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Analysis of energy occupying ratio of Coulomb explosion and thermal effect in picosecond pulse laser processing
Optics Communications 424 (2018) 190–197
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Analysis of energy occupying ratio of Coulomb explosion and thermal effect in picosecond pulse laser processing Zongji Zheng *, Chengjun Wu, Siyuan Liu, Xianbin Yang School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, PR China
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Keywords: Ten picosecond laser processing Coulomb explosion Thermal effect Numerical simulation Energy occupying ratio
ABSTRACT Molten material recasting may occur in ten picosecond laser processing although ultrashort-pulse processing is a kind of cold working method. It is also proved that experimental results do not fit expected processing results well in ten picosecond laser processing. What is more, some cracks on the surface of workpiece processed in ten picosecond laser can be observed. Aimed at above-mentioned facts processing in ten picosecond laser, a new hybrid model is raised. In this model, not only Coulomb explosion which is known to us but also thermal effect occurs in ten picosecond laser processing. Experiment method is used for analyzing the energy ratio of the two parts (Coulomb explosion and thermal effect). With OPENFOAM simulation software, the radius, topography and crack location of slots processed in different energy density are simulated. Finally, a comparison between simulation result and experimental result proves that this hybrid model is high degree of applicability and accuracy.
1. Introduction The application of laser ablation in different materials including metal is of great interest. With the appearance of ultrashort laser in 1990s, material/metal surface texturing gained a whole new dimension. From that moment, it became possible to touch three time regimes of pulse from femtosecond to nanosecond [1]. When time regimes of pulse are in fs–ns then laser processing can be divided into two categories, the first one is short-pulse laser processing, which is of high precision and efficiency. And the second one is ultrashort-pulse laser processing, which is of higher precision but lower efficiency [2–4]. For pursuing the precision, ultrashort-pulse laser is applied in more and more situations [5,6]. The major factor to distinguish short-pulse laser and ultrashort-pulse laser is the relationship between pulse duration and the relaxation time of materials. If the pulse duration is less than the relaxation time of materials, then the laser is defined as ultrashortpulse laser. Otherwise the laser is defined as short-pulse laser. And the relaxation time of materials depends on the property of their lattice, usually the critical value is about ten picoseconds. Usually ultrashortpulse laser processing is defined as a kind of cold ablation but sometimes processing with heat and short pulse laser processing is almost wholly due to thermal effect. For the past decades, the mechanism research of short pulse laser processing has already had quite a lot of previous accumulation, and it
has been verified on various materials by various processing methods. Many scholars have made a detailed analysis of thermal effect in short pulse laser ablation processing and the influencing factors of the processing. Chen et al. [7] Chose laser drilling process to make the efficient through holes in his research, which is based on hole drilling in silicon wafer by short pulse laser. Thermal and mechanical effects on silicon wafer induced by laser drilling were analyzed was characterized under optical microscopy, scanning electron microscopy and energy dispersive spectroscope. Aifei Pan et al. [8] Raised a two-dimensional thermochemical reaction model with temperature-dependent thermo-physical parameters on Si3N4 with 10 ns laser to investigate the ablated size, volume and surface morphology after single pulse. What is more, In SC Mishra’s paper [9], temporal evolutions of transmittance and reflectance signals, and incident radiation at various locations in the planar medium are studied for a wide range of the values of the extinction coefficient. The problem is analyzed using both the finite volume method and the discrete ordinates method. As a representative of cold ablation, mechanism and application of femtosecond pulse laser is widely studied. In Wang’s paper [10], the effects of processing parameters on the shape and morphology of microstructures in femtosecond laser fabrication of imprint roller are explored. An optimized fabrication process is proposed to acquire high accuracy microstructures. Menendez et al. [11] Studied Electrophoretic
* Correspondence to: Institute of Vibration and Noise Control, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China. E-mail addresses: [email protected] (Z. Zheng), [email protected] (X. Yang).
https://doi.org/10.1016/j.optcom.2018.04.045 Received 6 February 2018; Received in revised form 3 April 2018; Accepted 17 April 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
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mobility of laser-generated metal nanoparticles by laser scattering velocimetry and used the electrophoretic deposition of charged nanoparticles to generate nanoparticle-derived nanostructures on 3-dimensional micro-structured surfaces. Picosecond laser has characteristic of thermal accumulation and sometimes thermal will influence the topography of the materials. Liu [12,13] studied picosecond laser processing on porous structure with micro-size holes. After serious experiments, two kinds of porous structures were presented: periodic holes are formed from Coulomb Explosion during locally spatial modulated ablation, and random holes are formed from the burst of bubbles in overheated liquid during phase explosion. That means thermal effect exists in ps laser indeed. But even a large number of scholars have made much constructive experimental study of it, the study of picosecond pulse laser processing is still not enough. With the development of ultrashort laser technology, ten picosecond pulse laser can obtain dozens of micro joules energy. And in 10 ps laser the repetition frequency can reach MHz level. For common materials such as metal, semiconductor and dielectric, their relaxation time depends on the property of their lattice, usually the critical value is about ten picoseconds. So as long as laser duration is under ten picoseconds, there is no photon induction and thermal diffusion. Basic experimental research shows that picosecond laser is of high efficiency and owns unique implement advance. But as discussed above, 10 ps laser processing is a critical laser between hot and cold ablation. So this may lead to only merely hot ablation or totally cold ablation or even both. As a result of lying in the critical value, some phenomenon such as thermal stress and molten material recasting and surface crack may occur in picosecond laser processing. This is the main reason of the poor mechanism and controllability of picosecond laser. In accordance with the thermal annealing model (TAM), Lorazo et al. [14] Give a detailed description of the microscopic processes resulting from the interaction of a 308 nm, 10 ps, Gaussian pulse with a Si (100) substrate. What is more, in his paper, temperature gradient calculated by two-temperature model and pressure gradient due to thermal effect is obtained. In Wang’s paper [15], molecular dynamics (MD) simulations are conducted to study the thermal and thermomechanical phenomena induced by picosecond laser heating. He revealed thermal accumulation in picosecond processing and obtained temperature and strain due to thermal accumulation. They described the thermal accumulation and thermal effect in ten picosecond laser processing and explained the thermal effect in detail. Although the explanations are correct but concrete energy occupying ratio of Coulomb explosion and thermal effect is not obtained in their models. What is more, there is not necessary numerical verification for the thermal distribution. Based on this research status, in this paper, a new hybrid model for laser processing in 10 picosecond pulse duration and high pulse repetition is proposed. In this model, it is considered that both Coulomb explosion and thermal effect may take part in 10 picosecond laser processing. The energy occupying ratio of the two material removal method is related to the energy of each pulse according to our research. And the interpolation method is applied to estimate the relationship to guide the processing better.
Fig. 1. Molten material recasting.
Just take ten picosecond laser for experiments, when some energy densities are applied, an unusual phenomenon shown in Fig. 1 is observed through confocal laser scanning microscope that a large quantity of molten materials recast on the surface of the processed material. What is more, solid produced by condensation of a molten material is shaped like a droplet. The phenomenon means that phase transition occurs in processing procedure. But in former view, the main method of material removal in 10 picosecond laser does not include phase transition due to thermal effects. So the phenomenon does not fit the cold working characteristic of ultrashort-pulse laser. Another important phenomenon should be paid enough attention to. As it is known to us, laser is a kind of gauss light with very ultrashort action time so the affected area should be far less than the laser spot diameter after focusing. But it can be clearly seen in Fig. 2 through experiments that the affected area is almost equal to the spot diameter under several frequencies. It is clearly that the thermal effect plays a very important role in the processing procedure. What is more, in the previous point of view, the surface of workpiece processed in cold working method should be flat because there is almost no thermal stress in processing procedure. But the results from the experimental observation shown in Fig. 2 are not very optimistic. In some experimental groups, surface cracks are observed on the surface of the workpiece. It is obviously that the energy of the laser heating raises the temperature of the material, resulting in thermal stress which leads to the cracks of the surface of the material. In another word, there is also a thermal effect in 10 picosecond laser processing. One thing to be emphasized is that the total energy of the laser is certain. In the presence of the thermal effect, the energy of the Coulomb explosion is not the full source of energy. It is regrettable that the specific energy ratio is not yet conclusive. However, if the approximate energy ratio can be determined, the actual production process can be better guided and the quality of processing can be controlled more accurately. The main reason for the existence of thermal effect is that the occurrence of Coulomb explosion requires certain conditions: It is necessary to deliver enough energy to electrons in quite a short time. Only in this way can the electrons become excited electrons and convert the absorbed energy into the kinetic energy of the electrons. After that, the Coulomb force between the electrons and the nucleus traces the nuclear movement then the strong interaction force between the nuclei traces the other atomic movements and eventually removes the material. If the energy is not enough, it is obvious that Coulomb explosion can hardly happen. Therefore, the key issue is to determine the energy ratio of the Coulomb explosion and thermal effect in ultrashort-pulse laser.
2. Basic theory 2.1. Discussion about materials removal method in 10 picosecond laser processing In traditional view, ultrashort-pulse laser processing is defined as a kind of cold working method. And Coulomb explosion is the unique mechanism of action in processing procedure. But when the duration of laser is around ten picoseconds, the fact is that not only Coulomb explosion but also thermal effect plays an indispensable role in processing.
