Open Access
Add to BibSonomy
Abstract
The growing applicability of glass materials drives the development of novel processing methods, which usually lack comprehensive comparison to conventional or state-of-art ones. That is especially delicate for assessing the flexural strength of glass, which is highly dependent on many factors. This paper compares the traditional top-down laser ablation methods in the air to those assisted with a flowing water film using picosecond pulses. Furthermore, the bottom-up cutting method using picosecond and nanosecond pulses is investigated as well. The cutting quality, sidewall roughness, subsurface damage and the four-point bending strength of 1 mm-thick soda-lime glass are evaluated. The flexural strength of top-down cut samples is highly reduced due to heat accumulation-induced cracks, strictly orientated along the sidewall. The subsurface crack propagation can be reduced using water-assisted processing, leading to the highest flexural strength among investigated techniques. Although bottom-up cut samples have lower flexural strength than water-assisted, bottom-up technology allows us to achieve higher cutting speed, taper-less sidewalls, and better quality on the rear side surface and is preferable for thick glass processing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Direct laser ablation is one of the several laser-based techniques widely used for material cutting and milling. During the direct ablation process, a laser beam is focused into a spot, with a laser fluence exceeding the ablation threshold of the material. Ablation begins at the top of the workpiece and propagates down to the bottom surface as the material is removed layer by layer [1]. Direct ablation has the most significant advantage in cutting of small size glass parts with a complex shape, inner contours with a low radius of curvature, glasses coated with reflective coatings or highly absorptive (colourised) glasses with minimal chipping and crack formation. However, the power input into the material should be precisely controlled since the glass has a relatively low heat conductivity which, due to local heat accumulation caused stress gradients, makes glass prone to cracking and chipping as the laser power increases [2], and, in extreme cases, could result in the complete destruction of the workpiece. Also, cutting speed quickly deteriorates with increasing thickness of the workpiece, limiting direct glass ablation to applications where high throughput is not critical.
However, the water-assisted direct material ablation is a promising method of reducing the thermal damage in the material caused by the laser process [3]. Different approaches can be used to introduce water into the ablation zone by spraying water mist [4,5] or water jet [6] onto the surface of the workpiece, or submerging the workpiece into a still [7] or moving water flow [8,9]. The presence of liquid in the ablation zone improves the cooling of the material, decreasing both the temperature and the temperature gradient [9,10]. This, in turn, allows the introduction of higher laser power into the glass material, accelerating the laser process. Additionally, convection and bubble formation during the liquid boiling and forced water flow is reported to improve the removal of ablation products from the ablation zone, reducing the laser beam shielding and allowing more laser energy to reach the material [8].
Moreover, the fluid movement removes most of the ablated material, minimising contamination around the processed area [11]. Finally, the formation and collapse of cavitation bubbles and confined plasma recoil pressure generate shockwaves, contributing to the efficient removal of material [10,12]. As a result, the water-assisted direct material ablation has been shown to improve the throughput and processing quality in metals [9,11], semiconductors [10,13] and dielectrics [4,5,14].
Alternatively to top-down techniques, transparent materials can be processed via a bottom-up approach when the laser beam is focused at the bottom of a sample. The processing debris is removed through the backside [2,15–20]. Therefore, the interaction of debris with the incident laser beam and scattering by ablated channel is reduced. Furthermore, the processing efficiency can be significantly increased using long nanosecond pulses due to induction of thermal stresses and the resultant generation of large glass fractures [2,17], facilitated by enhanced absorption of ground milled surfaces [21]. However, due to the fracturing nature of the processing, significant chipping on surfaces may be unacceptable and residual cracks may reduce the strength of fabricated parts. Alternatively, shorter picosecond pulses may be applied to enhance the quality [17,18]. However, the bottom-up cutting could not entirely replace top-down techniques since it is only applicable for glasses with relatively high transmission and good front surface quality.
Before entering the industry, the emerging glass processing techniques should be carefully validated regarding the process throughput, strength and quality of fabricated parts. The strength is typically assessed using bending configurations, which outcome depends on the specimen dimensions, testing setup and loading rate [22]. Therefore, the same bending conditions should be followed for different processing methods for comparability. However, there is little consistent and comprehensive investigation of state-of-the-art laser glass cutting, as most researchers focus only on the visual inspection and throughput increase. The bending strength of thick glass (≥ 4 mm) cut by the controlled fracture technique was investigated by A. Zhimalov et al. [23]. H. Cheng et al. evaluated the strength of thin (≤ 100 μm) glass cut by picosecond laser dicing [24]. H. Shin et al. investigated the Bessel beam-assisted volumetric scribing and cleaving [25], top-down [26] and bottom-up ablation [27] techniques for cutting of thin (100 μm) alumina-borosilicate samples. J. Li et al. investigated the cutting of 1 mm-thick soda-lime glass via laser filamentation only and filamentation together with V-shaped grooving of glass surface [28]. Recently, J. Dudutis et al. have investigated the volumetric Bessel beam-assisted scribing with induced directional transverse cracks using 1064 nm-wavelength 300 ps pulses and bottom-up cutting using 532 nm-wavelength nanosecond pulses and compared them to the conventional techniques – mechanical scribing, diamond-saw and waterjet cutting [29]. In this paper, the other laser-based cutting approaches were investigated – the top-down cutting in the air and assisted with a water layer using picosecond pulses and bottom-up cutting approach using picosecond and nanosecond pulses at the wavelength of 1064 nm. The surface quality, subsurface damage, sidewall quality and flexural strength of 1 mm-thick specimens were assessed. Furthermore, the flexural strength was modelled numerically, considering edge flaws and subcritical crack growth before glass failure.
2. Materials and methods
The soda-lime glass sheets with a thickness of 1 mm were cut into 45 × 5 mm2 stripes, using four different laser-based cutting approaches: (i) the top-down cutting in the air (TDC), (ii) the water-assisted top-down cutting (WATDC), (iii) the bottom-up cutting using a picosecond laser (ps-BUC) and (iv) the bottom-up cutting using a nanosecond laser (ns-BUC).
2.1 Top-down cutting in the air and assisted with water
Direct front-side ablation experiments were carried out using a DPSS laser Atlantic (Ekspla) operating at 1064 nm radiation wavelength and a pulse duration of ∼10 ps (at full-width at half-maximum (FWHM)). The laser beam was focused on the glass sample with a 100 mm focal length f-theta lens [ Fig. 1(a)]. The laser beam had a spatial intensity distribution close to Gaussian. The diameter of the focused spot was the same in the air and water-assisted conditions. In both cases, the minimum beam diameter at the focus position was approximately equal to 28 µm (at e-2 intensity level). Glass cutting was realised by scanning the laser beam with the galvanometer scanner IntelliSCAN 14se from ScanLab.
