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Influence of laser energy distribution on laser surface microstructure processing
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Influence of laser energy distribution on laser surface microstructure processing
T
⁎
Xiaofang Xu , Xiaohan Yang, Jingbo Li, Sen Pan, Yong Bi, Yongfeng Gao School of Mechanical Engineering, Jiangsu University, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Surface microstructure Surface tension Laser energy density Gaussian distribution Uniform distribution
Laser surface microstructure can improve the friction properties, biomedical properties and optical properties of materials. In this paper, a two-dimensional finite element model based on temperature-dependent surface tension is proposed to study the effects of different laser energy density distributions on surface morphology. The results show that: when the laser energy density is applied to the molten pool under the Gaussian distribution and uniform distribution, respectively, the peak temperature of the molten pool surface is varied, and the difference of temperature gradient leads to the changes of surface tension. As the surface topography is mainly affected by the surface tension, different laser energy densities will produce different surface topography, therefore, its analysis will help us understand the formation mechanism of laser surface microstructures.
1. Instruction With the wide application of laser surface microstructure processing, a series of experimental and theoretical studies have emerged to explore the role of surface microstructure and the formation process. For example, Zhou et al. [1] analyzed the formation process of the surface topography and analyzed the mechanism of the pit formation by long pulse laser heating. Etsion, Yin B F, Hua X J and Andersson et al. [2–5] studied the effects of laser-induced surface microstructures on friction and wear. They found that the surface microstructures not only can improve the friction properties of materials, but also can extend the life of materials. Davide Scorticati et al. [6] deposited less than 400 nm aluminum on a borosilicate glass substrate, and used a laser to induce a periodic surface structure on aluminum surface to produce a regular nano-diffraction grating. They found that careful selection of suitable laser parameters can avoid harmful mechanical stresses, cracks and spalling. Vasylyev M A, et al. [7] irradiated dental chromealuminum alloy surface with a pulsed laser in the hydrogen atmosphere. They observed the influence of different energy densities on the surface morphology, and analyzed the main characteristics of the periodic structure. B S Yilbas et al. [8] performed laser gasassisted texturing on the surface of the silicon wafer and discovered that the micro-nano structure composed of the laser texture enhanced the surface hydrophobicity. They discovered that the laser surface microstructure would increase the surface microhardness and slightly lower the surface fracture toughness. In order to accomplish the experiment better, some numerical simulations were needed to discuss the thermal and mechanical effects of the material deformation process, and explain the interaction mechanism between laser and material. Shashank Sharma et al. [9] analysed the hole morphology under the laser energy density of the Gaussian distribution and the top hat distribution. It was found that the shape of the small holes occured significant deformation under the action of thermal and fluid mechanics, and the
⁎
Corresponding author at: School of Mechanical Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu Province, China. E-mail address: [email protected] (X. Xu).
https://doi.org/10.1016/j.ijleo.2019.163244 Received 20 May 2019; Accepted 16 August 2019 0030-4026/ © 2019 Published by Elsevier GmbH.
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
forces driving the melt movement in the molten pool were mainly physical force and surface force, but the model did not take into account the effects of hot capillary force and surface tension. S. Morville et al. [10] discussed the re-solidification geometry of the molten zone after a laser source heating which had a uniform distribution of laser energy density, they found that the liquid/gas interface shape was mainly controlled by the surface tension and the marangoni convection. Shen Hong et al. [11] established a twodimensional axisymmetric finite element model, and used the Gaussian distribution laser energy density as a numerical simulation heat source to discuss the formation of bumps in laser melting of stainless steel, they obtained that the formation of bumps was mainly affected by hot capillary force and surface tension. From the literature review, it was found that many literatures analysed the shape of the molten pool by simulation, and also discussed the surface morphology of the molten pool under different laser energy density. However, they often used the simplified models [12–15], which assumed that the top free surface of the weld pool was flat, ignoring the effects of heat