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Abstract
Laser ablation is widely used as a flexible and non-contact processing technology for the fabrication of fused silica. However, the introduction of thermal stress inevitably leads to crack growth and reduces the lifetime of fused silica. Due to the complicated coupling interaction and properties of fused silica, the unclear thermal stress formation is the bottleneck restricting further development of laser ablation. In this article, a three-dimensional multi-physics thermo-mechanical model was developed to reveal the evolution mechanism, and experiments were performed to validate the simulated results. The surface morphology evolution was elaborated during process cycles, with recoil pressure identified as the key factor in determining surface morphology. Moreover, thermal stress was quantified utilizing optical retardance and stress birefringence, effectively distinguishing between non-thermal and thermal stress induced by laser ablation. The theoretical simulations fit well with experimental measurements. Meanwhile, stress distribution and evolution behaviors were revealed under different processing parameters by this model. This work not only contributes to a profound understanding of the laser ablation process but also establishes a theoretical foundation for achieving high surface quality and non-thermal stress laser ablation.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the continuous development of modern optical technology, fused silica is widely used in high-power laser systems [1], extreme ultraviolet lithography systems [2], and astronomical telescopes [3], while surface quality demands are continuously increasing. However, the conventional contact grinding and polishing processes inevitably introduce polishing fluid contamination and sub-surface defects [4], which restricts the higher precision development of fused silica optics. Consequently, the non-contact, no-polishing fluid aid of laser is highly advantageous for fused silica optics fabrication [5].
Nowadays, two major types of laser processing methods are prevalent for machining fused silica optics. The first method is continuous-wave (CW) CO2 laser polishing, which has been used for reducing surface roughness based on the melting effect, and the temperature is below the evaporation temperature of fused silica [6–9]. The other one is pulsed CO2 laser ablation, where temperature exceeding the evaporation temperature is used to reduce form error and remove surface defect [10–12]. Pulsed laser ablation of fused silica results in a more precise and controlled material removal process compared to continuous-wave (CW) laser ablation, due to the intense, short bursts of energy delivered by pulsed lasers, which minimize heat-affected zones and reduce the risk of thermal damage to the material. Nonetheless, the thermal effect of these two methods inevitably induces negative residual stress, thereby leading to crack growth and shortening the lifetime of fused silica [13]. Therefore, it is necessary to have a thorough understanding of the thermal stress behaviors induced by CO2 laser processing.
In recent years, both experimental and theoretical studies have been conducted to gain insights into stress behavior under laser irradiation. Gallais et al. [14] first characterized the distribution of stresses and strains after quasi-successive CO2 laser polishing with 2.5 ns pulse duration, but the stress generation mechanism is not clear. Subsequently, Vignes et al. [15] established a two-dimensional finite element model to analyze the mechanism of residual stress distribution after 5 s long duration of CO2 laser polishing. However, the evolution behavior of stress is not considered during the polishing process. To further analyze the stress evolution process, Jiang et al. [16] employed a two-dimensional multi-physics coupled model to investigate the impact of temperature on residual stress during the quasi-consecutive CO2 laser polishing process utilizing a pulse length of 6.4 ns. However, the above studies primarily focus on the stress distribution results of the quasi-successive CO2 laser polishing process by two-dimensional model. There is no relevant study to fully describe the evolution process of temperature, morphology, and thermal stress during pulsed CO2 laser ablation by a three-dimensional model, which is an urgent challenge to solve.
In this work, the evolution behavior and properties of temperature, morphology, and stress during pulsed CO2 laser ablation on fused silica are explicated by using three-dimensional multi-physics thermo-mechanical simulation and experimental investigation. This research provides a significant contribution to understanding and explaining the ablation process, which can promote further development in laser ablation technology.
