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Abstract
With the development of industrial lasers and novel glass processing techniques, which offer high speed, quality and precision, this becomes an attractive alternative to conventional methods, such as mechanical scribing and cleaving, diamond saw and waterjet cutting, commonly used in the industry. However, the emerging techniques lack thorough validation with respect to well-established methods. To this end, we present a detailed comparison of different glass cutting methods, taking into account surface quality, side-wall roughness, residual stresses and flexural strength. In addition, samples were examined after fracture, and the flexural strength was estimated according to the quarter elliptical corner flaws, which were the main reason of glass failure. Two laser glass processing techniques were investigated – the rear-side glass processing with tightly focused nanosecond laser pulses and sub-nanosecond laser volumetric scribing with asymmetrical Bessel beam. Results were compared to mechanical scribing and breaking, diamond saw and waterjet cutting.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The conventional glass cutting techniques, such as a mechanical scribe and break method, are still widely used in the high-volume industrial production [1]. Although these technologies are well-established and offer high-speed processing at low cost, they do not meet the ever-growing demand for the fabrication of complex, miniaturised and high-quality parts. The laser-based processing has emerged as a very attractive tool, thanks to the precise and confined, both in space and time, energy deposition into the material, which ensure high processing accuracy together with low damage of the surrounding material. With the evolution of modern industrial lasers, laser-based technologies can provide high throughput as well.
The most efficient laser-based kerf-less methods are the controlled fracture technique [1] and glass scribing by introducing intra-volume voids, followed by the mechanical or thermal separation step [2]. The former technology generates smooth cutting surface with high flexural strength, but requires the accurate control of induced thermal stresses and is limited to low-curvature contours [3,4]. For the predictable separation, the second technique requires the generation of modifications through the large extent of the sample thickness. For this, the efficient use of Bessel optical beams, thanks to the large non-diffractive length and constant rebuilding due to the conical wavefront, has been demonstrated [5]. The Bessel beams allow scribing of samples up to 10 mm-thickness [6]. However, great efforts are being made to facilitate the separation of modified glass and to increase the processing efficiency. It was demonstrated that the asymmetrical intensity distribution induces transverse intra-volume cracks, which significantly facilitate glass cleaving at a high scribing speed [7]. The asymmetry may be introduced due to the manufacturing errors of the fabricated axicon [8,9], by axicon tilting operation [10,11], filtering of spatial frequencies [12,13], using diffractive optical elements, spatial light modulators [14] and deformable annular slits [15]. Since glass scribing processes are limited to simple and large-radius curvatures, ablation with the full material removal is preferable for complex contours. However, the efficient use of the most flexible technique – the front-side ablation – is limited to the sample thickness far below 1 mm due to debris accumulation and multiple beam reflections from tapered side-walls [16]. This limitation can be avoided via rear-side machining, or bottom-up approach, when processing debris is removed in the opposite direction, and the constant fluency is kept on the processed layer [17–19]. This approach is highly efficient when long nanosecond pulses are applied, and material is fractured into smaller pieces instead of being ablated [17,18]. Thus, the high material removal efficiency of 0.13 mm3/J for fused silica may be achieved [20]. That is several orders of magnitude higher comparing to the femtosecond laser single-shot ablation efficiency of 0.4 × 10−3 mm3/J [21].
There are little or no studies for comparison of the emerging techniques to conventional methods, especially regarding the flexural strength of the processed samples. Most of the research is dedicated to the mechanical scribing and breaking, grinding, polishing and controlled fracture techniques [4,22–24] with several recent studies, dedicated to laser-based processing of thin (≤ 100 µm) glasses [25–27]. However, the measured strength depends on the glass chemical composition, specimen dimensions, loading rate, environmental conditions and testing setup [28–30]. Therefore, different glass cutting methods have to be compared under the same experimental protocol. Moreover, it is of the prime importance to control the generated residual stresses in glass specimens, since they can reduce the strength of the material [31]. Furthermore, in optical applications, the stress-induced birefringence may impact the quality of laser beams, passing such elements. In addition, the fabricated parts may undergo cyclic loads, which can affect their quality and which influence needs to be investigated as well.
In this paper, we present the comprehensive characterisation of five different glass cutting methods in terms of the surface chipping and cracking, side-wall roughness, residual stresses in fabricated parts and resistance to the mechanical load. Two laser-based techniques were investigated – asymmetrical Bessel beam scribing and nanosecond laser rear-side machining and were compared to the three conventional processing technologies – mechanical scribing and breaking, diamond saw cutting and waterjet cutting.