transfer and fluid flow on the surface topography of the material. Therefore, a comprehensive model is needed to fully discussed the shape of the molten pool, the fluid flow characteristics in the molten pool, the surface topography characteristics of the molten pool after solidification under the Gaussian distribution and uniform distribution. In this paper, a finite element numerical model is established which based on the analysis of temperature-dependent material properties and surface tension. By comparing the thermal and mechanical characteristics of the molten pool under the laser energy density distributions of the Gaussian distribution and uniform distribution, respectively, the interaction mechanism between laser and material is analyzed, and the nature of the formation of surface microtopography is explored. 2. Numerical simulation 2.1. Control equation The transmission phenomena in solid and liquid regions are calculated by solving the conservation equations of mass, momentum and energy simultaneously (Eqs. (1)–(3)). →
ρ∇⋅(u ) = 0
(1)
→
ρ
→ → → → → → ∂u + ρ (u ⋅∇) u = ∇⋅[−pI + μ (∇u + (∇u)T )] − ρ (1 − β (T − Tm)) g + F ∂t
ρCP
→ ∂T + ρCP (u ⋅∇T ) = ∇⋅(k∇T ) ∂t
F = −C
(2)
(3)
(1 − fl )2 → u (fl3 + b)
(4)
⎧ 0, T ≤ Ts ⎪ T − Ts , Ts ≤ T ≤ Tl fl = ⎨ Tl − Ts ⎪1, T > Tl ⎩
(5) (kg / m3 ),
→ (N / m2 ), u
is the molten metal velocity (m / s ), Cp is the specific heat of Where ρ is the density of the material p is the pressure the material (J /(kg⋅K ) ), μ is the dynamic viscosity (Pa⋅s ), k is the thermal conductivity (W /(m⋅K ) ), β is the thermal expansion → coefficient(1/ K ), Tm is the melting temperature, I is the unit matrix, g is the gravity acceleration, T is the temperature (K ), F is the Darcy damping force, which is considered to dampen the velocity to zero when the temperature is lower than the melting temperature. This force induces isotropic permeability (Eqs. (4) and (5)) derived from the Kozeny − Carman equation which is also used to treat the mushy zone [16–18]. In addition, a large amount of heat the will be absorbed during the liquefaction process, called latent heat. In this paper, the equivalent specific heat capacity method is used to deal with the phase change problem. The formula is as follows [11]:
Cpeq = Cp + Lf (dfl / dt )
(6)
Cpeq
In Eq. (6), is the specific heat capacity of the latent heat converted material, Cp is the specific heat capacity of the material, Lf is the latent heat of fusion, and fl is the liquid volume fraction. The thermophysical parameters of Ti6Al4V are shown in Table 1 below. 2.2. Boundary condition setting 2.2.1. Energy boundary condition setting In the laser processing process, the boundary conditions of the upper surface are mainly set to laser heat flow, heat convection and heat radiation, while other boundary conditions are mainly set to heat convection. Eqs. ((7) and (8)) describe the laser thermal convection and the heat radiation, and the formulas are as follows: 2
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
Table 1 Material physical properties [19–21]. Property
Value
Liquidus temperature Solidus temperature Melting temperature Reference temperature Liquid phase density
1923K 1877K 1900K 1923K
Solid phase density
4200kg / m3
Reference phase density
3780kg / m3 29W /(m⋅k ) 21W /(m⋅k ) 831 J /(kg⋅K ) 670 J /(kg⋅K ) 2.86*10^5 J / kg 0.005Pa⋅s 1.4N / m −0.26*10^-3N / m/ K 8*10^-61/ K 0.7
3780kg / m3
Thermal conductivity of liquid phase Thermal conductivity of solid phase Specific heat of liquid phase Specific heat of solid phase Latent heat of fusion Dynamic viscosity of liquid phase Surface tension coefficient Temperature coefficient of surface tension Coefficient of thermal expansion Emissivity
4 − k∇T = αq − h [T − Tamb] − εσ [T 4 − Tamb ]
(7)
− k∇T = h (T − Tamb)
(8)
In Eq. (7), α is the laser absorption rate of the material to be irradiated, which is 0.432, and Tamb is the ambient temperature, which is 293.15 K . q represents the laser beam irradiance, and the last two equations represent the convection and radiant heat loss, respectively. In the computational domain (see Fig. 1, Eq. (8)), boundaries 1, 2, 3, and 4 are all subject to convective heat losses. 2.2.2. Free surface boundary condition setting In the case of two-phase flow, there is a surface tension that balances the total normal stress on both sides of the interface, that is the stress σ on the free surface of the top of the molten pool, which can be expressed as [22]
σ = γn (∇⋅n) − ∇γ = σn − σt
(9)
Where σn is the normal stress, σt is the tangential stress. In this paper, the surface tension γ depends on the temperature, and the surface tension gradient ∇γ can be expressed as [22]
σt = ∇γ =
∂γ ∇t T ∂T
(10)
Eq. (10) describes the Marangoni shear force term acting on the surface of the melt pool. The normal stress will act on the surface of the melt pool based on its curvature as follows [10]: →
→
σn = γn (∇⋅n) = −Pa n + κγn
(11)
Surface tension γ can be expressed as [21]
γ = γm − A γ (T − Tm)
(12)
In Eq. (12), γm is the surface tension, A γ is a constant in surface tension gradient and Tm is the melting temperature.