2. Theory and model
To comprehensively evaluate temperature, morphology, and thermal stress generated during the pulsed CO2 laser ablation process, a three-dimensional finite element model with a size of 5 mm × 2.5 mm × 0.5 mm has been established. In this model, the temperature field is calculated through three-dimensional transient thermal analysis. Subsequently, the temperature field serves as the initial condition for morphology and stress simulations. The mathematical model in this paper is established based on the following assumptions: (1) The material is isotropic and homogeneous; (2) the solid-liquid phase transition of the material is ignored; (3) the Marangoni effect and flow field are ignored.
The geometry and boundary conditions are shown in Fig. 1. Region A interacts directly with the laser, and the processing layer is influenced by the temperature field compared with the base. Therefore, for precision results, the mesh of region A is the finest part, and the maximum mesh size is 3 µm. The processing layer is finer than the base, and the maximum mesh size is 10 µm. In contrast, the base is divided into sparse mesh with a maximum mesh size of 50 µm. The Gaussian pulsed laser is applied on the top surface of fused silica and absorbed through the heat conduction inside the material. Heat is transmitted through heat conduction inside the material, and heat dissipation occurs through natural convection and radiation on the surface. The heat conduction governing equation is expressed as:
When the thermodynamic temperature of fused silica heated by CO2 laser exceeds the vaporization temperature, the fused silica is evaporated from the top surface, and part of the heat is taken away by evaporation. The evaporative heat flux can be expressed as [17]:
During the ablation process, the thermal expansion of fused silica occurs due to laser radiation, resulting in material displacement. The displacement s is expressed as [19]:
where ν is the Poisson ratio, and γ is the thermal expansion coefficient. The displacement s has components in the X-direction, Y-direction, and Z-direction. However, a single thermoelastic equation is insufficient to fully describe the changes during the cooling process of fused silica. On this basis, it is necessary to consider the viscoelasticity of the material to study the strain and stress over time. Therefore, a single-branch generalized Maxwell model is introduced to characterize the viscoelastic material to calculate the three-dimensional stress distribution of fused silica during the ablation process. The strain-displacement relationships in three directions are given by [20]:From the stress and strain results, we can calculate the distribution of stress birefringence in the material given by [14]:
In the simulation process, the fused silica parameters of thermal conductivity, specific heat capacity, and viscosity are considered and taken from Refs. [21–23], other parameters are listed in Table 1.
Table 1. Relevant parameters in this model
3. Experiments
The laser ablation experiments are conducted using CO2 laser processing equipment, which was independently built by ourselves, as shown in Fig. 2. The Gaussian beam wavelength is 10.6 µm, and the signal generator (FY6900, FeelElec) adjusts the output of the CO2 laser (Diamond Cx-10, Coherent). In our experiments, the signal generator modulates the laser to operate at a high modulation frequency (95 kHz) and duty cycle, to reach quasi-continuous output with an average power of 20 W, 25 W, 30 W, and 35 W. Then the quasi-CW laser beam is modulated into a rectangular pulse beam with a frequency of 1 kHz by an acousto-optic modulator. By changing the duty cycle through the acousto-optic modulator, ablation pulses with different pulse durations can be obtained. The pulse duration is precisely set in discrete temporal steps of less than 10 ns, representing the minimum pulse duration error. The achievable maximum power after the beam shaping process is 102 W for ablation experiments. The focused CO2 laser beam moves on the fused silica surface according to the F-theta lens with a radius of 83.5 µm (1/e2). Due to the rapid attenuation of light intensity within the fused silica, material removal does not occur throughout the entire Rayleigh length (2 mm) during ablation processing. In our experiment setup, the thickness of the material with temperature above the vaporization temperature in the heating region is only 100 nm. The sample is positioned on the precision three-dimensional mobile platform. The initial samples are ground and polished before experiments. Before every experiment, all samples (Heraeus Suprasil 311) with sizes of 20 mm × 20 mm × 6 mm need to be ultrasonically cleaned with deionized water and alcohol.
Fig. 2. Schematic diagram of laser ablation experiment platform. The microscopic images represent the morphology after laser ablation with laser power of 25 W and a scanning speed of 25.5 mm/s.