2. Materials and methods
The soda-lime glass sheets with a thickness of 1 mm were cut into 45 × 5 mm2 stripes, which were afterwards examined.
2.1 Laser-based glass cutting technologies
The investigated technologies are schematically shown in Fig. 1. Two laser-based techniques were investigated. In the first technique, glass samples were scribed using the asymmetrical Bessel beam and then cleaved manually. The fundamental harmonic (1064 nm) radiation of the DPSS laser Atlantic HE (from Ekspla) was used for the induction of volumetric modifications. The pulse width at FWHM, pulse energy and pulse repetition rate were 300 ps, 1.6 mJ and 1 kHz, respectively. An axicon with the apex angle of 170 deg was used to transform the incident Gaussian beam of 1.6-1.7 mm-radius at the 1/e2 intensity level into the quasi-non-diffractive Bessel-like beam. The tip of the axicon was rounded with the maximum shape error of 50 µm. Also, the cross-section of the axicon was slightly elliptical with the maximum ratio of the long and short axes equal to 1.021. As a result, the central core diameter reduced with the increase of the propagation distance (starting from 9 µm at the beginning to below 5 µm and 3.3 µm at propagation distances of 0.2 mm and 0.7 mm in air, respectively), after the axicon-generated Bessel beam was demagnified using the 4F optical system with the reduction factor of 6.5. Furthermore, the Bessel beam intensity distribution was asymmetrical in the transverse plane and induced directional intra-volume glass cracks while processing [Fig. 1]. The directional cracks allowed to increase the processing speed and reduce the required bending stress of the scribed material during the mechanical separation stage. The samples were mounted on linear stages ALS25020 (from Aerotech) to change their position relative to the laser beam. The scribing speed was set to 100 mm/s, resulting in the large distance of 100 µm between laser-induced modifications and the easiest separation (4 MPa) of glass plates with high quality. More details about Bessel beam processing could be found in Refs. [7,32].
In the second technique, samples were entirely cut by the rear-side machining. The second harmonic (532 nm) radiation of the DPSS nanosecond laser (from Ekspla) was used to conduct cutting experiments. The pulse duration at FWHM was 12.5 ns, the average laser power was 16 W, the pulse repetition rate was 200 kHz. The position of the focused laser beam was changed in the XY plane using a galvanometer scanner intelliSCAN 14 (from Scanlab). The laser beam was focused using a telecentric f-theta lens with the focal length of 80 mm. The diameter of the focused beam equalled to 10.5 µm at the 1/e2 intensity level. Samples were mounted on the positioning stage 8MT167-100 (from Standa) with a stepper motor to adjust the vertical position. The processing was initiated from the rear side of a sample. To increase the cutting kerf, which is required for material removal, the parallel contours were scanned in a layer-by-layer process, as shown in Fig. 1, while the vertical stage was continuously moving down at the fixed speed until the sample was cut through. The vertical speed was set to 0.09 mm/s, the scanning speed was set to 5000 mm/s, the kerf width was 0.075 mm, the intra-distance between the parallel lines was 0.025 mm. The effective cutting speed, calculated as the perimeter of a cut part, divided by processing time, was 9 mm/s. More details about the rear-side machining could be found in Refs. [18,20,33].
2.2 Conventional glass cutting technologies
Glass sheets were mechanically scribed and separated at Precizika Metrology using the tungsten carbide tip at the scribing speed of 100 mm/s and the scribing force of 27 N. In the case of diamond saw cutting, glass sheets were initially glued to stacks of 6 plates and then cut using a diamond disc at Eksma Optics. The cutting speed was 5 mm/s. The waterjet processing of samples was carried out by Waterjet AG.
Furthermore, the polishing procedure was applied to obtain the samples with non-damaged side-walls for comparison with that of the laser-based and conventional techniques. For this, samples were cut using the nanosecond laser rear-side machining, and then the 150 µm-thick layer was polished from each side of samples to remove residual cracks. The stacks of 6 samples were polished using the water solution with 1 µm-sized abrasive particles for 3 hours.
2.3 Sample characterisation
Glass samples were imaged using the scanning electron microscope (SEM) JSM-6490-LV (from JEOL). Cracks and chipping were evaluated by viewing the front or rear side of samples using the optical microscope Eclipse LV100 (from Nikon) and measuring the distance from the edge of a cut sample to the end of the visible defect (a crack or chip-out). In this context, cracks are related to volumetric defects, which typically start from the cut edge and spread into the bulk of the material. At the same time, chipping is related to the broken material from an edge, as a result of the glass cracking process. The largest cracks/chipping were defined for both sides of each sample by examining 60 samples for each method. Error bars appearing in graphs throughout the text represent the standard deviation.