2.2. Mathematical model 2.2.1. Governing equation & porous medium When the laser irradiates the surface of the workpiece, the workpiece melts and vaporizes while absorbing energy, so it is a system containing 191
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momentum conservation equations. PIMPLE can ensure the convergence of the equation maximally even a large time steps is selected. What is more, laser processing is a transient process, PIMPLE is the most suitable algorithm for this situation. 2.2.2. Energy equation The above system must also follow the energy conservation equation. Because this model takes into account both the traditional cold processing method and the thermal effect, so two-temperature equation and ordinary heat transfer equation are all needed. ( 2 ) ) ( 𝜕𝑇 1 𝜕 1 𝜕2 𝜕 (10) + + 𝑇𝑒 − 𝑔 𝑇𝑒 − 𝑇𝑙 + 𝑆1 𝐶𝑒 𝑒 = 𝑘 𝑒 𝜕𝑡 𝑟 𝜕𝑟 𝑟2 𝜕𝑧2 𝜕𝑟2 ( 2 ) ( ) 𝜕𝑇 1 𝜕 1 𝜕2 𝜕 𝐶𝑙 𝑙 = 𝑘 𝑙 + + 𝑇𝑙 + 𝑔 𝑇𝑒 − 𝑇𝑙 (11) 𝜕𝑡 𝑟 𝜕𝑟 𝑟2 𝜕𝑧2 𝜕𝑟2 ( ) 𝜕𝑇 𝜌𝑐𝑙 = ∇ ⋅ 𝑘𝑙 ∇𝑇 + 𝑆2 (12) 𝜕𝑡 𝐶𝑒 means the electron heat capacity of alumina, which is calculated by formula 𝐶𝑒 = 𝐶0 ∗𝑇 . In the equation, 𝐶0 means electron heat capacity constant and T means the temperature of electron. It means that 𝐶𝑒 is not a constant and varies with temperature.𝐶𝑙 means the lattice heat capacity of material. Usually it can be defined as 840 J∕(kg ⋅ ◦ C) for alumina. The total energy𝑆 is assigned to two equations, which are 𝑆1 and 𝑆2 , respectively. [ ( )2 ] 𝑆 = 𝐼0 {𝑒𝑥𝑝 −4 ln (2) (𝑡 − 𝑡0 )∕𝜏 } (1 − 𝑅) 𝛼𝑒𝑥𝑝(−𝛼𝑧) (13)
Fig. 2. Surface crack of workpiece.
three phase-gas, liquid, solid. So the system must conform to the governing equation of the fluid. The general form of governing equations for the conservation of mass, momentum equation used in the whole computational domains can be expressed in the following form: 𝜕(𝜌𝑢) 𝜕(𝜌𝑣) 𝜕(𝜌𝑤) + + =0 (1) 𝜕𝑥 𝜕𝑦 𝜕𝑧 𝜕(𝜌𝑢) 𝜕𝑝 + 𝑑𝑖𝑣 (𝜌𝑢𝑢) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑢) − (2) 𝜕𝑡 𝜕𝑥 𝜕𝑝 𝜕(𝜌𝑣) + 𝑑𝑖𝑣 (𝜌𝑣𝑢) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑣) − (3) 𝜕𝑡 𝜕𝑦 𝜕(𝜌𝑤) 𝜕𝑝 + 𝑑𝑖𝑣 (𝜌𝑤𝑢) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑤) − (4) 𝜕𝑡 𝜕𝑧 But in this model, The fluid part and solid part are coupling in this model, so the method of porous media is used to modify the momentum equation as:
(6)
(1 − 𝛾)2 𝐴 = −𝐶 𝛾3 + 𝑏
(7)
where 𝐴 is the porosity function, and 𝐶 is a large constant. To avoid division by zero in the solid phase, a small numerical constant 𝑏 is introduced [17]. And in this model, the large constant 𝐶 in the Darcy type source term in the momentum conservation equation is set to 1.6 × 106 kg∕m3 s and the small constant 𝑏 is set to 1.0 × 10−3 . 𝛾 is the phase fraction ranging from zero to one, it can be described by Eq. (8). ⎧0, ⎪ 𝑇 − 𝑇𝑠 , 𝛾=⎨ ⎪ 𝑇𝑙 − 𝑇𝑠 ⎩1,
𝑇 < 𝑇𝑠 𝑇𝑠 < 𝑇 < 𝑇 𝑙
(14)
𝑆2 = 𝑆 ∗ (1 − 𝑟𝑎𝑡𝑖𝑜)
(15)
The ratio is defined as the Coulomb explosion occupying ratio of Coulomb explosion, and the next section will focus on how to get this parameter. 𝛼 is the absorption coefficient while𝐼0 indicates the peak intensity of laser. The Eqs. (10), (11) describes the cold working methods. This equation could obtain the lattice temperature which can be used as the intermediate value for solving the phase field without thermal effect. As referred above, the energy equations are separated into electron energy equation and lattice energy equation. Obviously there is a connection between the two equations: electron–phonon coupling factor. Electron will transfer energy to lattice after absorbing quite large amount of energy from laser beam. So we must face a serious problem that if time step is large then the energy transferring in every iteration may be too much to get the correct results. The problem is due to numerical error so energy should be looped under every iteration to eliminate the error. Just take a 2D model for example, The discrete equation of Eq. (10) is described as 𝑒 𝑒 𝑒 𝑒 𝑒 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1 𝐶𝑒 × = 𝑘𝑒 × 𝛥𝑡 𝛥𝑥2) ( 𝑒 𝑙 − 𝑔 × 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗+1 + 𝑆1
𝜕(𝜌𝑈 ) + ∇ ⋅ (𝜌𝑈 𝑈 ) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑈 ) − ∇𝑝 + 𝐹𝜎 + 𝑆𝑚 (5) 𝜕𝑡 And the source term is previously proposed by Voller and Prakash [16] 𝑆𝑚 = 𝐴 (𝛾) ⋅ 𝑢
𝑆1 = 𝑆 ∗ 𝑟𝑎𝑡𝑖𝑜
𝐶𝑙 ×
(8)
𝑙 𝑙 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗
𝛥𝑡
𝑇𝑠 > 𝑇𝑙
= 𝑘𝑙 ×
𝑙 𝑙 𝑙 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1
𝛥𝑥2 𝑒 𝑙 + 𝑔 × (𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗+1 )
But we do not know the electron temperature of next iteration, so we add a loop under every iteration and amend the discrete equation as following:
VOF volume method is applied to determine the phase interface, and the solution of the phase equation depends on Eq. (9). 𝜕𝛾 + ∇ ⋅ (𝛼𝑈 ) = 0 (9) 𝜕t As described above, governing equations includes three equations: mass conservation equation, momentum conservation equation and energy equations. Usually several iterations are needed to get correct pressure and velocity field so called pressure–velocity correction. PIMPLE is chosen as the pressure–velocity correction algorithm in the model. We use PIMPLE algorithm to coupling the mass conservation and
𝐶𝑒 ×
𝑒 𝑒 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗
𝛥𝑡
= 𝑘𝑒 ×
𝑒 𝑒 𝑒 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1
− 𝑔× 𝐶𝑙 ×
192
𝑙 𝑇𝑖,𝑗+1
𝑙 − 𝑇𝑖,𝑗
𝛥𝑡
= 𝑘𝑙 ×
(
𝑒 𝑇𝑖,𝑗+1
2 𝛥𝑥 ) + 𝑆1
𝑙 − 𝑇𝑖,𝑗
𝑙 𝑙 𝑙 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1
𝛥𝑥2 𝑒 𝑙 + 𝑔 × (𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗 )
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The loop to couple the two equation is: Calculate the change of 𝑇𝑒 and it of 𝑇𝑙 between every loop, when the largest change is under a small constant then stop the loop and enter the next iteration. In this kind of algorithm, not only correct temperature could be got but also time steps could be set larger to save computing resource. Eq. (13) describes thermal processing, so it has an effect on the phase field and brings a thermal effect. In this model, when solving phase, first use Eqs. (10), (11) to solve the phase, then the final processing topography is obtained by solving Eq. (12) in the solution of Eqs. (10), (11). But only the actual lattice temperature obtained by Eq. (12) is used as a parameter for solving the thermal stress. In combination with Eqs. (1), (5), (10), (11), (12), the basic model is obtained. 2.2.3. Thermal stress & crack According to the mixture model, the thermal stress can also be simulated to test whether the crack appears. It can help us with better processing quality. Displacement is calculated in thermal elastic equation: ) ( ) [ ( 𝜕𝐷𝑧 𝜕𝐷𝑥 𝜕𝐷𝑦 𝜕𝐷 𝑛𝑦 + 𝜆 𝛿𝑥𝑦 𝑛𝑦 𝐺 + 𝜌 𝑥 𝑑𝑉 = ∮ ∫𝑣 𝜕𝑡2 𝜕𝑦 𝜕𝑥 𝜕𝑧 ] ( ) (16) − 𝛤 𝑎 𝑇 − 𝑇𝑟𝑒𝑓 𝛿𝑥𝑦 𝑛𝑦 𝑑𝑆 + 𝜌𝑓𝑥 𝑑𝑉 ∫𝑣
Fig. 3. Simulation flow chart.
solve the fields according to discrete equation. Another important point laser processing is a transient problem so another iteration should go through the above process for specified times to complete solving. The result got from last time iteration is the new initial field for the next iteration. All the description can be concluded in Fig. 3. In combination with operation above, the basic numerical model is obtained.
