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Abstract
An experimental and numerical study on 10 ps laser ablation of 316 L stainless steel up to 400 hundred pulse exposure has been carried out. In this simulation, the material removal threshold temperature has been carefully discussed depending on the different ablation driving mechanisms. The influence of the instantaneous material removal has also been considered which will affect the calculation of the next pulse’s absorption. For single-pulse ablation, the simulated ablation threshold Fsim = 0.26 J/cm2 is close to the fitted experimental result F0th = (0.29 ± 0.01) J/cm2. For multi-pulse ablation, the simulated ablation rate Rsim = 11.4 nm/pulse is close to the fitted experimental result Rexp = (12.4 ± 0.1) nm/pulse under 0.9 J/cm2 fluence, while the simulated ablation rate Rsim = 19.8 nm/pulse is slightly larger than the fitted experimental result Rexp = (16.1 ± 0.7) nm/pulse at 2.7 J/cm2, providing good agreement between theory and experiment for both single and multi-pulse ablation. This study could be used to predict the multi-pulse laser processing performance, especially with the help of a machine learning method to find the best parameters automatically.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Ultrafast laser whose pulse duration τ < 10 ps has been widely used in areas such as micro cutting [1], surface texturing [2], thin-film processing [3] due to the nature of ultrafast laser-material interactions with minimal heat conduction [4]. During the ultrafast laser ablation, the conduction electrons, excited by the single photon absorption, experience a dramatic increase of electron temperature Te during the pulse. Then, the electron energy transfers to the lattice through the electron-phonon interaction, leading to a nonequilibrium temperature stage [4,5] which is widely accepted by using the two-temperature model (TTM) [6] to evaluate.
During the past decade, a range of studies on ultrafast laser materials interaction, both theoretical and experimental have been carried out. For example, Metzner et al. [7] and Kumar et al. [8] studied the single pulse ablation on bulk metal by using TTM to predict the ablation depth and radius of single ultrashort pulse laser ablation of 316 L stainless steel and Ti6Al4V alloy respectively. The ablation on dielectric materials like fused silica can also be simulated by the TTM [9,10], as well as the thin-film ablation. For example, Thorstensen and Foss [11] analyze the variation of ablation thresholds when a silicon wafer is under different initial temperatures. Li et al. [12], and Olbrich et al. [13] predicted the ablation depth and radius on different thickness aluminium films, and a ‘gentle’ and ‘strong’ ablation crater were found when the film thickness is above 100 nm. Multi-layer thin film ablation can also be carried out. Zhou et al. [14] investigated the laser ablation on gold/glass film which was achieved by setting the electron insulation of electrons and thermal conduction in the glass layer as there are very few free electrons in dielectric materials. As a result, the two-temperature model is a powerful tool for studying the physics during ultrafast laser ablation on both bulk and thin films.
However, most of the studies on ultrafast TTM research are based on single-pulse ablation. For example, Leng et al. [15] integrated the single pulse laser energy and so equivalent to a multi-pulse for the numerical study. Zhang et al. [16] simulated the multi-pulse ablation on aluminium by assuming that the material removal rate is independent of pulse number due to the relatively low laser frequency (1 kHz). More recently, Kumar et al. [17] considered the material instantaneous removal rate during the simulation, experimentally and numerically investigating the 1-15 pulses high fluence femtosecond percussion drilling on Ti6Al4V alloy. Nevertheless, the accuracy of simulations remains challenging as the materials removal mechanisms and surface morphology changes during ablation will dramatically influence the accuracy of the simulation.
Moreover, the ‘gentle’ and ‘strong’ ablation [13,18] will occur when ‘low’ and ‘high’ laser fluence is applied during the ablation. For example, spallation, occurring for the laser fluence slightly above the ablation threshold at ‘low’ fluence, will induce a high compressive pressure region under the laser irradiation area [19]. This induced high pressure will lead to the fracture of multiple nanometer layers and surface expansion in the skin depth which will finally separate the liquid layer [20,21]. For high laser fluence, the phase explosion [22,23] at the material's thermodynamic critical temperature is more dominant which will result the target into liquid and vapour droplets [24–26]. Hence the materials removal threshold temperature Ts should be carefully selected according to the applied laser parameters. In the meantime, the temperature governs thermo-dynamic parameters such as latent heat of evaporation, coupling factor, thermal conductivity and developing surface profile which should also be considered to get a more precise numerical prediction.
