Nano‐Cracks and Glass Carving from Non‐Symmetrically Converging Shocks

A method is presented to carve into a glass submerged in water with laser‐induced surface and shock waves. It starts with an elliptic wave source that launches an elliptically converging Rayleigh and shock wave. At the wave focus a single microscopic crack with controlled location and orientation is induced that has a length of a few micrometers and a width of about 100 nm. Through successive surface waves, this crack may be extended along a specific direction which can be controlled by adjusting the distance, shape, and orientation of the laser focus. Here, either point‐like or elliptical laser foci are generated using a spatial light modulator. Furthermore, when the crack is guided along a closed circular path using a point like laser focus, a conchoidal hole may be carved through the glass slide demonstrated with a 160 µm thick cover slip. The shock waves are modeled in the fluid and the elastic waves in the glass in three dimensions with a finite‐volume framework that accounts for fluid‐structure interaction. The resulting pressures and stresses for both the elliptical and point‐like Rayleigh and shock wave sources are reported.


Introduction
To break glass along a line, one typically creates a small crack with a glass cutter and then applies a force on the sample for the crack to propagate and split the glass apart.While this method is simple and straightforward, an understanding of what exactly happens on the microscopic scale is far from complete.There contradicting views on the nature of fracture propagation in glasses exist.

DOI: 10.1002/apxr.202300030
For example, Guin and Wiederhorn [1] found using atomic force microscopy that the crack propagates in silicate glasses without forming a cavity at its tip suggesting a completely brittle fracture.While Célarié et al. [2] report on the nanoscale ductility in crack propagation thus fracture propagates similarly to that in metal, recently, Shen et al. [3] revealed that crack propagation in various glasses is dominated by self-organized nucleation, growth, and coalescence of nano-cavities resulting in nano-patterns on the crack's surface, arguing that these cavities confirm the presence of nanoscale ductility of brittle glasses.
There are different methods to generate cracks and modify the properties of glass.Some require direct contact like the case of indenters and others are contactless and rely on lasers or/and acoustic waves.[6][7][8] Nano-scratching is another technique based on indentation, but the tip that presses the surface moves laterally, generating microscopic channels on the material surface. [9]Recently, abrasive nanoparticles driven by ultrasonic vibration [10,11] have been used to study the hardness of materials and also for micro-machining.
Among the optical methods for micro structuring, the application of ultrashort laser pulses (femtoseconds) direct writing technology stands out.It has been widely used for the microfabrication of optical devices.The quality of the structures generally depends on the optical characteristics of both the experimental setup and the sample.The three main types of nano-scale modifications to materials: melting, high-density cavity, and nanograting, are based on the energy of the laser pulse used. [12]hock waves have also been used to damage materials like glass.Zhang and coworkers [13] studied the generation and propagation of leaky Rayleigh waves induced by a spherical shock wave at a water-glass interface.Symmetric convergent laser-induced shocks and acoustic waves have induced fracture in glass, [14] where a picosecond laser pulse shaped into a ring is absorbed by a gold coating deposited on the glass surface.The induced stresses resulted in the removal of a small fragment of the gold film (≈ 15 μm) at the center of the ring.Other studies with the same system [15] investigated glass failure at the nanosecond scale, generating craters with a depth of about 4-5 μm and a diameter of 10-20 μm.Their simulations estimated a tensile stress threshold of at least 6 GPa for borosilicate glass.
Other experiments with shocks and acoustic waves have used time delayed excitations, [16] including converging ring sources [17] where shock waves were induced in the liquid and Rayleigh waves in the solid.It was shown that the greatest damage induced on the surface was generated with the time delay corresponding constructive superposition from simultaneous focusing of Rayleigh waves.
