Open Access
Add to BibSonomy
Abstract
The machining-induced cracks and other defects on the surface of fused silica would incur damage when irradiated by intense lasers, which greatly shortens the service life of the fused silica optical components. The high absorption coefficient of fused silica for far-infrared lasers makes it possible to use low-energy CO2 lasers to melt and heal micro defects on the surface, and hence improve its damage threshold under the service conditions of extremely intense laser. However, the air in the cracks may evolve into bubbles during the laser healing process, but the law of crack morphology evolution and the bubble formation mechanism have not been clearly revealed. In this work, a simulation model of the healing process of fused silica surface cracks under the effect of low-energy CO2 laser is established. Three bubble formation mechanisms (i.e., the uneven fluidity caused by temperature gradient, the collapse effect caused by inclined cracks, and the internal cracks) are identified based on the simulation results of cracks with various original morphologies and characteristic structural parameters. The simulated fused silica morphology is consistent with the results of the laser healing experiment. This work can provide theoretical guidance for the optimization of optical manufacturing parameters of fused silica, as well as the CO2 laser healing and polishing strategies.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
For wavelengths in the near-infrared, visible light and ultraviolet bands, fused silica generally shows excellent transparency. It is an ideal optical material widely used in many occasions including portholes and solar panels in spacecrafts [1], as well as lens and shields in high-power laser systems [2]. However, under these working conditions, high-speed impact debris and high-power lasers can cause damage to the optical components. Fused silica is a typical hard and brittle material, during the process of grinding and mechanical polishing, cracks and other kinds of surface defects would be formed inevitably [3]. Under the extreme service conditions such as high-power lasers, these surface defects will exacerbate the degree of damage [4]. Therefore, it has great engineering practical value to realize the repairing of defects and damage sites on fused silica surfaces.
For far infrared lights, for example, CO2 laser with wavelength of 10.6 μm, fused silica has a high absorption coefficient of more than 80% due to the resonance excitation of the characteristic vibrational states of the SiO2 molecules [5]. On basis of this property, when irradiated by a far-infrared laser, the laser energy could be deposited in an area with the depth of several micrometers below the surface of fused silica, raising the local surface temperature to the melting and evaporation temperature in a short time. As a result, the micro material flow and ablation removal can be realized. Therefore, the CO2 laser processing technology has become the most competitive method for defect repairing [6–8], surface smoothing [9] and micro-structure fabrication [10,11] on fused silica surfaces.
Since CO2 laser repairing of fused silica surface defects become a research hotspot, a lot of research on the interaction mechanism between CO2 laser and fused silica, and the formation mechanism of the surface morphology has been previously reported. Feit et al. firstly proposed the theoretical models of heat conduction, melt flow, evaporation and gasification in CO2 laser repairing process [12]. Robin et al. measured the surface temperature of fused silica under different laser powers using an infrared camera and established a theoretical model for calculating the depth of the ablation crater [13]. Doualle et al. studied the influence of different heat source definition methods on the simulation results of the interaction between CO2 laser and fused silica, and calculated the temperature distribution, material ejection and distribution of residual stress. And these simulation results are consistent with the experimental results of infrared temperature, profile and photoelasticity measurements [14]. He et al. studied the mechanism of laser polishing of fused silica and pointed out that the surface tension plays a leading role in the surface smoothing process [9]. Tan et al. pointed out that material ablation and gasification recoil pressure are the formation reasons for the morphology of the laser repairing crater [15]. However, current researches mainly focus on the response of defect-free fused silica surface under the irradiation of CO2 laser. While few efforts have been made on the influence of surface cracks and other original defects on the surface morphology and surface quality of fused silica after CO2 laser processing.
In the process of CO2 laser irradiation, the original defects on the fused silica surface can lead to the formation of bubbles on the subsurface [16]. The existence of bubbles will cause near-field optical modulation on the repaired surface, which is seriously harmful to the promotion of laser damage threshold of fused silica optics. When the bubbles appear on the edge of the repairing crater, the modulation effect is most obvious [17,18]. Although it has been proved that, the formation of bubbles can be reduced by adjusting the CO2 laser irradiation strategy [19], as well as pretreating the component surface with hydrofluoric acid [20]. The mechanism of the laser healing process of micro-defects and the formation condition of bubbles have not been clearly explained.
This work focuses on the formation mechanism of bubbles in the healing process of micro-cracks involved in the non-evaporation interaction between low-energy CO2 laser and fused silica. Firstly, based on the equations of energy deposition, heat transfer, fluid flow, and material properties with respect to temperature, a multi-physics coupling model of electromagnetic field, temperature field, flow field and phase field was established for the crack healing process of fused silica under the irradiation of low-energy CO2 laser. The influence of temperature and viscosity gradient, surface tension, Marangoni effect, and gravity were all taken into consideration. A highlight of the model is the ability to track the evolution of surface cracks at every moment. Based on this model, the laser healing process of three typical surface defects (radial crack, Hertzian crack, and lateral crack) was then revealed, and the influence of crack characteristic parameters (e.g. depth and width) on the flow field distribution and bubble formation in the process of CO2 laser interaction was analyzed. Finally, a CO2 laser healing experiment was carried out on the ground fused silica surface. By comparing the surface morphology obtained by the experiment and simulation results, the reliability of the model is verified. This work is beneficial not only for the further understanding of CO2 laser repairing and healing mechanism of surface defects on fused silica optics, but also can provide effective guidance for optimizing the optical machining process of fused silica and establishing its machining quality control strategies.