In this work, an experimental and numerical study on multi-pulse, 10 ps laser ablation of a polished 316 L stainless steel is presented. The instantaneous material removal rate, surface morphology changes and the ablation threshold temperature were carefully considered to obtain more precise results yielding good agreement with experimental measurements. This 2D numerical computation for up to 400 hundred pulse exposure, closer to real-world application, can be further implemented into the machining learning process [27]. In this case, the desired results can be automatically chosen and transferred into the next calculation loop, which can save trial time and reduce manufacturing costs in the industry.
2. Methods
The experiment was carried out on a Nd:YVO4 seeded regenerative amplifier (High-Q IC-355-800 ps) laser which gives 5 kHz, 1064 nm, 10 ps linear polarized output beam. The beam energy was controlled by an attenuator system which is made by a halfwave plate and Glan laser polarizer. The beam was expanded through a diffraction limited telescope (M ∼ × 3) and guided to the input aperture of a galvo system (Nutfield XLR8-10) via a periscope and focused by a flat-field f-theta lens (f = 100 mm) on the sample which was supported on x,y,z stages (Aerotech). The pulse number was controlled by a fast-mechanical shutter (Thorlabs SH05) and the pulse energy was calibrated under the galvo using a power meter (Coherent, LM-3). The focal spot size radius (1/e2) is r0 = (11.1 ± 0.1 µm), and the input beam diameter (before the galvo system input aperture) Din is around 8 mm. More experimental details can be found in [3]. Each experimental data was measured 5 times and a Nikon DS-U2 microscope system coupled with the microscope NIS-Element D software and a WYKO NT1100 white light interferometer microscope was used to measure the 2D and 3D profiles of the ablated craters.
The numerical model proposed in this research combined TTM and material removal calculations, achieved by coefficient from PDE and deformed geometry module, respectively. The flowchart of the ablation simulation of 10 ps laser on 316 L stainless steel is shown in Fig. 1. When the first pulse (i = 1) with laser fluence F irradiates on the initial flat surface S, the amount of energy Q is absorbed in the material. Then, the electron temperature Te and lattice temperature Tl will be calculated individually which is detailed in Section 3.1. Once the lattice temperature is high enough, the material removal stage will occur which is achieved by the deformed geometry function described in the Sec 3.2. The calculation of the i-th pulse’s ablation will be finished when the number of the time loop j is large or equal to the steps for each pulse calculation Φ1, and the i + 1-th pulse calculation will start with the new surface morphology Si. If not, the calculation will continue with a time interval Δt. The whole loop will be finished until the calculated time step j is large or equal to the total time step Φ2.