Fig. 1. (a) The experimental setup. (b) Thin flowing water layer formation on the glass surface in WATDC.
In the case of WATDC, a commercially available airbrush (bottom-fed, double-action) was used to spray water mist on top of the glass sample, forming a flowing water film [see Fig. 1(b)]. Deionised water was used at room temperature. The nozzle was set at the inclination angle of 45 degrees, while the tip of the nozzle was fixed 10 mm above the glass surface. An airbrush was connected to a compressed air supply at 3 bars. The airflow compressed water into a thin liquid film. The thickest water layer was measured close to the nozzle tip (730 μm) and gradually thinned out as the distance increased. As the laser cut line was positioned within the water sprayed area, water film variation was inevitable, ranging from 670 µm to 320 µm. However, variation in water layer thickness had no significant effect on the ablation efficiency or cutting quality of 1 mm thick glass sheets throughout the length of the cut.
The laser beam was scanned parallel to the water flow. Cuts were slightly shifted away from the nozzle tip to avoid any energy losses caused by the laser beam shielding in the water mist. To cut through 1 mm thick glass sheets via the direct laser ablation, cuts were widened by scanning a sequence of parallel lines separated by a hatch jump dy [ Fig. 2(a)]. Scanning started from the same position at every layer and was bi-directional to reduce the time when the laser is turned off. Furthermore, the focal spot position was adjusted after every scan sequence to maintain the optimal laser fluence. The distance dz by which the focal plane was shifted was optimised for the fastest cut through of a 1 mm-thick glass sheet. After through cut, the same process was applied to the following cuts. Afterwards, TDC and WATDC cuts (solid lines in Fig. 2(b)) were cut perpendicularly (dashed lines) to fabricate rectangular glass samples with a trapezoidal cross-section due to tapered sidewalls. It should be noted that the cuts indicated by dashed lines do not affect the results of the sample investigation.
Fig. 2. Schematic representation for laser beam scanning strategies for top-down and bottom-up cutting techniques. In the case of TDC (a, b), the bi-directional lines were scanned in a sequence to widen a cutting kerf. Scanning the sequence multiple times produced a rectangular shaped cut through in an SLG glass workpiece. In the case of BUC (c, d), the closed concentric rectangles were scanned outwards and inwards (increasing and decreasing rectangles) to increase the cutting kerf.
Multiple laser parameters were optimised for the fastest glass cutting in the air and water-assisted environment: average laser power P, pulse energy E, laser fluence Fl, pulse repetition rate f, laser beam scanning speed v (or pitch dx), hatch jump dy, focal plane shift dz, and cutting kerf width at the top surface w. In addition, the effective cutting speed for samples with the thickness t was evaluated without taking into account the time spent on jumps:
where k is the number of loops.The highest effective cutting speed of 45 mm-length cuts in 1 mm thick SLG glass in water-assisted condition (WATDC) was 0.34 mm/s. The latter speed was achieved using the following laser parameter set: P = 30.6 W, E = 34 µJ, Fl = 11 J/cm2, f = 903 kHz, v = 4290 mm/s, dx = 4.75 μm, dy = 15 μm, dz = 4.4 μm, w = 0.415 mm. The cutting speed was limited by the maximum average power of the used laser. Thus, higher speeds could be achieved with more powerful lasers.
Cutting in the air (TDC) was slower than in water-assisted conditions (0.26 mm/s). Furthermore, glass shattered due to the heat accumulation if cuts were performed close to each other. Therefore, the average laser power was reduced to 19.2 W to avoid the shattering of a glass sample. This corresponded to a decrease in pulse repetition rate from 853 to 558 kHz since fluence was fixed at an optimal value of 11 J/cm2. Corrections in average laser power and pulse repetition rate decreased the glass effective cutting speed to 0.19 mm/s (P = 19.2W, E = 34 µJ, Fl = 11 J/cm2, f = 558 kHz, v = 1730 mm/s, dx = 3.1 μm, dy = 20 μm, dz = 7 μm, w = 0.85 mm). Notably, the optimal cutting width was ∼2 times larger to cut samples in the air.
2.2 Bottom-up cutting technique using ps and ns laser pulses
The fundamental harmonic radiation (1064 nm) of the DPSS picosecond and nanosecond lasers (Ekspla) was used to conduct BUC experiments. The laser beam was focused to the diameter of 20.8 µm at the 1/e2 intensity level using a telecentric f-theta lens with a focal length of 80 mm. The position of the focused laser beam was moved in the XY plane using a galvanometer scanner excelliSCAN 14 (Scanlab). Samples were mounted on the positioning stage 8MT167-100 (Standa) with a stepper motor to move a sample along the vertical direction. In contrast to the top-down cutting techniques, the closed concentric rectangles with the intra-distance of dy were scanned outwards and inwards to increase the cutting kerf [Fig. 2(c)]. At the same time, the vertical position of a sample was changed continuously at the constant speed vz. At the initial stage of the cutting, the beam waist position was set slightly below the rear surface. This distance is referred to as the beam offset. The position of the waist was calculated theoretically via raytracing.
In the case of ps-BUC, the laser pulse duration at FWHM was ∼10 ps. The processing regime was: P = 19.6 W, E = 49 µJ, Fl = 28.7 J/cm2 (at the beam waist position), f = 400 kHz, dx = 10 µm, dy = 20 µm, vz = 0.0074 mm/s, a milled depth per layer was 4.3 µm, w = 0.4 mm. The beam offset was 0.5 mm. The effective cutting speed was equal to 0.74 mm/s, obtained by dividing the length of a contour by the processing time. Therefore, jumps on the corners were taken into account. After the processing, redeposited debris on sidewalls was cleaned away using a cleaning tissue.
In the case of ns-BUC, the laser pulse duration at FWHM was 12.5 ns. The processing regime was: P = 26 W, E = 130 µJ, Fl = 76.5 J/cm2 (at the beam waist position), f = 200 kHz, dx = 15 µm, dy = 20 µm, vz = 0.0074 mm/s, a milled depth per layer was 7.1 µm, w = 0.4 mm). The beam offset was 0.3 mm. The effective cutting speed was equal to 0.9 mm/s.
2.3 Sample characterisation
The sidewall roughness of TDC, WATDC and ps-BUC samples was measured using the optical profiler S neox (Sensofar). In contrast, ns-BUC samples were evaluated using the stylus profiler Dektak 150 (Veeco). Roughness was measured along the laser beam scanning direction, using the sampling and evaluation lengths specified in the ISO 4288:1996 [30]. 40 samples were evaluated for each cutting technique. Error bars appearing in graphs represent the standard deviation.