2. Model and theory
2.1 Simulation model
Mechanical cracks of fused silica mainly include radial crack, lateral crack and Hertzian crack [3,21]. The morphological characteristics of these three types of cracks are shown in Fig. 1. Radial crack, which is perpendicular to the material surface and have a large aspect ratio, is generated by sharp abrasive particles. While lateral crack is formed when the external load disappears and the plastic deformation area of the material is relaxed. The lateral crack is a large-scale crack, which is parallel to the surface of the material. Hertzian crack is generated when blunt particles extrude the surface of the material. Its shape is a cone with a certain angle. The shape and size characteristics of these three types of cracks are the basis for establishing the crack healing model. After different grinding processes with different removal amounts, the depth range of cracks on the surface of fused silica can reach 0∼100 μm [22]. In order to find out the crack scale range applicable for CO2 laser treatment and provide guidance for determining the processing procedures of fused silica, the crack size in this work is set to be from a few microns to tens of microns.
Fig. 1. Morphology of surface cracks on ground fused silica: (a) radial crack; (b) lateral crack; (c) Hertzian cone crack.
Different from the evaporative repairing method by high-power lasers, the low-energy CO2 laser in this work is defined as: the laser energy is limited to control the maximum temperature of the fused silica surface below the evaporation temperature Tv. In this situation, the repairing and healing of defects are realized mainly by the micro-flow of the molten material. The calculation of material temperature involves laser energy deposition, heat transfer, and heat dissipation through convection and radiation. The calculation of micro-flow must take factors including material interface, phase change, surface tension (including capillary force and Marangoni force) and viscosity coefficient into consideration. Combining these factors, a laser-crack-healing model of fused silica coupled with laser energy field, temperature field, flow field, and phase field is established. The reason for introducing phase field is to track the interface between fused silica and air, so that the evolution processes of the crack and bubbles can be obtained. The schematic diagram is shown in Fig. 2.
Fig. 2. Schematic diagram of the laser healing model of fused silica surface cracks (where ϕ is the phase field variable used in finite element calculation: ϕ = 1 represents the fused silica area, ϕ = -1 represents the air area, and ϕ = 0 represents the interface between these two materials, i.e., the crack and the surface of fused silica).
The common finite element interface tracking methods include phase field method, level set method and moving grid method. The reasons for choosing the phase field method is: Firstly, in the crack healing process, there is a large, localized deformation. The moving mesh method is prone to mesh inversion and overlap. Another disadvantage of the moving mesh method is that it cannot simulate the evolution of bubbles after they are formed. Secondly, the effect of surface tension cannot be ignored in the crack healing process, but the level set method cannot take surface tension into consideration. Therefore, the phase field method is the most suitable method to track the evolution of the cracks.
In the model, the outer area of the material is set to be air, and the direction of gravity is set perpendicular to the material surface and towards the inside of the material. The ablation removal of materials is not involved in the process of low-energy laser healing. Although the molten material does slowly evaporate, and the change of the hypothetical temperature will make fused silica densify to a certain extent [23], the surface morphology change caused by evaporation and densification is only tens of nanometers [5], which has almost no influence on the final results. Therefore, the evaporation and densification of the material is ignored.
To properly consider the micro-flow of the material, the entire simulated area, especially the area near the crack, requires extremely fine meshing. A three-dimensional (3D) simulation model would be helpful for better modelling the crack healing process, but it will greatly increase the amount and cost of calculation. However, by comparing the simulated material flowing processes of fused silica without any surface defect by means of 2D and 3D models, it is found that for the simulation areas with symmetry, the modelled results of the 2D model are very close to those by the 3D model. Therefore, a two-dimensional axisymmetric simulation model is established to study the healing process of the symmetrical cracks.
