies. Consequently, investigation into the effect of coating material on the melt pool formation during laser heating becomes essential. In the present study, laser repetitive pulse heating of steel surface is simulated after incorporating the phase change and Marangoni flow in the melt pool for two laser intensity transverse mode patterns. The coating thickness is kept the same while coating material is changed in the simulations. The coating materials such as alumina (Al2O3), tungsten carbide (WC), and boron (B) are used in the simulations. Temporal variation of surface temperature in the vicinity of the irradiated spot is measured using a thermocouple and compared with numerical predictions.
T Tliquidus Tsolidus To t v vliq z
Temperature ðK Þ Liquid temperature ðK Þ Solid temperature ðK Þ Initial temperature ð1 CÞ Time ðsÞ Velocity vector m=s Liquid velocity in the mushy zone m=s Axial distance ðmÞ
Greek symbols:
a¼ b bl bE d
e r
k
rCps
Thermal diffusivity m=s2 Laser intensity transverse mode pattern The liquid fraction Volumetric thermal expansion coefficient 1=K 1 7 Absorption depth (6.17 10 ) m Porosity Density kg=m3
consecutive pulses is: 9 8 0, t¼0 > > > > > > > = < 1, t r r t rt f > f ðtÞ ¼ 0, t ¼ tp > > > > > > > > : 0, t p rt r t c ;
ð3Þ
where tr is the pulse rise time, tf is the pulse fall time, tp is the pulse length, tc is the end of cooling period. f(t) repeats when the second consecutive pulse begins, provided that time t ¼tf þtc corresponds to the starting time of the second pulse. The same mathematical arguments can apply for the other consecutive pulses after the second pulse. In the case of solid heating, two boundary conditions for each principal axis are specified. At a distance considerably away from the surface (at steel thickness), natural convection is assumed. However, at coating (tungsten carbide)–steel interface the continuity of flux and temperature is incorporated. The boundary
2. Mathematical analysis of heating The laser heating situation is shown in Fig. 1. Since the heated substrate material is stationary, the heat transfer equation in relation to the laser heating process can be written as:
rCp
@T ¼ ðrðkrTÞÞ þSo @t
ð1Þ
where Cp is the specific heat, k is the thermal conductivity, r is the density, and So is the volumetric heat source term and it is: 2 r So ¼ Io dð1r f ÞexpðdxÞexp b f ðtÞ a
ð2Þ
Io is laser peak intensity, d is the absorption depth, rf is the surface reflectivity, f(t) is the temporal distribution of the laser repetitive pulses, a is the Gaussian parameter, and b is the laser intensity transverse mode pattern. The temporal variation of the laser pulse shape, which is trapezium in time domain, resembles almost the actual laser pulse shape used in the industry. The laser pulse parameters used in the simulations are given in Table 1. The time function (f(t), Fig. 2) representing the
Fig. 1. A schematic view of laser heating situation, coordinate system, and the location of thermocouple.
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
49
Table 1 Laser pulse parameters used in the simulations for b ¼0.
Duty cycle 50%
Laser pulse length, tp (ms)
Cooling period, tc (ms)
Pulse rise time, tr (ms)
Pulse fall time, tf (ms)
Pulse intensity (W/m2) 1010
Guassian parameter, a (m)
1
1
0.156
0.070
0.6
3 10 4
1.5 tB= Begining of Heating Cycle
NORMALIZED INTENSITY
Duty Cycle = 0.5
tE= Ending of Heating Cycle
tf
tr 1
0.5 tc
tp
tB
0 0
1
tE 3
2 TIME (s)
4
Fig. 2. Laser repetitive two pulses for duty cycle of 0.5.
conditions, therefore, are: x at xt
x ¼ xt : Tðxt ,r,tÞ ¼ ht1 ðT st T o Þ þ esðT st 4 T 1 4 Þ
where xt is the thickness of the workpiece, which corresponds to the botttom surface, Tst is the bottom surface temperature, ht1 is the heat transfer coefficent (ht1 ¼20 W/m2 K), To is the ambient temperature (To ¼specified), and e is the surface emissivity. r at infinity)r ¼ 1 : Tðx,1,tÞ ¼ T o (specified) At symmetry axis)r ¼ 0 : @Tðx,0,tÞ ¼0 @r 4 4 At the surface)x ¼ 0 : k @T @x ¼ ht2 ðT s T 1 Þ þ esðT s T 1 Þ where ht2 is the heat transfer coefficient at the free surface and s is the Stefan–Boltzmann constant. The heat transfer coefficient predicted earlier is used in the present simulations (ht2 ¼104 W/ m2 K) [12]. At the coating–steel interface:
The enthalpy of the material is computed as the sum of the sensible enthalpy, h, and the latent heat, DH: H ¼ h þ DH
h ¼ href þ
where ka and ks are the thermal conductivity of tungsten carbide and steel, respectively, and L is the tungsten carbide coating thickness (L¼5, 7.5, 10 mm). The laser beam axis is the x-axis (Fig. 1). Eq. (1) is solved numerically with the appropriate boundary conditions to predict temperature field in the substrate material. However, to analyze the phase change problem, the enthalpy-porosity technique is used. In this case, the melt interface is tracked explicitly after defining a quantity called the liquid fraction, which indicates the fraction of the cell volume that is in liquid form. Based on the enthalpy balance, the liquid fraction is computed. The mushy zone is a region in which the liquid fraction lies between 0 and 1. The mushy zone is modeled as a ‘‘pseudo‘‘ porous medium in which the porosity decreases from 1 to 0 as the material solidifies. When the material has fully solidified in a cell, the porosity becomes zero and hence the velocities also drop to zero [13].
Z
T
cp dT
ð5Þ
T ref
and href is the reference enthalpy,T ref is the reference temperature, cp is the specific heat at constant pressure The liquid fraction, bl, can be defined as:
bl ¼ 0 if
T o T solidus
bl ¼ 1 if
T 4 T liquidus
bl ¼ @T @T ¼ ks x ¼ L : ka @x @x
ð4Þ
where
TT solidus T liquidus T solidus
if
T solidus o T o T liquidus
ð6Þ
Eq. (6) is referred to as the lever rule [13,14]. The latent heat content can now be written in terms of the latent heat of the material, Lh:
DH ¼ bl Lh
ð7Þ
The latent heat content can vary between zero (for a solid) and Lh (for a liquid). The enthalpy-porosity technique treats the mushy region (partially solidified region) as a porous medium. The porosity in each cell is set equal to the liquid fraction in that cell. In fully solidified regions, the porosity is equal to zero, which extinguishes the velocities in these regions. The flow in the mushy zone is governed by the Darcy law. In this case, as the porosity in the mushy zone decreases, the permeability and the velocity also decrease, i.e., when the mushy zone becomes completely solid at the interface of the mushy zone-solid phase, velocity reduces to zero. This behavior can be accounted for by defining the momen, tum sink as Sz ¼ A ðv Þ, where A is obtained from Carman–Kozeny
50
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Table 2 Material properties used in the simulations [16]. Temperature (K)
300
400
600
800
1000
1200
1500
Steel
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) L (J/kg)
477 14.9 8018 1766 1788 400,000
515 16.6 7968
557 19.8 7868
582 22.6 7769
611 25.4 7668
640 28 7568
682 31.7 7418
Alumina
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) Lh (J/kg)
786.19 37.06 3800 2260 2323 900,000
939.53 28.19 –
1019.86 21.81 –
1140.27 11.56 –
1190.84 8.63 –
1234.22 7.12 –
1254.52 6.66 –
Tungsten carbide
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) Lh (J/kg)
327 70.6 13101 2925 2925 192000
– – –
– – –
– – –
– – –
– – –
– – –
Boron
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) Lh (J/kg)
600 55.5 2500 2573 2600 52,000
1463 16.8
1892 10.6
2160 9.60
2383 9.85
2400 9.85
2400 9.85
equation [14], in which case, it is shown that A ¼
ð1bl Þ2 A ðbl 3 þ eÞ mush
[14].