3. Numerical modelling
3.1 Two temperature model
For 10 ps laser ablation in this work, the two-temperature model (TTM) [6] is used to predict the temporal and spatial distribution of the electron and lattice temperatures throughout the ablation. For a 2D axisymmetric case, the physical model is governed by the equations:
The numerical change of the phase state is considered by combining the latent heat of fusion HM and vaporization HV in the volumetric heat capacity of the lattice [13],
The volumetric heat capacity of the electron Ce, coupling factor G and electron thermal conductivity ke can be approximated as [7,29]:
3.2 Axisymmetric model building
In order to save the computation time, a 2D axisymmetric finite element model was built through COMSOL 5.2. The computation domain was set as 40 µm × 10 µm with 80 × 100 elements in r and z direction respectively, and both directional element ratio was set to 5, as shown in Fig. 2. Zero flux boundary conditions were set on the right and bottom surface of the computation domain. The symmetric axis was adopted to the Gaussian distribution center of the input laser, and the laser source was irradiated at the top surface of the domain for the first pulse ablation. However, the changeable domain surface will influence the start surface of the Beer-Lambert law. In this case, a modification of the Beer-Lambert law in Eq. (4) has changed into,
The depth of the focus ${Z_F} = \frac{{2.56{M^2}\lambda {f^2}}}{{D_{in}^2}} \approx 1\; mm,$ which is much larger than the µm scale in ablation depth of this work so that the spot size and incident laser intensity distribution were considered constant during the multi pulse ablation simulation. The deformed geometry module was used to simulate the instant material removal during the processing. Prescribed normal mesh velocity was added at the material top surface to estimate the deformation velocity of grid, ${v_{deform}}$, which can be determined by the energy balance at the top surface as [31]:
4. Results and discussion
4.1 Experimental results
The ablation threshold on stainless steel was measured using the following equations [37],
where D is the measured ablated crater diameter, r0 is the laser spot radius, Fth is the ablation threshold, F0 is the peak fluence and Ep is the pulse energy. Both single-pulse ablation and multi-pulse ablation were measured, and the pulse energy was set as Ep = 4 µJ, 6 µJ, …, 22 µJ. For multi-pulse ablation calculation, the ablated radius D was measured with the pulse energy Ep = 2.0 µJ, 4.0 µJ, …, 20.0 µJ and pulse number N = 1, 100, 200 and 400 pulses, respectively.A plot of D2 versus Ep is shown in Fig. 3(a), each data point was measured 5 times and error bars represent 1σ. The single pulse ablation threshold was fitted according to the model as Fth0(1) = (0.29 ± 0.01) J/cm2, which is close to Jaeggi et al. [38] result whose Fth0 = 0.31 J/cm2 and Zhao et al. [39] result whose Fth0 = 0.28 J/cm2 under the 10ps, 1064 nm laser’s irradiation. Similarly, the ablation thresholds of multi-pulse ablation were fitted as Fth0(100) = (0.16 ± 0.01) J/cm2, Fth0(200) = (0.14 ± 0.01) J/cm2 and Fth0(400) = (0.12 ± 0.01) J/cm2.
Fig. 3. The ablation threshold measurements of 10 ps 1064 nm laser on 316 L Stainless steel (a) Graph of squared ablation diameter D2 versus Ep for the single, 100, 200 and 400 pulse ablation (b) The incubation coefficient factor for 10 ps,1064 nm, 5 kHz ablation on 316 L Stainless Steel
The incubation model describes the relationship between the single-pulse ablation threshold Fth0(1) and the multi-pulse ablation threshold Fth(N) in form [39]
where S is the incubation coefficient and is measured as S = (0.85 ± 0.01), shown in Fig. 3(b). The typical values of S in the range between 0.8 and 0.9 were found with this method in the case of multi-shot laser ablation of metals at relatively low repetition rates (< 100 kHz) [40–42] and close to the value, S = 0.858 measured by Zhao et al. [39].The optical images and cross section profiles of multi-pulse ablation at fluence F = 0.9 J/cm2 and 2.7 J/cm2 are shown in Fig. 4. The spherically symmetric dark areas surrounding the ablation pits is due to the backward flux re-deposition during the multi-pulse ablation [43]. The ablated depth increases with pulse number, and a linear relationship could be found in both cases. The ablation depths were measured to be as follows: Dab = (0.91 ± 0.10) µm, (2.16 ± 0.13) µm, (4.61 ± 0.16) µm for laser fluence F = 0.9 J/cm2, and for laser fluence F = 2.7 J/cm2, Dab = (1.64 ± 0.09) µm, (3.39 ± 0.12) µm, (6.27 ± 0.29) µm at 100, 200 and 400 pulses respectively.