2.2 Governing equations
The interaction between CO2 laser and fused silica is mainly manifested as the temperature rise caused by the absorption of laser energy accompanied by multi-physical processes including phase change, heat transfer, and non-isothermal flow. For isotropic and homogeneous materials, the corresponding non-linear heat transfer equation can be expressed as:
The definition of heat source Q mainly includes body heat source and surface heat source [14]. In most of the previous publications in this field, only the surface temperature of fused silica is needed to be paid attention to. The definition of surface heat source is beneficial for simplifying the calculation, therefore it is generally adopted [9,11]. However, there is a certain difference in the temperature distribution calculated by the body and surface heat source definitions. When focusing on the healing process of cracks, the temperature gradient of the material will bring about a significant difference in the fluidity of the material. The body heat source definition, which is closer to the real situation of the energy deposition process under CO2 laser irradiation, is adopted in this work. The intensity distribution of the CO2 laser used in this work conforms to the Gaussian distribution, and the body heat source Q of the incident CO2 laser is represented as:
The fluid flow of fused silica and air can be described by Navier-Stokes equation:
To study the crack healing process, it is necessary to be enable the model to track the crack morphology at any moment. The phase field method can cope with the situation of large local deformation, and can take surface tension into consideration. Therefore, it is adopted in the model to track the interface between fused silica and air. The phase field equation can be expressed as:
According to the previous work by He et al. [9] and Tan et al. [15], surface tension plays a dominant role in the formation of the surface morphology in the interaction of CO2 laser and fused silica. In this work, the capillary force, which is the normal component of surface tension, can be expressed as:
while in the tangential direction, under the Marangoni effect: where κ is the curvature of surface profile, and ${\nabla _s}T$ is the temperature gradient.2.3 Material parameters and their variation with temperature
When the material temperature increases, parameters including thermal conductivity, heat capacity and viscosity of fused silica are not constant or change linearly. The change of material parameters with temperature has a great influence on the temperature field and flow field distribution in the healing process. Therefore, it is important to set reasonable material parameters in order to accurately simulate the crack healing process of fused silica.
The thermal conductivity of fused silica materials adopted in previous work were not the same [26–28]. The experimental data obtained by Combis et al. through an infrared camera [13,27] was adopted in this work, and the thermal conductivity is expressed as:
The specific heat capacity of fused silica is expressed as [29]:
Fused silica is a typical amorphous, and the temperature change have a great influence on its viscosity coefficient. Appropriate viscosity curve is necessary for accurately obtaining the flow characteristics. The relationship between the viscosity coefficient of fused silica and temperature in this work is [19]:
The rest fused silica parameters used in the model are shown in Table 1, and the parameters of air used in the model are referred to Ref. [30].
Table 1. The rest fused silica parameters used in the model
3. Results and discussion
3.1 Three representative bubble formation mechanisms
Based on the laser healing model established in Section 2, the healing process of radial crack, Hertzian crack and lateral crack on the surface of fused silica with different sizes was numerically analyzed under the irradiation of continuous CO2 laser with power P = 9 W and beam radius a = 0.3 mm. Three different bubble formation mechanisms were found, and the corresponding representative crack healing process are shown in Figs. 3∼5.
Fig. 3. A typical crack healing process of fused silica under CO2 laser (take radial crack as an example). The processes of gradually healing, formation of bubbles, and formation of surface pit due to the escape of the bubble are included.
The first bubble formation mechanism is related to the non-uniformity of fluidity along the depth. The healing process of a radial crack with a depth dl = 15 μm and an aspect ratio dl/wl = 10 is shown in Fig. 3. Under the effect of the laser, the length of the crack first gradually decreases. But as the distance from the surface increases, the temperature gradually decreases, resulting in a rapid increase in viscosity. Therefore, the crack evolved into several bubbles with different sizes: the closer to the surface, the larger the bubble volume. If the laser irradiation continues, the bubbles will move towards the material surface under the effect of buoyancy and flow field, and eventually some of the bubbles can escape from the material and leave a circular pit on the surface. There are four points to be noted:
- (1) Not all radial cracks will undergo a bubble formation process like this. The conditions for healing without bubbles formed will be elaborated in Section 3.2.
- (2) The existence of a surface pit is only a transient process. The molten fused silica has the property of flow and healing, and would continue to smooth the surface. But it can be expected that, the larger the pit formed, the longer the relaxation time required, and the easier to be observed in experiment.
- (3) Not all bubbles can finally float up to the surface of the material. It is found that bubbles do have certain movements after they are formed. But for most of them, e.g. bubbles 1 and 2 in Fig. 3, the change of position is too small to reach the surface. Which indicates that, it is not feasible to completely remove the residual bubbles inside the fused silica through long-term laser irradiation.
- (4) In previous works on the damage mitigation of fused silica using high-power CO2 lasers, a unique morphology of a Gaussian crater with a raised rim is observed as a result of the vaporization recoil pressure [15]. While in this work, under a low-energy CO2 laser, there is no violent material vaporization. Therefore, such morphology has not been observed.
The second bubble formation mechanism is related to the cracks with a certain angle. It is noticed that when a Hertzian crack is healed, bubble is inevitably formed at the end of the initial crack. Figure 4 shows the healing process of a shallow Hertzian crack with shape parameters of ac = 1 μm, wc = 0.5 μm, dc = 2 μm, θc = 30°. Although the overall healing effect is ideal and the surface after healing is smooth, tiny bubbles are left inside the material which is obviously undesirable. This is because the material above the crack (area I in Fig. 4) flows fast at first and tends to fill up the crack downwards during the laser healing process, while the movement below the crack (area II) is relatively slow, thus forming a collapse-like effect and wrapping the gas that cannot escape in time to form bubbles. Larger surface curvature and smaller flow resistance are the reasons for the faster material flow rate in area I.