The front surface directly faced the processing tool (disc, incoming laser beam, etc.). It should be noted that the exact side of polished samples and those that were processed with a diamond saw was indistinguishable. Furthermore, the effective crack width was evaluated by dividing the measured cracked area by the evaluation length for one selected sample for each method.
The side-wall roughness was measured using the stylus profiler Dektak 150 (from Veeco). The obtained surface profiles were post-processed according to the sampling and evaluation lengths, which are given in the ISO 4288:1996 specifications [Table 1] [34]. The filtering of longer spatial wavelengths was applied to separate the surface roughness from the surface waviness, taking the cut-off wavelength equal to the sampling length. 60 samples were evaluated for each method. 14-15 samples were evaluated after the vibration test. For waviness measurement, the evaluation length was set to 19.7 mm. Surface topographies were obtained using the optical profiler S neox (from Sensofar).
Table 1. Sampling lengths used to measure the average roughness of the side-wall [34].
Residual stress measurements were done at Ilis GmbH using the circularly-polarised polarimeter StrainScope flex with the telecentric optics of two different resolutions. The size of the measured field was 3.7 × 2.8 mm2 with the resolution of 0.003 mm/px and 9.6 × 7.2 mm2 with the resolution of 0.007 mm/px. Three samples were selected for each cutting method for evaluation.
The flexural strength of glass stripes was evaluated using the 4 point bending setup with the digital dynamometer FMI-S30A5 (from Alluris) and an additional lever, which extended the measuring range [ Fig. 2(a)]. The loading rate was 1.64 MPa/s. The bending stress was calculated according to the expression:
where F is the measured peak force at the breaking point, L = 30 mm and l = 16 mm are the outer and inner support spans, respectively, b = ∼5 mm and t = 1 mm are the width and thickness of a sample, respectively. The measured data were ranked in the ascending order (from i = 1 to n), and the failure probability of the specimen was calculated according to [35,36]:The failure probability was fitted by the two-parameter Weibull cumulative distribution function [37,38]:
where m and σ0 are the shape and scale parameters, respectively. To obtain these parameters, the Weibull cumulative distribution function was linearised by the double logarithmisation of both sides of (3): Then ln(-ln(1-P)) was plotted against ln(σ) and fitted linearly. The slope of the distribution defines the shape parameter m, which describes the variation of the data. Smaller data scattering is represented by the larger shape parameter or, the steeper slope. The scale parameter σ0 was calculated from the intercept mln(σ0). σ0 describes the bending stress, at which statistically ∼63% of samples will break. This value defines the flexural strength of specimens throughout the text unless otherwise stated.
Fig. 2. (a) Four-point bending setup with the illustration of a quarter elliptical crack at the corner of the bent sample. (b) Definition of the parametric angle ϕ of an elliptical crack.
Because the sign of stresses (compressive or tensile) depends on the glass stripe orientation relatively to support spans [Fig. 2(a)], both cases were studied, when the front or the rear surface faced the outer support span and, therefore, was tensioned. 15 samples were broken for each case. Samples after the vibration test were broken using such configuration, which gave the lowest flexural strength values before the vibration test.
The flexural strength of the material was estimated theoretically by taking into account the observed flaws in specimens during the post-mortem analysis of collected debris using an optical microscope. In the linear elastic fracture mechanics, defects (cracks) act as stress concentrators, characterised by the stress intensity factor, which depends on the load, configuration and size of the crack and sample. The instantaneous failure of the material is achieved, when the critical intensity factor or the fracture toughness KIc value is reached, which is equal to 0.75 MPa m1/2 for soda-lime glass [30,39]. The flexural strength was calculated using the stress intensity factor equations for a quarter elliptical crack in the flat plate [Fig. 2(a)] under the bending stress according to Newman and Raju [40]:
where a is the crack depth, Hc is the bending multiplier, Fc and Q are the boundary correction and shape factors. These factors depend on the crack depth a and width c, plate thickness t and parametric angle of an ellipse ϕ, which definition is shown in Fig. 2(b). Equation (5) was validated by Newman and Raju for 0.2 ≤ a/c ≤ 2, a/t < 1, 0 ≤ ϕ ≤ π/2 and c/b < 0.5. Comprehensive formulae could be found in [40].The resistance of samples to the mechanical cyclic load was investigated using the excitation vibrator 4806 with an amplifier [ Fig. 3(a)]. One side of samples was attached to the platform, which was excited for several hours by the swept sine signal in the range of 560-620 Hz. The displacement of samples was measured using U3B and U20B inductive sensors. The resonance frequency of the samples was in the range of 582-604 Hz, while the maximum oscillation amplitude of the opposite side of stripes reached 0.24 mm. An example of the measured displacement of a free end is shown in Fig. 3(b).