Therefore, the momentum sink due to the reduced porosity in the mushy zone takes the following form [13,14]: Sz ¼
ð1bl Þ2 3
ðbl þ eÞ
,
Amush ðv Þ
ð8Þ
where bl is the liquid volume fraction, e is a small number (0.001) to prevent division by zero, Amush is the mushy zone constant. The mushy zone constant measures the amplitude of the damping; the higher this value, the steeper the transition of the velocity of the material to zero as it solidifies. The liquid velocity can be found from the average velocity is determined from: , v liq
,
¼
v
ð9Þ
bl
The solution for temperature is essentially iteration between the energy equation (Eq. (3)) and the liquid fraction equation (Eq. (6)). Directly using Eq. (4) to update the liquid fraction usually results in poor convergence of the energy equation. However, the method suggested by Voller and Prakash [14] is used to update the liquid fraction based on the specific heat. The continuity and momentum equations in the melt layer are different than that corresponding to the mushy zone. Therefore, the conservation equations need to be incorporated to account for the flow field. This problem is governed by the axisymmetric Navier–Stokes equation. For laminar flow, the conservation equations are: Continuity
@u @x
þ 1r @ðrvÞ @r ¼ 0
r-dir
@v @t
m @v 1 @p þ u @v @x þ v @r ¼ r @r þ r
x-dir
@u @t
@u þu @u @x þ v @r
Energy
v þ 1r @r@ r @v @r r2 @u m @2 u 1 @p 1 @ ¼ r @x þ r @x2 þ r @r r @r þ g bE T þ Sx @2 v @x2
r @ðr@tHÞ þ r ðrvHÞ ¼ r ðkrTÞ þ So Sh
or
! @T @T @T @2 T 1 @ @T þu þv ¼a r þ So Sh þ @t @x @r r @r @r @x2
ð10Þ
where u and v are the component of the velocity in the radial r and axial x directions, respectively, p is the pressure, T is the temperature, a is the thermal diffusivity of the molten material, bE is the volumetric thermal expansion coefficient, which is formulated using the Boussinesq approximation, Sx is the momentum sink due to the reduced porosity in the mushy zone (Eq. (8)), and Sh is a phase related source term due to convection-diffusion phase change (Sh ¼ r @ðr@tDHÞ þ r ðrv_ DHÞ, where DH ¼ HrC p T) [14]. The term g bE T is the buoyancy term, which is used to introduce natural convection in the melt pool. The energy equation is similar to Eq. (3), provided that Eq. (10) is the enthalpy equation and being used for the phase change and the liquid phase during the laser heating process. Moreover, a zero reference temperature has been assumed for the buoyancy force term in the z-direction momentum equation. Boundary conditions for Eq. (10) are as follows: Free surface (at x ¼0): @T m @v @x ¼ sT @r
u¼0 k @T @x ¼ qloss where qloss includes the convective losses from the surface. The heat transfer coefficient is taken as ht ¼104 W/m2 K at the surface [12]. Axis of symmetry (at r ¼0): v¼0 ¼0
@u @r @T @r
¼0 Far field (solid):
T ¼ To where To is the ambient temperature. The equation m @v=@x ¼ sT @T=@r states the balance between the surface tension force and the viscous force on the free surface, where sT is the temperature coefficient of surface tension, which is a property of the material.
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
3. Numerical solution To discretise the governing equations, a control volume approach is introduced. The details of the numerical scheme are given in [15]. The calculation domain is divided into grids and a grid independence test is performed for different grid sizes and orientation. A non-uniform grid with 90 55 mesh points along x and r-axes, respectively, is employed after securing the grid independence. The finer grids are located near the irradiated spot center in the vicinity of the surface and grids become courser as the distance increases towards the bulk of substrate material. The central difference scheme is adopted for the diffusion terms. FLUENT CFD code [13] is used in the simulations and the convergence criterion for the residuals is set as k k1 9c c 9 r106 to terminate the simulations. Table 2 gives the thermal properties of material used in the simulations [16]. The laser energy is kept the same for all intensity distributions with different intensity transverse mode pattern. Fig. 3 shows laser intensity distribution for different values of the intensity transverse mode pattern (b). Moreover, the power is kept the same as the experimental value in the simulations; in which case the intensity transverse mode pattern b ¼0, i.e., Gaussian distribution with the parameter a¼2/3 R (R is a laser beam radius at the workpiece surface R¼0.3 mm) and power intensity Io ¼ 0.6 1010 W/m2.
4. Experimental The laser used in the experiment is a CO2 laser (LC-aIII-Amada) and delivering the maximum output power of 2000 W with adjustable duty cycle. Nitrogen emerging from a conical nozzle and co-axially with the laser beam is used. 127 mm focal lens is used to focus the laser beam, which results in the focal radius of 0.3 mm at the surface. The laser beam intensity distribution at the workpiece surface was Gaussian. The laser heating parameters are given in Table 3.
51
To validate temperature predictions, the fast response E-type surface thermocouple with a 0.025 mm bead was used to monitor the temporal variation of surface temperature at 0.2 mm away from the spot center of the laser pulse parameter b ¼0, which is Gaussian. The location of the thermocouple at 0.2 mm away from the spot center was necessary to avoid the melting of the thermocouple tip during the laser heating process. The thermocouple output was calibrated according to the previous study [17]. The experimental error was determined using the experimental repeatability; therefore, the experiments were repeated five times and the error was estimated in the order of 5%.
5. Results and discussion Laser induced melting of coated steel is simulated and influence of coating material on the melt pool characteristics are examined. Alumina, tungsten carbide, and boron are incorporated as coating material in the simulations. The study is extended to include the influence of laser intensity transverse mode pattern on the temperature field and melt pool size. The predictions are validated through thermocouple data. Fig. 4 shows temperature temporal variation of surface temperature for a single pulse of intensity transverse mode pattern b ¼ 0. Temperature profiles are obtained from the thermocouple data and present simulations. It is evident that both results are in good agreement. The small discrepancies between both results are due to the experimental error and the assumptions made in the simulations such as uniform properties. Fig. 5 shows temperature distribution along the depth (x-axis) for two different time periods, three coating materials and laser intensity transverse mode pattern b ¼ 0. Temperature attains significantly high value at the surface (x ¼0 m) at the end of the heating cycle of the 10th consecutive pulse (19 ms) for boron, then follows alumina and tungsten carbide. The attainment of high surface temperature is associated with the thermal diffusivity and absorption coefficient of boron and alumina which is lower than tungsten carbide (Table 2). In addition, temperature decay is sharp in the surface vicinity, which in turn results in high temperature gradients in this region. This is particularly true for the end of the heating cycle of the 10th pulse. Since temperature exceeds the melting temperature of the coating material along the depth of the coating, which is 7.5 mm. Since temperature below the coating is higher than the melting temperature of steel, melting also takes place in steel in the region close to the interface. Moreover, temperature decay becomes gradual beyond the depth x Z75 mm and temperature profiles in steel due to
1800 Predictions : x = 0 and r = 0.2 mm
Fig. 3. Laser intensity distribution along the radial direction at the surface for two intensity transverse mode patterns.
TEMPERATURE (K)
1500
Experiment : x = 0 and r = 0.2 mm
1200 900 600 300
Table 3 Laser heating parameters. Duty cycle
Power (W)
Nozzle gap (mm)
Nozzle diameter (m)
Focus diameter (m) (mm)
N2 pressure (kPa)
a (m)
0.5
170
1.5
1.5 10 3
0.3 10 3
300
0.2 10 3
0 0.0000
0.0005
0.0010 TIME (s)
0.0015
0.0020
Fig. 4. Temporal variation of surface temperature obtained from the simulations and thermocouple data for tungsten carbide coating and laser intensity transverse mode pattern b ¼ 0.