Fig. 1. Relationship between energy density and radial distance of laser under Gaussian distribution and uniform distribution. 3
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
2.3. Moving mesh In order to accurately predict the deformation of the molten pool, the ALE method is used. In this method, the displacement of the boundary node depends on the velocity of the fluid [10]. This condition can be described by the following equation: (13)
Vmesh⋅n = u⋅n
The above equation is used to describe the free surface motion (Boundary 2), with no-slip conditions applied on the remaining boundaries. 2.4. Laser energy distribution model establishment This paper mainly studies the influence of Gaussian distribution and uniform distribution on the surface morphology during laser processing. In order to obtain more accurate results, the same energy is used for processing. The laser heat source under Gaussian distribution can be expressed as a formula:
I (r ) = 2*I0 exp(
−2x 2 ) R2
(14)
The laser energy density under uniform distribution can be calculated by the energy which generated by the laser heat source with Gaussian distribution at the heating time of 0.2 ms . The laser power of the Gaussian distribution we chose is 300 W , and the laser beam radius R = 0.2mm . By solving Eq. (14), the laser heat source under uniform distribution conditions is expressed as:
I (r ) = 2.8559*10ˆ9[W / mˆ2]
(15)
The two laser energy density distributions are shown in Fig. 1, and the other boundary conditions are set as in the Gaussian distribution. 2.5. Mesh parameters and model calculation A geometric model with length of 600 μm and height of 80 μm is established, as shown in Fig. 2.The geometry is meshed using triangular element. In order to obtain more accurate results, the top boundary surface is meshed with maximum element size, and calibrate normal-sized elements in the rest area to calibrate general physics to save calculations the amount. The mesh smoothing algorithm used in this model is the Laplace method, which is further used to simulate the deformation of free surfaces. 3. Numerical simulation of laser energy Gaussian distribution and uniform distribution 3.1. Analysis of simulation process under Gaussian distribution Fig.3 shows the numerical simulation process under the condition of Gaussian distribution of laser energy. The model map are taken at 0.12ms , 0.16ms , 0.2ms , 0.21ms , 0.23ms , 0.26ms , 0.32ms , 0.45ms ,respectively. It can be found from Fig. 3 that the material has melted to form a molten pool at 0.12ms , the fluid in the molten pool flows toward the edge and forms a clockwise vortex. The surface topography of the central depression of the edge protrusion is formed, and the maximum velocity of the surface fluid reaches 3.41 m / s . When the heating time lasts to 0.16ms , the molten pool expands continuously, the thickness of the fluid in the molten pool increases, and the maximum velocity of the surface fluid also increases, reaching 4.48 m / s , the surface deformation is more obvious. At the end of the heating time 0.2ms , the fluid velocity in the molten pool reaches a maximum of 5.4 m / s , and the deformation is also more obvious. During the cooling phase, it is found that as the cooling time increases, the fluid in the molten pool solidifies from the edge to the center, the fluid velocity decreases and the final velocity is reduced to zero. However, the surface does not return to the flatness before processing, but a certain deformation occurs. 3.2. Analysis of simulation process under uniform distribution Fig.4 shows the numerical simulation process under the Gaussian distribution of laser energy. The model map are taken at 0.12ms , 0.16ms , 0.2ms , 0.21ms , 0.23ms , 0.26ms , 0.32ms ,respectively. It can be found from Fig. 4 that the material has melted to form a molten
Fig. 2. Schematic representation of the computational domain used in numerical simulation. 4
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
Fig. 3. Morphology of molten pool under Gaussian distribution.
pool at 0.12ms , the fluid in the molten pool flows toward the edge, the surface deformation is not very obvious, and the maximum velocity of the surface fluid reaches 0.4 m / s . When the heating time lasts to 0.16ms , the molten pool expands continuously, the thickness of the fluid in the molten pool increases, and the maximum velocity of the surface fluid also increases, reaching 0.86 m / s , the surface has a weak deformation. At the end of the heating time 0.2ms , the fluid velocity in the molten pool reaches a maximum of 1.51 m / s , and the deformation is also more obvious. During the cooling phase, it is found that as the cooling time increases, the fluid 5
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
Fig. 4. Morphology of molten pool under uniform distribution. 6
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
Fig. 5. Comparison of peak temperature of molten pool surface under Gaussian distribution and uniform distribution.
in the molten pool solidifies from the edge to the center, the fluid velocity decreases and the final velocity is reduced to zero. However, the surface does not return to the flatness before processing, but a certain deformation occurs. It can be found from Figs. 3 and 4 that the morphology of the molten pool under the two laser energy distributions is significantly different. The laser energy density Gaussian distribution is used for processing. The surface of the material begins to have a temperature gradient, which affects the surface tension. So the molten pool will flow from the center to the edge from the beginning, and the surface deformation is more obvious. In contrast, the morphology of the molten pool under the uniform distribution of Fig. 4 shows that the solid-liquid boundary of the molten pool is more flat, and the surface of the molten pool is relatively flat, which conforms to the morphology of the molten pool under uniform distribution. This phenomenon is mainly because the surface temperature under uniform distribution is almost the same, especially near the center of the molten pool. At the beginning of the heating stage, the center of the molten pool does not have much deformation.However, the heat transfer between the molten pool edge and the solid zone leads to the existence of temperature gradient. The heat transfer will continue to spread to the center, affecting the surface tension and the deformation of the molten pool surface. By comparing the two distributions, it is better to explain the factors affecting the surface topography, which have a great relationship with the temperature gradient during the laser melting process, that is, the surface tension has the strong dependence on temperature. 3.3. Comparison of simulation results under different distribution conditions Figs. 5–7 show a comparison of the surface temperature and deformation of the material under the laser energy Gaussian distribution and uniform distribution, respectively. Figs. 5 and 6 are the results of heating time 0.2 ms , and Fig. 7 is the result of solidification of the molten pools surface under the two distributions. As shown in Fig. 5, the temperature distribution is similar to the laser energy distribution, but due to the flow of fluid and the difference in heat transfer efficiency between solid and liquid phases, some irregular phenomena appear. Under the Gaussian distribution of laser energy, the center temperature is high and the edge temperature is low, and the highest temperature is higher than the temperature under uniform distribution. Under uniform distribution of laser energy, the intermediate temperature is basically flat, but the edge temperature is lower due to the heat transfer. Fig. 6 is a comparison of the surface velocity distribution. We can see that the velocity under the Gaussian distribution of the laser energy is much faster than that in the uniform distribution. It is mainly due to the higher surface temperature gradient of the material under the Gaussian distribution, the main driving force causing the fluid flow is the surface tension, which is affected by the temperature gradient. Therefore, the fluid velocity inside the molten pool under the Gaussian distribution is faster than the uniform distribution. Fig. 7 is a comparison of the surface deformation. It can be found that the deformation under the Gaussian distribution of the laser energy is much larger than that under the uniform distribution, so the generation of the surface deformation is related to the
Fig. 6. Comparison of surface velocity of molten pool under Gaussian distribution and uniform distribution. 7
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
Fig. 7. Comparison of surface morphology of molten pool under Gaussian distribution and uniform distribution.