The subscript means the phase state. 𝑇𝑙 and 𝑇𝑠 is the temperature of liquid and it of solid. 𝐷 is a field representing the displacement of every element. And the displacement is used for calculating the thermal stress. And 𝑎 is the coefficient of linear expansion. G, 𝜆 are Rahm coefficients and 𝛤 is the thermoelastic coefficient, which can be expressed by Eq. (17). ⎧ 𝐸 ⎪G = 2(1 + 𝜇) ⎪ ⎪ 𝜇𝐸 ⎨𝜆 = (1 + 𝜇)(1 − 2𝜇) ⎪ ⎪ 𝐸 ⎪𝛤 = 1 − 2𝜇 ⎩
2.3. Interpolation method to calculate energy ratio (17)
Till now the problem that has not been solved in the model is the parameter ‘‘ratio’’. A comparison between simulation and experiment is made to calculate the energy ratio. Following paragraph will clarify the general idea of how to get the energy ratio. First, a threshold should be obtained according to the experimental results. If the energy input of unit duration exceeds this threshold, Coulomb explosion is considered as the dominating way of material removal. And the energy occupying ratio of Coulomb is set as 99.9%. If the energy of a unit pulse is under the threshold, it is considered that the Coulomb explosion coexists with the thermal effect. Then, numerical simulation is carried out in this case in order to calculate the energy ratio. As it is known to us, the influence area of thermal effect is larger than that of Coulomb explosion. And the size of the slot width is determined by the thermal effect when there is a negligible thermal effect. Therefore, only the material removal caused by the thermal effect is calculated in the simulation to get approximate slot width. Then the energy in unit pulse in simulation is constantly adjusted until the slot width almost fits experimental data. Then the energy is extracted, and the energy is determined as the energy of the thermal effect. Finally, these results are interpolated as interpolation points for cubic spline curves. In this way, the relationship between energy ratio and energy in unit pulse can be obtained. The equipment used in processing is the picosecond laser generator shown in Fig. 4. And the observation equipment is the confocal microscope shown in Fig. 5. Several groups of experiments are set up by the control variable method. Processing parameters are as shown in Table 1. The processing method is laser scanning. Laser power, scanning speed, pulse width, laser wavelength and material are kept unchanged. Only the frequency is changed so as to control the change of the exact energy in unit pulse. In the end, the topography of the workpiece was measured by a confocal microscope, as shown in Fig. 6.
Once the displacement is obtained, the thermal stress can be solved by Eq. (18): ∇ ⋅ 𝜎 = ∇ ⋅ (𝐺∇D) + ∇ ⋅ [𝐺(∇𝐷)𝑇 + 𝜆𝐼𝑡𝑟(∇𝐷)]
(18)
Then the stress in the direction of 𝑥 and 𝑦 is extracted in order to determine where the crack would appear: |𝜎𝑥𝑥 | > 𝜎𝑏 𝑜𝑟 ||𝜎𝑦𝑦 || > 𝜎𝑏 | | | |
(19)
where 𝜎𝑏 is the tensile strength of material (for aluminum oxide the value is 1.9 × 108 pa). 2.2.4. Simulation method In the simulation, OPENFOAM is applied to obtain the numerical results. OPENFOAM is a software which could complete some user defined operation such as equation construction and discretion and even iterative solution method. But just like all computational fluid dynamics simulation software, we have to go through the main modules: create mesh, set the equations to be solve, equations discretization and solve the field in OPENFOAM. In this simulation in the article, the zone to be calculated is a cuboid area so hex mesh is chosen to ensure mesh quality. A meshcreator file is included in the program. And then all the equations to be solved are included. Exactly all the iteration and coupling process are defined in the form of self-programming. Till now, the equations are presented as differential forms. The most important process is equations discretization. We should choose the difference scheme and change equations into discrete equations. Then put initial field value into mesh so that all the variables are stored on the mesh. The final step is surely to 193
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Optics Communications 424 (2018) 190–197
Fig. 4. Experimental equipment (a) picosecond laser generator, (b) experimental station. Table 1 Experimental processing parameters. Laser power
Scan speed
Pulse width
Frequency
Wave length
Material
50 W
1 mm/s
1e-11s
500–100 KHz
1064 nm
Al2 O3
When frequency reaches 100 KHz, the energy is almost wholly used for Coulomb explosion effect so that the topography is the smoothest among all experimental groups above. It is valid to consider that when the 100 KHz frequency is used, the Coulomb explosion has occupied a dominant position. The energy of the unit pulse corresponding to the 100 KHz can be set as the threshold mentioned in the preceding paragraph. And the energy occupying power of the Coulomb explosion and thermal effect is obtained by using cubic spline interpolation. And the five points in Table 1 are selected as the interpolation points. The energy occupying ratios at these frequencies are roughly calculated by simulation. In addition to the energy in the unit pulse, all the simulation parameters and experimental parameters are set to the same. As shown in Table 2, the energy of each experimental group is obtained by simulation. The ‘‘ratio’’ in the table means the energy ratio of the Coulomb explosion. Final interpolated equation is obtained as Eq. (20). Power in the equation means the energy of each pulse, the unit is 1 × 107 w. Ratio in the equation means the energy ratio of the Coulomb explosion.
Fig. 5. Confocal microscope.
ratio ⎧−0.0198(𝑝𝑜𝑤 − 0.1)3 + 0.1398(𝑝𝑜𝑤 − 0.1)2 ⎪ ⎪ − 0.0553(𝑝𝑜𝑤 − 0.1) + 0.001, ⎪−0.0198(𝑝𝑜𝑤 − 1)3 + 0.0864(𝑝𝑜𝑤 − 1)2 ⎪ = ⎨ + 0.1482(𝑝𝑜𝑤 − 1) + 0.05, ⎪−0.0108(𝑝𝑜𝑤 − 2.5)3 − 0.0025(𝑝𝑜𝑤 − 2.5)2 ⎪ ⎪ + 0.274(𝑝𝑜𝑤 − 2.5) + 0.4, ⎪0.999, ⎩
0.1 < 𝑝𝑜𝑤𝑒𝑟 < 1 1 < 𝑝𝑜𝑤𝑒𝑟 < 2.5 (20) 2.5 < 𝑝𝑜𝑤𝑒𝑟 < 5 𝑝𝑜𝑤𝑒𝑟 > 5
3. Results and discussion The model has been established, but it is necessary for the model to be verified. Hence, the following validation procedures are set. First several different frequencies are selected and then the results of simulation are compared with experimental results. Finally, the model will be verified in several different aspects. Simulation is under the frequencies of 50 KHz, 350 KHz and 250 KHz in order to conclude each segment in Eq. (20). The laser parameters are the same as the experimental parameters, as shown in Table 1. And the data in Table 3 is the result of the interpolation obtained from Eq. (20) described in the previous article. The following simulation results are obtained through OPENFOAM software. And then the results are compared with the results obtained from the experiments. The contrast diagrams are shown in Figs. 7–9.
Fig. 6. Experimental groups.
From the left to the right of the figure, the frequency of the laser is 500 KHz, 400 KHz, 300 KHz, 200 KHz, 150 KHz, 100 KHz. As shown in the figure, it is difficult to process on the workpiece under a laser of 500 KHz frequency because the laser power is almost fully applied in hot ablation (The heat-affected zone is large). With the frequency decreasing, laser power during per pulse increases. So the Coulomb explosion takes more and more part in processing with smoother topography. 194
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Optics Communications 424 (2018) 190–197 Table 2 The energy occupying ratio of each experimental group obtained by simulation (The ‘‘ratio’’ in the table means the energy ratio of the Coulomb explosion). Frequency (KHz)
500
400
300
200
100
Power/pulse (W) Ratio (%) Coulomb (w) Thermal (W)
1 × 107 0.1 1 × 104 9.99 × 106
1.25 × 107 6.25 0.078 × 107 1.172 × 107
1.6 × 107 15 0.24 × 107 1.36 × 107
2.5 × 107 37.5 9.38 × 106 1.56 × 107
5 × 107 99.9 4.995 × 107 5 × 104
Fig. 7. Comparison between simulation and experimental result processing in 350 KHz. (a) simulation, (b) experiment.
Fig. 8. Comparison between simulation and experimental result processing in 150 KHz. (a) simulation, (b) experiment.
Fig. 9. Comparison between simulation and experimental result processing in 50 KHz. (a) simulation, (b) experiment.
The comparison between simulation and experiment in this paper is mainly taken into consideration from the following three aspects. The first is the width of the slot obtained by laser scanning. The second is the surface topography of the workpiece after laser scanning, and the third is the position of the surface crack after the scanning.