The quality of the edges at the front and rear surfaces of the cut samples was assessed using the optical microscope Eclipse LV100NDA (Nikon). The front surface is defined as one, which directly faces the incident laser beam. The maximum width of chipping and damaged area at both edges was defined for both surfaces in the central part (length of ∼20 mm) of 40 glass beam-shaped samples and averaged. The effective damage/cracking width was evaluated by measuring the ablated or cracked area at the edge, dividing by the characterisation length. 20 samples were evaluated for this case.
The flexural (bending) strength of cut samples was evaluated using the four-point bending setup, shown in Fig. 3(a). The distance between inner and outer supports, l and L, which faced the non-damaged glass surface, was equal to 16 mm and 30 mm, respectively. The force F at the breaking point was measured using the digital dynamometer FMI-S30A5 (Alluris) and an additional lever, extending the measuring range. The loading rate was 0.79 MPa/s. The bending stress was calculated according to the expression [31]:
where M is the bending moment, I is the moment of inertia, y is the distance to the neutral axis. For example, for samples with a trapezoidal cross-section (i.e. top-down cut samples with a tapered sidewall, as illustrated in Fig. 3(b)), the distance from the neutral axis to the front surface with a lower width is equal to [31]: where b1 and b2 are the sample width at the rear, and front surfaces (∼5 mm), t = ∼1 mm is the thickness of a beam. The moment of inertia can be calculated as [31]: For a sample with a rectangular cross-section (i.e. BUC samples), the distance y to the neutral axis equals half the plate thickness.Fig. 3. (a) Four-point bending setup, illustrating a plane crack and a chip-out on the edge of the tensioned surface. a and c denote the length and depth of a crack. (b) The trapezoidal cross-section of a sample.
After bending tests, results were arranged in ascending order. The failure probability of the ith sample was calculated according to [32]:
where n is the total amount of specimens. Failure probability was fitted by the two-parameter Weibull cumulative distribution function [33]: where m and σ0 are the shape and scale parameters, respectively. To estimate these parameters, ln(-ln(1-Pi)) was plotted against ln(σi) and fitted linearly by the least-squares method [34]. The shape parameter describes data scattering, which is reduced with an increase of the m value. The scale parameter σ0 defines the bending stress, at which there is a 63% probability to break a sample. The scale parameter was used to define the flexural strength of samples throughout the text unless otherwise stated. The glass failure originates at the tensioned side, which faces the outer supports. The flexural strength of both sides was evaluated, investigating 20 samples for each side.Additional samples were immersed in the 5% hydrofluoric acid (HF) solution to visualise the formation of subsurface cracks [35].
3. Results and discussion
3.1 Sidewall quality
Profiles of laser-cut samples, mechanically cleaved perpendicularly to a cut sidewall, are shown in Fig. 4. Both top-down cutting techniques, in the air (TDC) and water-assisted (WATDC), gave tapered sidewalls. Shallow ablated trenches have parabolic edges at the beginning of cutting due to the Gaussian intensity distribution [36]. After multiple layers, the reflection and scattering of the incident laser beam by an ablated groove and an increased projection on the sidewall take place as well, finally giving a typical V shape [36,37]. However, WATDC allowed decreasing the taper angle to 10 deg, compared to 16 deg, achieved in the air.
Fig. 4. The images of cleavage planes, obtained using an optical microscope. Samples were etched in a 5% HF solution for 10 min (TDC, WATDC) and 5 min (BUC). The solid red line in TDC shows ray propagation according to Snell’s law. Laser beam propagation direction is from top to bottom. Large cracks, mists, surface deviations, visible at the front and rear sides, are cleaving artefacts.
Furthermore, the optimal kerf for the fastest cutting was 2 times narrower in the WATDC technique due to the lower taper angle. Water-assisted processing results in higher plasma pressure, generation of stronger shock waves and the additional impact of cavitation bubble collapse and formation of liquid jets [11,38], leading to mechanical erosion and more efficient debris removal. As a result, steeper craters are formed [39]. Furthermore, the water layer may assist the beam transportation to the ablated zone due to the refractive index mismatch reduction between a channel and glass. Notably, the non-linear self-focusing in water could be excluded due to too low peak power of 2.5 MW, which was slightly below critical [40], equal to 3.1 MW, taking the non-linear refractive index n2 = 4.1 × 10−20 m2/W [41].
In contrast to TDC, the bottom-up techniques cut taper-less sidewalls due to constant processing conditions for every milled layer excluding surfaces. Compared to top-down techniques, the material was removed in the opposite direction, reducing the interaction with the laser beam. Furthermore, in BUC, the laser beam propagation to the interaction area was not affected by the shape of the fabricated channel.
The refraction and diffraction of the incident laser beam by the tapered sidewall [42,43] of TDC and WATDC samples led to the induction of subsurface modifications beneath the sidewall, seen in Fig. 4. For more detailed investigation, samples were etched in a 5% HF solution. The length of modifications was over 100 µm, and their direction followed Snell’s law for TDC samples considering air/glass interface. Since the sidewall was wavy in the case of TDC, the damage traces were more pronounced in zones, where the angle of incidence was lower, in agreement with a decrease of the Fresnel reflection coefficient. Spicular intra-volume modifications are attributed to the generation of high-density plasma of free electrons by laser radiation, leaked through the air/glass interface in the channel [42–44]. The induced modifications are speckled, therefore, are genuinely volumetric.
The analysis of the refraction angle, judged by spicular damage of WATDC samples, indicated that the refractive index of the material in the channel during laser processing is closer to the refractive index of air rather than water. Because of the short time separation between subsequent pulses (1.1 µs) and relatively low scanning speed (4.3 µm/µs) in comparison to the vapour bubble expansion rate of ∼10 µm/µs and the collapse time of cavitation bubbles of tens of microseconds [45], subsequent laser pulses interact with the bubble, which affects the beam propagation to the ablation site [46].
Spicular damage was absent in bottom-up cut samples, agreeing with results of BUC using femtosecond pulses by H. Shin et al. [27]. Furthermore, the pump-probe experiments by D. Grossmann et al. [44] revealed that energy deposition could be localised close to a crater by optimising processing parameters in the rear side ablation using picosecond pulses. In our case, only the subsurface cracks emanated from the sidewall were visible (see inset images in Fig. 4), with a length larger in the case of nanosecond pulses. In contrast to speckled modifications of TDC, herein etched paths were uniform, coming from sidewalls, and could be attributed to thermally induced subsurface cracks during processing. In the case of ps-BUC, cracks pointed slightly towards the front surface. Therefore, they counter-propagated to the incoming laser radiation. However, no clear direction of cracks was found for ns-BUC.