fluid velocity in the molten pool. As shown in Fig. 7, the surface deformation diameter is closer to the laser beam diameter under laser energy uniform distribution conditions, and the deformation interval is larger than the Gaussian distribution condition, but the surface deformation diameter under the laser energy Gaussian distribution is not easy to measure, as the change of surface deformation with lasting of the heating time is obvious. 4. Conclusions In this paper, a two-dimensional finite element analysis model is proposed to study the effect of laser energy distribution on the surface morphology of the molten pool. From the numerical simulation, it can be concluded that the laser energy distribution has a great influence on the morphology of the molten pool. The surface deformation of the molten pool under laser energy Gaussian distribution is larger than that under uniform distribution, and the surface morphology is strongly affected by the surface tension which is the temperature dependent. At the same time, the melting pool diameter under the Gaussian distribution of laser energy is obviously changed with the increase of heating time, but the variation of the molten pool diameter under the uniform distribution is small, which close to the laser beam diameter. Acknowledgments This work is supported by Chinese National Natural Science Foundation: Research on the electron nonequilibrium heat transport by femtosecond laser controllable excitation and the barrier elimination mechanism in metal films, and the Jiangsu Government Scholarship for Overseas Studies (No. JS-2018-253). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
J. Zhou, H. Shen, Y.Q. Pan, X.H. Ding, Experimental study on laser microstructures using long pulse, Optics Lasers Eng. 78 (2016) 113–120. I. Etsion, State of the art in laser surface texturing, ASME J. Tribol. 127 (1) (2005) 248–253. B.F. Yin, X.D. Li, Y.H. Fu, Y. Wang, Research on tribological performance of cylinder liner by micro-laser surface texturing, Adv. Sci. Lett. 4 (4-5) (2011) 1318–1324 7. X.J. Hua, Z. Puo, C. Julius, J.G. Sun, Experimental analysis of friction and wear of laser microtextured surface filled with composite solid lubricant and lubricated with grease on sliding surfaces, ASME J. Tribol. 139 (2017) 021609. P. Andersson, J. Koskinen, S.E. Varjus, Y. Gerbig, H. Haefke, S. Georgiou, W. Buss, Microlubrication effect by laser-textured steel surfaces, Wear 262 (3-4) (2007) 369–379. D. Scorticati, G. Romer, D.F. de. Lange, Ultra-short-pulsed laser-machined nanogratings of laser-induced periodic surface structures on thin molybdenum layers, J. Nanophotonics 6 (2012) 063528. M.A. Vasylyev, V.A. Tinkov, V.S. Filatova, Generation of the periodic surface structures on the dental Co-Cr-Mo alloy by Nd:YAG laser in an inert atmosphere, Appl. Surf. Sci. 258 (10) (2012) 4424–4427. B.S. Yilbas, H. Ali, M. Khaled, Characteristics of laser textured silicon surface and effect of mud adhesion on hydrophobicity, Appl. Surf. Sci. 351 (2015) 880–888. S. Sharma, Y. Pachaury, S.N. Akhtar, J. Ramkumar, A study on hydrodynamics of melt expulsion in pulsed Nd:YAG laser drilling of titanium, Proceedings of the 2015 COMSOL Conference, Pune, India, 2019. S. Morville, M. Carin, M. Muller, M. Gharbi, P. Peyre, D. Carron, P. Lemasson, R. Fabbro, 2D axial-symmetric model for fluid flow and heat transfer in the melting and resolidification of a vertical cylinder, Proceedings of the 2010 COMSOL Conference, Paris, France, 2019. H. Shen, Y. Pan, J. Zhou, Z. Yao, Forming mechanism of bump shape in pulsed laser melting of stainless steel, J. Heat Transfer 139 (2017) 062301. H.X. Liu, Z.B. Shen, X. Wang, H.J. Wang, Numerical simulation and experimentation of a novel micro scale laser high speed punching, Int. J. Mach. Tools Manuf. 50 (2010) 491–494. H.X. Liu, Z.H. Huang, C.X. Gu, Z.B. Shen, X. Wang, Experiment and numerical simulation of laser shock micro dents, Int. J. Surf. Sci. Eng. 8 (1) (2014). X.G. Cui, X.H. Wang, G.C. Yin, C.D. Xia, C. Fang, W.F. Zhang, C.Y. Cui, Three-dimensional (3-D) temperature distribution simulation of Fiber laser butt welding of AISI 304 stainless steel, Laser Eng. 39 (3-6) (2018) 355–377. J. Li, X. Wang, Numerical simulation of the influence of the bulges around laser surface textures on the tribological performance, Tribol. Trans. 