Fig. 3. (a) The vibration setup of processed samples. (b) An example of the measured displacement of a free end of a specimen versus time.
According to the Euler–Bernoulli theory, the stress in a bent beam can be calculated by taking the second derivative of the displacement w along the Y-axis [41]:
where E is Young's modulus (72 GPa), and h is the distance from the neutral axis. The maximum stresses are induced at the specimen surfaces (h = t/2 = 0.5 mm). The beam displacement along X direction was calculated using the free vibration solution for a beam with one end fixed and the other one free, oscillating at natural frequencies [41]. The displacement was scaled according to the maximum measured oscillation amplitude Δy of the free end of a beam.3. Results and discussion
3.1 Surface cracks and chipping
The side-wall images of processed and separated samples are presented in Fig. 4. The Bessel beam induces micro-channels in the volume of glass with the cracked area between the adjacent modifications. The modifications are produced slightly below the front surface. Therefore, the thin undamaged layer is formed after cleaving. In the case of mechanical scribing and breaking, the median cracks are visible below the front surface, which is in contact with a tool during the scribing process. The average crack penetration along the normal to the surface plane is 216 µm; beyond this, the damage-free layer is generated. In the case of the rear-side machining, diamond saw and waterjet cutting, the regular rough structure is created on the side-wall. However, this layer could be removed during polishing. The waterjet cutting was the only one technology amongst tested, which gave tapered edge (about 4-5 deg deviation from a perpendicular angle), similarly to the front-side ablation process.
The images of the front and rear surfaces and the measurement of maximum surface cracks/chipping width perpendicular to the side-wall are presented in Fig. 5. Note that the exact side could not be identified for samples processed with a diamond saw. Therefore, all data are included in a single column bar. Other samples had the largest cracks/chipping on the front surface.
Fig. 5. (a) The optical microscope images of samples cut using different techniques. The letters “F” and “R” stand for the front and rear surfaces, respectively. (b) Surface chipping/cracks width evaluation for different glass cutting methods.
It is evident that glass cracks and chipping on the rear surface of the mechanically scribed samples occur due to the breaking operation since this side remains undamaged during the scribing step. In the case of Bessel beam volumetric scribing, the height of the non-damaged zone close to the front surface is lower in comparison to mechanical scribing [Fig. 4]. The chipping is also lower due to probably the lower bending load, required to separate sheets. In these experiments, the modified glass sheets were separated manually. However, lower chipping could be possibly achieved by using bending setups that provide uniform load or special expansion tapes, used in the separation stage of stealth-diced semiconductor wafers [42].
The lowest maximum cracks/chipping were generated with the Bessel beam laser scribing and separation - the average maximum crack/chipping width was 57 µm and 35 µm on the front and rear surfaces, respectively. The largest cracks/chipping of 187 µm were generated with waterjet cutting. However, as the occurrence of glass cracking and chipping is a stochastic process, the effective crack width, estimated by integrating the damaged area and dividing by the evaluation length for a single sample, was from 3 to 6 times lower compared to the average maximum crack/chipping width. Crack examination before and after vibration tests showed that surface cracks were not affected by the cyclic mechanical load.
3.2 Side-wall surface roughness evaluation
The measured side-wall topographies and average surface roughness Ra are presented in Fig. 6. The largest average surface roughness of 4.1 µm was measured for the Bessel beam scribing and separation. In the case of the laser rear-side machining technique and waterjet cutting, the average roughness was 1.4 µm and 1.9 µm, respectively. The diamond saw allowed to achieve the 0.15 µm roughness. Even lower roughness of 11 nm was achieved using the mechanical scribe and break method, which affects only the upper layer while the remaining smooth plain is created during fracture. However, in this case, the large average surface waviness Wa of 5.2 µm was observed, while the waviness was equal to 1.6 µm and 1 µm for Bessel beam scribing and separation and rear-side machining, respectively. For the rest of conventional methods, diamond saw and waterjet cutting, the side-wall average waviness was 0.2 µm and 0.9 µm, respectively. The average surface roughness and waviness of polished samples were 4 nm and 0.2 µm, respectively. The surface roughness of vibrated samples was comparable to the measurements before the vibration test, and slight variations of the mean value were within the standard deviation.
Fig. 6. The measured side-wall surface topographies and average roughness. The size of the topography is 338 µm x 283 µm (width x height).