52
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Fig. 5. Temperature distribution inside the substrate material along the depth for laser pulse intensity transverse mode pattern b ¼0, two heating periods and different coating materials.
Fig. 6. Temperature distribution inside the substrate material along the depth for laser pulse intensity transverse mode pattern b ¼0, two heating periods and different coating materials.
different coating materials become almost the same. It should be noted that the size of the mushy zone between the liquid and solid phases is not visible from the figure. This is attributed to the high energy density deposition during the short duration of laser heating pulses. In the case of end of cooling period of the 10th pulse (t¼ 20 ms) temperature reduces considerably. The high rate of temperature decay is associated with the conduction, convection and radiation heat losses from the laser irradiated region. Since the temperature gradient is high in the heated region, conduction heat transfer from heated region to solid bulk is considerable while contributing to sharp temperature decay in the cooling period. Fig. 6 shows temperature distribution along the depth of the irradiated region for the laser intensity transverse mode pattern b ¼1. The behavior of temperature curves are similar to those shown in Fig. 5, provided that peak temperature and the temperature decay along the depth are not the same. This is attributed to the laser peak intensity, which moves away from the irradiated spot center for the laser intensity transverse mode pattern b ¼1 (Fig. 3). The differences in the behavior of temperature curves due to different laser intensity transverse mode pattern are more pronounced during the heating cycle of the pulse. Since internal energy gain of the substrate material and temperature rise in the surface vicinity is associated with
Fig. 7. Temperature distribution inside the substrate material along the radial distance for laser pulse intensity transverse mode pattern b ¼0, two heating periods and different coating materials.
absorption of the incident laser energy, change in laser intensity distribution results in large change in the peak temperature at the coating surface. Fig. 7 shows temperature distribution along the radial direction for different time periods, three materials, and laser intensity transverse mode pattern b ¼0. Temperature decays gradually in the central region of the irradiated spot around the symmetry axis where temperature is considerably high. As the distance in the radial direction increases away from the symmetry axis, temperature decay becomes sharp. This is attributed to the laser pulse intensity distribution at the workpiece surface, which is Gaussian. This is more pronounced at the end of heating period of 10th pulse (t ¼19 ms) for tungsten carbide and alumina coatings. In the case of Tungsten Carbide, due to relatively high thermal diffusivity and low absorption coefficient, temperature becomes lower at the surface as compared to other coating materials. In the case of end of the cooling period (t ¼20 ms), temperature drops significantly at the surface for all coating materials and temperature difference becomes small. This is attributed to the internal energy gain of the coating from the irradiated field, which ceases at the end of the heating period. Since laser beam power is switched off in the cooling cycle, heat losses due to convection, radiation and conduction from the surface lower temperature significantly at the surface region. Fig. 8 shows surface temperature distribution in the radial direction for the laser intensity transverse mode pattern b ¼1. Temperature distribution at the surface follows almost the laser pulse intensity distribution during the heating cycle (t ¼9 ms). This is attributed to the material response to the incident laser radiation. The peak temperature exceeds the melting temperature of the coating material for alumina and boron; therefore, melting in the surface region is evident. However, no evidence of mushy zone is observed from the temperature profiles. This indicates that the small size of mushy zone is present between the liquid and solid phases, which may not be seen clearly from temperature curves. In the cooling cycle, absorption of incident radiation ceases so that temperature drops significantly at the surface. In this case, the peak temperature remains below the melting temperature of the substrate material. Fig. 9(a) and (b) shows temporal variation of surface temperature for different coating materials for b ¼0 and b ¼1, respectively. Temperature increases first and reduces later during each pulse, which appears as oscillation in temperature profile with progressing time. Since the duty cycle is 50%, the heating cycle is
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Fig. 8. Temperature distribution inside the substrate material along the radial distance for laser pulse intensity transverse mode pattern b ¼ 1, two heating periods and different coating materials.
Fig. 9. (a) Temporal variation of temperature at the irradiated spot center for laser pulse intensity transverse mode pattern b ¼0 and different coating materials. (b) Temporal variation of temperature at the irradiated spot center for laser pulse intensity transverse mode pattern b ¼1 and different coating materials.
1 ms while the cooling cycle ends after 1 ms of the heating cycle of the pulse. Therefore, the total heating and cooling durations of each pulse is 2 ms. Temperature rises sharply during the early period of heating cycle and temperature rise becomes gradual as
53
the time progresses towards the end of heating cycle. This is attributed to absorption of incident beam in the early heating period; in which case, internal energy increase becomes rapid, which produces the rise of surface temperature at the same rate. As the heating period progresses, heat conduction from the irradiated region to the solid bulk increases because of high temperature gradient developed during the initial period of the heating cycle. In the case of cooling cycle, temperature reduces sharply due to cease of the laser power. However, the slope of temperature decay changes slightly towards the end of the cooling cycle. This change is associated with the phase change in the irradiated center; in which case, the slope of temperature decay changes in the vicinity of the melting temperature of the coating material. In the case of laser intensity transverse mode pattern b ¼ 1, temperature rise is considerably smaller than that of b ¼0, since the peak intensity shifts away from the irradiated spot center for the laser intensity transverse mode pattern b ¼1 (Fig. 3). Surface temperature difference at the irradiated spot center becomes smaller for b ¼1 than that of b ¼0. Fig. 10(a) and (b) shows temperature contours and phase changed regions in the coating and in the base material for three coating materials and two laser transverse mode patterns, respectively. In the case of b ¼0, temperature reaches beyond the melting temperature in the coating for alumina and boron while it does not reach the melting temperature of tungsten carbide. In addition, temperature reaches above the melting temperature of the base material below the coating for all coating materials. Consequently, tungsten carbide coating remains in the solid phase while underlying steel undergoes a melting at the interface region. This is associated with the melting temperature of tungsten carbide, which is high. The presence of mushy zone is visible for steel; however, mushy zone size is considerably small for the coating materials. Although continuity of heat flux and temperature is considered at the coating and the base material interface, the behavior of temperature profiles in the coating and the base material is notably different, which is attributed to differences in thermal properties of the coating and the base material. In the case of laser intensity transverse mode pattern b ¼ 1, temperature profiles in the coating and substrate material become different than those shown in Fig. 10(a). This is because of the laser power intensity distribution at the workpiece surface, which is non-Gaussian (Fig. 3). The melt pool moves away from the irradiated spot center towards the location of the peak laser power intensity. Since the peak laser power intensity is low for laser intensity transverse mode pattern b ¼1, coating does not undergo melting all along its thickness, which is also true for alumina and boron coatings. In addition, the melt pool depth becomes shallower and the melt pool width grow to be wider than those corresponding to the laser intensity transverse mode pattern b ¼0. The melt depth and width in the base material are also modified by the laser pulse intensity distribution for laser intensity transverse mode pattern b ¼1. However, the mushy zone thickness for all laser intensity transverse mode patterns remains almost the same for alumina and boron coatings. Fig. 11(a) and (b) shows velocity vectors in the melt pool produced in the coating for the laser intensity transverse mode pattern b ¼0 and b ¼1. The flow field developed in the melt pool is associated with the Marangoni and shear driven flows due to the surface tension force and the rate of flow strain variation in the melt pool. The flow behavior in alumina and boron coatings is similar and a circulation cell is formed in the melt pool. In the case of laser intensity transverse mode pattern b ¼0, velocity magnitude is higher than that corresponding to b ¼1. This is attributed to the melt depth; in which case, the melt pool is shallow for b ¼1 and the convection current developed due to rate of fluid strain variation in the melt pool becomes weaker
54
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Fig. 10. (a) Temperature contours and melt pool in the surface vicinity for laser pulse intensity transverse mode pattern b ¼ 0 and different coating materials. (b)Temperature contours and melt pool in the surface vicinity for laser pulse intensity transverse mode pattern b ¼ 1 and different coating materials.