Fig. 4. The optical images and cross section profile of 10 ps laser ablation on 316 L stainless steel at 100, 200 and 400 pulses. (a) F = 0.9 J/cm2 (b) 2.7 J/cm2
4.2 Numerical results
In this work, a range of laser fluence were used. Due to the different driving mechanisms (spallation and phase explosion) at ‘low’ and ‘high’ laser fluence, the threshold temperature Ts in Eq. (12) should be carefully considered. The threshold temperature Ts was first set as the material’s thermodynamic critical temperature Tc for all fluence, Ts = Tc, and the electron and lattice temperature along with a time scale of 100 ps at center point (0,0) in Fig. 1 was calculated and shown in Fig. 5(a).The corresponding calculated maximum electron temperature Te = 11,300 K, 15,200 K, 18,900 K while the lattice temperature takes 10.3 ps, 7.2 ps, 6.1 ps to reach the critical temperature of the stainless steel at fluence F = 0.9, 1.8 and 2.7 J/cm2, respectively. When laser fluence F = 0.9 J/cm2, the maximum Te = 11300 K which is close to the Ts = 9324 K. There will be only a small amount of the material reaches the Tc while the rest of the materials remain the solid or liquid state. In this case, it may not be physically reasonable to use Tc as threshold temperature for material removal. Moreover, at ‘low’ fluence regime, the spallation is predominated, and the materials are removed mainly by the laser-induced pressure [20,21]. When ‘high’ laser fluence F ≥ 0.9 J/cm2 is applied, the maximum Te is much larger than the critical temperature Tc and the lattice temperature Tl indicates a mixture of liquid and gas material whose phenomena is predominated by the phase explosion. In this case, the threshold temperature Ts is set as the evaporation temperature, Ts = TV = 3300 K while the laser fluence F < 0.9, and Ts = Tc = 9324 K when laser fluence F ≥ 0.9 J/cm2. In addition, a logarithmic form of temperature-time dependence in a second periodic (100 ps – 10 µs) when the laser fluence F = 2.7 J/cm2 is also shown in Fig. 5(a). It could be seen that the lattice and electron temperature both reached the room temperature at 7.27 µs whereas the inter-pulse period is 0.2 ms in this work. Therefore, the possible heat accumulation in the multi-pulse ablation has not been considered in this simulation.
Fig. 5. The electron and lattice temperature at laser spot center (0,0). (a) laser fluence F = 0.9, 1.8 and 2.7 J/cm2. (b) laser fluence F = 0.25, 0.26, 0.27 and 0.28 J/cm2, and ablation threshold is recognized at 0.26 J/cm2 due to the lattice temperature at this fluence first reaching the evaporation temperature of the 316 L Stainless Steel (Tv = 3300 K). (c) A validation of the quantity of the used transport coefficient with the TTM.
The lattice and electron temperature at ‘low’ laser fluence near the ablation threshold are calculated to test this assumption, and the fluence where the lattice temperature just reaches the evaporation temperature Tv is considered as the ablation threshold for 316 L stainless steel. Figure 5(b) shows the electron and lattice temperature with an inset yellow region, enlarged. The lattice temperature just rises above the evaporation temperature (Tv = 3300 K) at the laser fluence F = 0.26 J/cm2, which is close to the experimental measurement Fth0(1) = (0.29 ± 0.01) J/cm2, whereas the ablation threshold when critical temperature Tc is used is calculated as Fsim =0.61 J/cm2 (not shown). This simulation result supports our assumption that at ‘low’ laser fluence, the ablation threshold temperature should be chosen as evaporation temperature Tv instead of the critical temperature (Tc) which is relevant at ‘high’ laser fluence. To verify the quantity of the used transport coefficient with the TTM, a comparison of the electron and lattice temperature along 100 ps with our and Wang et al. [18] work are shown in Fig. 5(c). It could be seen that our work has a good fit with Wang et al.’s work. The slight difference might contribute to the constant reflectivity R = 0.51 in Wang et al.’s work.
The distribution of 2D lattice temperature at ‘high’ laser fluence F = 2.7 J/cm2 under multi-pulse ablation is shown in Fig. 6. At 5 ps delay after the first pulse ablation, the maximum surface temperature raised to ∼ 6500 K, but there is no material removal since the surface temperature is below the critical temperature, Tc. Then the temperature continues to rise until Tc at 7.5 ps delay when phase explosion and material removal occurs. An obvious surface depression can be observed at 25 ps, which is deeper and wider at 50 ps delay, and further evaporation after 50 ps delay is negligible. In this case, the recessional surface profile of the i-th pulse at 100 ps is exported as a txt. file and inserted in the i + 1-th pulse ablation’s calculation, as shown in Eq. (10). In this case, a more accurate material removal region can be simulated. Hence, an iterative calculation can be carried out for higher pulse numbers.