3.1. Width of seam
First, the slot width between the simulation results and the experimental results should be verified. The width of the simulated slot is 195
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Table 3 Interpolation result of energy occupying ratio of experimental groups (The ‘‘ratio’’ in the table means the energy ratio of the Coulomb explosion). Frequency (KHz)
50
150
350
Power/pulse (W) Ratio (%) Coulomb (w) Thermal (W)
1 × 108 99.9 1 × 106 9.9 × 107
3.3 × 107 57.5 1.4025 × 107 1.8975 × 107
1.43 × 107 12.81 1.2468 × 107 0.1832 × 107
Table 4 Comparison between simulation and experimental result of seam width. Frequency (KHz)
50
150
350
Simulation width (μm) Experimental width (μm) Error (%)
12 11.8 1.69
33 34.3 3.79
56 54.7 2.37
Fig. 10. Solid particles that fall back to the workpiece.
compared with the actual width measured by the confocal microscope. The results are shown in Table 4. It can be seen from the table above that all errors of slot width between simulation and experiments are less than five percents, which can preliminarily prove that the former interpolation method is of less error and feasible. It has been mentioned in the previous paragraph that the width of the slots depends mainly on the effect of the thermal effect when the thermal effect occupies a position that cannot be ignored. This is due to two major characteristics of hot ablation One is that the requirement of the heat effect to remove the material is relatively low. Material only needs to continuously absorb the heat to reach the melting point or the boiling point. But only when the energy in per pulse exceeds the energy threshold, can Coulomb explosion happen. Therefore, there is a smaller affected area in Coulomb explosion ablation than in hot ablation. The second is that the thermal effect has the role of heat transfer. Processed area in the center of gauss light will continuously transmit energy into the surrounding area, helping the surrounding area to complete the material removal faster. Therefore, when the frequency increases from 50 KHz to 350 KHz, the slot width changes from 11.8 μm to 54.7 μm. To sum up, it can be proved that the energy occupying ratio obtained by Eq. (20) is credible through the comparison of the simulation and the experiment.
problem that needs to be explained is why there is no such change in the diameter of the hole in Fig. 7. This is because the laser power used in 50 KHz is large enough, and Coulomb explosion almost dominates the whole process. As it is known to us, Coulomb explosion is a kind of cold working. Thus, there is no such high pressure gradient like in 50 KHz. So, there will not be a lot of flying particles, which is a good explanation for why the processing aperture has not changed in Fig. 7. The change of the diameter of the slot in the laser scanning process is also a qualitative analysis parameter for the energy ratio. From Figs. 7–9, it can be seen that the change rule of the simulation is basically the same as that of the experiment, which further proves the credibility of the simulation. 3.3. Thermal stress & crack The occurrence of the crack is due to the effect of thermal stress. So the analysis of the position of the crack is also an analysis of the energy ratio. It should be noticed that crack usually appears after hole processed. Some data is distilled from the simulation results to find the location of stress concentration region (150 KHz is applied in the simulation). As is depicted in Fig. 11, when temperature reaches 1720 degrees Kelvin, the thermal stress in direction x is about −1.948 × 108 (pa) in the stress concentration region while 1.9 × 108 (pa) is the tensile strength of aluminum oxide. The stress concentration region is near the processing region so cracks surely appear in this region and develop along scanning direction. As shown in Fig. 12, the simulation result fits the experimental result very well.
3.2. Topography Surface topography is another important factor determined by the energy ratio. It can be seen from Figs. 7 and 8 that the diameter of the slot varies with the processing direction and there is a regular change. The diameter changes from large to small, and then rises to large again. It is necessary to explain the cause of this phenomenon. This is because when there is a thermal effect, there will be a large number of phase transitions. The material will be liquefied or vaporized, or directly sublimated. Phase transitions will raise the vapor pressure to about 10 atmospheres [18]. Then, the pressure causes the splash of the molten pool and the jet of a part of the solid particles. After that, these particles will cover over the surface of the workpiece, and some falling particles will also block the laser. As shown in Fig. 10, this phenomenon has been observed in our experiments. The floc in the picture is the falling particles. Part of the energy of the laser will be used to process these particles, which leads to the fact that the actual laser energy on the surface of the workpiece is not as much as expected. Hence, the processing procedure of laser scanning can be summed up as follows: the laser starts to process at the surface, then the surface particles fly out, and the energy of the actual workpiece is reduced. Later, the laser continues to process in order to eliminate the continuously produced particles. In the end, the laser continues to move forward, and the processing state is back to the initial state. The energy of the actual irradiation on the workpiece has experienced a procedure from large to small then to large, so the diameter of the hole is of such a similar periodic regularity. Another
4. Conclusion In this paper, a new mixture model with mixed processing procedure processed in ten picosecond pulse laser is proposed. Thermal effect material removal method is mixed with Coulomb explosion material removal method in ten picosecond pulse laser processing in the model. Some approximation and fitting methods are applied to identify how much energy is applied in thermal material removal and Coulomb explosion. First, pre-experiments are made to identify the range where thermal material removal and Coulomb explosion emerge in the same laser processing procedure. Then, an approximate equation, explaining how the ratio between thermal effect and Coulomb explosion varies with energy in unit pulse, is confirmed through interpolation. In the end, the simulation data is compared with the experiment data. Based on the governing equation, the energy equation and the stress equation, a numerical simulation model is set up. The process of laser scanning is simulated, and the main data such as temperature field, phase field, stress field and so on are solved. Afterwards the model is verified from the following three directions, namely the width of the 196
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Fig. 11. Numerical simulation of thermal stress (a) temperature of workpiece (b) thermal stress of workpiece. [2] Y. Ding, J. Shao, X. Li, H. Tian, L. Miao, H. Liu, Controllable formation of nanogaps in thin metallic film by rear side irradiation with ultrashort pulsed laser, Physica E 44 (2) (2011) 430–434. [3] K. Paivasaari, J.J. Kaakkunen, M. Kuittinen, T. Jaaskelainen, Enhanced optical absorptance of metals using interferometric femtosecond ablation, Opt. Express 15 (21) (2007) 13838–13843. [4] W.Q. Han, L. Wu, Klie. R, Y. Zhu, Enhanced optical absorption induced by dense nanocavities inside titania nanorods, Adv. Mater. 19 (18) (2007) 2525–2529. [5] Y.B. Gerbig, I.U. Ahmed, D.G. Chetwynd, H. Haefke, Topography-related effects on the lubrication of nanostructured hard surfaces, Tribol. Int. 39 (9) (2006) 945–952. [6] J. Cui, L. Yang, W. Yang, X. Mei, W. Wang, C. Hou, Nanospot soldering polystyrene nanoparticles with an optical fiber probe laser irradiating a metallic afm probe based on the near-field enhancement effect, Acs Appl. Mater. Interfaces 7 (4) (2015) 2294. [7] Y.H. Chen, W.C. Lo, T.Y. Kuo, Thermal effect characterization of laser-ablated silicon-through interconnect, in: Electronic Systemintegration Technology Conference, Vol. 1, IEEE, 2006, pp. 594–599. [8] A.F. Pan, W.J. Wang, X.S. Mei, K.D. Wang, W.Q. Zhao, T.Q. Li, Laser thermal effect
Fig. 12. Surface crack on workpiece.
on silicon nitride ceramic based on thermo-chemical reaction with temperaturedependent thermo-physical parameters, Appl. Surf. Sci. 375 (2016) 90–100. [9] S.C. Mishra, R. Muthukumaran, S. Maruyama, Comparison of the thermal effects of the transport of a short-pulse laser and a multi-pulse laser through a participating medium, Int. J. Heat Mass Transfer 55 (21–22) (2012) 5583–5596. [10] W. Wang, X. Mei, G. Jiang, Control of microstructure shape and morphology in femtosecond laser ablation of imprint rollers, Int. J. Adv. Manuf. Technol. 41 (5–6)
slot, the surface topography of the processed surface and the surface crack caused by thermal stress. The surface topography has been studied from the qualitative point of view. The slot width is quantitatively studied. And the location of the surface crack is analyzed by nature and quantitative analysis method. The causes of these phenomena are analyzed from the theoretical point of view and the theoretical analysis is verified from the experimental point of view. And fortunately, the simulation model fits experiment well. The results indicate the mixture model is more accurate than traditional model. Finally, the following conclusions are obtained: (1) Not only Coulomb explosion but also thermal effect may play an important role in ten picosecond pulse laser processing procedure. (2) Errors between simulation model and experiment model are less than 5%, the accuracy is proved to be fine and the simulation model is credible.
(2009) 504–512. [11] A. Menendez-Manjon, J. Jakobi, K. Schwabe, J.K. Krauss, S. Barcikowski, Mobility of nanoparticles generated by femtosecond laser ablation in liquids and its application to surface patterning, J. Laser Micro 4 (2) (2008) 95–99. [12] Liu Bin, et al., Formation of porous structure with subspot size under the irradiation of picosecond laser pulses, J. Nanomater. 2 (2013) 11. [13] Liu Bin, et al., Porous microstructures induced by picosecond laser scanning irradiation on stainless steel surface, Opt. Lasers Eng. 78 (2016) 55–63. [14] P. Lorazo, L.J. Lewis, M. Meunier, Simulation of picosecond pulsed laser ablation of silicon: the molecular-dynamics thermal-annealing model, in: Photonics West 2001LASE, International Society for Optics and Photonics, 2001. [15] X. Wang, X. Xu, Molecular dynamics simulation of thermal and thermomechanical phenomena in picosecond laser material interaction, Int. J. Heat Mass Transfer 46 (1) (2003) 45–53.