In the present manuscript, we propose a novel non-contact method to nano-structure borosilicate glass in a controlled way.A shaped laser pulse focuses into the liquid close to the glass substrate; unlike direct laser writing methods, the laser energy is not deposited within the substrate.A nano-sized crack is induced via the convergence of laser-induced elliptical shock and surface waves.The direction of the cracks are along the minor axis of the ellipse with a width on the order of 100 nm, which allows control via the orientation of the elliptically shaped laser pulse.The optical detection of the nanosized crack relies on the observation of the induced cavitation when it is exposed to the acoustic waves.We also demonstrate the controlled propagation of those cracks drawing different geometric shapes with sizes of tens of microns.
Repeated exposure to the shocks and surface waves can carve the glass drilling out a piece of the substrate.

Experimental Setup
The experimental setup was based on previous works [16,17] and was shown as a schematic in Figure 1A.The laser pulse (Orion, New Wave, 6 ns) was shaped into an elliptical ring using a spatial light modulator (SLM, Hamamatsu, X10468-01).The sizes of the major (104 μm) and minor (78 μm) axes in the focal plane are controlled through the hologram displayed on the SLM screen, which could be easily modified in real-time to change the shape of the laser pulse.
The liquid (ink, EPSON T6643, Magenta) with a similar density and viscosity as water, was bounded by a microscope slide of 1 mm thickness at the top and a microscope slide of 160 μm thickness at the bottom.The properties of the glass are provided by the manufacturer:  = 2230 kg m −3 ,  = 0.2 and E = 63 GPa (Fisherbrand, www.fishersci.com).The thickness of the liquid layer was about 80 μm, set by a spacer (double-sided tape) placed between both glass substrates.As the top glass substrate was far from where the laser pulse was focused, it was not shown in Figure 1A.
The shaped pulse was focused at the bottom of a liquid container by a microscope objective (Olympus, 10×, NA 0.4).Due to the low intensity of the pulse within the glass, the laser pulse by itself does not damage the substrate.Instead, it was linearly absorbed in the dyed liquid forming an elliptic ring bubble.Consequently, a shock wave front with the shape of the elliptical torus bubble was emitted.The outer front propagates outward from the bubble and diverges, thus decaying in amplitude over time.The inner front wave propagates inward from the elliptical bubble, leading to energy focusing near the center of the ellipse.In Figure 1A, the laser bubble in water was shown in blue, while the convergence of the inner shock wave front was shown in shades of red.Since the laser-induced bubble was formed at the bottom of the liquid, the bubble expansion loads this surface almost instantaneously, resulting in an energy transfer that deforms the surface and generates the Rayleigh wave.
The energy of the elliptically shaped laser beam was set to (202 ± 7) μJ, measured between the SLM and the dichroic mirror of the inverted microscope.This energy was used to induce crack formation.
Later, to propagate circularly the induced crack, the hologram displayed on the SLM screen was modified to induce the formation of a single spherical bubble of 12 μm radius, which leads to the formation of a shock wave in the liquid and a Rayleigh wave on the solid surface.The energy of the laser pulse was set to (300 ± 8 μJ).
To capture the fast dynamics of the events, stroboscopic photography was used.For illumination, a second laser pulse was used with a wavelength of 532 nm that was converted to 690 nm using a dye cell.The pulse illuminates the sample, and propagates through the dichroic mirror of the microscope, after which the light reaches a CCD camera (Sensicam QE).
The fracture topology was measured via areal confocal microscopy (Mahr nanofocus &mu;surf custom P).As the measurement principle makes use of the light reflected at the sample surface, reflectivity was increased by sputtering the glass samples with a thin gold layer (thickness approximately 40 nm).A difficulty encountered with the fracture topologies here was that planar surfaces may easily overexpose the camera sensor while curved surfaces were underexposed as they reflect light out of the microscope's objective aperture.This has been solved by performing measurements of the same region four times with increasing light intensity.The data was combined choosing at each pixel position the darkest measurement run that still yielded a reliable result which has been performed with a Matlab script.