3.3 Residual stress evaluation
The residual stresses in specimens, measured with high-resolution optics, are presented in Fig. 7(a). The largest stresses are generated close to the processed edge with the magnitude, depending on the cutting technology. The maximum stresses (the mean value for 3 samples) were 14 MPa for specimens, cut with the Bessel beam and rear-side machining technique. However, the maximum stress was reduced to 4.5 MPa after the polishing step, when the damaged layer was removed. The largest stresses of 19 MPa were measured in the mechanically scribed and separated samples. The lowest residual stresses among tested technologies were measured for diamond saw-cut samples and equalled to 7.4 MPa. The residual stresses in waterjet-cut samples were comparable to laser-based cutting and equalled to 12 MPa.
Fig. 7. (a) The measured residual stresses in glass plates, viewing the specimen surface close to the processed edge. (b) The average residual stress dependence on the distance to the edge. The inset graphs represent the residual stresses over the whole width of specimens, obtained using an optical configuration with a larger field of view.
The residual stresses, averaged over the 4 mm-distance along the edge for a single sample, are presented in Fig. 7(b). The maximum values of averaged stresses were reduced by the factor of 3.6-4, comparing to the largest measured stresses. However, the trend remained the same with the largest stresses generated in mechanically scribed and separated samples and the lowest stresses in diamond saw-cut and polished samples.
The inset graphs in Fig. 7(b) show the residual stresses over the full width of specimens, measured using optics with the larger field of view. The stress profiles are typically U-shaped with the largest stresses generated up to 50 µm-distance from the edge and the lowest value in the middle of specimens, except for the rear-side machining with the lowest value at 0.7 mm distance from the edge. In the middle of the sample, the largest stresses were measured for the rear-side machining and equalled to 0.2 MPa, but this value decreased below 0.003 MPa after a polishing step. The similar stress value was obtained only with mechanical scribing and separation (0.004 MPa). The measured stresses in the middle of the samples, cut using Bessel beam, diamond-saw and waterjet, were in the range of 0.03-0.06 MPa.
3.4 Flexural strength evaluation
The measured flexural strength of glass samples with two-parameter Weibull cumulative distribution fits is presented in Fig. 8. Summarised data are given in Table 2. The flexural strength depends on which side of glass plates is under tension. The flexural strength of laser-scribed and separated samples was 127 MPa and 67 MPa when the front and rear sides were tensioned, respectively. This is an expected result since there was an undamaged layer below the front surface. In the bending setup, the largest tensile stresses are generated at the tensioned surface and linearly decreases with the increase of the distance from this surface until the middle of a sample, when stresses change from tensile to compressive ones, as shown in the inset picture in Fig. 8. Therefore, the tensile stress is reduced by the factor of 0.6-0.8 acting upon cracks that are buried 100-200 µm beneath the tensioned surface in comparison to cracks, which are close to the surface. As a result, higher bending load is required to fracture a specimen.
Fig. 8. The failure probability of samples cut using different technologies versus applied bending stress. Solid and dashed lines represent the Weibull fit of the experimental data (open dots). The inset graph in the rear-side machining case represents the average flexural strength dependence on the sample width. The solid dark cyan curve in the inset graph represents the modelled flexural strength with the corner crack a = c = 60 µm.
Table 2. The flexural strength of samples cut with different technologies.
The lower dependence on the side orientation was observed for the rear-side machining technique as the measured flexural strength was 101 MPa and 83 MPa for the front and rear sides, respectively. This assuredly overcomes the waterjet cutting technique, which gives the flexural strength of 61 MPa and 74 MPa for the front and rear sides, respectively. The flexural strength of samples, cut using the rear-side technique, was enhanced by 1.6-1.9 times to 161 MPa after the polishing procedure, which removed a damaged layer from edges. The largest flexural strength among tested cutting techniques was measured for the rear-side of mechanically scribed and separated samples, which was equal to 181 MPa. The edge close to the rear-side of scribed samples is created during the separation stage. Thus, it has a lower density of flaws and the zone of large median cracks, seen in Fig. 4, is under compression. However, the flexural strength of the front side is considerably lower and equal to 134 MPa, which is comparable to diamond saw-cut samples (137 MPa). It is also important to note that these techniques resulted in the higher scattering of data with the Weibull shape parameter below 10, while laser scribing and separation, rear-side machining and waterjet cutting ensured more predictable failure with the shape parameter in the range of 10 to 21. The theoretical strength of glass is ∼30 GPa [30]. Therefore, the strength is reduced by the factor of 166 for the rear side of mechanically scribed and separated samples and 493 of the front side of waterjet-cut samples.