56 (2013) 1011–1018. M. Courtois, M. Carin, P. Le Masson, S. Gaied, M. Balabane, A new approach to compute multi-reflections of laser beam in a keyhole for heat transfer and fluid flow modelling in laser welding, J. Phys. D Appl. Phys. 46 (2013). H. Shen, D. Feng, Z. Yao, Modeling of underwater laser drilling of alumina, J. Manuf. Sci. Eng. 139 (2016) 041008. Y. Zhang, Z. Shen, X. Ni, Modeling and simulation on long pulse laser drilling processing, Int. J. Heat Mass. Transfer 73 (2014) 429–437. K.C. Mills, Recommended Values of Thermophysical Properties for Selected Commercial, Woodhead Publishing Ltd, Cambridge, 2002. C. Panwisawas, Y. Sovani, R.P. Turner, J.W. Brooks, H.C. Basoalto, I. Choquet, Modelling of thermal fluid dynamics for fusion welding, J. Mater. Process. Technol. 252 (2018) 176–182. S. Sharma, V. Mandal, S.A. Ramakrishna, J. Ramkumar, Numerical simulation of melt hydrodynamics induced hole blockage in Quasi-CW Fiber laser micro-drilling of TiAl6V4, J. Mater. Process. Technol. 262 (2018) 131–148. D.A. Willis, X. Xu, Transport Phenomena and Droplet Formation During Pulsed Laser Interaction With Thin Films, ASME J. Heat Transfer 122 (4) (2000) 763–770.
8
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Influence of laser energy distribution on laser surface microstructure processing
T
⁎
Xiaofang Xu , Xiaohan Yang, Jingbo Li, Sen Pan, Yong Bi, Yongfeng Gao School of Mechanical Engineering, Jiangsu University, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Surface microstructure Surface tension Laser energy density Gaussian distribution Uniform distribution
Laser surface microstructure can improve the friction properties, biomedical properties and optical properties of materials. In this paper, a two-dimensional finite element model based on temperature-dependent surface tension is proposed to study the effects of different laser energy density distributions on surface morphology. The results show that: when the laser energy density is applied to the molten pool under the Gaussian distribution and uniform distribution, respectively, the peak temperature of the molten pool surface is varied, and the difference of temperature gradient leads to the changes of surface tension. As the surface topography is mainly affected by the surface tension, different laser energy densities will produce different surface topography, therefore, its analysis will help us understand the formation mechanism of laser surface microstructures.
1. Instruction With the wide application of laser surface microstructure processing, a series of experimental and theoretical studies have emerged to explore the role of surface microstructure and the formation process. For example, Zhou et al. [1] analyzed the formation process of the surface topography and analyzed the mechanism of the pit formation by long pulse laser heating. Etsion, Yin B F, Hua X J and Andersson et al. [2–5] studied the effects of laser-induced surface microstructures on friction and wear. They found that the surface microstructures not only can improve the friction properties of materials, but also can extend the life of materials. Davide Scorticati et al. [6] deposited less than 400 nm aluminum on a borosilicate glass substrate, and used a laser to induce a periodic surface structure on aluminum surface to produce a regular nano-diffraction grating. They found that careful selection of suitable laser parameters can avoid harmful mechanical stresses, cracks and spalling. Vasylyev M A, et al. [7] irradiated dental chromealuminum alloy surface with a pulsed laser in the hydrogen atmosphere. They observed the influence of different energy densities on the surface morphology, and analyzed the main characteristics of the periodic structure. B S Yilbas et al. [8] performed laser gasassisted texturing on the surface of the silicon wafer and discovered that the micro-nano structure composed of the laser texture enhanced the surface hydrophobicity. They discovered that the laser surface microstructure would increase the surface microhardness and slightly lower the surface fracture toughness. In order to accomplish the experiment better, some numerical simulations were needed to discuss the thermal and mechanical effects of the material deformation process, and explain the interaction mechanism between laser and material. Shashank Sharma et al. [9] analysed the hole morphology under the laser energy density of the Gaussian distribution and the top hat distribution. It was found that the shape of the small holes occured significant deformation under the action of thermal and fluid mechanics, and the
⁎
Corresponding author at: School of Mechanical Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu Province, China. E-mail address: [email protected] (X. Xu).
https://doi.org/10.1016/j.ijleo.2019.163244 Received 20 May 2019; Accepted 16 August 2019 0030-4026/ © 2019 Published by Elsevier GmbH.