To characterize the processing results, the form error is measured using a white light interferometer (NanoCam Sq, 4D Technology). The microscopic images are obtained with an Olympus microscope (OLYMPUS BX53). The stress is measured by an imaging high-precision polarizer (StrainMatic M4/150.10, ILIS Gmbh), which utilizes the property of stress birefringence based on the phase retardance between the two polarized light along the two directions of stress. Additionally, we carried out a series of laser ablation experiments to verify the reliability of the simulated model. All the parameters in laser ablation experiments are consistently processed with those used in the simulated model.
4. Results and discussion
4.1 Surface morphology analysis and validation
To verify the effectiveness of the simulated thermodynamic fields, we first obtained the experimental and simulated laser ablation surface morphology of ten pulse cycles (10000 µs). The experimental results with laser power of 25 W and scanning speed of 25.5 mm/s were measured with a 20× mirror white light interferometer (Fig. 3(a)), while the calculated results are shown in Fig. 3(b). The experiment was carried out using the same laser ablation parameters described in the simulated model. It can be seen that the morphology distribution between the experiment and calculation agrees very well. In Fig. 3(c), the experimental and simulated morphology corresponding to the cross-section of the dotted black line was illustrated. As the laser moves along the direction of the laser scanning path, the ablation depth increases gradually until the laser is turned off. In addition, a significant cumulative effect can be found during the ablation process. The cumulative effect is related to scanning speed, which influences the overlapping rate between each pulse. The impact of different scanning speeds on the surface morphology was simulated, as shown in Fig. 3(d). It can be seen that the morphology after laser ablation has a large residual height h (the fluctuation degree of the ablated surface when the ablation depth is stable) under high scanning speed (Fig. 3(e)). As the scanning speed decreases, the ablated morphology becomes relatively smooth. Moreover, the comparison of maximum ablation depth H between the experiment and simulation is obtained under different scanning speeds, and the calculated results fit well with the experimental results.
Fig. 3. (a) Experimental surface morphology under the laser power of 25 W and scanning speed of 25.5 mm/s; (b) Simulated surface morphology under the laser power of 25 W and scanning speed of 25.5 mm/s; (c) Experimental and simulated morphology corresponds to the cross-section of the dotted black line; (d) Simulation results of surface morphology under scanning speeds of 6 mm/s, 12.5 mm/s, 25.5 mm/s and 51 mm/s with the same laser power. The partially enlarged image represents the bottom residual height h of 51 mm/s. (e) Simulated and experimental maximum depth and residual height under different scanning speeds; (f) Simulated and experimental maximum depth and residual height under different laser powers.
Similarly, the simulated and experimental maximum ablation depth and residual height under different laser powers are illustrated in Fig. 3(f). The simulated results agree well with the experimental results, which effectively demonstrates the rationality of this model. The maximum ablation depth H and residual height h increase with the increase of laser power on account of the increase in energy per unit region. Thus, it is necessary to increase the laser power and reduce the scanning speed to ensure the surface quality after laser ablation.
To further explore the critical factor influencing surface morphology, we calculated the removal velocity at the same processing position with different scanning speeds and laser powers. With the increase of laser power, the same position undergoes the same number of velocity increments (Fig. 4(a)), and the removal velocity increases during the first pulse duration (interaction time for the first pulse reaching the fused silica target) in Fig. 4(c). However, as the scanning speed increases, the same position undergoes different numbers of velocity increments (Fig. 4(b)). The removal velocity with different scanning speeds maintains a similar trend and value during the first pulse duration (Fig. 4(d)).
Fig. 4. (a) Removal velocity under different laser powers in simulation; (b) Removal velocity under different scanning speeds in simulation; (c) Relationship between removal velocity and time during the first pulse duration under different laser powers; (d) Relationship between removal velocity and time during the first pulse duration under different scanning speeds.