Fig. 4. Typical healing process of a Hertzian crack. Although the depth of the crack is only 2 μm, at which the impact of uneven fluidity is little, bubbles are formed at the corner of the crack.
Based on this results, three methods can be proposed to suppress the formation of such bubbles. The first method is to strictly limit the angle of the cracks generated during grinding. The second is to pretreat the component, e.g. etching with HF [31], to increase the opening width of the cracks and reduce the curvature at the crack edge. And the third is, by adjusting the laser parameters, optimize the material state for better healing effect. For example, in Ref. [19], before heating the crack to the melting temperature, irradiate it with a long-term CO2 laser with lower energy to make sure the gas in the crack is well discharged can achieve a better result with fewer bubbles.
The third bubble formation mechanism is closely related to lateral cracks. Figure 5 shows the deformation of a lateral crack with original parameters of al = 2 μm, dl = 2 μm, wl = 0.5 μm, under the effect of CO2 laser. In 0.5 s of laser irradiation, the crack gradually shrinks toward the center, and the shape of its bottom is close to a sphere. Since lateral cracks are generated from the interior of the material as a result of relaxation, most of them do not have openings on the surface. Therefore, the air in the lateral crack can hardly escape, and the bubble formed are much larger than radial cracks and Hertzian cracks which have larger surface openings.
Fig. 5. A Typical evolution process of lateral crack under the effect of CO2 laser: (a) evolution of morphology; (b) variation curve of maximum surface height; (c) pressure distribution around the bubble at 0.4 s. The crack gradually shrinks into a large bubble, and the expansion of the bubble causes the surface to rise.
It can be observed in Fig. 5(a) that, the material surface above the bubble is obviously higher than the original surface when the material is melted and begins to flow. The maximum surface height shows a trend of increasing firstly and then decreasing (Fig. 5(b)). According to calculation, the volume of the bubble increases by 35% at 0.3 s compared with the initial crack. This is caused by the increase of gas pressure resulted from the temperature rise. Obvious pressure concentration is observed around and directly above the bubble (Fig. 5(c)). Considering that, the depth of the bubble is only reduced by 0.09 μm, the main reason for the rise of the material surface is the thermal expansion of the bubble.
When the laser loading time exceeds 0.3 s, obvious bubble expansion can still be observed. But the surface height of the material stops increasing but begin to decrease. This phenomenon is the result of the surface smoothing effect dominated by surface tension, which can be used to reduce the surface roughness of fused silica components [9,32].
In summary, the non-uniformity of fluidity, the inclination angle of the crack, and the internal cracks are the reasons for the formation of bubbles during the laser healing process of fused silica. For radial cracks and Hertzian cracks, limiting the depth of cracks and avoiding inclined cracks during manufacturing process can help avoid the formation of bubbles. Lateral cracks are not able to be healed. Therefore, they must either be completely avoided during the manufacturing process, or be removed using rigorous methods before laser polishing.
3.2 Influence of crack parameters on healing process: a case study of radial crack
In order to develop the manufacturing strategy to suppress the residual bubbles and improve the material performance of fused silica after low-energy CO2 laser treatment, it is necessary to find out the specific conditions for bubble formation. In this work, radial cracks were selected as the research object, and two characteristic parameters, crack depth and crack opening width, were selected to study their effects on the laser healing process.
Figure 6 shows the healing process of radial cracks with different initial depth dl and the same aspect ratio dl/wl = 10 under the irradiation of continuous CO2 laser with power P = 9 W and radius a = 0.3 mm. The dl and wl here refer to the original parameters of the crack before healing. According to the summarized results of crack healing for various crack depth dl increasing from 0 to 40 μm, the results of crack healing can be divided into three stages:
- (1) When dl ≤ 13 μm, take 10 μm as an example (Figs. 6(a)∼6(d), the crack can be healed perfectly with no bubbles formed in the whole process. Therefore, in the manufacturing process of fused silica optical components, the depth of the cracks should be controlled within this range to facilitate the subsequent CO2 laser treatment for healing the cracks.
- (2) When dl is 13∼30 μm, the crack can be healed under the action of laser, but several spherical bubbles will be formed at the same time, as shown in Fig. 3 and Figs. 6(e)∼6(h). 13 μm is the transition threshold for the first stage (no bubbles formed) and the second (with bubbles left in the healed material).
- (3) When dl exceeds 30 μm, there will be almost no healing effect at the area far away from the surface within 0.5s. But the melted material around the surface will quickly seal the crack. As a result, most of the air will be trapped inside the material and a large droplet-shaped bubble will be formed (shown in Figs. 6(i)∼6(l)). If the laser irradiation time continues to increase, the major of the bubble would gradually shrink to become more spherical, and a part of the gas at the tail will separate out to form tiny bubbles.