Acknowledgments
[16] V.R. Voller, C. Prakash, A fixed grid numerical modelling methodology for convection–diffusion mushy region phase-change problems, Int. J. Heat Mass Transfer 30 (8) (1987) 1709–1719. [17] F. Rösler, D. Brüggemann, Shell-and-tube type latent heat thermal energy storage: Numerical analysis and comparison with experiments, Heat Mass Transfer 47 (8) (2011) 1027–1033. [18] Charles J. Knight, Theoretical modeling of rapid surface vaporization with back
This work was supported by The National Key Research and Development Program of China (grant no. 2016YFB1102500). References
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[1] B.N. Chichkov, C. Momma, S. Nolte, F.V. Alvensleben, A. Tünnermann, Femtosecond, picosecond and nanosecond laser ablation of solids, Appl. Phys. A 63 (2) (1996) 109–115.
197
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Analysis of energy occupying ratio of Coulomb explosion and thermal effect in picosecond pulse laser processing Zongji Zheng *, Chengjun Wu, Siyuan Liu, Xianbin Yang School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, PR China
ARTICLE
INFO
Keywords: Ten picosecond laser processing Coulomb explosion Thermal effect Numerical simulation Energy occupying ratio
ABSTRACT Molten material recasting may occur in ten picosecond laser processing although ultrashort-pulse processing is a kind of cold working method. It is also proved that experimental results do not fit expected processing results well in ten picosecond laser processing. What is more, some cracks on the surface of workpiece processed in ten picosecond laser can be observed. Aimed at above-mentioned facts processing in ten picosecond laser, a new hybrid model is raised. In this model, not only Coulomb explosion which is known to us but also thermal effect occurs in ten picosecond laser processing. Experiment method is used for analyzing the energy ratio of the two parts (Coulomb explosion and thermal effect). With OPENFOAM simulation software, the radius, topography and crack location of slots processed in different energy density are simulated. Finally, a comparison between simulation result and experimental result proves that this hybrid model is high degree of applicability and accuracy.
1. Introduction The application of laser ablation in different materials including metal is of great interest. With the appearance of ultrashort laser in 1990s, material/metal surface texturing gained a whole new dimension. From that moment, it became possible to touch three time regimes of pulse from femtosecond to nanosecond [1]. When time regimes of pulse are in fs–ns then laser processing can be divided into two categories, the first one is short-pulse laser processing, which is of high precision and efficiency. And the second one is ultrashort-pulse laser processing, which is of higher precision but lower efficiency [2–4]. For pursuing the precision, ultrashort-pulse laser is applied in more and more situations [5,6]. The major factor to distinguish short-pulse laser and ultrashort-pulse laser is the relationship between pulse duration and the relaxation time of materials. If the pulse duration is less than the relaxation time of materials, then the laser is defined as ultrashortpulse laser. Otherwise the laser is defined as short-pulse laser. And the relaxation time of materials depends on the property of their lattice, usually the critical value is about ten picoseconds. Usually ultrashortpulse laser processing is defined as a kind of cold ablation but sometimes processing with heat and short pulse laser processing is almost wholly due to thermal effect. For the past decades, the mechanism research of short pulse laser processing has already had quite a lot of previous accumulation, and it
has been verified on various materials by various processing methods. Many scholars have made a detailed analysis of thermal effect in short pulse laser ablation processing and the influencing factors of the processing. Chen et al. [7] Chose laser drilling process to make the efficient through holes in his research, which is based on hole drilling in silicon wafer by short pulse laser. Thermal and mechanical effects on silicon wafer induced by laser drilling were analyzed was characterized under optical microscopy, scanning electron microscopy and energy dispersive spectroscope. Aifei Pan et al. [8] Raised a two-dimensional thermochemical reaction model with temperature-dependent thermo-physical parameters on Si3N4 with 10 ns laser to investigate the ablated size, volume and surface morphology after single pulse. What is more, In SC Mishra’s paper [9], temporal evolutions of transmittance and reflectance signals, and incident radiation at various locations in the planar medium are studied for a wide range of the values of the extinction coefficient. The problem is analyzed using both the finite volume method and the discrete ordinates method. As a representative of cold ablation, mechanism and application of femtosecond pulse laser is widely studied. In Wang’s paper [10], the effects of processing parameters on the shape and morphology of microstructures in femtosecond laser fabrication of imprint roller are explored. An optimized fabrication process is proposed to acquire high accuracy microstructures. Menendez et al. [11] Studied Electrophoretic
* Correspondence to: Institute of Vibration and Noise Control, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China. E-mail addresses: [email protected] (Z. Zheng), [email protected] (X. Yang).
https://doi.org/10.1016/j.optcom.2018.04.045 Received 6 February 2018; Received in revised form 3 April 2018; Accepted 17 April 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
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Optics Communications 424 (2018) 190–197
mobility of laser-generated metal nanoparticles by laser scattering velocimetry and used the electrophoretic deposition of charged nanoparticles to generate nanoparticle-derived nanostructures on 3-dimensional micro-structured surfaces. Picosecond laser has characteristic of thermal accumulation and sometimes thermal will influence the topography of the materials. Liu [12,13] studied picosecond laser processing on porous structure with micro-size holes. After serious experiments, two kinds of porous structures were presented: periodic holes are formed from Coulomb Explosion during locally spatial modulated ablation, and random holes are formed from the burst of bubbles in overheated liquid during phase explosion. That means thermal effect exists in ps laser indeed. But even a large number of scholars have made much constructive experimental study of it, the study of picosecond pulse laser processing is still not enough. With the development of ultrashort laser technology, ten picosecond pulse laser can obtain dozens of micro joules energy. And in 10 ps laser the repetition frequency can reach MHz level. For common materials such as metal, semiconductor and dielectric, their relaxation time depends on the property of their lattice, usually the critical value is about ten picoseconds. So as long as laser duration is under ten picoseconds, there is no photon induction and thermal diffusion. Basic experimental research shows that picosecond laser is of high efficiency and owns unique implement advance. But as discussed above, 10 ps laser processing is a critical laser between hot and cold ablation. So this may lead to only merely hot ablation or totally cold ablation or even both. As a result of lying in the critical value, some phenomenon such as thermal stress and molten material recasting and surface crack may occur in picosecond laser processing. This is the main reason of the poor mechanism and controllability of picosecond laser. In accordance with the thermal annealing model (TAM), Lorazo et al. [14] Give a detailed description of the microscopic processes resulting from the interaction of a 308 nm, 10 ps, Gaussian pulse with a Si (100) substrate. What is more, in his paper, temperature gradient calculated by two-temperature model and pressure gradient due to thermal effect is obtained. In Wang’s paper [15], molecular dynamics (MD) simulations are conducted to study the thermal and thermomechanical phenomena induced by picosecond laser heating. He revealed thermal accumulation in picosecond processing and obtained temperature and strain due to thermal accumulation. They described the thermal accumulation and thermal effect in ten picosecond laser processing and explained the thermal effect in detail. Although the explanations are correct but concrete energy occupying ratio of Coulomb explosion and thermal effect is not obtained in their models. What is more, there is not necessary numerical verification for the thermal distribution. Based on this research status, in this paper, a new hybrid model for laser processing in 10 picosecond pulse duration and high pulse repetition is proposed. In this model, it is considered that both Coulomb explosion and thermal effect may take part in 10 picosecond laser processing. The energy occupying ratio of the two material removal method is related to the energy of each pulse according to our research. And the interpolation method is applied to estimate the relationship to guide the processing better.
Fig. 1. Molten material recasting.
Just take ten picosecond laser for experiments, when some energy densities are applied, an unusual phenomenon shown in Fig. 1 is observed through confocal laser scanning microscope that a large quantity of molten materials recast on the surface of the processed material. What is more, solid produced by condensation of a molten material is shaped like a droplet. The phenomenon means that phase transition occurs in processing procedure. But in former view, the main method of material removal in 10 picosecond laser does not include phase transition due to thermal effects. So the phenomenon does not fit the cold working characteristic of ultrashort-pulse laser. Another important phenomenon should be paid enough attention to. As it is known to us, laser is a kind of gauss light with very ultrashort action time so the affected area should be far less than the laser spot diameter after focusing. But it can be clearly seen in Fig. 2 through experiments that the affected area is almost equal to the spot diameter under several frequencies. It is clearly that the thermal effect plays a very important role in the processing procedure. What is more, in the previous point of view, the surface of workpiece processed in cold working method should be flat because there is almost no thermal stress in processing procedure. But the results from the experimental observation shown in Fig. 2 are not very optimistic. In some experimental groups, surface cracks are observed on the surface of the workpiece. It is obviously that the energy of the laser heating raises the temperature of the material, resulting in thermal stress which leads to the cracks of the surface of the material. In another word, there is also a thermal effect in 10 picosecond laser processing. One thing to be emphasized is that the total energy of the laser is certain. In the presence of the thermal effect, the energy of the Coulomb explosion is not the full source of energy. It is regrettable that the specific energy ratio is not yet conclusive. However, if the approximate energy ratio can be determined, the actual production process can be better guided and the quality of processing can be controlled more accurately. The main reason for the existence of thermal effect is that the occurrence of Coulomb explosion requires certain conditions: It is necessary to deliver enough energy to electrons in quite a short time. Only in this way can the electrons become excited electrons and convert the absorbed energy into the kinetic energy of the electrons. After that, the Coulomb force between the electrons and the nucleus traces the nuclear movement then the strong interaction force between the nuclei traces the other atomic movements and eventually removes the material. If the energy is not enough, it is obvious that Coulomb explosion can hardly happen. Therefore, the key issue is to determine the energy ratio of the Coulomb explosion and thermal effect in ultrashort-pulse laser.