Numerical Model
For the numerical simulations, a finite-volume solver of two compressible, viscous fluids was coupled to a solver for a linear elastic solid.One of the fluids represents water, and the other was the gas within the bubble, which represents the bubble created by the laser in the experiments.All changes of state were treated as adiabatic, assuming that the presented dynamics were faster than any significant heat exchanges.Indeed, for nanosecond laser-induced microbubbles similar to those gener- ated in the experiments of the present investigation, Quinto-Su et al. [18] has shown that the rise in temperature was only a few Kelvin.The elastic solid represents the microscope slide made of glass that neighbors the created bubble.The solver CavBubbleF-siFoam was a modified version of fsiFoam, which was found in the fluid-structure interaction package [19] in the OpenFOAM version foam-extend-4.0. [20]Details on the solver method could be found in Refs., [17, 21] where it was used to simulate similar configurations.
The parameters characterizing the properties of the two fluids involved and of the elastic solid, as well as the initial conditions are given in Table 1.The fluid domain containing the liquid and the bubble has a thickness of 80 μm and was sandwiched between a rigid boundary and the elastic solid plate, which has a thickness of 160 μm.On the opposite side of the plate, another gas-filled fluid domain with a thickness of 80 μm was placed which was bounded by an open boundary, allowing the plate to move freely with respect to the liquid-filled fluid domain.The outer boundaries far from the region of interest were open boundaries, representing an infinitely extended domain.
Two simulation cases with different initial bubble shapes were presented, where advantage of their respective symmetries were taken.In the first case, the seeded bubble was an elliptical torus, as seen in Figure 1, and thus has two symmetry planes, the x-z and y-z planes.Thus, only a quarter of the full domain was simulated.The computational mesh was initiated as a cubic grid with a grid parameter of 20 μm.In the liquid-filled domain near the bubble, the cells were successively split into 8 cells of halved grid parameter for 4 iterations to reach a grid parameter of 1.25 μm.The initial conditions were chosen to match the experimentally observed shock wave dynamics.The initial length of the major semi-axis was 52 μm, while that of the minor semi-axis was 39 μm.The ellipse width was 5 μm, which was close to the diffraction limit of the microscope objective that was used in the experiment.The center of the bubble was placed 2.5 μm above the elastic solid wall, such that they were in contact.
In the second case, a small spherical bubble was seeded on the (vertical) z-axis, in which case the configuration was axisymmetric.Thus, a quasi-2D simulation could be employed, and the governing equations only need to be solved in the x-z plane.For the computational mesh a square grid with a grid parameter of 1 μm was used.The initial bubble radius was chosen to be 12 μm and its center was placed 12 μm above the solid wall such that they again were in contact.In both cases, the initial bubble pressure was chosen to be 1.69 GPa, such that the initial gas density was equal to the liquid density, implying that the laser energy absorption happens much faster than the bubble expansion, as it was done in Refs.[14, 16, 17] This resembles the very fast energy deposition from the nanosecond laser pulse used in the experiment.Our solver was additionally validated by a close match of the shock wave propagation with the experimental observation.The initial sizes of the bubbles (radius, and/or minor axis and major axis, depending on the case) were chosen such that the shock wave position over time closely matches that observed in the experiments.

Nano-Crack Generation
Figure 1B depicts the dynamics of the elliptical bubble and its shock wave emission in top view.At the top of each frame, strobe photographs are shown, while at the bottom, frames extracted from the simulation are presented.Both, the simulated and the experimental frames are cropped along y = 0 for ease of comparison.The frames from the simulation are extracted from a slice in the x-y plane at z = 2.5 μm.The bubble appears gray.The size of the bubble and the locations of the pressure wave front show a good agreement between simulations and experiments.
In the first two frames, corresponding to 10 and 16 ns, we find an expanding laser-induced bubble that has emitted a shock wave front with the shape of the bubble (elliptical torus), propagating with a velocity close to 1900 m s −1 .The convergent shock wave front is indicated with an arrow.