The removal velocity, recoil pressure, and light pressure during the first pulse duration are shown in Fig. 5. When the recoil pressure is applied, the velocity field increases rapidly. As the recoil pressure disappears, the maximum velocity decreases instantly. The removal velocity keeps a similar trend with the recoil pressure rather than the light pressure. Therefore, the recoil pressure generated by evaporation plays a leading role in laser ablation and determines the ablated morphology.
Fig. 5. Removal velocity, recoil pressure, and light pressure under laser power of 25 W and scanning speed of 25.5 mm/s during the first pulse duration.
4.2 Stress birefringence analysis and validation
To compare the calculated thermal stress with the experimental results, the thermal stress is linked with stress birefringence, which is calculated by dividing the optical retardance of linearly polarized plane waves by the sample thickness. Hence, the optical retardance after one pulse cycle is firstly calculated to verify, shown in Fig. 6. In Fig. 6(a), the optical retardance along the X-direction and Y-direction were symmetrically distributed like a petal. Along the X-direction, it is about zero in the center of the ablation area. It decreases rapidly to the minimum of −0.0028 nm at the edge of the heated region (Fig. 6(c)). With the distance further growing, the retardance gradually increases in the outer part of the heated region to about 0 nm. While along the Y-direction, the optical direction shows an opposite distribution. The optical retardance rapidly increases from approximately 0 nm to 0.0031 nm in the heated region and gradually decreases to approximately 0 nm. The simulated results were in good agreement with Jiang et al. [16] and Yang et al. [28] experiments results, which proves the validity of the stress fields in this model.
Fig. 6. (a-b) Simulated optical retardance and temperature distribution after one pulse cycle (1000 µs); (c) X-direction and Y-direction optical retardance correspond to the cross-section; (d) X-direction and Y-direction temperature correspond to the cross-section. The X-coordinate distance represents the distance to the origin of the coordinates.
Figures 7(a-b) show the measurement results of stress birefringence before and after laser ablation. The initial stress birefringence is 0.52 nm/cm, while the maximum value after laser ablation (vscan =25.5 mm/s) increases to 0.62 nm/cm. The simulated results of stress birefringence after 20 pulse cycles are shown in Fig. 7(c), where the maximum stress birefringence is 0.66 nm/cm. Subsequently, we compared the maximum simulated and experimental stress birefringence results under different scanning speeds and laser powers, shown in Figs. 7(d-e). To obtain the error bars of maximum stress birefringence, we measured the maximum stress birefringence at three different regions randomly and averaged the maximum stress birefringence of the three regions. The error bars represent the standard deviation from the average maximum stress birefringence. Under the same processing parameters, the calculated results fit well with the experimental results. Moreover, we simulated with higher scanning speeds exceeding 51 mm/s to obtain the equilibrium line, which can divide the non-thermal and thermal stress regions, shown in Fig. 7(f). The equilibrium line is obtained by comparing the maximum stress birefringence before and after laser processing at different laser powers and scanning speeds according to experimental and simulated results. When the laser power and scanning speed are at the equilibrium line, the maximum stress birefringence is approximately the same as before laser ablation. Therefore, the maximum non-thermal stress depth of single processing is approximately 600 nm, according to the analysis in section 4.1. This is of great significance to guiding the laser ablation experiments without negative thermal effects.
Fig. 7. (a) Initial stress birefringence result without laser ablation; (b) Experimental stress birefringence result with laser power of 25 W and scanning speed of 25.5 mm/s; (c) Simulated stress birefringence result with laser power of 25 W and scanning speed of 25.5 mm/s after 20 pulse cycles; (d) Variation of the maximum simulated and experimental stress birefringence concerning scanning speeds; (e) Variation of the maximum simulated and experimental stress birefringence concerning laser powers; (f) Non-thermal stress and thermal stress region at different scanning speeds and laser powers. The curve represents the equilibrium line to divide the region with and without thermal stress.