2. Basic theory 2.1. Discussion about materials removal method in 10 picosecond laser processing In traditional view, ultrashort-pulse laser processing is defined as a kind of cold working method. And Coulomb explosion is the unique mechanism of action in processing procedure. But when the duration of laser is around ten picoseconds, the fact is that not only Coulomb explosion but also thermal effect plays an indispensable role in processing.
2.2. Mathematical model 2.2.1. Governing equation & porous medium When the laser irradiates the surface of the workpiece, the workpiece melts and vaporizes while absorbing energy, so it is a system containing 191
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momentum conservation equations. PIMPLE can ensure the convergence of the equation maximally even a large time steps is selected. What is more, laser processing is a transient process, PIMPLE is the most suitable algorithm for this situation. 2.2.2. Energy equation The above system must also follow the energy conservation equation. Because this model takes into account both the traditional cold processing method and the thermal effect, so two-temperature equation and ordinary heat transfer equation are all needed. ( 2 ) ) ( 𝜕𝑇 1 𝜕 1 𝜕2 𝜕 (10) + + 𝑇𝑒 − 𝑔 𝑇𝑒 − 𝑇𝑙 + 𝑆1 𝐶𝑒 𝑒 = 𝑘 𝑒 𝜕𝑡 𝑟 𝜕𝑟 𝑟2 𝜕𝑧2 𝜕𝑟2 ( 2 ) ( ) 𝜕𝑇 1 𝜕 1 𝜕2 𝜕 𝐶𝑙 𝑙 = 𝑘 𝑙 + + 𝑇𝑙 + 𝑔 𝑇𝑒 − 𝑇𝑙 (11) 𝜕𝑡 𝑟 𝜕𝑟 𝑟2 𝜕𝑧2 𝜕𝑟2 ( ) 𝜕𝑇 𝜌𝑐𝑙 = ∇ ⋅ 𝑘𝑙 ∇𝑇 + 𝑆2 (12) 𝜕𝑡 𝐶𝑒 means the electron heat capacity of alumina, which is calculated by formula 𝐶𝑒 = 𝐶0 ∗𝑇 . In the equation, 𝐶0 means electron heat capacity constant and T means the temperature of electron. It means that 𝐶𝑒 is not a constant and varies with temperature.𝐶𝑙 means the lattice heat capacity of material. Usually it can be defined as 840 J∕(kg ⋅ ◦ C) for alumina. The total energy𝑆 is assigned to two equations, which are 𝑆1 and 𝑆2 , respectively. [ ( )2 ] 𝑆 = 𝐼0 {𝑒𝑥𝑝 −4 ln (2) (𝑡 − 𝑡0 )∕𝜏 } (1 − 𝑅) 𝛼𝑒𝑥𝑝(−𝛼𝑧) (13)
Fig. 2. Surface crack of workpiece.
three phase-gas, liquid, solid. So the system must conform to the governing equation of the fluid. The general form of governing equations for the conservation of mass, momentum equation used in the whole computational domains can be expressed in the following form: 𝜕(𝜌𝑢) 𝜕(𝜌𝑣) 𝜕(𝜌𝑤) + + =0 (1) 𝜕𝑥 𝜕𝑦 𝜕𝑧 𝜕(𝜌𝑢) 𝜕𝑝 + 𝑑𝑖𝑣 (𝜌𝑢𝑢) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑢) − (2) 𝜕𝑡 𝜕𝑥 𝜕𝑝 𝜕(𝜌𝑣) + 𝑑𝑖𝑣 (𝜌𝑣𝑢) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑣) − (3) 𝜕𝑡 𝜕𝑦 𝜕(𝜌𝑤) 𝜕𝑝 + 𝑑𝑖𝑣 (𝜌𝑤𝑢) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑤) − (4) 𝜕𝑡 𝜕𝑧 But in this model, The fluid part and solid part are coupling in this model, so the method of porous media is used to modify the momentum equation as:
(6)
(1 − 𝛾)2 𝐴 = −𝐶 𝛾3 + 𝑏
(7)
where 𝐴 is the porosity function, and 𝐶 is a large constant. To avoid division by zero in the solid phase, a small numerical constant 𝑏 is introduced [17]. And in this model, the large constant 𝐶 in the Darcy type source term in the momentum conservation equation is set to 1.6 × 106 kg∕m3 s and the small constant 𝑏 is set to 1.0 × 10−3 . 𝛾 is the phase fraction ranging from zero to one, it can be described by Eq. (8). ⎧0, ⎪ 𝑇 − 𝑇𝑠 , 𝛾=⎨ ⎪ 𝑇𝑙 − 𝑇𝑠 ⎩1,
𝑇 < 𝑇𝑠 𝑇𝑠 < 𝑇 < 𝑇 𝑙
(14)
𝑆2 = 𝑆 ∗ (1 − 𝑟𝑎𝑡𝑖𝑜)
(15)
The ratio is defined as the Coulomb explosion occupying ratio of Coulomb explosion, and the next section will focus on how to get this parameter. 𝛼 is the absorption coefficient while𝐼0 indicates the peak intensity of laser. The Eqs. (10), (11) describes the cold working methods. This equation could obtain the lattice temperature which can be used as the intermediate value for solving the phase field without thermal effect. As referred above, the energy equations are separated into electron energy equation and lattice energy equation. Obviously there is a connection between the two equations: electron–phonon coupling factor. Electron will transfer energy to lattice after absorbing quite large amount of energy from laser beam. So we must face a serious problem that if time step is large then the energy transferring in every iteration may be too much to get the correct results. The problem is due to numerical error so energy should be looped under every iteration to eliminate the error. Just take a 2D model for example, The discrete equation of Eq. (10) is described as 𝑒 𝑒 𝑒 𝑒 𝑒 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1 𝐶𝑒 × = 𝑘𝑒 × 𝛥𝑡 𝛥𝑥2) ( 𝑒 𝑙 − 𝑔 × 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗+1 + 𝑆1
𝜕(𝜌𝑈 ) + ∇ ⋅ (𝜌𝑈 𝑈 ) = 𝑑𝑖𝑣 (𝜂 ⋅ 𝑔𝑟𝑎𝑑𝑈 ) − ∇𝑝 + 𝐹𝜎 + 𝑆𝑚 (5) 𝜕𝑡 And the source term is previously proposed by Voller and Prakash [16] 𝑆𝑚 = 𝐴 (𝛾) ⋅ 𝑢
𝑆1 = 𝑆 ∗ 𝑟𝑎𝑡𝑖𝑜
𝐶𝑙 ×
(8)
𝑙 𝑙 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗
𝛥𝑡
𝑇𝑠 > 𝑇𝑙
= 𝑘𝑙 ×
𝑙 𝑙 𝑙 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1
𝛥𝑥2 𝑒 𝑙 + 𝑔 × (𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗+1 )
But we do not know the electron temperature of next iteration, so we add a loop under every iteration and amend the discrete equation as following:
VOF volume method is applied to determine the phase interface, and the solution of the phase equation depends on Eq. (9). 𝜕𝛾 + ∇ ⋅ (𝛼𝑈 ) = 0 (9) 𝜕t As described above, governing equations includes three equations: mass conservation equation, momentum conservation equation and energy equations. Usually several iterations are needed to get correct pressure and velocity field so called pressure–velocity correction. PIMPLE is chosen as the pressure–velocity correction algorithm in the model. We use PIMPLE algorithm to coupling the mass conservation and
𝐶𝑒 ×
𝑒 𝑒 𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗
𝛥𝑡
= 𝑘𝑒 ×
𝑒 𝑒 𝑒 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1
− 𝑔× 𝐶𝑙 ×
192
𝑙 𝑇𝑖,𝑗+1
𝑙 − 𝑇𝑖,𝑗
𝛥𝑡
= 𝑘𝑙 ×
(
𝑒 𝑇𝑖,𝑗+1
2 𝛥𝑥 ) + 𝑆1
𝑙 − 𝑇𝑖,𝑗
𝑙 𝑙 𝑙 𝑇𝑖+1,𝑗+1 − 2 × 𝑇𝑖,𝑗+1 + 𝑇𝑖−1,𝑗+1
𝛥𝑥2 𝑒 𝑙 + 𝑔 × (𝑇𝑖,𝑗+1 − 𝑇𝑖,𝑗 )
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Optics Communications 424 (2018) 190–197
The loop to couple the two equation is: Calculate the change of 𝑇𝑒 and it of 𝑇𝑙 between every loop, when the largest change is under a small constant then stop the loop and enter the next iteration. In this kind of algorithm, not only correct temperature could be got but also time steps could be set larger to save computing resource. Eq. (13) describes thermal processing, so it has an effect on the phase field and brings a thermal effect. In this model, when solving phase, first use Eqs. (10), (11) to solve the phase, then the final processing topography is obtained by solving Eq. (12) in the solution of Eqs. (10), (11). But only the actual lattice temperature obtained by Eq. (12) is used as a parameter for solving the thermal stress. In combination with Eqs. (1), (5), (10), (11), (12), the basic model is obtained. 2.2.3. Thermal stress & crack According to the mixture model, the thermal stress can also be simulated to test whether the crack appears. It can help us with better processing quality. Displacement is calculated in thermal elastic equation: ) ( ) [ ( 𝜕𝐷𝑧 𝜕𝐷𝑥 𝜕𝐷𝑦 𝜕𝐷 𝑛𝑦 + 𝜆 𝛿𝑥𝑦 𝑛𝑦 𝐺 + 𝜌 𝑥 𝑑𝑉 = ∮ ∫𝑣 𝜕𝑡2 𝜕𝑦 𝜕𝑥 𝜕𝑧 ] ( ) (16) − 𝛤 𝑎 𝑇 − 𝑇𝑟𝑒𝑓 𝛿𝑥𝑦 𝑛𝑦 𝑑𝑆 + 𝜌𝑓𝑥 𝑑𝑉 ∫𝑣
Fig. 3. Simulation flow chart.