The negative pressures (induced by the Rayleigh wave) reach the center first (t ≈ 16 ns).Thus, at t = 18 ns they are already diverging, while the positive pressures are still converging toward the The top and bottom fronts (y-axis) of the inner shock wave front reach the center first, before the side fronts (x-axis).At 18 ns, we observe two large pressures along the major axis (p = 1050 MPa at x = ± 8 μm, y = 0).Later, at 22 ns, the highest pressure overall is reached when the two high pressure regions converge at the center creating an elongated focus (p = 1090 MPa, at x = 0 and along a line of 10 μm on the minor axis).In the next frames, 28 ns and 34 ns, the inner shock wave front has passed through the center and is now diverging.As a result from the superposition of converging and diverging waves and the higher positive pressure amplitudes, negative pressures are diminished for later times.Due to the convergence of the waves, in the time interval shown in Figure 1B (10-34 ns), the maximum values of pressure in the liquid and stresses in the solid are reached.
Figure 1C depicts the evolution of the stresses  xx (left),  yy (center) and  zz (right) on a line on the surface of the solid along the major axis (above), and along the minor axis (below).The vertical and horizontal axes are the spatial and temporal coordinates, respectively.The spatial coordinate ranges from -15 to 15 μm, while the temporal coordinate ranges from 5 to 35 ns.A region of positive stress (i.e., tensile stress) is observed, followed by a region of negative stress (i.e., compressive stress).Although similar, the stresses on the two axes show several differences.
The positive stress is induced by the Rayleigh wave, which propagates with a velocity of about 3200 m s −1 .For  xx , the maximum value is 650 MPa, reached at 15 ns.It is approximately constant along 4 μm on the major axis and along 2 μm on the minor axis.For  yy , the maximum value is 875 MPa, reached at The strongest compressive stress for  xx ,  yy , and  zz is reached along a line on the surface in the direction of the minor axis, −5 μm < y < 5 μm.These minima for the stresses in the solid are reached only 1 and 2 ns after the greatest pressure in the liquid is reached, due to the convergence of the shock wave.The videos in Supporting Information show the dynamics of the bubble and the shock wave fronts for almost 100 ns, both for the simulation and for the experiment.The dynamics in the x-y plane are shown for the pressure p (z = 2.5 μm), as well as the stress components  xx ,  yy , and  zz separately (z = 0).Additionally, a 3D view is given showing the pressure in the fluid, along with each of these stress components separately.
The waves induced by the elliptical laser torus bubble create lines on the surface with almost constant values of tensile and compressive stresses.In comparison, for a circular ring bubble (rotational symmetry case), the convergence of a Rayleigh wave and a shock wave induces stresses with maximum and minimum values at the center of convergence, which rapidly decays in the radial direction. [17]igure 2A depicts how a nano-crack is generated through a sequence of successive experimental runs of the elliptical laser focus shown in Figure 1.After wave focusing, a rarefaction wave induces tension in the liquid that is strong enough to nucleate cavitation at the position of the crack.Thus the crack becomes visible by the presence of small bubbles which is accomplished by recording the images at 15 ns, after the time of Rayleigh wave focusing.
After 19 repetitions, no damage to the glass is observed.After the 20th run a small bubble at the center becomes visible.In the subsequent runs, a vertical line of small bubbles expands, indicating that the crack has now grown vertically.As the propagating shock wave is of high-pressure amplitude as it reaches the center, it collapses the nucleated bubbles, limiting the lifetime of the bubbles to the interval between the high stresses induced by the Rayleigh wave and the high pressure induced by the convergent shock wave.For the present experiments, this duration is less than 10 ns.The direction of the nano-crack, along the ellipse's minor axis, is explained by the strong and approximately constant compression in  xx ,  yy , and  zz over 10 μm along the minor axis mentioned above (Figure 1C).