Fig. 6. Laser healing process of radial cracks with different depths: (a)∼(d) dl = 10 μm, the crack is perfectly healed; (e)∼(h) dl = 20 μm, several spherical bubbles are formed; (i)∼(l) dl = 40 μm, the crack cannot be healed, and a large droplet-shaped bubble is formed.
Figure 7 shows the flow field distribution around the three radial cracks shown in Fig. 6 at 0.2 s after the laser is applied. The difference in the flow field distribution is the basis to choose 30 μm as the key point to divide the second and third stage.
Fig. 7. The flow field of radial cracks with different depths after laser irradiation of 0.2 s. (a)∼(c) are the overall flow field with different original crack depths of 10, 20, and 40 μm; (d)∼(f) are the corresponding flow field around the crack. The scale of the arrows is logarithmic rather than linear, which can help easier observe the flow trend but do not represent the absolute magnitude of velocity.
For shallow cracks in the first depth range (0∼13 μm), the melted material flows from both sides along the bottom of the molten pool to the center and then moves upward (Fig. 7(a)), forming a flow trend towards the material surface. As a result, the cracks can be gradually healed outward from the deepest point.
For cracks with medium depth (13∼30 μm), different flow trends are observed at the two ends of the crack. The two positions at which the crack heals first are marked in Fig. 7(e). Because of the larger depth, there is a large temperature gradient between the two ends of the crack. The area close to the surface has higher temperature and lower viscosity, so surface tension plays a dominant role in forming a tendency to flow from the surface towards inner area. While for the area far away from the surface, it has lower temperature and higher viscosity. And the flow property of the molten pool plays the leading role, and at 0.2 s there is a slight reduction in the depth of the crack. The former leads to the sealing of the crack, while the latter divides the long gap in the material into several spherical bubbles.
For cracks deeper than 30 μm, the depth of the crack exceeds that of the molten pool. Therefore, the flow trend formed by the property of the molten pool is same to the surface tension. The crack is too deep that temperature at the bottom does not reach the melting temperature. As a result, the viscosity coefficient at the bottom is very large. Most of the air in the crack is trapped, and can only evolve slowly into a droplet-shaped bubble instead of spheres (Fig. 6(l)). In this case, the CO2 laser healing cannot effectively improve the surface quality of the material.
The healing process of radial cracks with different opening widths wl under the action of laser is also simulated, and the critical states of wl = 4 μm and wl = 5 μm are shown in Figs. 8(a)∼8(c) and Figs. 8(d)∼8(f) respectively. The depths dl of these cracks are all 20 μm. The result shows that, under such healing conditions, cracks with wl less than 4 μm will form bubbles, but when wl exceeds 5 μm, the crack can be healed flawlessly. Based on this, in the actual laser healing process, the pretreatment methods which can broaden the crack width will significantly improve the healing quality.
Fig. 8. Influence of crack width on the laser healing process and bubble formation: (a)∼(c) the healing process of the crack with dl = 20 μm and wl = 4 μm; (d)∼(f) the healing process of the crack with the same depth but wl = 5 μm; (g) the healing speed of cracks with different widths obtained by comparing the residual depth at 0.25 s and 0.3 s.
It is usually assumed that a crack with a larger width will cost longer time to be healed. However, comparing the crack morphology after laser irradiation of 0.3 s (Fig. 8(b) and Fig. 8(e), it is found that the depth of the wider crack with wl = 5 μm is smaller than that of the 4 μm crack under the same laser parameters, indicating that it heals faster. To find out the cause of this phenomenon, the residual depths of cracks with different widths at t = 0.25 s and 0.3 s were counted and shown in Fig. 8(g). The reason for choosing these two time points is to allow as many cracks as possible in a stable healing process. The larger the difference between the crack depths at these two time points, the faster the crack healing speed. The result shows that, the healing speed of cracks with wl from 4 μm to 7 μm first increases and then decreases. It reaches the maximum value around 4.5 μm. The reason for that is: firstly, when the crack is wider, the more mass is needed to fill it, resulting in the healing speed to be slower. The curve for crack width ranging from 5 μm to 7 μm is consistent with this trend. Secondly, as the crack widens, the mass of the central area irradiated by the laser is reduced, while the total input energy remains constant. As a result, the energy absorbed by per unit volume increases. Therefore, in the central local area around the crack, the temperature of the crack with wl = 5 μm (2513 K at t = 0.25 s) is a little higher than that of the 4 μm (2503 K) and 3 μm (2453 K) cracks, in which case the material has better fluidity and can correspondingly heal the crack faster.
In summary, perfect healing can be achieved when the crack depth dl ≤ 13 μm. When dl > 13 μm, the air in the crack will be trapped and bubbles will be formed. Increasing the width of the crack can improve the possibility of crack being healed. And properly increasing the crack width can accelerate the healing process.