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
forces driving the melt movement in the molten pool were mainly physical force and surface force, but the model did not take into account the effects of hot capillary force and surface tension. S. Morville et al. [10] discussed the re-solidification geometry of the molten zone after a laser source heating which had a uniform distribution of laser energy density, they found that the liquid/gas interface shape was mainly controlled by the surface tension and the marangoni convection. Shen Hong et al. [11] established a twodimensional axisymmetric finite element model, and used the Gaussian distribution laser energy density as a numerical simulation heat source to discuss the formation of bumps in laser melting of stainless steel, they obtained that the formation of bumps was mainly affected by hot capillary force and surface tension. From the literature review, it was found that many literatures analysed the shape of the molten pool by simulation, and also discussed the surface morphology of the molten pool under different laser energy density. However, they often used the simplified models [12–15], which assumed that the top free surface of the weld pool was flat, ignoring the effects of heat transfer and fluid flow on the surface topography of the material. Therefore, a comprehensive model is needed to fully discussed the shape of the molten pool, the fluid flow characteristics in the molten pool, the surface topography characteristics of the molten pool after solidification under the Gaussian distribution and uniform distribution. In this paper, a finite element numerical model is established which based on the analysis of temperature-dependent material properties and surface tension. By comparing the thermal and mechanical characteristics of the molten pool under the laser energy density distributions of the Gaussian distribution and uniform distribution, respectively, the interaction mechanism between laser and material is analyzed, and the nature of the formation of surface microtopography is explored. 2. Numerical simulation 2.1. Control equation The transmission phenomena in solid and liquid regions are calculated by solving the conservation equations of mass, momentum and energy simultaneously (Eqs. (1)–(3)). →
ρ∇⋅(u ) = 0
(1)
→
ρ
→ → → → → → ∂u + ρ (u ⋅∇) u = ∇⋅[−pI + μ (∇u + (∇u)T )] − ρ (1 − β (T − Tm)) g + F ∂t
ρCP
→ ∂T + ρCP (u ⋅∇T ) = ∇⋅(k∇T ) ∂t
F = −C
(2)
(3)
(1 − fl )2 → u (fl3 + b)
(4)
⎧ 0, T ≤ Ts ⎪ T − Ts , Ts ≤ T ≤ Tl fl = ⎨ Tl − Ts ⎪1, T > Tl ⎩
(5) (kg / m3 ),
→ (N / m2 ), u
is the molten metal velocity (m / s ), Cp is the specific heat of Where ρ is the density of the material p is the pressure the material (J /(kg⋅K ) ), μ is the dynamic viscosity (Pa⋅s ), k is the thermal conductivity (W /(m⋅K ) ), β is the thermal expansion → coefficient(1/ K ), Tm is the melting temperature, I is the unit matrix, g is the gravity acceleration, T is the temperature (K ), F is the Darcy damping force, which is considered to dampen the velocity to zero when the temperature is lower than the melting temperature. This force induces isotropic permeability (Eqs. (4) and (5)) derived from the Kozeny − Carman equation which is also used to treat the mushy zone [16–18]. In addition, a large amount of heat the will be absorbed during the liquefaction process, called latent heat. In this paper, the equivalent specific heat capacity method is used to deal with the phase change problem. The formula is as follows [11]:
Cpeq = Cp + Lf (dfl / dt )
(6)
Cpeq
In Eq. (6), is the specific heat capacity of the latent heat converted material, Cp is the specific heat capacity of the material, Lf is the latent heat of fusion, and fl is the liquid volume fraction. The thermophysical parameters of Ti6Al4V are shown in Table 1 below. 2.2. Boundary condition setting 2.2.1. Energy boundary condition setting In the laser processing process, the boundary conditions of the upper surface are mainly set to laser heat flow, heat convection and heat radiation, while other boundary conditions are mainly set to heat convection. Eqs. ((7) and (8)) describe the laser thermal convection and the heat radiation, and the formulas are as follows: 2