To determine the probability of crack generation ϕ as a function of the number of repeated shots N, the experiment is repeated n = 50 times, each time in a new region of the glass.Continuing the experiments for many more runs after the initial crack is formed results in cracks in other directions and eventually the ejection of small glass fragments.

Controlled Crack Patterns
Figure 3A shows the process of creating a 150 μm long vertical crack.A first nano-crack is created in the center of the elliptical laser-induced bubble.Then a motorized stage moves the glass downward by about 5 μm and a second bubble is created.This is repeated 30 times.The movement can be seen by following the movement of marks on the glass, see the blue and red dashed circles in Figure 3A.While multiple shots (E(N) = 17.92, mean of the cumulative distribution function) are needed to initiate the first crack, each successive shot of the laser propagates the crack further.
To visualize the crack, we change the hologram to create a smaller circular bubble that launches a radially outgoing Rayleigh wave.The stresses of this wave nucleate small bubbles all over the line, see Figure 3B.The photograph is recorded 50 ns after the generation of the laser-induced bubble.While the shock wave in the liquid visible as a dark circle in the image has not reached the crack, the Rayleigh wave already has reached the crack and expanded the bubbles.
The resulting crack is further characterized using scanning electron microscopy (SEM), see Figure 3C.Here, the nonconductive glass surface has been coated with ≈ 10 nm thick gold layer.The SEM image reveals a width of the crack of less than 100 nm.
The orientation of the crack can be changed by displaying different digital holograms on the SLM during the experiments.Together with the ability to translate the glass sample with the motorized stage, linear cracks can be arranged into patterns.This feature is demonstrated in Figure 4.There we have oriented cracks along the sides of a square and an equilateral triangle.
To visualize the crack patterns within the means of the experimental setup, we again changed the hologram to create a smaller circular bubble and varied the timing of the image recording.Figure 4 is the overlay of several photographs taken with different delay times (15-85 ns) to fully observe the bubbles induced on the crack positions on the created pattern.Since the bubbles formed on the crack reach their maximum size shortly before the shock wave reaches that position, the photos are circularly cropped close to the position of the shock wave.
By increasing the laser energy (with constant ellipse size) the number of shots needed to induce a crack is reduced, and eventually a single shot would be required.However, we did not use higher energies because it prevented good control when expanding the crack.Once the damage was induced with higher energy, extending it detached small shard of glass (≈ 3 μm, i.e., visible) along the crack.In each frame, the vertical nano-crack is observed in the center of the elliptical laser bubble.The sample is moved upward in steps of 5 μm using a motorized stage.On the right, two marks in the glass with a distance of 150 μm are labeled.The nano-crack grows downward.In the bottom row, a second fixed mark in the glass is labeled.B) visualization of the finished 150 μm long crack using a smaller circular laser pulse shape.The emitted Rayleigh wave causes tension in the liquid, inducing cavitation bubbles, which make the path of the crack visible.C) SEM photograph of the crack (SEI, 5 kV, x50000).

Carving
Zhang et al. [13] showed that concentric circle-like patterns can be created on a glass surface from pre-existing flaws via shock wave impact generated with a Nano-Pulse Lithotripsy probe.They observe and study circumferential crack propagation induced by the symmetric radial stress.
In this section, we study the circular propagation of the crack induced by the described elliptical configuration.Once the crack in the center of the ellipse is observed, the shots with that configuration are stopped.
The hologram displayed on the SLM screen is modified to induce a single spherical bubble at the bottom of the liquid.The crack is placed at a distance d from the position where the laser-induced bubble is created, as shown in Figure 5A.The laser pulse, with an energy of (300 ± 8) μJ, induces a spherical bubble and the emission of a shock wave.Almost instantaneously, the bubble expansion loads the surface which results in an energy transfer that deforms the glass surface, and causes the formation of a surface acoustic wave (Rayleigh wave).This is represented schematically in Figure 5A, where the red shaded circular lines represent either the shock wave or the Rayleigh wave emitted by the bubble.As in the previous case, those waves allow us to observe the crack through small bubbles nucleated on it.