3.3 Laser healing experiment and model verification
To verify the simulation model and results, a laser scanning healing experiment was carried out on a ground fused silica surface. The sample used is Corning 7980. The peak power of the CO2 laser is 55 W, the laser frequency is 10 kHz, the duty cycle is 40%, and the beam radius is 0.5 mm. The laser moved in a 10 mm × 10 mm area by the control of the galvanometer scanning system, and the scanning speed is 5 mm/s, the track pitch is 90 μm. Under such parameters, the maximum surface temperature and the depth of the molten after the laser irradiation of 0.2 s are calculated to be 2522 K and 32 μm (calculated in a laser heating model with the same laser parameters as used in the experiment, as well as the same material parameters and heat governing equations in the crack healing model). Which is close to the material state under the same laser irradiation time in Figs. 3∼8 (around 2500 K and 25 μm).
A microscopic imaging system and a white light interferometer were used to obtain the surface image and morphology of the sample after healing. The results are shown in Fig. 9.
Fig. 9. Surface and subsurface morphology of fused silica after CO2 laser healing: (a) surface image obtained by polarized optical microscopy; (b) surface morphology obtained by ZYGO Newview 8200 white light interferometer; (c) microscopic image obtained by focusing at the subsurface.
As shown in the polarized optical image in Fig. 9(a), there are several conspicuous circular spots (marked 1∼4) on the surface of the fused silica after laser healing. According to the three-dimensional morphology image Fig. 9(b), these spots are pits on the surface of the material. The shape of the pits are standard circles with smooth edges, indicating that they are formed after the bubble escaped, rather than formed by material collapse. This finding verifies the simulation result in Fig. 3 that, under the laser irradiation, the bubbles formed will float towards the material surface. And some of the bubbles can escape and leave pits on the surface of fused silica.
Abundant dots can be also seen in the polarized optical image Fig. 9(a). These dots generally distributed around the surface pits, mostly present local continuity and directionality. By focusing the microscope to the sub-surface area, as shown in Fig. 9(c), it is found that there are circular shadows under these dots. Considering that, the shape of original crack is close to a canyon with a certain length. During the healing process, the crack is divided along the length direction. Therefore, these continuously distributed bubbles are formed, and the trajectory of the bubble distribution is the trace of the original crack.
Several convex areas (marked I∼III) can be found in Fig. 9(b). All of them appear at places with dense bubbles, indicating that their formation is induced by the bubbles rather than the flow of the melted fused silica itself. It has been predicted in Fig. 5 that, the thermal expansion of the bubbles in the subsurface of fused silica would cause the surface to bulge. These convex areas on the surface are formed by the same mechanism. After the laser irradiation is over, the heat of the melted material will rapidly transfer to the main body, leading to a rapid cooling and solidification. But the expanded bubbles do not have enough time to relax to the volume under normal pressure. Therefore, the deformed surface is preserved.
In summary, form the results in Fig. 3 and Fig. 5, surface pits formed by the escape of bubbles, as well as convex areas formed by the thermal expansion of bubbles, have been predicted. These observations are consistent with the results of laser healing experiment. And these special surface morphologies have an evident correlation with the distribution of bubbles, indicating that they are formed by the healing of cracks. Based on these results, the reliability of the laser healing model of fused silica can be verified.
4. Conclusion
In this work, a model of the low-energy CO2 laser healing process of surface cracks on ground fused silica is established by taking energy deposition, heat transfer, microflow and defect morphology into consideration. Based on this model, the healing processes of radial cracks, lateral cracks and Hertzian cracks are simulated, and three bubble formation mechanisms are identified. Firstly, excessive crack depth would lead to large temperature gradients at different positions of the crack. The area near the surface heals quickly and the air in the crack would be trapped to form bubbles. Secondly, for inclined cracks, the upper side has greater surface tension and lower viscosity, which can trap the air in the corner of the crack. Thirdly, for lateral cracks which do not have opening on the surface, they are not able to be healed and would shrink to huge spherical bubbles. Therefore, during the manufacturing process of fused silica optical components, the depth and inclination of the defects formed during mechanical processing should be strictly controlled. Based on these results, pretreatment methods like HF etching, which can widen the crack and expose defects that are difficult to heal, are proposed to increase the surface quality and material performance after laser healing.
Radial crack is taken as an example to reveal the critical conditions for crack healing. For cracks with an aspect ratio of 10, the condition for healing without bubble formation is that the crack depth dl is less than 13 μm. When 13 μm < dl < 30 μm, spherical bubbles will be formed; when dl > 30 μm, the crack is not able to be healed. For cracks with a depth of 15 μm, the condition for perfect healing is that the crack width is more than 5 μm. It is also found that a slight increase in width can accelerate the healing process. The crack healing conditions identified in this work can provide important guidance for the determination of technological parameters of the crack healing process in practical engineering.
Special surface morphologies including the surface pits after the bubbles escape, and the convex areas caused by the thermal expansion of the bubbles are predicted by the established model. Through the laser healing experiment, the formation of these morphologies induced by the healing of cracks are proved. Thus, the reliability of the laser healing model is verified.