The topographies of sidewalls with the indicated laser beam propagation direction during processing are shown in Fig. 5. The measured sidewall roughness along the cutting direction, perpendicular to the beam propagation, is presented in Fig. 6(a). The lowest average roughness Ra of 0.28 µm was measured for TDC samples, which was 2.8 times smaller compared to WATDC (0.77 µm). The mechanical erosion of WATDC sidewalls could lead to higher roughness [11]. Furthermore, thermal effects play an essential role in TDC as well. Due to the high pulse repetition rate, the time separation between subsequent pulses (1.8 µs) in TDC was lower than the thermal diffusion time (e.g. several microseconds for borosilicate glass [42,47]). Therefore, the heat accumulation took place, considering the high overlap of laser-irradiated spots of 89% (1-dx/2ω0) 100%). Assistance with water allowed a higher pulse repetition rate, resulting in shorter time separation between pulses (1.1 µs), although the overlap was slightly lower (83%). Water-spraying allows to reduce the temperature in the processing zone as well as removes processing debris, which accumulation on sidewalls could contribute to the heat accumulation. Compared to top-down techniques, the lower overlap and repetition rate were used in bottom-up cutting techniques (28% and 200 kHz for ns-BUC and 52% and 400 kHz for ps-BUC).
Fig. 5. Topographies of cut sidewalls measured using an optical profiler. The area size is 1.77 mm x 1 mm. Red arrows indicate laser beam propagation direction during processing – from top to bottom in the case of TDC and WATDC and from left to right in the case of ps-BUC and ns-BUC.
Fig. 6. (a) The average roughness Ra and average peak-to-valley distance Rz of sidewalls measured along the laser beam scanning direction. Error bars indicate standard deviation. (b) The front side surface of the nearly cut channels. Scale bars are 100 µm-long.
In the case of ps-BUC (lower left image in Fig. 5), the short tapered zone could be observed close to the front surface, starting from about 50 µm-depth. The height of this layer is about 20 µm. Judging from optical microscope images of the front surface of nearly cut samples (see Fig. 6(a)), this phenomenon was caused by the mixed rear side ablation with the front side ablation, which starts when the focal position of the laser beam is close enough to the front surface. As a result, the fluence is high enough to damage the material, enhancing radiation absorption and disrupting the further beam propagation to the bottom-up ablated channel. The threshold fluence for the front side ablation could also be lowered by subsurface cracks [48], originating from the groove top and propagating to the surface. However, the micro taper was absent in the case of nanosecond pulses, where the chamfered edges were formed due to glass chipping, typical for this type of material processing [49]. Therefore, lower peak intensity leads to more localised energy deposition on the crater at the bottom side [44]. Indeed, in the case of ps-BUC, the peak intensity at the beam waist position was more than 400 times larger compared to ns-BUC (Ipeak ∼ 2.7 × 1012 W/cm2 vs 5.8 × 109 W/cm2), whereas the threshold intensity is only ∼35 times larger for picosecond pulses, according to τ1/2 the dependence of the damage fluence [50].
Consequently, the front-side ablation was less pronounced using nanosecond pulses. Nanosecond laser processing results in a rougher milled surface with longer subsurface cracks, enhancing the laser intensity locally [48,51,52]. Therefore, the rougher surface can be processed with lower fluence compared to smooth surfaces [21]. Furthermore, longer cracks lead to higher stress intensity. Therefore, the material is more prone to cracking [53]. Furthermore, the cracking and chipping process may hinder the front side ablation since the material is fractured into the larger debris using nanosecond pulses [17].
The average roughness of ps-BUC samples was slightly larger than WATDC samples and equalled 1.03 µm. ns-BUC samples had the largest roughness of 3.2 µm – more than twice larger than the bottom-up technique (Ra ∼ 1.4 µm) using the 532 nm-wavelength nanosecond laser in our previous research [29]. The average peak-to-valley distance (Rz roughness) was 8-9.4 times larger than Ra for investigated techniques [Fig. 6(a)].
3.2 Surface damage
Exemplary surface images of cut samples are shown in Fig. 7. The front-side surface quality was clearly better for the picosecond-laser made TDC and WATDC samples compared to the BUC samples, especially fabricated by nanosecond pulses, where the dominant cutting mechanism is the local cracking of the material. The measured maximum surface damage width is presented in Fig. 8(a). The maximum width was measured for each edge of the investigated specimens and then averaged. The mean damage width of the front side of TDC and WATDC samples was 12 µm and 22 µm, respectively. These values were considerably lower than the mean damage width of ps-BUC and ns-BUC samples (50 µm and 102 µm).
Fig. 7. The images of the front and rear sides of cut samples. The upper right image illustrates the induction of rear side damage in TDC and WATDC.
Fig. 8. (a) The mean maximum surface damage width. (b) The effective damage width, obtained by dividing the damaged area by the evaluation length. Error bars indicate standard deviation.
The quality of the rear-side surface of TDC and WATDC samples was worse compared to the front side, which is typical for the top-down ablation of transparent materials [26,54–57]. Two different modification zones could be observed in both top-down techniques: (i) the uniformly damaged zone close to the edge, caused by the laser ablation with light escaping through the flat bottom of a channel; (ii) speckled periodical surface damage at longer distances from the edge, which is a result of the light refraction and diffraction at the tapered sidewall as schematically illustrated in the upper right image in Fig. 7. However, due to lack of uniformity and sample-to-sample variation, these tracks were not considered in damage width measurements, provided in Fig. 8(a). The mean width of the uniform rear-side surface damage was equal to 51 µm and 58 µm for TDC and WATDC techniques, respectively. The uneven ablation-driven rear-side surface damage was not observed in ps-BUC and ns-BUC samples due to the taper-less milling process and higher scattering losses by rougher sidewalls.
In contrast to the top-down techniques, the surface quality of BUC samples was better at the rear side. The mean maximum damage width was equal to 20 µm and 96 µm on the rear side of ps-BUC and ns-BUC samples, respectively. The degradation of BUC samples at the front surface could be caused by the initiation of the front side ablation mentioned in the previous section and the shattering of a thin glass layer at the very end of cutting.
The effective damage width, calculated by dividing the damaged area by the evaluation length, is shown in Fig. 8(b). Effective width was significantly reduced for BUC samples compared to maximum defects. For example, the rear side effective damage width was reduced to 8 µm and 21 µm for ps-BUC and ns-BUC, outperforming TDC and WATDC techniques (34 µm and 44 µm). Severe glass cracking and chipping are stochastic processes, occurring accidentally along a cut edge.
3.3 Flexural strength
Laser-cut samples were broken using the four-point bending set up at the loading rate of 0.79 MPa/s. The failure probability of samples for the applied bending stress with two-parameter Weibull cumulative distribution fits are shown in Fig. 9. Summarised data are given in Table 1.