The overview of the flexural strength of samples cut with different technologies found in the literature is presented in Table 3. The strength of laser-cut samples, presented in this paper, is lower in comparison to femtosecond laser-ablated 0.1 mm-thick aluminoborosilicate glass with the flexural strength of 280 MPa and 240 MPa when the front and rear-sides are tensioned, respectively, reported by H. Shin and D. Kim [26]. The same authors achieved even higher flexural strength values of 370 MPa and 400 MPa for the front and rear-sides, respectively, using femtosecond laser Bessel beam scribing [27]. However, the authors used a three-point bending setup, which gives higher values in comparison to the four-point bending [43]. Furthermore, the strength is higher for thinner samples [25,28]. Also, the flexural strength is highly dependent on the loading rate [39,44,45]. The evident difference between experimental conditions is that H. Shin and D. Kim reported the flexural strength of 550 MPa of mechanically scribed and separated mirror-like glass surface [27], which is 3 times larger than measured for samples, cut with the same technique in this paper. For comparison, J. Li et al. reported the 112.1 MPa flexural strength of 1 mm-thick soda-lime samples, which were scribed via laser filamentation-induced volumetric modifications [46]. Authors reported a 16% reduction in the force, required to cleave modified samples, compared to ground ones. In comparison, asymmetrical Bessel beam scribing, presented in this paper, reduces the breaking force by the factor of 30 [7].
J. Li et al. reported that the breaking force could be significantly reduced when V-grooves are formed in addition to volumetric modifications. However, in this case, the flexural strength decreased to 95-105 MPa [46], which is comparable to rear-side machining, presented in this paper. Therefore, it can be concluded that the higher quality intra-volume scribing using shorter pulses results in the higher stress, required to separate modified samples. For instance, Jenne et al. reported the ∼54 MPa breaking stress of 1 mm-thick sample, scribed with the fs-ps Bessel beam [14]. Sub-nanosecond asymmetrical Bessel beam, presented in this paper, allows more than 13 times easier separation (4 MPa) [7].
Table 3. The overview of the flexural strength of samples cut with different technologies.
3.5 Post-mortem analysis
The post-mortem analysis of recollected samples after breaking revealed that in most cases, the origin of failure was flaws on the corner or edge of a processed sample [Figs. 9(a)–9(f), 9(h) and 9(i)]. This depended on the size of flaws generated during processing and was the failure reason for samples, cut using rear-side machining and waterjet cutting, and for the rear-side of laser-scribed and separated samples. However, the failure of samples with higher flexural strength in some cases started from the front and rear surface further from the edge (an example is shown in Fig. 9(g)), depending on which side was tensioned. This occurred mostly for the rear side of mechanically scribed and separated samples (5 of 11) and samples, cut with a diamond saw (4 of 21 samples). One case of cracks, emanating from the surface, was observed for the front side of mechanically and laser-scribed and separated samples.
Fig. 9. The post-mortal images of broken specimens obtained using scanning electron (b, e, i) and optical microscopes (a, c, d, f-h). In optical microscope images, the fractured plane is shown. Red arrows indicate the origin of the failure. Blue arrows show the tilted SEM image of the corresponding flaw. Scale bars are 100 µm-length unless otherwise stated.
The occurring flaws during manufacturing, processing and inappropriate handling reduce the flexural strength of the whole sample. The theoretically estimated flexural strength of the specimen with an idealised quarter elliptical crack on the corner under the bending load is presented in Fig. 10(a). Sample dimensions were selected according to experimental conditions (1 mm thickness, 5 mm width). Note that dashed lines enclose the region of the validated crack aspect ratio 0.2 ≤ a/c ≤ 2 for equations, derived by Newman and Raju [40]. The inset graph in Fig. 10(a) shows the variation of the stress intensity factor along the crack front for the applied bending stress of 100 MPa. The largest intensity factor is at the surface or a side-wall, depending on the crack aspect ratio. The largest intensity factor, resulting into the minimal flexural strength, was taken for calculations, and the dark cyan solid line on the estimated flexural strength 2D map determines the zone with the parametric angle equal to 0 deg (top) and 90 deg (bottom). Data suppose that the size of flaws in the case of the quarter circular crack (a = c) should lay in the range of 13-103 µm since the experimentally measured average flexural strength was between 60-165 MPa for different technologies.