Fig. 11. (a) Velocity vectors in the coating melt pool for laser pulse intensity transverse mode pattern b ¼0 and different coating materials. (b) Velocity vectors in the coating melt pool for laser pulse intensity transverse mode pattern b ¼1 and different coating materials.
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
than that of b ¼0. Moreover, no free surface exist for the underlying steel substrate, no Marangoni flow is generated. In addition, density variation due to temperature change in the melt pool of steel is small, no visible convection current driven circulation is observed.
55
Acknowledgements The authors acknowledge the support of King Fahd University of Petroleum and Minerals Dhahran Saudi Arabia. References
6. Conclusion Laser controlled melting of coated carbon steel surface is simulated using the control volume approach. Temperature predictions are validated through the thermocouple data. The phase change during the laser heating is incorporated using the enthalpy porosity method. The Marangoni flow in the melt pool is considered in the numerical simulations. The study is extended to include the influence of the laser intensity transverse mode pattern (b) on the melting characteristics. It is found that the peak temperatures corresponding to boron and alumina are higher than that of tungsten carbide coating. This is associated with high thermal diffusivity and high absorption coefficient of tungsten carbide. Surface temperature increase is significant during the initial period of heating cycle of the laser pulse while in the cooling cycle temperature decay is sharp due to the cease of laser power. The influence of laser intensity distribution on temperature profiles is considerable, since radial distribution of surface temperature follows almost the laser intensity distribution at the workpiece surface. Boron and alumina coatings melt completely during the heating cycle of 10th pulse for laser intensity transverse mode pattern b ¼0. In addition, steel beneath the coating undergoes melting at the interface region. Although coating remains in the solid phase for tungsten carbide, underlying steel melts while forming a melt pool at the interface region. The size of the melt pool is influenced by the laser intensity transverse mode pattern; in which case, the orientation of the melt pool changes from the irradiated spot center for the laser pulse parameter b ¼1. The depth of the melt pool becomes shallow influencing the Marangoni flow in the melt pool. In general, a circulation cell is developed and the velocity magnitude in the melt pool attains higher values for the laser intensity transverse mode pattern b ¼0 than that corresponding to b ¼1.
[1] Zhang Y, Faghri A. Vaporization, melting and heat conduction in the laser drilling process. International Journal of Heat and Mass Transfer 1999;42:1775–90. [2] Yang LX, Peng X, Wang BX. Numerical modeling and experimental investigation on the characteristics of molten pool during laser processing. International Journal Heat Mass transfer 2001;44:4465–73. [3] Chung H, Das S. Numerical modeling of scanning laser-induced melting, vaporization and resolidification in metals subjected to step heat flux input. International Journal of Heat and Mass Transfer 2004;47:4153–64. [4] Tani G, Tomesani L, Campana G. Prediction of melt geometry in laser cutting. Applied Surface Science 2003;208–209:142–7. [5] Li JF, Li L, Stott FH. Comparison of volumetric and surface heating surfaces in the modeling of laser melting of ceramic materials. International Journal of Heat and Mass Transfer 2004;47:1159–74. [6] Konrad C, Zhang Y, Shi Y. Melting and resolidification of a subcooled metal powder particle subjected to nanosecond laser heating. International Journal of Heat Mass Transfer 2007;50:2236–45. [7] Krishnan S, Murthy JY, Garimella SV. Analysis of solid-liquid phase change under pulsed heating. The ASME Journal of Heat Transfer 2007;129:395–9. [8] Safdar S, Li L, Sheikh MA, Liu Z. An analysis of the effect of laser beam geometry on laser transformation hardening. Journal of Manufacturing Science and Engineering 2006;128:659–67. [9] Shen ZH, Zhang SY, Lu J, Ni XW. Mathematical modeling of laser induced heating and melting in solids. Optics and Laser Technology 2001;33:533–7. [10] Yilbas BS, Mansoor SB. Laser pulse heating and phase changes in the irradiated region: temperature dependent thermal properties case. International Journal of Thermal Sciences 2009;48:761–72. [11] Shuja SZ, Yilbas BS, Khan S. Laser consecutive pulse heating and phase change: influence of spatial distribution of laser pulse intensity on melting. International Journal of Thermal Sciences 2009;48:1960–6. [12] Shuja SZ, Yilbas BS. Pulsative heating of surfaces. International Journal of Heat and Mass Transfer 1998;41:3899–918. [13] Fluent Inc 2005 Fluent Users Guide. [14] Voller VR, Prakash C. A fixed-grid numerical modeling methodology for convection-diffusion mushy region phase-change problems. International Journal of Heat Mass Transfer 1987;30:1709–20. [15] Patankar SV. Numerical heat transfer. New York: McGraw-Hill; 1980. [16] Incropera FP, DeWitt DP. Fundamentals of heat and mass transfer. fourth ed. New York: John Wiley & Sons; 1996 p829 830. [17] Yilbas BS, Davies R, Gorur A, Yilbas Z, Begh , Kalkat M, et al. Study into the measurement and prediction of penetration time during CO2 laser cutting process. Proceedings of the Institution of Mechanical Engineers Part B 1990;204:105–13.
Contents lists available at SciVerse ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Laser induced heating of coated carbon steel sheets: Consideration of melting and Marangoni flow S.Z. Shuja, B.S. Yilbas n ME Department, KFUPM Box 1913, Dhahran 31261, Saudi Arabia
a r t i c l e i n f o
abstract
Article history: Received 2 February 2012 Received in revised form 19 July 2012 Accepted 25 July 2012 Available online 12 October 2012
Laser induced melting of coated carbon steel workpiece is simulated. The coating materials include tungsten carbide, alumina, and boron are incorporated in the simulations. The coating thickness is kept constant at 7.5 mm in the analysis. The enthalpy porosity method is used to account for the phase change in the irradiated region. The study is extended to include the influence of laser intensity transverse mode pattern (b) on the resulting melting characteristics. It is found that peak temperature predicted at the surface is higher for alumina and boron coatings than that of tungsten carbide coating. The influence of the laser intensity transverse mode pattern on the melting characteristics is considerable. Surface temperature predicted agrees with the thermocouple data. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Laser Melting Marangoni flow
1. Introduction Laser controlled melting is widely used in surface treatment of engineering materials. Lasers provide precision of operation, fast processing, and low cost. In laser surface treatment of metals, in general, repetitive pulses are used and the size of the melt depends on the duty cycle of repetitive pulses, laser pulse intensity distribution at the workpiece surface, and the properties of the substrate material. The use of controlled melting is to form homogeneous and fine structures at the surface. Depending on the surface condition prior to laser treatment, homogeneous and fine structures can be formed. Carbides and Ceramics layers/ coatings on the metallic substrate surfaces can be treated by a laser to generate fine structures in the surface region of the metallic substrates. However, thermal response of the surface to the laser heating pulse changes for different coating materials. Consequently, investigation into effect of laser pulse parameters on laser induced melt formation in the coating layer becomes fruitful. Considerable research studies were carried out to examine laser heating and melt formation at the surface. Phase change and conduction heating in relation to laser drilling were examined by Zang and Faghri [1]. The location of the solid-liquid interface was obtained through solving energy equation at the interface and findings revealed that heat conduction reduced the melt layer thickness. A model study on characteristics of molten pool during laser processing was carried out by Yang et al. [2]. The Marangoni
n
Corresponding author. Tel.: þ966 3 860 4481; fax: þ966 3 860 2949. E-mail address: [email protected] (B.S. Yilbas).