In the future work, to verify the model quantitatively, typical defects would be created artificially for the laser healing experiment. In that case, more persuasive evidence would be provided. At the same time, more surface microstructures, e.g. scratches, surface pits, etc., as well as their characteristic parameters will be taken into consideration.
Funding
National Natural Science Foundation of China (51775147, 52175389); Consolidation Program for Fundamental Research (2019JCJQZDXX00); Young Elite Scientists Sponsorship Program by CAST (2018QNRC001); China Postdoctoral Science Foundation (2018T110288); Natural Science Foundation of Heilongjiang Province (YQ2021E021); Science Challenge Project (TZ2016006-0503-01); Self-Planned Task of State Key Laboratory of Robotics and System (HIT) (SKLRS201718A, SKLRS201803B); Southwest University of Science and Technology (19kfzk03).
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.
References
1. G. Drolshagen, “Impact effects from small size meteoroids and space debris,” Adv. Space Res. 41(7), 1123–1131 (2008). [CrossRef]
2. P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016). [CrossRef]
3. T. Suratwala, L. Wong, P. Miller, M. D. Feit, J. Menapace, R. Steele, P. Davis, and D. Walmer, “Sub-surface mechanical damage distributions during grinding of fused silica,” J. Non-cryst. Solids 352(52-54), 5601–5617 (2006). [CrossRef]
4. J. Cheng, M. Chen, W. Liao, H. Wang, J. Wang, Y. Xiao, and M. Li, “Influence of surface cracks on laser-induced damage resistance of brittle KH2PO4 crystal,” Opt. Express 22(23), 28740–28755 (2014). [CrossRef]
5. A. Temmler, C. B. Weingarten, B. Schober, and E. Uluz, “Investigation on laser beam figuring of fused silica using microsecond pulsed CO2 laser radiation,” Appl. Surf. Sci. 555, 149609 (2021). [CrossRef]
6. E. Mendez, K. M. Nowak, H. J. Baker, F. J. Villarreal, and D. R. Hall, “Localized CO2 laser damage repair of fused silica optics,” Appl. Optics 45(21), 5358–5367 (2006). [CrossRef]
7. S. T. Yang, M. J. Matthews, S. Elhadj, D. Cooke, G. M. Guss, V. G. Draggoo, and P. J. Wegner, “Comparing the use of mid-infrared versus far-infrared lasers for mitigating damage growth on fused silica,” Appl. Optics 49(14), 2606–2616 (2010). [CrossRef]
8. Z. Fang, Y. a. Zhao, W. Sun, Z. Li, G. Hu, X. Liu, D. Li, and J. Shao, “CO2 laser mitigation of the ultraviolet laser damage site on a fused silica surface,” Opt. Eng. 53(8), 084107 (2014). [CrossRef]
9. T. He, C. Wei, Z. Jiang, Y. Zhao, and J. Shao, “Super-smooth surface demonstration and the physical mechanism of CO2 laser polishing of fused silica,” Opt. Lett. 43(23), 5777–5780 (2018). [CrossRef]
10. K. L. Wlodarczyk, N. J. Weston, M. Ardron, and D. P. Hand, “Direct CO2 laser-based generation of holographic structures on the surface of glass,” Opt. Express 24(2), 1447–1462 (2016). [CrossRef]
11. L. J. Zhao, J. Cheng, Z. Y. Yin, H. Yang, Q. Liu, C. Tan, W. Liao, M. Chen, and X. Yuan, “Rapid CO2 laser processing technique for fabrication of micro-optics and micro-structures on fused silica materials,” Proc. Inst. Mech. Eng. Part B-J. Eng. Manuf, 0954405420937534 (2020).
12. M. Feit and A. M. Rubenchik, “Mechanisms of CO2 laser mitigation of laser damage growth in fused silica,” Proc. of SPIE 4932, 91 (2003). [CrossRef]
13. L. Robin, P. Combis, P. Cormont, L. Gallais, D. Hebert, C. Mainfray, and J.-L. Rullier, “Infrared thermometry and interferential microscopy for analysis of crater formation at the surface of fused silica under CO2 laser irradiation,” J. Appl. Phys. 111(6), 063106 (2012). [CrossRef]
14. T. Doualle, L. Gallais, P. Cormont, D. Hebert, P. Combis, and J. L. Rullier, “Thermo-mechanical simulations of CO2 laser-fused silica interactions,” J. Appl. Phys. 119(11), 113106 (2016). [CrossRef]
15. C. Tan, L. J. Zhao, M. J. Chen, J. Cheng, C. Wu, Q. Liu, H. Yang, Z. Yin, and W. Liao, “Experimental and theoretical investigation of localized CO2 laser interaction with fused silica during the process of surface damage mitigation,” Results Phys. 16, 102936 (2020). [CrossRef]
16. G. Guss, I. Bass, V. Draggoo, R. Hackel, S. Payne, M. Lancaster, and P. Mak, “Mitigation of growth of laser initiated surface damage in fused silica using a 4.6-micron wavelength laser,” Proc. of SPIE 6403, 64030M (2007). [CrossRef]
17. C. L. Zhang, C. M. Liu, X. Xiang, W. Dai, Z. G. Wang, L. Li, X. D. Yuan, S. B. He, and X. T. Zu, “Near-field modulated simulation of repaired site contained crack or bubble in fused silica subsurface,” Acta Phys. Sin. 61, 124214 (2012).