Fig. 10. (a) The estimated flexural strength for glass specimens with a quarter elliptical corner crack with the depth a and width c. The black dashed lines enclose the 0.2 ≤ a/c ≤ 2 region. The dark cyan solid line determines the zone with the parametric angle equal to 0 deg (top) and 90 deg (bottom). The inset graph shows the stress intensity factor dependence on the parametric angle ϕ for the different crack aspect ratio a/c (depth/width) in micrometres. (b) The experimentally measured flexural strength versus estimated according to the post-mortal analysis of quarter elliptical corner flaws in glass specimens, cut using different technologies. The solid and open dots show that the front or the rear side is under tension, respectively.
In Fig. 10(b), we have compared the experimentally measured and estimated flexural strength, according to the size of corner flaws, measured during the post-mortem analysis. The calculated Pearson correlation coefficient was equal to 0.84. The measured mean flaw depth and width of laser-scribed and separated samples was 162 µm and 39 µm, respectively. Note that the aspect ratio of cracks in laser-scribed and separated samples was equal to 4.5 and slightly dropped out from the validation window in Fig. 10(a). The mean flaw size for rear-side-machined samples was a = 42 µm, c = 45 µm for the front surface and a = 61 µm, c = 105 µm for the rear surface. These values were considerably lower compared to waterjet cutting with a = 112 µm, c = 95 µm for the front surface and a = 74 µm, c = 90 µm for the rear surface. The similar flaw size of a = 22 µm, c = 49 µm was observed for the front-side of mechanically scribed and separated samples, and samples, cut with a diamond saw (a = 24 µm, c = 31 µm). Not surprisingly, these techniques gave similar values of the flexural strength. In most cases, the measured flexural strength was higher than estimated according to the flaw size. This could be explained by the fact that the actual flaws expand along the specimen edge. Therefore, they are more chips-outs rather than ideally planar cracks (this could be seen in SEM images in Figs. 9(b), 9(e) and 9(i)). Furthermore, the series of parallel cracks/chips along the edge also reduces the stress intensity factor due to the shielding effect, which depends on the ratio of cack size and distance between cracks [47].
The mean width of flaws, measured during the post-mortem analysis, is considerably lower in comparison to the average maximum crack/chipping width, presented in section 3.1, except for the rear side of laser-scribed samples. In the case of the rear side of rear-side-machined and diamond saw-cut samples, the width of flaws was comparable to the effective crack width, while for other techniques, post-mortal flaws were larger. Furthermore, the strength of samples could not be compared solely in terms of the surface cracks/chipping width, as the depth and shape of cracks play an essential role as well. The average surface roughness is also not a reliable parameter in assessing strength. Although the specimens with the best side-wall quality (mechanically scribed, saw-cut and polished) demonstrated the largest flexural strength, the strength of the waterjet-cut samples was lower in comparison to the laser-scribed and separated samples, which had 2 times larger average roughness.
The inset graph in Fig. 8 in the rear-side machining case represents the average flexural strength for different sample width, which varies from 1 mm to 10 mm when the rear-side of samples was tensioned. The variation of the measured values was modest as predicted by the theoretical estimation for specimens, having quarter circular cracks with a = c = 60 µm, shown as the dark cyan solid curve in the inset graph. Therefore, the generated flaws during glass processing determine the flexural strength of the whole sample.
3.6 Vibration tests
Glassy parts installed in machines, for instance, scales in optical encoders [48,49], may undergo vibrations during operation. However, the vibrations herein are typically considered as a cause of the measuring inaccuracies, ignoring that they may affect the quality and strength of parts during the long-term excitation. For this, we have carried out the vibration tests at harsh conditions, exciting the glass plates resonantly to reach the amplitude of 0.24 mm, which corresponds to the vibration speed of 0.7 m/s and the acceleration of 2500 m/s2 – much higher values than allowed in machines according to standards (such as ISO 20816).
The instant fracture of glass occurs when the critical stress intensity factor is reached. However, the subcritical crack growth may occur in the ambient atmosphere due to the crack corrosion effect because of the chemical reaction of water molecules with silica at the crack front [30]. The growth rate depends on the applied stress and environmental conditions, however, below the threshold stress intensity Kth, which is in the range of 0.2-0.3 MPa m1/2 for soda-lime glass, cracks do not grow [30]. The main mechanisms that arrest the growth of cracks in the soda-lime glass below the threshold are thought to be crack-tip blunting and ion-exchange reactions [50,51].