0030-3992/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2012.07.029
effect was incorporated in the model used to predict flow field in the melt pool. Numerical modeling of laser induced melting and re-solidification in metals were investigated by Chung and Das [3]. They derived relations for the time corresponding to the melting initiation and the melt depth. The analytical model for the evaluation of the melt geometry in laser cutting process was introduced by Tani et al. [4]. They proposed the relation between the dross attachment and the melt flow in the kerf. The comparison of volumetric and surface heat sources in relation to laser melting of ceramic surfaces was carried oute by Li et al. [5]. The findings revealed that the model study incorporating the volumetric heat source was more accurate than that incorporating the surface heat source for the melt size predictions. Melting and resolidification of a subcooled metal powder particle subjected to a nanosecond laser heating pulse were studied by Konrad et al. [6]. They used an integral approximation method to locate the solid–liquid interface during the melting and solidification process. The solid-liquid phase change under pulse heating was investigated by Krishnan et al. [7]. The coupled effect of pulse width and natural convection in the melt pool was found to have a profound effect on the overall melting behavior. The influence of non-conventional laser beam geometries during laser melting of metallic materials was examined by Saftar et al. [8]. They presented temperature distribution, melt pool geometry, flow velocity, and heating/cooling rates after incorporating the Marangoni effect in the melt pool. Laser induced heating and melting due to laser irradiation onto solid surface were investigated by Shen et al. [9]. They indicated the presence of temperature gradient discontinuity across the solid–melt interface and conduction heat transfer into solid limited the melt pool size in the laser irradiated region. Yilbas and Mansoor [10] and Shuja
48
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Nomenclature a Amush cp H h href ht Io k L Lh r rf Sx Sh So
Gaussian parameter ðmÞ Mushy zone constant Specific heat capacity J=kg K Total enthalpy ðJÞ Enthalpy J=kg K Reference enthalpy J=kg 2 Heat transfer coefficient W=m K 2 Laser peak power intensity W=m Thermal conductivity W=m K Coating thickness ðmÞ Latent heat of melting J=kg Radial distance ðmÞ Reflection coefficient Momentum sink per unit mass flow rate m=s Phase source term per unit mass flow related rate m=s Source term W=m3
et al. [11] investigated the phase change due to laser heating pulses. Although they incorporated the Marangoni flow in the resulting melt pool, laser processing of coating layer located at the base material surface was not considered in the model studies. Consequently, investigation into the effect of coating material on the melt pool formation during laser heating becomes essential. In the present study, laser repetitive pulse heating of steel surface is simulated after incorporating the phase change and Marangoni flow in the melt pool for two laser intensity transverse mode patterns. The coating thickness is kept the same while coating material is changed in the simulations. The coating materials such as alumina (Al2O3), tungsten carbide (WC), and boron (B) are used in the simulations. Temporal variation of surface temperature in the vicinity of the irradiated spot is measured using a thermocouple and compared with numerical predictions.
T Tliquidus Tsolidus To t v vliq z
Temperature ðK Þ Liquid temperature ðK Þ Solid temperature ðK Þ Initial temperature ð1 CÞ Time ðsÞ Velocity vector m=s Liquid velocity in the mushy zone m=s Axial distance ðmÞ
Greek symbols:
a¼ b bl bE d
e r
k
rCps
Thermal diffusivity m=s2 Laser intensity transverse mode pattern The liquid fraction Volumetric thermal expansion coefficient 1=K 1 7 Absorption depth (6.17 10 ) m Porosity Density kg=m3
consecutive pulses is: 9 8 0, t¼0 > > > > > > > = < 1, t r r t rt f > f ðtÞ ¼ 0, t ¼ tp > > > > > > > > : 0, t p rt r t c ;
ð3Þ
where tr is the pulse rise time, tf is the pulse fall time, tp is the pulse length, tc is the end of cooling period. f(t) repeats when the second consecutive pulse begins, provided that time t ¼tf þtc corresponds to the starting time of the second pulse. The same mathematical arguments can apply for the other consecutive pulses after the second pulse. In the case of solid heating, two boundary conditions for each principal axis are specified. At a distance considerably away from the surface (at steel thickness), natural convection is assumed. However, at coating (tungsten carbide)–steel interface the continuity of flux and temperature is incorporated. The boundary
2. Mathematical analysis of heating The laser heating situation is shown in Fig. 1. Since the heated substrate material is stationary, the heat transfer equation in relation to the laser heating process can be written as:
rCp
@T ¼ ðrðkrTÞÞ þSo @t
ð1Þ
where Cp is the specific heat, k is the thermal conductivity, r is the density, and So is the volumetric heat source term and it is: 2 r So ¼ Io dð1r f ÞexpðdxÞexp b f ðtÞ a
ð2Þ
Io is laser peak intensity, d is the absorption depth, rf is the surface reflectivity, f(t) is the temporal distribution of the laser repetitive pulses, a is the Gaussian parameter, and b is the laser intensity transverse mode pattern. The temporal variation of the laser pulse shape, which is trapezium in time domain, resembles almost the actual laser pulse shape used in the industry. The laser pulse parameters used in the simulations are given in Table 1. The time function (f(t), Fig. 2) representing the
Fig. 1. A schematic view of laser heating situation, coordinate system, and the location of thermocouple.
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
49
Table 1 Laser pulse parameters used in the simulations for b ¼0.
Duty cycle 50%
Laser pulse length, tp (ms)
Cooling period, tc (ms)
Pulse rise time, tr (ms)
Pulse fall time, tf (ms)
Pulse intensity (W/m2) 1010
Guassian parameter, a (m)
1
1
0.156
0.070
0.6
3 10 4
1.5 tB= Begining of Heating Cycle
NORMALIZED INTENSITY
Duty Cycle = 0.5
tE= Ending of Heating Cycle
tf
tr 1
0.5 tc
tp
tB
0 0
1
tE 3
2 TIME (s)
4
Fig. 2. Laser repetitive two pulses for duty cycle of 0.5.
conditions, therefore, are: x at xt
x ¼ xt : Tðxt ,r,tÞ ¼ ht1 ðT st T o Þ þ esðT st 4 T 1 4 Þ
where xt is the thickness of the workpiece, which corresponds to the botttom surface, Tst is the bottom surface temperature, ht1 is the heat transfer coefficent (ht1 ¼20 W/m2 K), To is the ambient temperature (To ¼specified), and e is the surface emissivity. r at infinity)r ¼ 1 : Tðx,1,tÞ ¼ T o (specified) At symmetry axis)r ¼ 0 : @Tðx,0,tÞ ¼0 @r 4 4 At the surface)x ¼ 0 : k @T @x ¼ ht2 ðT s T 1 Þ þ esðT s T 1 Þ where ht2 is the heat transfer coefficient at the free surface and s is the Stefan–Boltzmann constant. The heat transfer coefficient predicted earlier is used in the present simulations (ht2 ¼104 W/ m2 K) [12]. At the coating–steel interface:
The enthalpy of the material is computed as the sum of the sensible enthalpy, h, and the latent heat, DH: H ¼ h þ DH
h ¼ href þ
where ka and ks are the thermal conductivity of tungsten carbide and steel, respectively, and L is the tungsten carbide coating thickness (L¼5, 7.5, 10 mm). The laser beam axis is the x-axis (Fig. 1). Eq. (1) is solved numerically with the appropriate boundary conditions to predict temperature field in the substrate material. However, to analyze the phase change problem, the enthalpy-porosity technique is used. In this case, the melt interface is tracked explicitly after defining a quantity called the liquid fraction, which indicates the fraction of the cell volume that is in liquid form. Based on the enthalpy balance, the liquid fraction is computed. The mushy zone is a region in which the liquid fraction lies between 0 and 1. The mushy zone is modeled as a ‘‘pseudo‘‘ porous medium in which the porosity decreases from 1 to 0 as the material solidifies. When the material has fully solidified in a cell, the porosity becomes zero and hence the velocities also drop to zero [13].