Fig. 9. The failure probability versus applied bending stress on samples, cut using different technologies. Experimentally measured data are shown as open dots. Solid and dashed lines show the fitted Weibull cumulative distribution. Dash dotted lines in the second graph from the top represent the mechanical scribing and cleaving [29]. Dashed lines in WATDC and ns-BUC graphs were taken from the previous research using the mechanical score and break method and the 532 nm-wavelength nanosecond laser BUC [29]. Horizontal dotted lines show a 63% probability to break samples (Weibull scale parameter).
Table 1. The flexural strength of samples cut with different technologies.
The highest flexural strength of 134 MPa (Weibull scale parameter) was on the front side of WATDC samples. The strength was similar to the processed edge of mechanically scribed and cleaved samples (134 MPa [29]). However, the strength of WATDC samples was still far lower than the strength of the opposite side of the mechanically scribed surface (181 MPa [29]), which had the mirror-like quality obtained during a cleaving stage. However, in the case of laser-based WATDC, the shape parameter is larger compared to mechanically scribed and separated samples (12 (front side) and 9 (rear side) versus 5 and 4, respectively [29]). The probability curves of WATDC intersects with the failure probability curve of the front side of mechanically scribed and cleaved samples at 128-133 MPa. Therefore, WATDC samples were broken more predictably with a lower failure probability below this bending stress value. Considering much more conservative requirements than a 63% probability of failure for most applications, WATDC overcomes mechanical scribing and cleaving method.
It should be mentioned that in previous research in [29], samples were broken at a higher loading rate (1.64 MPa/s). The influence of the loading rate will be discussed in section 3.5. According to numerical calculations, this would give a slight (∼4%) difference.
The flexural strength of the front and rear sides of TDC samples in the air was significantly reduced and equal to 89 MPa and 77 MPa, respectively. This result was comparable to ns-BUC samples (84 MPa and 81 MPa). However, TDC samples were broken more predictably, having the shape parameter (10 and 21) larger than ns-BUC samples (8). The flexural strength of ns-BUC samples was comparable to the strength of the rear side of the samples, cut using the BUC technique with the 532 nm-wavelength nanosecond laser (the probability curves are dashed lines in Fig. 9) in [29]. However, the strength of the front side was higher using the 532 nm-wavelength [29]. The flexural strength of bottom-up cut samples using picosecond pulses was lower than WATDC samples but larger than ns-BUC and TDC samples. Also, the shape parameter was large (13 and 19).
Post mortal analysis revealed that the failure during bending mainly was initiated at the edge of a sample. However, we found 4 WATDC rear-side-tensioned samples, which failure originated away from the edge up to 1 mm distance. Judging that this phenomenon occurred only for rear-side tensioning, and etched pits in HF-treated samples were visible up to the comparable distance from the edge, this type of failure could be caused by the speckled damage seen on the rear side.
3.4 Flexural strength dependence on the cutting quality
To investigate the influence of the surface damage and sidewall roughness on the flexural strength of cut samples, data were collected from the current and previous research in [29]. Overall, 9 different technologies were compared: laser-based TDC, WATDC, ps-BUC, ns-BUC at 1064 nm-wavelength in this paper and Bessel beam-assisted volumetric scribing and cleaving, ns-BUC (532 nm), waterjet, diamond-saw, mechanical scribing and cleaving in [29]. We did not observe the direct correlation between the front or rear side surface quality and measured flexural strength among different techniques, even though it could explain some results. For instance, the worse quality of the rear side surface of TDC and WATDC samples could explain the decrease in strength of this side. However, contradictory results are observed for samples cut by different techniques. For instance, WATDC samples demonstrated the largest strength, although their surface quality was worse than TDC. The measured maximum or effective surface damage width mainly results from chipping during processing or rear-side surface ablation, which generate blunt flaws with the reduced stress intensity factor, and, therefore, having a lower impact on the flexural strength of specimens [35].
It could be observed in Fig. 10 that, with some exceptions, the strength of specimens deteriorates with the increase of the sidewall roughness Rz. That was the only quantitative parameter that allowed us to assess the flexural strength of different specimens in a non-destructive manner. This is an expected result since a rougher surface is supposed to have larger defects, which act as local stress concentrators [58]. However, TDC showed discrepant results – their mechanical strength was low, despite the low surface damage and sidewall roughness.
Fig. 10. The mean flexural strength versus average peak-to-valley distance (Rz) of non-etched sidewalls. Error bars indicate standard deviation. Data related to Bessel beam-assisted volumetric scribing and cleaving, ns-BUC (532 nm) milling, waterjet, diamond-saw cutting, mechanical scribing and cleaving were collected from [29].
For further investigation, samples were etched in a 5% HF solution to reveal the subsurface flaws. SEM images of the sidewalls of non-etched and etched samples are shown in Fig. 11. In the case of TDC, the long straight cracks at the normal direction to the surface appeared after only 1 min of etching. After 2 minutes of etching, cracks vanished near the front side, indicating their shorter depth. Therefore, this would explain the higher flexural strength of this side. In the case of WATDC, cracks were shorter, and sidewalls of specimens consisted of local damage sites, which interconnect only at a short range. Etching of ps-BUC and ns-BUC samples resulted in the worm-like morphology of sidewalls. After long etching, some cracks interconnected together, but their direction was not as strict as in the TDC case.
Long cracks in TDC could be developed by the thermal accumulation [42,59], while initial cracking could be possibly onset by induced stress waves in the vicinity of the bottom of the ablated trench [60]. Sidewall heating increases with an increase of the ablated depth since the laser beam is always scanned along the same path in the XY plane. This could explain the increase of cracks density at the bottom of the sidewall. Furthermore, the projection of the laser beam on the tapered sidewall gives an elongated heated zone with a more uniform distribution of induced stresses, resulting in well-orientated cracks. On the contrary, thermal effects are significantly reduced in WATDC due to efficient cooling and mechanically assisted material removal [10]. As a result, the development of cracks by subsequent laser beam passes is reduced.
In BUC techniques, we could expect that cracks in the sidewall are not continuously opened as in the case of TDC due to the reverse cutting direction. Also, at lower overlaps of laser-irradiated spots, micro notches should dominate over planar cracks, as demonstrated in [42]. The likely nature of notches is the intersection of cracks originated from different sites, causing large debris to chip out.
For sidewall roughness evaluation, one etched specimen was measured using an optical profiler at different positions for each method. The average peak to valley distance Rz increased with the etching duration since the penetration of flaws into the material is larger than could be measured using a profiler. However, at very long etching durations, we would expect the coalescence of individual etched pits, which would lead to the roughness decrease [35]. After 5 min of etching, the largest roughness was of an ns-BUC sample, equalling 39 µm. The lowest roughness of 7 µm was measured for a TDC sample.