solve the fields according to discrete equation. Another important point laser processing is a transient problem so another iteration should go through the above process for specified times to complete solving. The result got from last time iteration is the new initial field for the next iteration. All the description can be concluded in Fig. 3. In combination with operation above, the basic numerical model is obtained.
The subscript means the phase state. 𝑇𝑙 and 𝑇𝑠 is the temperature of liquid and it of solid. 𝐷 is a field representing the displacement of every element. And the displacement is used for calculating the thermal stress. And 𝑎 is the coefficient of linear expansion. G, 𝜆 are Rahm coefficients and 𝛤 is the thermoelastic coefficient, which can be expressed by Eq. (17). ⎧ 𝐸 ⎪G = 2(1 + 𝜇) ⎪ ⎪ 𝜇𝐸 ⎨𝜆 = (1 + 𝜇)(1 − 2𝜇) ⎪ ⎪ 𝐸 ⎪𝛤 = 1 − 2𝜇 ⎩
2.3. Interpolation method to calculate energy ratio (17)
Till now the problem that has not been solved in the model is the parameter ‘‘ratio’’. A comparison between simulation and experiment is made to calculate the energy ratio. Following paragraph will clarify the general idea of how to get the energy ratio. First, a threshold should be obtained according to the experimental results. If the energy input of unit duration exceeds this threshold, Coulomb explosion is considered as the dominating way of material removal. And the energy occupying ratio of Coulomb is set as 99.9%. If the energy of a unit pulse is under the threshold, it is considered that the Coulomb explosion coexists with the thermal effect. Then, numerical simulation is carried out in this case in order to calculate the energy ratio. As it is known to us, the influence area of thermal effect is larger than that of Coulomb explosion. And the size of the slot width is determined by the thermal effect when there is a negligible thermal effect. Therefore, only the material removal caused by the thermal effect is calculated in the simulation to get approximate slot width. Then the energy in unit pulse in simulation is constantly adjusted until the slot width almost fits experimental data. Then the energy is extracted, and the energy is determined as the energy of the thermal effect. Finally, these results are interpolated as interpolation points for cubic spline curves. In this way, the relationship between energy ratio and energy in unit pulse can be obtained. The equipment used in processing is the picosecond laser generator shown in Fig. 4. And the observation equipment is the confocal microscope shown in Fig. 5. Several groups of experiments are set up by the control variable method. Processing parameters are as shown in Table 1. The processing method is laser scanning. Laser power, scanning speed, pulse width, laser wavelength and material are kept unchanged. Only the frequency is changed so as to control the change of the exact energy in unit pulse. In the end, the topography of the workpiece was measured by a confocal microscope, as shown in Fig. 6.
Once the displacement is obtained, the thermal stress can be solved by Eq. (18): ∇ ⋅ 𝜎 = ∇ ⋅ (𝐺∇D) + ∇ ⋅ [𝐺(∇𝐷)𝑇 + 𝜆𝐼𝑡𝑟(∇𝐷)]
(18)
Then the stress in the direction of 𝑥 and 𝑦 is extracted in order to determine where the crack would appear: |𝜎𝑥𝑥 | > 𝜎𝑏 𝑜𝑟 ||𝜎𝑦𝑦 || > 𝜎𝑏 | | | |
(19)
where 𝜎𝑏 is the tensile strength of material (for aluminum oxide the value is 1.9 × 108 pa). 2.2.4. Simulation method In the simulation, OPENFOAM is applied to obtain the numerical results. OPENFOAM is a software which could complete some user defined operation such as equation construction and discretion and even iterative solution method. But just like all computational fluid dynamics simulation software, we have to go through the main modules: create mesh, set the equations to be solve, equations discretization and solve the field in OPENFOAM. In this simulation in the article, the zone to be calculated is a cuboid area so hex mesh is chosen to ensure mesh quality. A meshcreator file is included in the program. And then all the equations to be solved are included. Exactly all the iteration and coupling process are defined in the form of self-programming. Till now, the equations are presented as differential forms. The most important process is equations discretization. We should choose the difference scheme and change equations into discrete equations. Then put initial field value into mesh so that all the variables are stored on the mesh. The final step is surely to 193
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Fig. 4. Experimental equipment (a) picosecond laser generator, (b) experimental station. Table 1 Experimental processing parameters. Laser power
Scan speed
Pulse width
Frequency
Wave length
Material
50 W
1 mm/s
1e-11s
500–100 KHz
1064 nm
Al2 O3
When frequency reaches 100 KHz, the energy is almost wholly used for Coulomb explosion effect so that the topography is the smoothest among all experimental groups above. It is valid to consider that when the 100 KHz frequency is used, the Coulomb explosion has occupied a dominant position. The energy of the unit pulse corresponding to the 100 KHz can be set as the threshold mentioned in the preceding paragraph. And the energy occupying power of the Coulomb explosion and thermal effect is obtained by using cubic spline interpolation. And the five points in Table 1 are selected as the interpolation points. The energy occupying ratios at these frequencies are roughly calculated by simulation. In addition to the energy in the unit pulse, all the simulation parameters and experimental parameters are set to the same. As shown in Table 2, the energy of each experimental group is obtained by simulation. The ‘‘ratio’’ in the table means the energy ratio of the Coulomb explosion. Final interpolated equation is obtained as Eq. (20). Power in the equation means the energy of each pulse, the unit is 1 × 107 w. Ratio in the equation means the energy ratio of the Coulomb explosion.
Fig. 5. Confocal microscope.
ratio ⎧−0.0198(𝑝𝑜𝑤 − 0.1)3 + 0.1398(𝑝𝑜𝑤 − 0.1)2 ⎪ ⎪ − 0.0553(𝑝𝑜𝑤 − 0.1) + 0.001, ⎪−0.0198(𝑝𝑜𝑤 − 1)3 + 0.0864(𝑝𝑜𝑤 − 1)2 ⎪ = ⎨ + 0.1482(𝑝𝑜𝑤 − 1) + 0.05, ⎪−0.0108(𝑝𝑜𝑤 − 2.5)3 − 0.0025(𝑝𝑜𝑤 − 2.5)2 ⎪ ⎪ + 0.274(𝑝𝑜𝑤 − 2.5) + 0.4, ⎪0.999, ⎩
0.1 < 𝑝𝑜𝑤𝑒𝑟 < 1 1 < 𝑝𝑜𝑤𝑒𝑟 < 2.5 (20) 2.5 < 𝑝𝑜𝑤𝑒𝑟 < 5 𝑝𝑜𝑤𝑒𝑟 > 5
3. Results and discussion The model has been established, but it is necessary for the model to be verified. Hence, the following validation procedures are set. First several different frequencies are selected and then the results of simulation are compared with experimental results. Finally, the model will be verified in several different aspects. Simulation is under the frequencies of 50 KHz, 350 KHz and 250 KHz in order to conclude each segment in Eq. (20). The laser parameters are the same as the experimental parameters, as shown in Table 1. And the data in Table 3 is the result of the interpolation obtained from Eq. (20) described in the previous article. The following simulation results are obtained through OPENFOAM software. And then the results are compared with the results obtained from the experiments. The contrast diagrams are shown in Figs. 7–9.
Fig. 6. Experimental groups.