Z
T
cp dT
ð5Þ
T ref
and href is the reference enthalpy,T ref is the reference temperature, cp is the specific heat at constant pressure The liquid fraction, bl, can be defined as:
bl ¼ 0 if
T o T solidus
bl ¼ 1 if
T 4 T liquidus
bl ¼ @T @T ¼ ks x ¼ L : ka @x @x
ð4Þ
where
TT solidus T liquidus T solidus
if
T solidus o T o T liquidus
ð6Þ
Eq. (6) is referred to as the lever rule [13,14]. The latent heat content can now be written in terms of the latent heat of the material, Lh:
DH ¼ bl Lh
ð7Þ
The latent heat content can vary between zero (for a solid) and Lh (for a liquid). The enthalpy-porosity technique treats the mushy region (partially solidified region) as a porous medium. The porosity in each cell is set equal to the liquid fraction in that cell. In fully solidified regions, the porosity is equal to zero, which extinguishes the velocities in these regions. The flow in the mushy zone is governed by the Darcy law. In this case, as the porosity in the mushy zone decreases, the permeability and the velocity also decrease, i.e., when the mushy zone becomes completely solid at the interface of the mushy zone-solid phase, velocity reduces to zero. This behavior can be accounted for by defining the momen, tum sink as Sz ¼ A ðv Þ, where A is obtained from Carman–Kozeny
50
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Table 2 Material properties used in the simulations [16]. Temperature (K)
300
400
600
800
1000
1200
1500
Steel
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) L (J/kg)
477 14.9 8018 1766 1788 400,000
515 16.6 7968
557 19.8 7868
582 22.6 7769
611 25.4 7668
640 28 7568
682 31.7 7418
Alumina
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) Lh (J/kg)
786.19 37.06 3800 2260 2323 900,000
939.53 28.19 –
1019.86 21.81 –
1140.27 11.56 –
1190.84 8.63 –
1234.22 7.12 –
1254.52 6.66 –
Tungsten carbide
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) Lh (J/kg)
327 70.6 13101 2925 2925 192000
– – –
– – –
– – –
– – –
– – –
– – –
Boron
Cp (J/kg K) k (W/m K) r (kg/m3) Tsolidus (K) Tliquidus (K) Lh (J/kg)
600 55.5 2500 2573 2600 52,000
1463 16.8
1892 10.6
2160 9.60
2383 9.85
2400 9.85
2400 9.85
equation [14], in which case, it is shown that A ¼
ð1bl Þ2 A ðbl 3 þ eÞ mush
[14].
Therefore, the momentum sink due to the reduced porosity in the mushy zone takes the following form [13,14]: Sz ¼
ð1bl Þ2 3
ðbl þ eÞ
,
Amush ðv Þ
ð8Þ
where bl is the liquid volume fraction, e is a small number (0.001) to prevent division by zero, Amush is the mushy zone constant. The mushy zone constant measures the amplitude of the damping; the higher this value, the steeper the transition of the velocity of the material to zero as it solidifies. The liquid velocity can be found from the average velocity is determined from: , v liq
,
¼
v
ð9Þ
bl
The solution for temperature is essentially iteration between the energy equation (Eq. (3)) and the liquid fraction equation (Eq. (6)). Directly using Eq. (4) to update the liquid fraction usually results in poor convergence of the energy equation. However, the method suggested by Voller and Prakash [14] is used to update the liquid fraction based on the specific heat. The continuity and momentum equations in the melt layer are different than that corresponding to the mushy zone. Therefore, the conservation equations need to be incorporated to account for the flow field. This problem is governed by the axisymmetric Navier–Stokes equation. For laminar flow, the conservation equations are: Continuity
@u @x
þ 1r @ðrvÞ @r ¼ 0
r-dir
@v @t
m @v 1 @p þ u @v @x þ v @r ¼ r @r þ r
x-dir
@u @t
@u þu @u @x þ v @r
Energy
v þ 1r @r@ r @v @r r2 @u m @2 u 1 @p 1 @ ¼ r @x þ r @x2 þ r @r r @r þ g bE T þ Sx @2 v @x2
r @ðr@tHÞ þ r ðrvHÞ ¼ r ðkrTÞ þ So Sh
or
! @T @T @T @2 T 1 @ @T þu þv ¼a r þ So Sh þ @t @x @r r @r @r @x2
ð10Þ
where u and v are the component of the velocity in the radial r and axial x directions, respectively, p is the pressure, T is the temperature, a is the thermal diffusivity of the molten material, bE is the volumetric thermal expansion coefficient, which is formulated using the Boussinesq approximation, Sx is the momentum sink due to the reduced porosity in the mushy zone (Eq. (8)), and Sh is a phase related source term due to convection-diffusion phase change (Sh ¼ r @ðr@tDHÞ þ r ðrv_ DHÞ, where DH ¼ HrC p T) [14]. The term g bE T is the buoyancy term, which is used to introduce natural convection in the melt pool. The energy equation is similar to Eq. (3), provided that Eq. (10) is the enthalpy equation and being used for the phase change and the liquid phase during the laser heating process. Moreover, a zero reference temperature has been assumed for the buoyancy force term in the z-direction momentum equation. Boundary conditions for Eq. (10) are as follows: Free surface (at x ¼0): @T m @v @x ¼ sT @r
u¼0 k @T @x ¼ qloss where qloss includes the convective losses from the surface. The heat transfer coefficient is taken as ht ¼104 W/m2 K at the surface [12]. Axis of symmetry (at r ¼0): v¼0 ¼0
@u @r @T @r
¼0 Far field (solid):
T ¼ To where To is the ambient temperature. The equation m @v=@x ¼ sT @T=@r states the balance between the surface tension force and the viscous force on the free surface, where sT is the temperature coefficient of surface tension, which is a property of the material.
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
3. Numerical solution To discretise the governing equations, a control volume approach is introduced. The details of the numerical scheme are given in [15]. The calculation domain is divided into grids and a grid independence test is performed for different grid sizes and orientation. A non-uniform grid with 90 55 mesh points along x and r-axes, respectively, is employed after securing the grid independence. The finer grids are located near the irradiated spot center in the vicinity of the surface and grids become courser as the distance increases towards the bulk of substrate material. The central difference scheme is adopted for the diffusion terms. FLUENT CFD code [13] is used in the simulations and the convergence criterion for the residuals is set as k k1 9c c 9 r106 to terminate the simulations. Table 2 gives the thermal properties of material used in the simulations [16]. The laser energy is kept the same for all intensity distributions with different intensity transverse mode pattern. Fig. 3 shows laser intensity distribution for different values of the intensity transverse mode pattern (b). Moreover, the power is kept the same as the experimental value in the simulations; in which case the intensity transverse mode pattern b ¼0, i.e., Gaussian distribution with the parameter a¼2/3 R (R is a laser beam radius at the workpiece surface R¼0.3 mm) and power intensity Io ¼ 0.6 1010 W/m2.
4. Experimental The laser used in the experiment is a CO2 laser (LC-aIII-Amada) and delivering the maximum output power of 2000 W with adjustable duty cycle. Nitrogen emerging from a conical nozzle and co-axially with the laser beam is used. 127 mm focal lens is used to focus the laser beam, which results in the focal radius of 0.3 mm at the surface. The laser beam intensity distribution at the workpiece surface was Gaussian. The laser heating parameters are given in Table 3.
51
To validate temperature predictions, the fast response E-type surface thermocouple with a 0.025 mm bead was used to monitor the temporal variation of surface temperature at 0.2 mm away from the spot center of the laser pulse parameter b ¼0, which is Gaussian. The location of the thermocouple at 0.2 mm away from the spot center was necessary to avoid the melting of the thermocouple tip during the laser heating process. The thermocouple output was calibrated according to the previous study [17]. The experimental error was determined using the experimental repeatability; therefore, the experiments were repeated five times and the error was estimated in the order of 5%.