3.5 Simulation of the flexural strength
The flexural strength was modelled according to linear elastic fracture mechanics, based on the simplified assumption that the planar quarter elliptical cracks originate on the edge having the length a and depth c (see the inset image in Fig. 12), and specimens are instantaneously broken when the critical stress intensity factor is reached (KI = KIC), which is typically equal to 0.75 MPa m1/2 for soda-lime glass [22]. Since samples were not instantaneously loaded in our experiments (the loading rate was 0.79 MPa/s), the subcritical crack growth was considered:
Fig. 12. Solid and dashed lines show the simulated flexural strength versus crack depth c for different crack lengths a (5–200 µm). Solid and dashed lines represent 0.79 MPa/s and 1.64 MPa/s loading rates, respectively. It should be noted that some values drop out from the validation range 0.2 ≤ a/c ≤ 2 by Newman and Raju [64]. Solid dots represent experimental data, assuming that the crack width is equal to the measured average peak-to-valley distance Rz of sidewalls etched in a 5% HF solution for 1 min (TDC front side), 2 min (TDC rear side and WATDC) and 5 min (BUC). Error bars indicate standard deviation.
The modelled flexural strength dependence on the crack depth c is shown in Fig. 12 as solid and dashed lines, representing 0.79 MPa/s and 1.64 MPa/s loading rates, respectively. The latter loading rate was used in our previous experiments [29]. Thus, at a larger loading rate, we would expect only slightly larger strength values (∼4%), which is within error bars of the measured flexural strength.
It is observed that the flexural strength strongly depends on the crack length, explaining the low strength of TDC samples, which have long straight cracks on the sidewall observed after etching [Fig. 11], even though their depth is lower compared to other methods, judged by the fast vanishing of traces of cracks and low surface roughness after etching. The experimental data was plotted in Fig. 12, assuming that the crack depth is equal to the sidewall roughness Rz after etching in a 5% HF solution for 1 min (TDC front side), 2 min (TDC rear side and WATDC) and 5 min (BUC). One sample was investigated per each method and etching duration using an optical profiler. Shorter etching durations were selected for TDC and WATDC due to the fast vanishing of traces of etched cracks in these techniques. Their roughness further increased with the increase of etching time with pitted morphology, seen in Fig. 11, probably due to the opening and coalescence of intra-volume speckled damage. In comparison, cracks were visible for BUC techniques even after 5 min etching. For this duration, the Rz values were 39 µm and 17 µm for ns-BUC and ps-BUC samples, respectively, comparable to the visible cracks observed of cleavage planes of separated samples [Fig. 4]. Fairly good correspondence was observed between measured and modelled flexural strength for TDC. The strength was underestimated for WATDC and BUC samples, assuming that the length of cracks reaches several tens of micrometres. The etched-out cracks are not strictly perpendicular to the surface. As a result, cracks were not in the pure opening mode, and the stress intensity factor for this mode was reduced [65].
4. Summary and conclusions
In this paper, we have comprehensively investigated different laser-based techniques for 1 mm-thick soda-lime glass cutting. The traditional top-down cutting technique in the air (TDC) was compared to the top-down cutting assisted with spraying a thin water layer (WATDC) using a picosecond laser and the bottom-up cutting using picosecond and nanosecond pulses (ps-BUC and ns-BUC) at the wavelength of 1064 nm. In addition, the cutting quality and the flexural strength using the four-point bending setup at a loading rate of 0.79 MPa/s was investigated.
Top-down cutting techniques gave the lowest sidewall roughness and the excellent quality of the front side surface compared to the bottom-up techniques. For example, the average roughness of TDC and WATDC samples was equal to 0.28 µm and 0.77 µm, respectively, while the mean maximum damage width was equal to 12 µm and 22 µm. However, the quality at the rear side of top-down samples was poor, with speckled modifications extending over 100 µm from the cut edge. Furthermore, the intra-volume subsurface modifications were observed beneath the ablated sidewall. Both phenomena were caused by the laser beam transmission and propagation effects through the tapered sidewall.
On the contrary, speckled surface and volumetric modifications were absent in BUC techniques. Herein only cracks, propagated from the channel were observed, having the length of tens of micrometres. The surface quality was comparable on both sides of ns-BUC samples with the mean maximum damage width of 100 µm. However, the quality can be enhanced using picosecond pulses. Therefore, considering the tapered sidewall and severe rear-side damage during the top-down cutting, the bottom-up approach is preferable for thick glass cutting. Furthermore, the achieved processing speed is larger in bottom-up cutting.
TDC samples demonstrated significantly deteriorated strength to 89 MPa and 77 MPa (Weibull scale parameter) of the front and rear sides, which is unexpected due to the highest visual quality. The etching of samples in a HF solution revealed straight and long cracks in the sidewall, which could be generated and opened due to thermal accumulation during processing. Numerical modelling justified a strong influence of the crack length along the sidewall on the flexural strength. Therefore, care must be taken when assessing the strength of samples only by roughness as an indicator of a flaw depth.
The front side of WATDC samples demonstrated the highest flexural strength of 134 MPa due to the localised mechanical impact and an efficient sample cooling with flowing water, preventing the growth of cracks. Considering this, WATDC technology would be an excellent tool for manufacturing small-sized parts from thin glass plates.
Funding
Lietuvos Mokslo Taryba (LMTLT) (01.2.2-LMT-K-718-01-0003).
Acknowledgments
This project has received funding from European Regional Development Fund (project No 01.2.2-LMT-K-718-01-0003) under a grant agreement with the Research Council of Lithuania (LMTLT).