From the left to the right of the figure, the frequency of the laser is 500 KHz, 400 KHz, 300 KHz, 200 KHz, 150 KHz, 100 KHz. As shown in the figure, it is difficult to process on the workpiece under a laser of 500 KHz frequency because the laser power is almost fully applied in hot ablation (The heat-affected zone is large). With the frequency decreasing, laser power during per pulse increases. So the Coulomb explosion takes more and more part in processing with smoother topography. 194
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Optics Communications 424 (2018) 190–197 Table 2 The energy occupying ratio of each experimental group obtained by simulation (The ‘‘ratio’’ in the table means the energy ratio of the Coulomb explosion). Frequency (KHz)
500
400
300
200
100
Power/pulse (W) Ratio (%) Coulomb (w) Thermal (W)
1 × 107 0.1 1 × 104 9.99 × 106
1.25 × 107 6.25 0.078 × 107 1.172 × 107
1.6 × 107 15 0.24 × 107 1.36 × 107
2.5 × 107 37.5 9.38 × 106 1.56 × 107
5 × 107 99.9 4.995 × 107 5 × 104
Fig. 7. Comparison between simulation and experimental result processing in 350 KHz. (a) simulation, (b) experiment.
Fig. 8. Comparison between simulation and experimental result processing in 150 KHz. (a) simulation, (b) experiment.
Fig. 9. Comparison between simulation and experimental result processing in 50 KHz. (a) simulation, (b) experiment.
The comparison between simulation and experiment in this paper is mainly taken into consideration from the following three aspects. The first is the width of the slot obtained by laser scanning. The second is the surface topography of the workpiece after laser scanning, and the third is the position of the surface crack after the scanning.
3.1. Width of seam
First, the slot width between the simulation results and the experimental results should be verified. The width of the simulated slot is 195
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Optics Communications 424 (2018) 190–197
Table 3 Interpolation result of energy occupying ratio of experimental groups (The ‘‘ratio’’ in the table means the energy ratio of the Coulomb explosion). Frequency (KHz)
50
150
350
Power/pulse (W) Ratio (%) Coulomb (w) Thermal (W)
1 × 108 99.9 1 × 106 9.9 × 107
3.3 × 107 57.5 1.4025 × 107 1.8975 × 107
1.43 × 107 12.81 1.2468 × 107 0.1832 × 107
Table 4 Comparison between simulation and experimental result of seam width. Frequency (KHz)
50
150
350
Simulation width (μm) Experimental width (μm) Error (%)
12 11.8 1.69
33 34.3 3.79
56 54.7 2.37
Fig. 10. Solid particles that fall back to the workpiece.
compared with the actual width measured by the confocal microscope. The results are shown in Table 4. It can be seen from the table above that all errors of slot width between simulation and experiments are less than five percents, which can preliminarily prove that the former interpolation method is of less error and feasible. It has been mentioned in the previous paragraph that the width of the slots depends mainly on the effect of the thermal effect when the thermal effect occupies a position that cannot be ignored. This is due to two major characteristics of hot ablation One is that the requirement of the heat effect to remove the material is relatively low. Material only needs to continuously absorb the heat to reach the melting point or the boiling point. But only when the energy in per pulse exceeds the energy threshold, can Coulomb explosion happen. Therefore, there is a smaller affected area in Coulomb explosion ablation than in hot ablation. The second is that the thermal effect has the role of heat transfer. Processed area in the center of gauss light will continuously transmit energy into the surrounding area, helping the surrounding area to complete the material removal faster. Therefore, when the frequency increases from 50 KHz to 350 KHz, the slot width changes from 11.8 μm to 54.7 μm. To sum up, it can be proved that the energy occupying ratio obtained by Eq. (20) is credible through the comparison of the simulation and the experiment.
problem that needs to be explained is why there is no such change in the diameter of the hole in Fig. 7. This is because the laser power used in 50 KHz is large enough, and Coulomb explosion almost dominates the whole process. As it is known to us, Coulomb explosion is a kind of cold working. Thus, there is no such high pressure gradient like in 50 KHz. So, there will not be a lot of flying particles, which is a good explanation for why the processing aperture has not changed in Fig. 7. The change of the diameter of the slot in the laser scanning process is also a qualitative analysis parameter for the energy ratio. From Figs. 7–9, it can be seen that the change rule of the simulation is basically the same as that of the experiment, which further proves the credibility of the simulation. 3.3. Thermal stress & crack The occurrence of the crack is due to the effect of thermal stress. So the analysis of the position of the crack is also an analysis of the energy ratio. It should be noticed that crack usually appears after hole processed. Some data is distilled from the simulation results to find the location of stress concentration region (150 KHz is applied in the simulation). As is depicted in Fig. 11, when temperature reaches 1720 degrees Kelvin, the thermal stress in direction x is about −1.948 × 108 (pa) in the stress concentration region while 1.9 × 108 (pa) is the tensile strength of aluminum oxide. The stress concentration region is near the processing region so cracks surely appear in this region and develop along scanning direction. As shown in Fig. 12, the simulation result fits the experimental result very well.
3.2. Topography Surface topography is another important factor determined by the energy ratio. It can be seen from Figs. 7 and 8 that the diameter of the slot varies with the processing direction and there is a regular change. The diameter changes from large to small, and then rises to large again. It is necessary to explain the cause of this phenomenon. This is because when there is a thermal effect, there will be a large number of phase transitions. The material will be liquefied or vaporized, or directly sublimated. Phase transitions will raise the vapor pressure to about 10 atmospheres [18]. Then, the pressure causes the splash of the molten pool and the jet of a part of the solid particles. After that, these particles will cover over the surface of the workpiece, and some falling particles will also block the laser. As shown in Fig. 10, this phenomenon has been observed in our experiments. The floc in the picture is the falling particles. Part of the energy of the laser will be used to process these particles, which leads to the fact that the actual laser energy on the surface of the workpiece is not as much as expected. Hence, the processing procedure of laser scanning can be summed up as follows: the laser starts to process at the surface, then the surface particles fly out, and the energy of the actual workpiece is reduced. Later, the laser continues to process in order to eliminate the continuously produced particles. In the end, the laser continues to move forward, and the processing state is back to the initial state. The energy of the actual irradiation on the workpiece has experienced a procedure from large to small then to large, so the diameter of the hole is of such a similar periodic regularity. Another
4. Conclusion In this paper, a new mixture model with mixed processing procedure processed in ten picosecond pulse laser is proposed. Thermal effect material removal method is mixed with Coulomb explosion material removal method in ten picosecond pulse laser processing in the model. Some approximation and fitting methods are applied to identify how much energy is applied in thermal material removal and Coulomb explosion. First, pre-experiments are made to identify the range where thermal material removal and Coulomb explosion emerge in the same laser processing procedure. Then, an approximate equation, explaining how the ratio between thermal effect and Coulomb explosion varies with energy in unit pulse, is confirmed through interpolation. In the end, the simulation data is compared with the experiment data. Based on the governing equation, the energy equation and the stress equation, a numerical simulation model is set up. The process of laser scanning is simulated, and the main data such as temperature field, phase field, stress field and so on are solved. Afterwards the model is verified from the following three directions, namely the width of the 196
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Fig. 11. Numerical simulation of thermal stress (a) temperature of workpiece (b) thermal stress of workpiece. [2] Y. Ding, J. Shao, X. Li, H. Tian, L. Miao, H. Liu, Controllable formation of nanogaps in thin metallic film by rear side irradiation with ultrashort pulsed laser, Physica E 44 (2) (2011) 430–434. [3] K. Paivasaari, J.J. Kaakkunen, M. Kuittinen, T. Jaaskelainen, Enhanced optical absorptance of metals using interferometric femtosecond ablation, Opt. Express 15 (21) (2007) 13838–13843. [4] W.Q. Han, L. Wu, Klie. R, Y. Zhu, Enhanced optical absorption induced by dense nanocavities inside titania nanorods, Adv. Mater. 19 (18) (2007) 2525–2529. [5] Y.B. Gerbig, I.U. Ahmed, D.G. Chetwynd, H. Haefke, Topography-related effects on the lubrication of nanostructured hard surfaces, Tribol. Int. 39 (9) (2006) 945–952. [6] J. Cui, L. Yang, W. Yang, X. Mei, W. Wang, C. Hou, Nanospot soldering polystyrene nanoparticles with an optical fiber probe laser irradiating a metallic afm probe based on the near-field enhancement effect, Acs Appl. Mater. Interfaces 7 (4) (2015) 2294. [7] Y.H. Chen, W.C. Lo, T.Y. Kuo, Thermal effect characterization of laser-ablated silicon-through interconnect, in: Electronic Systemintegration Technology Conference, Vol. 1, IEEE, 2006, pp. 594–599. [8] A.F. Pan, W.J. Wang, X.S. Mei, K.D. Wang, W.Q. Zhao, T.Q. Li, Laser thermal effect
Fig. 12. Surface crack on workpiece.
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slot, the surface topography of the processed surface and the surface crack caused by thermal stress. The surface topography has been studied from the qualitative point of view. The slot width is quantitatively studied. And the location of the surface crack is analyzed by nature and quantitative analysis method. The causes of these phenomena are analyzed from the theoretical point of view and the theoretical analysis is verified from the experimental point of view. And fortunately, the simulation model fits experiment well. The results indicate the mixture model is more accurate than traditional model. Finally, the following conclusions are obtained: (1) Not only Coulomb explosion but also thermal effect may play an important role in ten picosecond pulse laser processing procedure. (2) Errors between simulation model and experiment model are less than 5%, the accuracy is proved to be fine and the simulation model is credible.
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Acknowledgments
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