4.3 Analysis of stress distribution and evolution process
To further study the evolution of residual thermal stress during the laser ablation process, the Von Mises stress distribution and five representative points position a-e along the laser scanning path with laser power of 25 W and scanning speed of 25.5 mm/s were shown in Figs. 8(a-b) according to the simulated model. Points a and b are located in front of the scanning path. The maximum Von Mises stresses of each cycle gradually decrease during the first five cycles and then gradually maintain stability. Points c is in the middle of the scanning path, where the maximum Von Mises stress of each cycle increases gradually, reaching a maximum in the fifth cycle before gradually decreasing. Points d and e are located at the end of the scanning path, and their maximum Von Mises stresses increase during ten pulse cycles. The Von Mises stresses of the five typical points after 10000 µs are illustrated in Fig. 8(c). The maximum Von Mises stress value at point c is higher than other points, and the stress tends to concentrate in the middle region, implying high thermal susceptibility in the middle of the scanning path.
Fig. 8. Stress distribution along laser scanning path from simulation results. (a) Von Mises stress distribution and the position in point a (100 µm distance in front of the initial point of the scanning path), point b (the initial point of the scanning path), point c (the middle point of the scanning path), point d (the tail point of the scanning path), and point e (100 µm away from the tail point of the scanning path) with laser power of 25 W and scanning speed of 25.5 mm/s at 10000 µs; (b) Von Mises stress at different points at different times; (c) Von Mises stress of points a-e at 10000 µs; (d) Temperature and different stress distribution at point c. The blue and orange regions represent the tensile stress zone and the compressive stress zone, respectively.
Although the locations of the maximum stresses can be obtained from the above results, the Von Mises stresses can only exhibit the equivalent stress amplitude and cannot separate the tensile stress (positive value) and compressive stress (negative value) due to the root mean square of calculation formula. In contrast, the stress components in different directions can distinguish the tensile stress and compressive stress according to the value. Thus, the stress distribution and temperature changes at point c are shown in Fig. 8(d) to determine the key factor influencing the stress distribution. Combined with the σx, σy, σz, and τ, the time with significant changes from compressive to tension stress can be easily separated. The X-direction stress σx translates from tensile stress to compressive stress after five cycles once the maximum temperature exceeds the strain point temperature (1874K) [16]. Similarly, the Y-direction stress σy and Z-direction stress σz show the same trend. Specifically, the shear stress τ appears the opposite trend. The stress results at 10000 µs demonstrate that the X-direction stress σx and Y-direction σy values are considerable, and the X-direction stress σx presents a maximum value compared with the other stresses. This implies that the stress is mainly distributed on the surface and along the scanning path direction.
As discussed above, X-direction stress σx and Y-direction stress σy with the tension stress significantly contribute to residual thermal stress generation. To analyze these two stress evolution behaviours, the stress distribution at the end of the tenth pulse duration (t = 9050 µs) was first described in Figs. 9(a-b). This time point (t = 9050 µs) is at the end of the tenth pulse duration. It represents the time when the material has just finished heating and is ready to cool. Comparing different stresses along typical lines 1-3 shown in Figs. 9(c-d), laser ablation produces a large tensile stress in front of the scanning path while other areas show compressive. Additionally, the position where the laser has just been turned off has a larger stress range than the region that has been cooled. In Figs. 9(e-f), the stresses along typical lines 4-7 show that they were symmetrically distributed at the sides with respect to the X-axis, and the stress in the centre is less than the outer region along line 6, which is a similar conclusion of optical retardance results in section 4.2.
Fig. 9. (a) σx stress distribution at 9050 µs with laser power of 25 W and scanning speed of 25.5 mm/s and the position of line-1 (alone the X-direction in the middle and surface of the scanning path), line-2 (at the margin of the scanning path along the X-direction on the surface), and line-3 (at the outer region of the scanning path along the X-direction on the surface); (b) σy stress distribution at 9050 µs with laser power of 25 W and scanning speed of 25.5 mm/s and the position of line-4 (at the initial side of the scanning path along the Y-direction on the surface), line-5 (50 µm away from the initial side of the scanning path along the Y-direction on the surface), line-6 (50 µm away from the tail side of the scanning path along the Y-direction on the surface), and line-7 (at the tail side of the scanning path along the Y-direction on the surface); (c) σx stress distribution along typical lines 1-3; (d) σy stress distribution along typical lines 1-3; (e) σx stress distribution along typical lines 4-7; (f) σy stress distribution along typical lines 4-7.