Optik - International Journal for Light and Electron Optics 199 (2019) 163244
X. Xu, et al.
Table 1 Material physical properties [19–21]. Property
Value
Liquidus temperature Solidus temperature Melting temperature Reference temperature Liquid phase density
1923K 1877K 1900K 1923K
Solid phase density
4200kg / m3
Reference phase density
3780kg / m3 29W /(m⋅k ) 21W /(m⋅k ) 831 J /(kg⋅K ) 670 J /(kg⋅K ) 2.86*10^5 J / kg 0.005Pa⋅s 1.4N / m −0.26*10^-3N / m/ K 8*10^-61/ K 0.7
3780kg / m3
Thermal conductivity of liquid phase Thermal conductivity of solid phase Specific heat of liquid phase Specific heat of solid phase Latent heat of fusion Dynamic viscosity of liquid phase Surface tension coefficient Temperature coefficient of surface tension Coefficient of thermal expansion Emissivity
4 − k∇T = αq − h [T − Tamb] − εσ [T 4 − Tamb ]
(7)
− k∇T = h (T − Tamb)
(8)
In Eq. (7), α is the laser absorption rate of the material to be irradiated, which is 0.432, and Tamb is the ambient temperature, which is 293.15 K . q represents the laser beam irradiance, and the last two equations represent the convection and radiant heat loss, respectively. In the computational domain (see Fig. 1, Eq. (8)), boundaries 1, 2, 3, and 4 are all subject to convective heat losses. 2.2.2. Free surface boundary condition setting In the case of two-phase flow, there is a surface tension that balances the total normal stress on both sides of the interface, that is the stress σ on the free surface of the top of the molten pool, which can be expressed as [22]
σ = γn (∇⋅n) − ∇γ = σn − σt
(9)
Where σn is the normal stress, σt is the tangential stress. In this paper, the surface tension γ depends on the temperature, and the surface tension gradient ∇γ can be expressed as [22]
σt = ∇γ =
∂γ ∇t T ∂T
(10)
Eq. (10) describes the Marangoni shear force term acting on the surface of the melt pool. The normal stress will act on the surface of the melt pool based on its curvature as follows [10]: →
→
σn = γn (∇⋅n) = −Pa n + κγn
(11)
Surface tension γ can be expressed as [21]
γ = γm − A γ (T − Tm)
(12)
In Eq. (12), γm is the surface tension, A γ is a constant in surface tension gradient and Tm is the melting temperature.
Fig. 1. Relationship between energy density and radial distance of laser under Gaussian distribution and uniform distribution. 3
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2.3. Moving mesh In order to accurately predict the deformation of the molten pool, the ALE method is used. In this method, the displacement of the boundary node depends on the velocity of the fluid [10]. This condition can be described by the following equation: (13)
Vmesh⋅n = u⋅n
The above equation is used to describe the free surface motion (Boundary 2), with no-slip conditions applied on the remaining boundaries. 2.4. Laser energy distribution model establishment This paper mainly studies the influence of Gaussian distribution and uniform distribution on the surface morphology during laser processing. In order to obtain more accurate results, the same energy is used for processing. The laser heat source under Gaussian distribution can be expressed as a formula:
I (r ) = 2*I0 exp(
−2x 2 ) R2
(14)
The laser energy density under uniform distribution can be calculated by the energy which generated by the laser heat source with Gaussian distribution at the heating time of 0.2 ms . The laser power of the Gaussian distribution we chose is 300 W , and the laser beam radius R = 0.2mm . By solving Eq. (14), the laser heat source under uniform distribution conditions is expressed as:
I (r ) = 2.8559*10ˆ9[W / mˆ2]
(15)
The two laser energy density distributions are shown in Fig. 1, and the other boundary conditions are set as in the Gaussian distribution. 2.5. Mesh parameters and model calculation A geometric model with length of 600 μm and height of 80 μm is established, as shown in Fig. 2.The geometry is meshed using triangular element. In order to obtain more accurate results, the top boundary surface is meshed with maximum element size, and calibrate normal-sized elements in the rest area to calibrate general physics to save calculations the amount. The mesh smoothing algorithm used in this model is the Laplace method, which is further used to simulate the deformation of free surfaces. 3. Numerical simulation of laser energy Gaussian distribution and uniform distribution 3.1. Analysis of simulation process under Gaussian distribution Fig.3 shows the numerical simulation process under the condition of Gaussian distribution of laser energy. The model map are taken at 0.12ms , 0.16ms , 0.2ms , 0.21ms , 0.23ms , 0.26ms , 0.32ms , 0.45ms ,respectively. It can be found from Fig. 3 that the material has melted to form a molten pool at 0.12ms , the fluid in the molten pool flows toward the edge and forms a clockwise vortex. The surface topography of the central depression of the edge protrusion is formed, and the maximum velocity of the surface fluid reaches 3.41 m / s . When the heating time lasts to 0.16ms , the molten pool expands continuously, the thickness of the fluid in the molten pool increases, and the maximum velocity of the surface fluid also increases, reaching 4.48 m / s , the surface deformation is more obvious. At the end of the heating time 0.2ms , the fluid velocity in the molten pool reaches a maximum of 5.4 m / s , and the deformation is also more obvious. During the cooling phase, it is found that as the cooling time increases, the fluid in the molten pool solidifies from the edge to the center, the fluid velocity decreases and the final velocity is reduced to zero. However, the surface does not return to the flatness before processing, but a certain deformation occurs. 3.2. Analysis of simulation process under uniform distribution Fig.4 shows the numerical simulation process under the Gaussian distribution of laser energy. The model map are taken at 0.12ms , 0.16ms , 0.2ms , 0.21ms , 0.23ms , 0.26ms , 0.32ms ,respectively. It can be found from Fig. 4 that the material has melted to form a molten
Fig. 2. Schematic representation of the computational domain used in numerical simulation. 4
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Fig. 3. Morphology of molten pool under Gaussian distribution.