18. C. L. Zhang, C. M. Yao, and C. D. Wang, “Laser intensification induced by air bubbles below nonideal repaired damage site,” Optik 127(5), 3105–3108 (2016). [CrossRef]
19. L. J. Zhang, C. C. Zhang, J. Chen, Y. Bai, Y. L. Jiang, X. L. Jiang, H. J. Wang, X. Y. Luan, X.-D. Yuan, and W. Liao, “Formation and control of bubbles during the mitigation of laser-induced damage on fused silica surface,” Acta Phys. Sin. 67, 016103 (2018).
20. Z. Cao, C. Wei, X. Cheng, Y. Zhao, X. Peng, Z. Jiang, and J. Shao, “Ground fused silica processed by combined chemical etching and CO2 laser polishing with super-smooth surface and high damage resistance,” Opt. Lett. 45(21), 6014–6017 (2020). [CrossRef]
21. Y. G. Li, N. Zheng, H. B. Li, J. Hou, X. Y. Lei, X. H. Chen, Z. G. Yuan, Z. Z. Guo, J. A. Wang, Y. B. Guo, and Q. A. Xu, “Morphology and distribution of subsurface damage in optical fused silica parts: Bound-abrasive grinding,” Appl. Surf. Sci. 257(6), 2066–2073 (2011). [CrossRef]
22. D. W. Camp, M. R. Kozlowski, L. M. Sheehan, M. A. Nichols, M. Dovik, R. G. Raether, and I. M. Thomas, “Subsurface damage and polishing compound affect the 355-nm laser damage threshold of fused silica surfaces,” Proc. of SPIE 3244, 356 (1998). [CrossRef]
23. C. Zhang, L. Zhang, X. Jiang, B. Jia, W. Liao, R. Dai, J. Chen, X. Yuan, and X. Jiang, “Influence of pulse length on heat affected zones of evaporatively-mitigated damages of fused silica optics by CO2 laser,” Opt. Laser. Eng. 125, 105857 (2020). [CrossRef]
24. L. J. Zhao, J. Cheng, M. J. Chen, X. D. Yuan, W. Liao, H. J. Wang, Q. Liu, and H. Yang, “Toward little heat-affected area of fused silica materials using short pulse and high power CO2 laser,” Results Phys. 12, 1363–1371 (2019). [CrossRef]
25. R. M. Vignes, T. F. Soules, J. S. Stolken, R. R. Settgast, S. Elhadj, and M. J. Matthews, “Thermomechanical Modeling of Laser-Induced Structural Relaxation and Deformation of Glass: Volume Changes in Fused Silica at High Temperatures,” J. Am. Cream. Soc. 96(1), 137–145 (2013). [CrossRef]
26. C. Tan, L. J. Zhao, M. J. Chen, J. Cheng, H. Yang, Q. Liu, Z. Yin, and W. Liao, “Formation mechanism of surface morphology in the process of CO2 pulsed laser processing of fused silica optics,” Opt. Laser Technol. 138, 106838 (2021). [CrossRef]
27. P. Combis, P. Cormont, L. Gallais, D. Hebert, L. Robin, and J.-L. Rullier, “Evaluation of the fused silica thermal conductivity by comparing infrared thermometry measurements with two-dimensional simulations,” Appl. Phys. Lett. 101(21), 211908 (2012). [CrossRef]
28. S. T. Yang, M. J. Matthews, S. Elhadj, V. G. Draggoo, and S. E. Bisson, “Thermal transport in CO2 laser irradiated fused silica: In situ measurements and analysis,” J. Appl. Phys. 106(10), 103106 (2009). [CrossRef]
29. T. Doualle, D. Hebert, P. Combis, C. Hecquet, L. Gallais, and J.-L. Rullier, “Comparison between fused silica of type II and III after surface heating with a CO2 laser,” Appl. Phys. A-Mater. 122, 90 (2016). [CrossRef]
30. F. Cardarelli, Materials Handbook 8: Gases and Liquids (Harbin Institute of Technology, 2014).
31. T. Liu, K. Yang, Z. Zhang, L. Yan, B. Huang, H. Li, C. Zhang, X. Jiang, and H. Yan, “Hydrofluoric acid-based etching effect on surface pit, crack, and scratch and laser damage site of fused silica optics,” Opt. Express 27(8), 10705–10728 (2019). [CrossRef]
32. D. Wang, F. Fan, M. Liu, T. Tan, H. Li, and Y. Li, “Top-hat and Gaussian laser beam smoothing of ground fused silica surface,” Opt. Laser Technol. 127, 106141 (2020). [CrossRef]