5. Results and discussion Laser induced melting of coated steel is simulated and influence of coating material on the melt pool characteristics are examined. Alumina, tungsten carbide, and boron are incorporated as coating material in the simulations. The study is extended to include the influence of laser intensity transverse mode pattern on the temperature field and melt pool size. The predictions are validated through thermocouple data. Fig. 4 shows temperature temporal variation of surface temperature for a single pulse of intensity transverse mode pattern b ¼ 0. Temperature profiles are obtained from the thermocouple data and present simulations. It is evident that both results are in good agreement. The small discrepancies between both results are due to the experimental error and the assumptions made in the simulations such as uniform properties. Fig. 5 shows temperature distribution along the depth (x-axis) for two different time periods, three coating materials and laser intensity transverse mode pattern b ¼ 0. Temperature attains significantly high value at the surface (x ¼0 m) at the end of the heating cycle of the 10th consecutive pulse (19 ms) for boron, then follows alumina and tungsten carbide. The attainment of high surface temperature is associated with the thermal diffusivity and absorption coefficient of boron and alumina which is lower than tungsten carbide (Table 2). In addition, temperature decay is sharp in the surface vicinity, which in turn results in high temperature gradients in this region. This is particularly true for the end of the heating cycle of the 10th pulse. Since temperature exceeds the melting temperature of the coating material along the depth of the coating, which is 7.5 mm. Since temperature below the coating is higher than the melting temperature of steel, melting also takes place in steel in the region close to the interface. Moreover, temperature decay becomes gradual beyond the depth x Z75 mm and temperature profiles in steel due to
1800 Predictions : x = 0 and r = 0.2 mm
Fig. 3. Laser intensity distribution along the radial direction at the surface for two intensity transverse mode patterns.
TEMPERATURE (K)
1500
Experiment : x = 0 and r = 0.2 mm
1200 900 600 300
Table 3 Laser heating parameters. Duty cycle
Power (W)
Nozzle gap (mm)
Nozzle diameter (m)
Focus diameter (m) (mm)
N2 pressure (kPa)
a (m)
0.5
170
1.5
1.5 10 3
0.3 10 3
300
0.2 10 3
0 0.0000
0.0005
0.0010 TIME (s)
0.0015
0.0020
Fig. 4. Temporal variation of surface temperature obtained from the simulations and thermocouple data for tungsten carbide coating and laser intensity transverse mode pattern b ¼ 0.
52
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Fig. 5. Temperature distribution inside the substrate material along the depth for laser pulse intensity transverse mode pattern b ¼0, two heating periods and different coating materials.
Fig. 6. Temperature distribution inside the substrate material along the depth for laser pulse intensity transverse mode pattern b ¼0, two heating periods and different coating materials.
different coating materials become almost the same. It should be noted that the size of the mushy zone between the liquid and solid phases is not visible from the figure. This is attributed to the high energy density deposition during the short duration of laser heating pulses. In the case of end of cooling period of the 10th pulse (t¼ 20 ms) temperature reduces considerably. The high rate of temperature decay is associated with the conduction, convection and radiation heat losses from the laser irradiated region. Since the temperature gradient is high in the heated region, conduction heat transfer from heated region to solid bulk is considerable while contributing to sharp temperature decay in the cooling period. Fig. 6 shows temperature distribution along the depth of the irradiated region for the laser intensity transverse mode pattern b ¼1. The behavior of temperature curves are similar to those shown in Fig. 5, provided that peak temperature and the temperature decay along the depth are not the same. This is attributed to the laser peak intensity, which moves away from the irradiated spot center for the laser intensity transverse mode pattern b ¼1 (Fig. 3). The differences in the behavior of temperature curves due to different laser intensity transverse mode pattern are more pronounced during the heating cycle of the pulse. Since internal energy gain of the substrate material and temperature rise in the surface vicinity is associated with
Fig. 7. Temperature distribution inside the substrate material along the radial distance for laser pulse intensity transverse mode pattern b ¼0, two heating periods and different coating materials.
absorption of the incident laser energy, change in laser intensity distribution results in large change in the peak temperature at the coating surface. Fig. 7 shows temperature distribution along the radial direction for different time periods, three materials, and laser intensity transverse mode pattern b ¼0. Temperature decays gradually in the central region of the irradiated spot around the symmetry axis where temperature is considerably high. As the distance in the radial direction increases away from the symmetry axis, temperature decay becomes sharp. This is attributed to the laser pulse intensity distribution at the workpiece surface, which is Gaussian. This is more pronounced at the end of heating period of 10th pulse (t ¼19 ms) for tungsten carbide and alumina coatings. In the case of Tungsten Carbide, due to relatively high thermal diffusivity and low absorption coefficient, temperature becomes lower at the surface as compared to other coating materials. In the case of end of the cooling period (t ¼20 ms), temperature drops significantly at the surface for all coating materials and temperature difference becomes small. This is attributed to the internal energy gain of the coating from the irradiated field, which ceases at the end of the heating period. Since laser beam power is switched off in the cooling cycle, heat losses due to convection, radiation and conduction from the surface lower temperature significantly at the surface region. Fig. 8 shows surface temperature distribution in the radial direction for the laser intensity transverse mode pattern b ¼1. Temperature distribution at the surface follows almost the laser pulse intensity distribution during the heating cycle (t ¼9 ms). This is attributed to the material response to the incident laser radiation. The peak temperature exceeds the melting temperature of the coating material for alumina and boron; therefore, melting in the surface region is evident. However, no evidence of mushy zone is observed from the temperature profiles. This indicates that the small size of mushy zone is present between the liquid and solid phases, which may not be seen clearly from temperature curves. In the cooling cycle, absorption of incident radiation ceases so that temperature drops significantly at the surface. In this case, the peak temperature remains below the melting temperature of the substrate material. Fig. 9(a) and (b) shows temporal variation of surface temperature for different coating materials for b ¼0 and b ¼1, respectively. Temperature increases first and reduces later during each pulse, which appears as oscillation in temperature profile with progressing time. Since the duty cycle is 50%, the heating cycle is
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Fig. 8. Temperature distribution inside the substrate material along the radial distance for laser pulse intensity transverse mode pattern b ¼ 1, two heating periods and different coating materials.
Fig. 9. (a) Temporal variation of temperature at the irradiated spot center for laser pulse intensity transverse mode pattern b ¼0 and different coating materials. (b) Temporal variation of temperature at the irradiated spot center for laser pulse intensity transverse mode pattern b ¼1 and different coating materials.