Fig. 6. The temporal distribution of 2D lattice temperature and developing surface profile at laser fluence F = 2.7 J/cm2 under 1st, 2nd and 3rd pulse ps ablation.
The developing surface recession at laser fluence F = 2.7 J/cm2 under 1st, 50th, 100th, 200th, 300th and 400th pulses at 50 ps is shown in Fig. 7. After the first pulse irradiation, a 0.021 µm deep and 8.77 µm radius crater has been formed. Then, the depth increased to 1.03 µm, 2.04 µm, 4.03 µm, 6.02 µm, 7.97 µm while the ablation radii increased to 9.33 µm, 10.04 µm, 10.49 µm, 10.74 µm, 11.01 µm after 50, 100, 200, 300 and 400 pulse exposure, respectively. In particular, the ablation rate almost follows a linear increase, but the increments of the ablated radius are decreasing which illustrates the incubation effect of multi-pulse ablation.
Fig. 7. The surface temperature and recession at laser fluence F = 2.7 J/cm2 under 1st, 50th, 100th, 200th, 300th and 400th pulses at 50 ps.
The experiential and numerical ablated rate of 10 ps (1064 nm) laser on 316 L stainless steel is also compared and shown in Fig. 8. For ‘low’ fluence F = 0.9 J/cm2, the simulated ablated rate Rsti-l = 11.4 nm/pulse is close the calculated experimental result Rexp-l = (12.4 ± 0.1) nm/pulse. The simulated and experimental ablated depth at 100, 200, 300 and 400 pulses are Dsim-l = 1.15 µm, 2.28 µm, 3.40 µm, 4.52 µm and Dexp-l = (0.91 ± 0.10) µm, (2.16 ± 0.13) µm, (3.72 ± 0.14) µm, (4.61 ± 0.16) µm, respectively. It could be seen that the simulated results were first larger than the experimental results, then it became lower than the experimental results after 350 pulses ablation, with good agreement. This change might result in the increased laser absorption due to the increased effect of surface roughness which is only necessary when the pulse number is high at low laser fluence [44].
Fig. 8. Log10-log10 figure of pulse number versus simulated and experimental results of ablation depth under 0.9 J/cm2 and 2.7 J/cm2 fluence at 10 ps (1064 nm @5kHz) laser ablation on 316 L stainless steel.
However, the simulated results at ‘high’ fluence F = 2.7 J/cm2, Rsti-h = 19.8 nm/pulse, are ∼ 20% higher than the calculated experimental result Rexp-h = (16.1 ± 0.7) nm/pulse, and the simulated and experimental ablated depth at 100, 200, 300 and 400 pulses exposure are Dsim-h = 2.06 µm, 4.05 µm, 6.04 µm, 7.99 µm and Dexp-h =(1.64 ± 0.09) µm, (3.39 ± 0.12) µm, (4.92 ± 0.25) µm, (6.27 ± 0.29) µm, respectively. This difference might be caused by the inaccuracy in calculated reflectivity around and above an electron temperature of 25,000 K [30], while reflectivity reduces with the increasing pulse number and surface roughness [45]. The backward flux re-deposition [43] might also reduce the effective ablation rate/pulse, especially at ‘high’ fluence, as ‘thicker’ oxidization layer needs to be removed for multi-pulse ablation [46]. In our previous study on stainless steel with incident fluence F = 9.0 J/cm2 and 10 ps pulse length, the plasma lifetime (1/e) was measured as (9.2 ± 1.0) ns, yielding an electron temperature Te ∼ 7500 K after 40 ns delay [43]. The possible plasma shielding might also influence the final absorption during the laser ablation which might cause errors in the calculation results.