Figure 5B shows the progression of the circularly propagating crack, each photograph is labeled with the corresponding experimental run number.The dark circle in the center is the laser bubble, while the blurred dark line is the emitted shock wave.The Rayleigh wave is not visible in the photographs.To observe the small bubbles on the crack, the photographs are taken at a delay of 35 ns after the generation of the laser bubble, only the last one (45 runs) is taken with a delay of 45 ns, where the approximately circular damage has closed completely.
Figure 5C shows the damage created after 54 experimental runs performed in the same position.The full frame is not large enough to observe the entire fracture.In the subsequent 55th run, a piece of glass is completely detached, remarkably in one piece.
The detachment can be seen by the blurred thick line on the bottom and the several curved conchoidal marks.The fracture is further analyzed via the surface topology presented in Figure 5C  The fracture reaches a depth of z = −50 μm near the perimeter of the circular hole, measured at a radial distance of about 75 μm from the perimeter of the circle, or 175 μm measured from the center of the circle (x = y = 0).This depth is reached with an approximate rotational symmetry.From z = −50 μm to the bottom side of the glass (z = −160 μm), the propagation of the damage is not axisymmetric, but shows only an approximate planar symmetry with respect to the y-z plane.The lateral outer edge of the damage is at x ≈ ± 380 μm, top is at y ≈ 215 μm, and the bottom is at y ≈ −250 μm.
The conchoidal marks appear as half circles in the area where the first surface crack is placed.These marks grow to form a shape similar to the ends of a cardioid that closes in the zone where the circular crack has closed on the surface.
In Figure 6, we show a cross-section (x-z plane) of an axisymmetric finite-volume simulation of a circular bubble.The liquid in which the bubble is induced and the shock wave is emitted is shown on the top.The elastic plate where the Rayleigh wave is transmitted is shown on the bottom.In the solid, the maximum radial stress over the full simulation time (200 ns) is shown.As expected, the highest stresses are reached on the surface of the glass.Nevertheless, at the bottom of the glass, a region in which large radial stresses are reached extends laterally for about 300 μm.That region reaches a height of about 50 μm.The simulation and the corresponding maximum stress distribution may explain the conchoidal fracture of Figure 5D.The radial stress  xx creates the complex fracture, but the vertical stress  yy eventually causes its detachment.Even so, in the experiment the situation is more complex.As the damage grows, the distribution of maximum stress changes with each shot.
We identify the curvilinear marks as shell-like or conchoidal marks. [22]The conchoidal marks are typical in isotropic rocks such as obsidian and limestone.As is explained by Li and Moelle, [23] an individual conchoidal mark is a ridge delineated by a change of fracture orientation.If the conchoidal marks are periodically repeated, the result is a conchoidal structure.McJunkins and Thornton [22] has described how the characteristic lines be- tween the conchoidal marks represent the locations of maximum tensile stress.
In Figure 7, a close-up of the marks on the glass is observed using confocal microscopy.We identify hackle marks [24] intersecting conchoidal marks perpendicularly.The hackle marks are parallel to the crack propagation.
We also study the experimental case without an initial crack.There only a circular laser bubble is created in the liquid sample close to the glass surface.Using the same laser energy as for the case presented in Figure 5, the conchoidal structure is observed, but the crater has just half of the size compared to the previous case.The number of shots necessary to detach the conchoidal structure is significantly larger if there is no initial crack, with 156 shots compared to the previous 55.

Conclusion
We have developed a simple tool for micro-and nano-structuring on glass in a controlled way using shaped laser-induced shocks and surface waves.In contrast to existing direct-writing methods, energy is not deposited directly into the glass.The laser pulse focuses into the liquid, close to the solid surface, which leads to the formation of shock waves in the liquid and Rayleigh waves in the glass.The results are compared with finite-volume simulations with reasonable agreement.