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. M. Kumkar, L. Bauer, S. Russ, M. Wendel, J. Kleiner, D. Grossmann, K. Bergner, and S. Nolte, “Comparison of different processes for separation of glass and crystals using ultrashort pulsed lasers,” Proc. SPIE 8972, 897214 (2014). [CrossRef]
2. P. Gečys, J. Dudutis, and G. Račiukaitis, “Nanosecond Laser Processing of Soda-Lime Glass,” J. Laser Micro/Nanoengineering 10(3), 254–258 (2015). [CrossRef]
3. V. Tangwarodomnukun and C. Dumkum, “Experiment and analytical model of laser milling process in soluble oil,” Int J Adv Manuf Technol 96(1-4), 607–621 (2018). [CrossRef]
4. E. Markauskas and P. Gečys, “Thin water film assisted glass ablation with a picosecond laser,” Procedia CIRP 74, 328–332 (2018). [CrossRef]
5. E. Markauskas, L. Zubauskas, and P. Gečys, “Efficient milling and cutting of borosilicate glasses through a thin flowing water film with a picosecond laser,” J. Manuf. Process. 68, 898–909 (2021). [CrossRef]
6. V. Tangwarodomnukun, P. Likhitangsuwat, O. Tevinpibanphan, and C. Dumkum, “Laser ablation of titanium alloy under a thin and flowing water layer,” Int. J. Mach. Tools Manuf. 89, 14–28 (2015). [CrossRef]
7. S. van der Linden, R. Hagmeijer, and G. R. B. E. Römer, “Picosecond pulsed underwater laser ablation of silicon and stainless steel: Comparing crater analysis methods and analysing dependence of crater characteristics on water layer thickness,” Appl. Surf. Sci. 540, 148005 (2021). [CrossRef]
8. W. Charee and V. Tangwarodomnukun, “Dynamic features of bubble induced by a nanosecond pulse laser in still and flowing water,” Opt. Laser Technol. 100, 230–243 (2018). [CrossRef]
9. I. Nicolae, M. Bojan, C. Viespe, and D. Miu, “Repetition Rate Effects in Picosecond Laser Microprocessing of Aluminum and Steel in Water,” Micromachines 8(11), 316 (2017). [CrossRef]
10. G. Y. Mak, E. Y. Lam, and H. W. Choi, “Liquid-immersion laser micromachining of GaN grown on sapphire,” Appl. Phys. A 102(2), 441–447 (2011). [CrossRef]
11. N. Krstulović, S. Shannon, R. Stefanuik, and C. Fanara, “Underwater-laser drilling of aluminum,” Int J Adv Manuf Technol 69(5-8), 1765–1773 (2013). [CrossRef]
12. O. Supponen, D. Obreschkow, M. Tinguely, P. Kobel, N. Dorsaz, and M. Farhat, “Scaling laws for jets of single cavitation bubbles,” J. Fluid Mech. 802, 263–293 (2016). [CrossRef]
13. H. Liu, F. Chen, X. Wang, Q. Yang, H. Bian, J. Si, and X. Hou, “Influence of liquid environments on femtosecond laser ablation of silicon,” Thin Solid Films 518(18), 5188–5194 (2010). [CrossRef]
14. Y. Li, S. Qu, and Z. Guo, “Fabrication of microfluidic devices in silica glass by water-assisted ablation with femtosecond laser pulses,” J. Micromech. Microeng. 21(7), 075008 (2011). [CrossRef]
15. Y. Li, K. Itoh, W. Watanabe, K. Yamada, D. Kuroda, J. Nishii, and Y. Jiang, “Three-dimensional hole drilling of silica glass from the rear surface with femtosecond laser pulses,” Opt. Lett. 26(23), 1912–1914 (2001). [CrossRef]
16. D. J. Hwang, T. Y. Choi, and C. P. Grigoropoulos, “Liquid-assisted femtosecond laser drilling of straight and three-dimensional microchannels in glass,” Appl. Phys. A 79(3), 605–612 (2004). [CrossRef]
17. D. Ashkenasi, T. Kaszemeikat, N. Mueller, A. Lemke, and H. J. Eichler, “Machining of glass and quartz using nanosecond and picosecond laser pulses,” Proc. SPIE 8243, 82430M (2012). [CrossRef]
18. Z. K. Wang, W. L. Seow, X. C. Wang, and H. Y. Zheng, “Effect of laser beam scanning mode on material removal efficiency in laser ablation for micromachining of glass,” J. Laser Appl. 27(S2), S28004 (2015). [CrossRef]
19. V. Tomkus, V. Girdauskas, J. Dudutis, P. Gečys, V. Stankevič, and G. Račiukaitis, “High-density gas capillary nozzles manufactured by hybrid 3D laser machining technique from fused silica,” Opt. Express 26(21), 27965–27977 (2018). [CrossRef]
20. S. Schwarz, S. Rung, C. Esen, and R. Hellmann, “Ultrashort pulsed laser backside ablation of fused silica,” Opt. Express 29(15), 23477–23486 (2021). [CrossRef]
21. K. Nagayama, Y. Kotsuka, T. Kajiwara, T. Nishiyama, S. Kubota, and M. Nakahara, “Pulse laser ablation of ground glass,” Shock Waves 17(3), 171–183 (2007). [CrossRef]
22. M. Haldimann, A. Luible, and M. Overend, Structural Use of Glass (International Association for Bridge and Structural Engineering, 2008).
23. A. B. Zhimalov, V. F. Solinov, V. S. Kondratenko, and T. V. Kaplina, “Laser cutting of float glass during production,” Glas. Ceram. 63(9-10), 319–321 (2006). [CrossRef]
24. H.-C. Cheng, K.-H. Li, C.-Y. Shih, and W.-H. Chen, “Characterization of the Flexural Strength and Fatigue Life of Ultrathin Glass After Dicing,” IEEE Trans. Components, Packag. Manuf. Technol. 8(12), 2213–2221 (2018). [CrossRef]
25. H. Shin and D. Kim, “Strength of ultra-thin glass cut by internal scribing using a femtosecond Bessel beam,” Opt. Laser Technol. 129, 106307 (2020). [CrossRef]
26. H. Shin and D. Kim, “Cutting thin glass by femtosecond laser ablation,” Opt. Laser Technol. 102, 1–11 (2018). [CrossRef]
27. H. Shin, J. Noh, and D. Kim, “Bottom-up cutting method to maximize edge strength in femtosecond laser ablation cutting of ultra-thin glass,” Opt. Laser Technol. 138, 106921 (2021). [CrossRef]
28. J. Li, E. Ertorer, and P. R. Herman, “Ultrafast laser burst-train filamentation for non-contact scribing of optical glasses,” Opt. Express 27(18), 25078–25090 (2019). [CrossRef]
29. J. Dudutis, J. Pipiras, R. Stonys, E. Daknys, A. Kilikevičius, A. Kasparaitis, G. Račiukaitis, and P. Gečys, “In-depth comparison of conventional glass cutting technologies with laser-based methods by volumetric scribing using Bessel beam and rear-side machining,” Opt. Express 28(21), 32133–32151 (2020). [CrossRef]
30. “Geometrical Product Specifications (GPS) - Surface texture: Profile method - Rules and procedures for the assessment of surface texture,” ISO 4288:1996 (1996).