Subsequently, the stress distribution after ten cycles (t = 10000 µs) was described in Fig. 10. This time point (t = 10000 µs) is at the end of the tenth processing cycle. It represents the material has finished cooling during one processing cycle and is ready to heat. At the end of the tenth cycle, the stresses at the tail of the scanning path along typical lines 1-3 change from tensile to primarily compressive during the cool process (Figs. 10(c-d)). Similarly, the stresses at the tail of the scanning path along typical lines 4-7 show the same variation trend from tensile to mainly compressive (Figs. 10(e-f)). Plus, the stress at the tail of the scanning path has a higher value than the stress in front of the scanning path. The maximum tensile stress occurs at the edges of both sides of the heated region, while the inside of the heated region is compressive stress (Fig. 10(f)). The above analysis implies that the cooling process mainly affects the tail position of the scanning path so that the thermal stress experiences a transition from tensile to compressive. However, fused silica usually exhibits intrinsically higher compressive strength (1150 Mpa) [29] than tensile strength (50 Mpa) [30]. Thus, the tensile stress occurring at the edges easily induces fused silica damage, and it should be avoided by adjusting ablation processing parameters.
Fig. 10. (a) σx stress distribution at 10000 µs with laser power of 25 W and scanning speed of 25.5 mm/s; (b) σy stress distribution at 10000 µs with laser power of 25 W and scanning speed of 25.5 mm/s; (c) σx stress distribution along typical lines 1-3; (d) σy stress distribution along typical lines 1-3; (e) σx stress distribution along typical lines 4-7; (f) σy stress distribution along typical lines 4-7. The position of lines 1-7 is the same in Fig. 9. The blue and orange regions represent the tensile stress zone and the compressive stress zone, respectively.
4.4 Temperature and stress distribution under different processing parameters
To analyze the thermal sensitivity at different processing parameters, the simulated Von Mises stresses and temperature distributions are extracted at three typical points A-C under different scanning speeds and laser powers along a single scanning path (Fig. 11(a) and Fig. 12(a)). With a decrease in scanning speed, the Von Mises stresses after 10000 µs at three typical points increase gradually. The pulse numbers of maximum temperature above the structural transition temperature of 1350 K also increase during the ablation process, shown in Figs. 11(b-d). This is because a decrease in scanning speed will lead to an increase in the overlapping rate between laser pulses, leading to more obvious heat accumulation.
Fig. 11. (a) Von Mises stress distributions at 9050 µs under different scanning speeds and the position of point A (the initial point of the scanning path), point B (the middle point of the scanning path), and point C (the tail point of the scanning path); (b-d) Von Mises stress and temperature changing with time at points A-C with different scanning speeds.
Fig. 12. (a) Temperature distributions at 9050 µs under different laser powers and the position of points A-C is the same in Fig. 11; (b-d) Von Mises stress and temperature changing with time at points A-C with different laser powers.
Moreover, the surface temperature increases gradually when pulsed laser irradiates on the surface of fused silica. After the laser beam is turned off, the surface temperature drops to below the structural transition temperature of 1350 K in tens of microseconds. The substrate can be completely cooled in the pulse duration cycle so that the thermal effect will not change the structure of the fused silica. Plus, the evaporation will also take away lots of heat to avoid the accumulation of thermal stress. Therefore, laser ablation can achieve non-thermal stress processing compared with the initial stress without laser processing, which proves the conclusion of section 4.2.