Other physics (for example, spallation, phase transition, stress confinement and density-dependent collision frequency) which has not been considered in this model, will also bring the errors into the results. For 316 L stainless steel under 10 ps pulse duration, the heating time τheat is defined by the pulse duration which is longer than the mechanical expansion time, τheat ≈ τ > τmech, as the 316 L stainless steel’s typical electron-photon interaction time τep is around 1-3 ps [29] and the mechanical expansion time τmech is around 5 ps [47]. In this case, the low heat conduction and high electron-phonon coupling will confine the laser energy near the surface, contributing to the laser-induced stress relaxation and the thermoelastic stress which is large enough to cause the photomechanical spallation [48]. This photothermal phase explosion can cause around a 25% drop in energy specific ablation volume (ESAV) which is the ratio of the removal volume Vabl and the irradiated pulse energy Ep, compared with the ESAV at 0.9 J/cm2 and 2.7 J/cm2 under 10 ps pulse duration [47]. Hence, the ablation efficiency will decrease as the increment of the laser fluence. As our model has not considered the influence of the spallation and phase explosion, it could bring a relatively large error at ‘high’ fluence.
Moreover, the phase transition during the ablation will influence the material’s optical properties which are related to the varying electron collision frequencies. The electron-electron collision frequency υee is often proportional to the electron temperature υee ${\propto} {T_e}^2$ and the electron-ion collision frequency is directly proportional to the lattice temperature υei ${\propto} $ Tl [49]. In this case, the density changes of the 316 L stainless steel within lattice temperature, density decrease, and solid-liquid phase transition, all influencing optics via varying collision frequencies which will bring additional differences between the simulation and experiment. It was found that there is a nearly constant upward shift of the effective electron frequency υeff along with the increase of the electron temperature, and an abrupt increase of the υeff will occur when the solid material transfer into liquid. reflecting the major decrease of thermal conductivity [50]. This density-dependent collision and plasma frequency will dramatically affect the real part of material dielectric function Δɛr [50] and further influence the total absorption through the ablation. In this case, without considering the density dependence in this model will bring larger errors at high laser fluence, as there is a more obvious density change at high fluence ablation [46]. As a result, without considering the ultrafast laser ablation efficiency by stress confinement [51] and the material’s optical properties change due to the density transition [50] will bring the errors in this simulation, and higher errors could be found at 2.7 J/cm2 whose absorption has been more impacted as previous discussion.
5. Conclusions
This method yields encouraging results although representing an approximate picture of the complex ablation process as the single and multiple pulse ablation exposure has been studied experimentally and numerically. The material removal module was used to simulate the instantaneous material removal, which can obtain a more accurate result. Material removal mechanisms such as spallation and phase explosion under different laser fluences have been carefully considered. The threshold temperature Ts was set as evaporation temperature Ts =Tv = 3300 K for fluence F < 0.9 J/cm2, and the critical temperature Ts =Tc = 9324 K for fluence F ≥ 0.9 Jcm−2 according to the different ablation driving mechanisms under the ‘low’ and ‘high’ laser fluence. In this case, an excellent agreement between experiment and simulation could be achieved as the predicted single pulse ablation threshold Fsim = 0.26 J/cm2 is close to the experimental measurement F0th(1) = (0.29 ± 0.01) J/cm2. The resulting recession surface parameters were used in an iterative procedure to increase the accuracy of the total absorption after multi-pulse exposure. and 1 to 400 pulses ablation were performed with instant material removal at different temporal scales. By using this method, the predicted ablation rate for multi-pulse ablation, Rsti-l = 11.4 nm/pulse is close to the experimental result Rsti-l = (12.4 ± 0.1) nm/pulse at 0.9 J/cm2, while at higher laser fluence F = 2.7 J/cm2, the simulated and calculated experimental ablated rate are Rsti-h = 19.8 nm/pulse and Rexp-h = (16.1 ± 0.7) nm/pulse, respectively. This method is a very versatile tool optimized for variable materials: it works across different industrial applications, for example, thin-film processing, laser-induced periodic spatial structure formation, laser drilling, which can save the trial and error costs in manufacturing. Furthermore, this model can be implemented into the machining learning process [27], which can directly choose the desired results and transfer them into the next calculation.
Funding
Wenzhou Major Scientific and Technological Innovation Project (ZG2022008); Jiangsu Provincial Key Research and Development Program (BE2022143).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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