31. F. S. Merritt and J. T. Ricketts, Building Design and Construction Handbook (McGraw-Hill Professional, 2000).
32. J. D. Sullivan and P. H. Lauzon, “Experimental probability estimators for Weibull plots,” J. Mater. Sci. Lett. 5(12), 1245–1247 (1986). [CrossRef]
33. W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech. 18(3), 293–297 (1951). [CrossRef]
34. K. C. Datsiou and M. Overend, “Weibull parameter estimation and goodness-of-fit for glass strength data,” Struct. Saf. 73, 29–41 (2018). [CrossRef]
35. M. Kolli, M. Hamidouche, N. Bouaouadja, and G. Fantozzi, “HF etching effect on sandblasted soda-lime glass properties,” J. Eur. Ceram. Soc. 29(13), 2697–2704 (2009). [CrossRef]
36. M. Sun, U. Eppelt, S. Russ, C. Hartmann, C. Siebert, J. Zhu, and W. Schulz, “Numerical analysis of laser ablation and damage in glass with multiple picosecond laser pulses,” Opt. Express 21(7), 7858–7867 (2013). [CrossRef]
37. S. Butkus, E. Gaižauskas, L. Mačernytė, V. Jukna, D. Paipulas, and V. Sirutkaitis, “Femtosecond Beam Transformation Effects in Water, Enabling Increased Throughput Micromachining in Transparent Materials,” Appl. Sci. 9(12), 2405 (2019). [CrossRef]
38. A. Kruusing, “Underwater and water-assisted laser processing: Part 1—general features, steam cleaning and shock processing,” Opt. Lasers Eng. 41(2), 307–327 (2004). [CrossRef]
39. L. M. Wee, E. Y. K. Ng, A. H. Prathama, and H. Zheng, “Micro-machining of silicon wafer in air and under water,” Opt. Laser Technol. 43(1), 62–71 (2011). [CrossRef]
40. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
41. C. B. Marble, J. E. Clary, G. D. Noojin, S. P. O’Connor, D. T. Nodurft, A. W. Wharmby, B. A. Rockwell, M. O. Scully, and V. V. Yakovlev, “Z-scan measurements of water from 1150 to 1400 nm,” Opt. Lett. 43(17), 4196 (2018). [CrossRef]
42. M. Sun, U. Eppelt, C. Hartmann, W. Schulz, J. Zhu, and Z. Lin, “Damage morphology and mechanism in ablation cutting of thin glass sheets with picosecond pulsed lasers,” Opt. Laser Technol. 80, 227–236 (2016). [CrossRef]
43. C. Kalupka, D. Großmann, and M. Reininghaus, “Evolution of energy deposition during glass cutting with pulsed femtosecond laser radiation,” Appl. Phys. A 123(5), 376 (2017). [CrossRef]
44. D. Grossmann, M. Reininghaus, C. Kalupka, M. Jenne, and M. Kumkar, “In-situ microscopy of front and rear side ablation processes in alkali aluminosilicate glass using ultra short pulsed laser radiation,” Opt. Express 25(23), 28478–28488 (2017). [CrossRef]
45. J. Long, M. H. Eliceiri, L. Wang, Z. Vangelatos, Y. Ouyang, X. Xie, Y. Zhang, and C. P. Grigoropoulos, “Capturing the final stage of the collapse of cavitation bubbles generated during nanosecond laser ablation of submerged targets,” Opt. Laser Technol. 134, 106647 (2021). [CrossRef]
46. D. Zhang, B. Gökce, S. Sommer, R. Streubel, and S. Barcikowski, “Debris-free rear-side picosecond laser ablation of thin germanium wafers in water with ethanol,” Appl. Surf. Sci. 367, 222–230 (2016). [CrossRef]
47. M. Sakakura, M. Terazima, Y. Shimotsuma, K. Miura, and K. Hirao, “Heating and rapid cooling of bulk glass after photoexcitation by a focused femtosecond laser pulse,” Opt. Express 15(25), 16800–16807 (2007). [CrossRef]
48. N. Bloembergen, “Role of Cracks, Pores, and Absorbing Inclusions on Laser Induced Damage Threshold at Surfaces of Transparent Dielectrics,” Appl. Opt. 12(4), 661–664 (1973). [CrossRef]
49. V. Tomkus, V. Girdauskas, J. Dudutis, P. Gečys, V. Stankevič, and G. Račiukaitis, “Impact of the wall roughness on the quality of micrometric nozzles manufactured from fused silica by different laser processing techniques,” Appl. Surf. Sci. 483, 205–211 (2019). [CrossRef]
50. B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996). [CrossRef]
51. L. Zhang, W. Chen, and L. Hu, “Systematic investigation on light intensification by typical subsurface cracks on optical glass surfaces,” Appl. Opt. 52(5), 980–989 (2013). [CrossRef]
52. 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]
53. M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser-induced surface damage,” Proc. SPIE 5273, 264–272 (2004). [CrossRef]
54. S. Russ, C. Siebert, U. Eppelt, C. Hartmann, B. Faißt, and W. Schulz, “Picosecond laser ablation of transparent materials,” Proc. SPIE 8608, 86080E (2013). [CrossRef]
55. A. R. Collins and G. M. O’Connor, “Mechanically inspired laser scribing of thin flexible glass,” Opt. Lett. 40(20), 4811–4814 (2015). [CrossRef]
56. X. Sun, J. Zheng, C. Liang, Y. Hu, H. Zhong, and J. Duan, “Improvement of rear damage of thin fused silica by liquid-assisted femtosecond laser cutting,” Appl. Phys. A 125(7), 461 (2019). [CrossRef]
57. S. Indrišiūnas, E. Svirplys, J. Jorudas, and I. Kašalynas, “Laser Processing of Transparent Wafers with a AlGaN/GaN Heterostructures and High-Electron Mobility Devices on a Backside,” Micromachines 12(4), 407 (2021). [CrossRef]
58. P. P. Kist, I. L. Aurélio, M. Amaral, and L. G. May, “Effect of the bur grit size on the flexural strength of a glass-ceramic,” Cerâmica 62(362), 121–127 (2016). [CrossRef]
59. K. L. Wlodarczyk, A. Brunton, P. Rumsby, and D. P. Hand, “Picosecond laser cutting and drilling of thin flex glass,” Opt. Lasers Eng. 78, 64–74 (2016). [CrossRef]
60. Y. Ito, R. Shinomoto, K. Nagato, A. Otsu, K. Tatsukoshi, Y. Fukasawa, T. Kizaki, N. Sugita, and M. Mitsuishi, “Mechanisms of damage formation in glass in the process of femtosecond laser drilling,” Appl. Phys. A 124(2), 181 (2018). [CrossRef]
61. P. Dwivedi and D. J. Green, “Indentation Crack-Shape Evolution during Subcritical Crack Growth,” J. Am. Ceram. Soc. 78(5), 1240–1246 (1995). [CrossRef]
62. R. Dugnani and R. Zednik, “Flexural strength by fractography in modern brittle materials,” J. Am. Ceram. Soc. 96(12), 3908–3914 (2013). [CrossRef]
63. L. Ma, H. Sun, and R. Dugnani, “Shape Evolution of Unstable, Flexural Cracks in Brittle Materials,” J. Mater. Eng. Perform. 29(2), 1311–1320 (2020). [CrossRef]
64. J. James, C. Newman, and I. S. Raju, “Stress-Intensity Factor Equations for Cracks in Three-Dimensional Finite Bodies Subjected to Tension and Bending Loads,” NASA Technical Memorandum 85793 (1984).
65. T. L. Anderson, Fracture Mechanics (CRC Press, 2005).