1 ms while the cooling cycle ends after 1 ms of the heating cycle of the pulse. Therefore, the total heating and cooling durations of each pulse is 2 ms. Temperature rises sharply during the early period of heating cycle and temperature rise becomes gradual as
53
the time progresses towards the end of heating cycle. This is attributed to absorption of incident beam in the early heating period; in which case, internal energy increase becomes rapid, which produces the rise of surface temperature at the same rate. As the heating period progresses, heat conduction from the irradiated region to the solid bulk increases because of high temperature gradient developed during the initial period of the heating cycle. In the case of cooling cycle, temperature reduces sharply due to cease of the laser power. However, the slope of temperature decay changes slightly towards the end of the cooling cycle. This change is associated with the phase change in the irradiated center; in which case, the slope of temperature decay changes in the vicinity of the melting temperature of the coating material. In the case of laser intensity transverse mode pattern b ¼ 1, temperature rise is considerably smaller than that of b ¼0, since the peak intensity shifts away from the irradiated spot center for the laser intensity transverse mode pattern b ¼1 (Fig. 3). Surface temperature difference at the irradiated spot center becomes smaller for b ¼1 than that of b ¼0. Fig. 10(a) and (b) shows temperature contours and phase changed regions in the coating and in the base material for three coating materials and two laser transverse mode patterns, respectively. In the case of b ¼0, temperature reaches beyond the melting temperature in the coating for alumina and boron while it does not reach the melting temperature of tungsten carbide. In addition, temperature reaches above the melting temperature of the base material below the coating for all coating materials. Consequently, tungsten carbide coating remains in the solid phase while underlying steel undergoes a melting at the interface region. This is associated with the melting temperature of tungsten carbide, which is high. The presence of mushy zone is visible for steel; however, mushy zone size is considerably small for the coating materials. Although continuity of heat flux and temperature is considered at the coating and the base material interface, the behavior of temperature profiles in the coating and the base material is notably different, which is attributed to differences in thermal properties of the coating and the base material. In the case of laser intensity transverse mode pattern b ¼ 1, temperature profiles in the coating and substrate material become different than those shown in Fig. 10(a). This is because of the laser power intensity distribution at the workpiece surface, which is non-Gaussian (Fig. 3). The melt pool moves away from the irradiated spot center towards the location of the peak laser power intensity. Since the peak laser power intensity is low for laser intensity transverse mode pattern b ¼1, coating does not undergo melting all along its thickness, which is also true for alumina and boron coatings. In addition, the melt pool depth becomes shallower and the melt pool width grow to be wider than those corresponding to the laser intensity transverse mode pattern b ¼0. The melt depth and width in the base material are also modified by the laser pulse intensity distribution for laser intensity transverse mode pattern b ¼1. However, the mushy zone thickness for all laser intensity transverse mode patterns remains almost the same for alumina and boron coatings. Fig. 11(a) and (b) shows velocity vectors in the melt pool produced in the coating for the laser intensity transverse mode pattern b ¼0 and b ¼1. The flow field developed in the melt pool is associated with the Marangoni and shear driven flows due to the surface tension force and the rate of flow strain variation in the melt pool. The flow behavior in alumina and boron coatings is similar and a circulation cell is formed in the melt pool. In the case of laser intensity transverse mode pattern b ¼0, velocity magnitude is higher than that corresponding to b ¼1. This is attributed to the melt depth; in which case, the melt pool is shallow for b ¼1 and the convection current developed due to rate of fluid strain variation in the melt pool becomes weaker
54
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
Fig. 10. (a) Temperature contours and melt pool in the surface vicinity for laser pulse intensity transverse mode pattern b ¼ 0 and different coating materials. (b)Temperature contours and melt pool in the surface vicinity for laser pulse intensity transverse mode pattern b ¼ 1 and different coating materials.
Fig. 11. (a) Velocity vectors in the coating melt pool for laser pulse intensity transverse mode pattern b ¼0 and different coating materials. (b) Velocity vectors in the coating melt pool for laser pulse intensity transverse mode pattern b ¼1 and different coating materials.
S.Z. Shuja, B.S. Yilbas / Optics & Laser Technology 47 (2013) 47–55
than that of b ¼0. Moreover, no free surface exist for the underlying steel substrate, no Marangoni flow is generated. In addition, density variation due to temperature change in the melt pool of steel is small, no visible convection current driven circulation is observed.
55
Acknowledgements The authors acknowledge the support of King Fahd University of Petroleum and Minerals Dhahran Saudi Arabia. References
6. Conclusion Laser controlled melting of coated carbon steel surface is simulated using the control volume approach. Temperature predictions are validated through the thermocouple data. The phase change during the laser heating is incorporated using the enthalpy porosity method. The Marangoni flow in the melt pool is considered in the numerical simulations. The study is extended to include the influence of the laser intensity transverse mode pattern (b) on the melting characteristics. It is found that the peak temperatures corresponding to boron and alumina are higher than that of tungsten carbide coating. This is associated with high thermal diffusivity and high absorption coefficient of tungsten carbide. Surface temperature increase is significant during the initial period of heating cycle of the laser pulse while in the cooling cycle temperature decay is sharp due to the cease of laser power. The influence of laser intensity distribution on temperature profiles is considerable, since radial distribution of surface temperature follows almost the laser intensity distribution at the workpiece surface. Boron and alumina coatings melt completely during the heating cycle of 10th pulse for laser intensity transverse mode pattern b ¼0. In addition, steel beneath the coating undergoes melting at the interface region. Although coating remains in the solid phase for tungsten carbide, underlying steel melts while forming a melt pool at the interface region. The size of the melt pool is influenced by the laser intensity transverse mode pattern; in which case, the orientation of the melt pool changes from the irradiated spot center for the laser pulse parameter b ¼1. The depth of the melt pool becomes shallow influencing the Marangoni flow in the melt pool. In general, a circulation cell is developed and the velocity magnitude in the melt pool attains higher values for the laser intensity transverse mode pattern b ¼0 than that corresponding to b ¼1.
[1] Zhang Y, Faghri A. Vaporization, melting and heat conduction in the laser drilling process. International Journal of Heat and Mass Transfer 1999;42:1775–90. [2] Yang LX, Peng X, Wang BX. Numerical modeling and experimental investigation on the characteristics of molten pool during laser processing. International Journal Heat Mass transfer 2001;44:4465–73. [3] Chung H, Das S. Numerical modeling of scanning laser-induced melting, vaporization and resolidification in metals subjected to step heat flux input. International Journal of Heat and Mass Transfer 2004;47:4153–64. [4] Tani G, Tomesani L, Campana G. Prediction of melt geometry in laser cutting. Applied Surface Science 2003;208–209:142–7. [5] Li JF, Li L, Stott FH. Comparison of volumetric and surface heating surfaces in the modeling of laser melting of ceramic materials. International Journal of Heat and Mass Transfer 2004;47:1159–74. [6] Konrad C, Zhang Y, Shi Y. Melting and resolidification of a subcooled metal powder particle subjected to nanosecond laser heating. International Journal of Heat Mass Transfer 2007;50:2236–45. [7] Krishnan S, Murthy JY, Garimella SV. Analysis of solid-liquid phase change under pulsed heating. The ASME Journal of Heat Transfer 2007;129:395–9. [8] Safdar S, Li L, Sheikh MA, Liu Z. An analysis of the effect of laser beam geometry on laser transformation hardening. Journal of Manufacturing Science and Engineering 2006;128:659–67. [9] Shen ZH, Zhang SY, Lu J, Ni XW. Mathematical modeling of laser induced heating and melting in solids. Optics and Laser Technology 2001;33:533–7. [10] Yilbas BS, Mansoor SB. Laser pulse heating and phase changes in the irradiated region: temperature dependent thermal properties case. International Journal of Thermal Sciences 2009;48:761–72. [11] Shuja SZ, Yilbas BS, Khan S. Laser consecutive pulse heating and phase change: influence of spatial distribution of laser pulse intensity on melting. International Journal of Thermal Sciences 2009;48:1960–6. [12] Shuja SZ, Yilbas BS. Pulsative heating of surfaces. International Journal of Heat and Mass Transfer 1998;41:3899–918. [13] Fluent Inc 2005 Fluent Users Guide. [14] Voller VR, Prakash C. A fixed-grid numerical modeling methodology for convection-diffusion mushy region phase-change problems. International Journal of Heat Mass Transfer 1987;30:1709–20. [15] Patankar SV. Numerical heat transfer. New York: McGraw-Hill; 1980. [16] Incropera FP, DeWitt DP. Fundamentals of heat and mass transfer. fourth ed. New York: John Wiley & Sons; 1996 p829 830. [17] Yilbas BS, Davies R, Gorur A, Yilbas Z, Begh , Kalkat M, et al. Study into the measurement and prediction of penetration time during CO2 laser cutting process. Proceedings of the Institution of Mechanical Engineers Part B 1990;204:105–13.