pool at 0.12ms , the fluid in the molten pool flows toward the edge, the surface deformation is not very obvious, and the maximum velocity of the surface fluid reaches 0.4 m / s . When the heating time lasts to 0.16ms , the molten pool expands continuously, the thickness of the fluid in the molten pool increases, and the maximum velocity of the surface fluid also increases, reaching 0.86 m / s , the surface has a weak deformation. At the end of the heating time 0.2ms , the fluid velocity in the molten pool reaches a maximum of 1.51 m / s , and the deformation is also more obvious. During the cooling phase, it is found that as the cooling time increases, the fluid 5
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Fig. 4. Morphology of molten pool under uniform distribution. 6
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Fig. 5. Comparison of peak temperature of molten pool surface under Gaussian distribution and uniform distribution.
in the molten pool solidifies from the edge to the center, the fluid velocity decreases and the final velocity is reduced to zero. However, the surface does not return to the flatness before processing, but a certain deformation occurs. It can be found from Figs. 3 and 4 that the morphology of the molten pool under the two laser energy distributions is significantly different. The laser energy density Gaussian distribution is used for processing. The surface of the material begins to have a temperature gradient, which affects the surface tension. So the molten pool will flow from the center to the edge from the beginning, and the surface deformation is more obvious. In contrast, the morphology of the molten pool under the uniform distribution of Fig. 4 shows that the solid-liquid boundary of the molten pool is more flat, and the surface of the molten pool is relatively flat, which conforms to the morphology of the molten pool under uniform distribution. This phenomenon is mainly because the surface temperature under uniform distribution is almost the same, especially near the center of the molten pool. At the beginning of the heating stage, the center of the molten pool does not have much deformation.However, the heat transfer between the molten pool edge and the solid zone leads to the existence of temperature gradient. The heat transfer will continue to spread to the center, affecting the surface tension and the deformation of the molten pool surface. By comparing the two distributions, it is better to explain the factors affecting the surface topography, which have a great relationship with the temperature gradient during the laser melting process, that is, the surface tension has the strong dependence on temperature. 3.3. Comparison of simulation results under different distribution conditions Figs. 5–7 show a comparison of the surface temperature and deformation of the material under the laser energy Gaussian distribution and uniform distribution, respectively. Figs. 5 and 6 are the results of heating time 0.2 ms , and Fig. 7 is the result of solidification of the molten pools surface under the two distributions. As shown in Fig. 5, the temperature distribution is similar to the laser energy distribution, but due to the flow of fluid and the difference in heat transfer efficiency between solid and liquid phases, some irregular phenomena appear. Under the Gaussian distribution of laser energy, the center temperature is high and the edge temperature is low, and the highest temperature is higher than the temperature under uniform distribution. Under uniform distribution of laser energy, the intermediate temperature is basically flat, but the edge temperature is lower due to the heat transfer. Fig. 6 is a comparison of the surface velocity distribution. We can see that the velocity under the Gaussian distribution of the laser energy is much faster than that in the uniform distribution. It is mainly due to the higher surface temperature gradient of the material under the Gaussian distribution, the main driving force causing the fluid flow is the surface tension, which is affected by the temperature gradient. Therefore, the fluid velocity inside the molten pool under the Gaussian distribution is faster than the uniform distribution. Fig. 7 is a comparison of the surface deformation. It can be found that the deformation under the Gaussian distribution of the laser energy is much larger than that under the uniform distribution, so the generation of the surface deformation is related to the
Fig. 6. Comparison of surface velocity of molten pool under Gaussian distribution and uniform distribution. 7
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Fig. 7. Comparison of surface morphology of molten pool under Gaussian distribution and uniform distribution.
fluid velocity in the molten pool. As shown in Fig. 7, the surface deformation diameter is closer to the laser beam diameter under laser energy uniform distribution conditions, and the deformation interval is larger than the Gaussian distribution condition, but the surface deformation diameter under the laser energy Gaussian distribution is not easy to measure, as the change of surface deformation with lasting of the heating time is obvious. 4. Conclusions In this paper, a two-dimensional finite element analysis model is proposed to study the effect of laser energy distribution on the surface morphology of the molten pool. From the numerical simulation, it can be concluded that the laser energy distribution has a great influence on the morphology of the molten pool. The surface deformation of the molten pool under laser energy Gaussian distribution is larger than that under uniform distribution, and the surface morphology is strongly affected by the surface tension which is the temperature dependent. At the same time, the melting pool diameter under the Gaussian distribution of laser energy is obviously changed with the increase of heating time, but the variation of the molten pool diameter under the uniform distribution is small, which close to the laser beam diameter. Acknowledgments This work is supported by Chinese National Natural Science Foundation: Research on the electron nonequilibrium heat transport by femtosecond laser controllable excitation and the barrier elimination mechanism in metal films, and the Jiangsu Government Scholarship for Overseas Studies (No. JS-2018-253). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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