The first mode of glass plates was excited during vibration tests. The modelled shapes of the 1st (633 Hz), 2nd (3969 Hz) and 3rd (11112 Hz) modes of the oscillating beam with one end fixed is shown in Fig. 11(a). The highest stresses are induced at the fixed end, as shown in Fig. 11(b). However, in the four-point bending setup, the examined area is between the inner support spans, since it is under the highest load. In our case, this area starts at 7-14 mm-distance from the fixed end. The dependence of stress and stress intensity factor on the maximum displacement for the first mode is shown in Fig. 11(c). The stress intensity factor was calculated according to the corner quarter elliptical crack model with the crack size of a = 112 µm and c = 95 µm (mean values for waterjet-cut samples with the largest cracks and stress intensity factor). It is seen that the stress intensity factor was at or below the threshold value for 0.24 mm-displacement. Therefore, the growth of cracks could not occur during experiments. Furthermore, the failure of a beam may possibly occur at the clamping position before the induction of measurable defects in glass plates at some distance from the fixed end, where the largest stresses are induced. However, more uniform treatment may be achieved by the excitation of higher modes [Fig. 11(b)].
Fig. 11. (a) The modelled shapes of the 1st (633 Hz), 2nd (3969 Hz) and 3rd (11112 Hz) modes of the oscillating beam with one end fixed. (b) The corresponding stresses at the surface of glass plates. Red dashed vertical lines indicate the support spans at the closest possible position to the fixed end during four-point bending tests. (c) The dependence of the induced stress and stress intensity factor on the maximum displacement of a sample, oscillating in the first mode.
Although the vibration tests had a negligible impact on the surface cracks/chipping and the processed edge roughness, we have observed the increase of the flexural strength by ∼3% of mechanically and laser-scribed and separated samples [Table 2]. The flexural strength of samples, cut with a waterjet, increased by 1.6%, while the flexural strength of samples, cut via rear-side machining and with a diamond saw, slightly reduced (< 0.4%). However, the largest drop of 13% was observed for polished samples. Moreover, the shape parameter increased for all techniques except the mechanical scribing and separation. Therefore, vibrated samples fractured more predictably, resulting in the steeper cumulative distribution function [Fig. 8].
Our findings are in good correspondence to the reported increase of the flexural strength for damaged glass samples, which experienced static or dynamic pre-loading [52,53]. The strength of soda-lime glass could be potentially increased, as long as the stress intensity factor is below the threshold value and cracks do not further grow. However, the influence of the surface morphology as an outcome of different cutting techniques, applied maximum stress intensity, loading duration etc. has to be investigated in more details in the future.
4. Summary and conclusions
In this report, we have comprehensively characterised the emerging laser-based glass cutting methods – Bessel beam scribing and separation and nanosecond laser rear-side machining and compared to conventional techniques – mechanical scribing and separation, diamond saw and waterjet cutting. The 1 mm-thick soda-lime glass specimens were characterised in terms of surface cracking/chipping, side-wall roughness, residual stresses and resistance to mechanical load.
The sub-nanosecond Bessel beam scribing and separation with induced transverse cracks offers a high processing speed with the lowest surface cracks and chipping. However, the side-wall roughness is relatively high (Ra = 4.1 µm), and the flexural strength is 67 MPa and 127 MPa, depending on the tensioned side (the rear or the front side, respectively) since the flexural strength increases as the cracks are buried below the surface. The flexural strength could be potentially increased using shorter pulse durations due to more delicate energy deposition into the material, however, at the expense of glass cleavability. A common drawback of scribing-based methods is cutting straight and large-radius curvatures only. Rear-side machining approach, which allows entirely cutting of complicated contours, offers higher flexural strength (83 MPa and 101 MPa for the rear and front side), reduced average side-wall roughness (1.4 µm), but generates large surface cracks/chipping (140 µm) and high residual stresses. Although the general quality and mechanical resistivity were lower compared to mechanical scribing and separation and diamond-saw cutting, this approach overcame the waterjet cutting, which produced tapered edges, the largest surface cracks/chipping (188 µm), higher side-wall roughness (1.9 µm) and the lowest flexural strength (61 MPa and 74 MPa for the front and rear side) among tested techniques. Furthermore, the polishing procedure of laser-machined samples increased the flexural strength to 161 MPa and reduced residual stresses to 4.5 MPa. Therefore, the cutting surface finishing is essential.
The post-mortem analysis revealed that in most cases, the fatal fracture originated from the corner, especially when the side-wall was severely damaged due to the cutting procedure. The experimentally measured flexural strength of samples coincided well with the estimated values, according to the corner elliptical crack model, taking into account the size of flaws, which were measured after the sample fracture. However, the surface cracks/chipping width could not be solely used to compare the flexural strength of specimens, as the depth and shape of cracks play an essential role as well.
Acknowledgements
We are grateful to Ilis GmbH for their help with sample stress measurements.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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