Similarly, with an increase in laser power, the Von Mises stresses after 10000 µs at three typical points, and the pulse numbers of maximum temperature above 1350 K increase gradually, shown in Figs. 12(b-d). These results agree well with the experimental results in Figs. 7(d-e). Moreover, the temperature significantly implicates the Von Mises stress and maintains a similar variation tendency. Thus, the Von Mises stresses can be reduced by controlling the material temperature and reducing thermal gradients.
According to the analysis in section 4.3, the stress after laser ablation is mainly distributed on the surface, and the Von Mises stress is equivalent stress, which cannot distinguish stress direction. Thus, the X-direction stress σx and Y-direction stress σy at point C are shown in Figs. 13(a-b). When the scanning speed is 6 mm/s, 12.5 mm/s, and 25.5 mm/s, the X-direction stress σx and Y-direction stress σy translate from tensile to compressive after the fifth cycle, and then it keeps compressive. The X-direction stress σx value and Y-direction stress σy value at 10000 µs increase with the rise of scanning speed. However, the X-direction stress σx and Y-direction stress σy keep tensile during ten cycles when the scanning speed is 51 mm/s. Although the stress value of 51 mm/s at 10000 µs is the minimum, fused silica is very sensitive to tensile stress, and choosing this scanning speed is not a good choice for fused silica fabrication. Similarly, the X-direction stress σx and Y-direction stress σy at different laser powers exhibit the same variation trend, shown in Figs. 13(c-d). When the laser power increases from 20 W to 25 W, the stresses change from tensile to compressive at 10000 µs. As the laser power rises from 25 W to 35 W, the stresses grow gradually and keep compressive. Therefore, choosing the appropriate scanning speed and laser power is necessary to maintain compressive and minimum stress during laser ablation.
Fig. 13. (a) X-direction stress σx distribution at point C with different scanning speeds; (b) Y-direction stress σy distribution at point C with different scanning speeds; (c) X-direction stress σx distribution at point C with different laser powers; (d) Y-direction stress σy distribution at point C with different laser powers. The blue and orange regions represent the tensile and compressive stress zones, respectively.
5. Conclusion
In this study, a three-dimensional thermo-mechanical simulated model provides new insights into revealing the surface morphology and stress evolution behavior during the pulsed CO2 laser ablation process. Some innovative conclusions are obtained as follows:
- (1) With a decrease in scanning speed and an increase in laser power, the maximum ablation depth and residual height increase gradually. Plus, recoil pressure generated by evaporation is the key factor influencing the removal velocity and surface morphology.
- (2) This model quantified the stress birefringence, and it was symmetrically distributed like a petal. The maximum stress birefringence increases with a decrease in scanning speed and an increase in laser power. Plus, the equilibrium line of non-thermal and thermal stress region is obtained, and the maximum non-thermal stress depth of single processing is calculated as 600 nm when the processing parameters are on the equilibrium line.
- (3) The residual thermal stress is mainly distributed on the surface and along the direction of the scanning path. In addition, the stress in the heated region changes from tensile to compressive during the cool process, and the tensile stress occurs at the edges of the heated region.
- (4) With an increase in scanning speed and a decrease in laser power, the temperature and Von Mises stress after ten cycles decrease gradually. Choosing the appropriate scanning speed and laser power is necessary to ensure that both X-direction stress and Y-direction stress are minimum and compressive.
Experimental measurements demonstrate that the proposed model can precisely predict the morphology and stress fields during the pulsed CO2 laser ablation process, and these findings provide a promising possibility for fabricating high-precision and non-thermal stress fused silica by laser ablation.
Funding
Member of Youth Innovation Promotion Association of the Chinese Academy of Sciences (2022246); Key projects of the Joint Fund for Astronomy of National Natural Science Funding of China (U1831211); Natural Science Foundation of Shanghai (21ZR1472000); National Natural Science Youth Foundation of China (62205352); Shanghai Sailing Program (20YF1454800); National Key Research and Development Program of China (2022YFB3403403).
Acknowledgements
The authors would like to thank the referees for their valuable suggestions and comments that have helped improve the paper.
Disclosures
The authors declare no competing interests.
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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