A directed nano-crack with a width of less than 100 nm can be created by focusing a pulsed, elliptically shaped laser beam.The nano-crack is created by repeated loading (≈ 18 events) in the direction of the minor axis of the ellipse.The crack can be propagated by displacing the sample and changing the rotation angle of the laser ellipse which is digitally controlled in real-time with the SLM.In this way, arbitrary shapes can be engraved on the glass surface (e.g., triangle, square).The presented method, as it is not dependent on ablation, produces much fewer unwanted material fragments, in comparison with other methods for microand nano-structuring.Also, as the technique relies on "cutting" along a surface rather than gradually removing material, larger volumes should be easier to carve.In future studies, this technique, together with others of fine measurement, could help to determine the nature of the propagation of damage in this type of material (brittle or ductile).
Since the width of the crack is too small to observe with optical microscopy, we utilize the nucleation of secondary cavitation bubbles in the crack, thereby indicating its location.
Focusing the laser into a point near a crack, generates diverging shocks and surface waves with a circular shape propagating the crack around the focused spot and eventually closing a loop.This also generates several conchoidal marks in the glass, leading to the formation of a conchoidal structure.Hackle marks, perpendicular to the conchoidal marks, are also observed.The crater size is determined by the initial distance between the nano-crack and the laser-induced bubble.The biggest crater radius observed with the energy used in this manuscript was about 115 μm.The smallest radius, of about 50 μm, was observed in a case in which no previous crack was induced.
To fully explain the conchoidal structure, a simulation would require to consider the repeated loading and changes on the glass structure.However, the calculated maximum radial stresses on the glass (Figure 6) help understand the structure of the crater.
In future work, we could use objective lenses with shorter focal lengths to reduce the length and width of the shaped laser pulse, which might yield even better control of the crack.
Another possible future experiment could involve trying to observe the crack generating mechanism, but that will require combining our asymmetrical acoustic wave excitation with other techniques.
This non-contact method of crack generation and propagation may be used for micro-structuring delicate surfaces.It would be interesting to expand it from amorphous to crystalline materials where currently microcracks are induced through thermal ablation. [25]

Figure 1 .
Figure 1.A) Schematic of the experimental setup.The laser bubble in water is shown in blue, while the propagation of the wavefront is shown in shades of red.B) Dynamics of the elliptical bubble.The top of each frame is a strobe photograph, while the bottom is extracted from a finite-volume method simulation.The size of the individual frames is 200 μm × 200 μm.C) Stresses on the surface of the solid (z = 0) close to the center to which the waves converge.In the top row for a line on the major axis (x = -15-x = 15 μm), in the bottom row for a line on the minor axis (y = -15-y = 15 μm).

Table 1 .
Simulation fluid and solid parameters, including surface tension , dynamic viscosity μ and parameters of the Tait equation of state, as well as the elastic modulus E, Poisson's ratio  and density . [N m −1 ] μ[mPa s] p 0 [Pa]  0 [kg m −3 ] 13 ns.It is approximately constant along 10 μm on the major axis and along 2 μm on the minor axis.For  zz , the maximum value is 132 MPa, reached at 17 ns.It is approximately constant along 6 μm on both axes.The negative stress is induced by the shock wave, which propagates slower than the Rayleigh wave, with a velocity of about 1900 m s −1 .The minimum value for  xx is −1230 MPa, reached at 24 ns.For  yy , the minimum value is −1120 MPa, reached at 23 ns.For  zz , the minimum value is −1077 MPa, reached at 23 ns.Similar maximum values are reached along 10 μm on the minor axis and only along 2 μm on the major axis.In absolute value, the maximum compressive stress (-1230 MPa for  xx ) is 1.4 times larger than the maximum tensile stress (875 MPa for  yy ).The values for this ratio (|Max.Tensile stress/Max.Compressive stress|) are 1.89, 1.28, and 8.16, for each component,  xx ,  yy , and  zz , respectively.

Figure 2 .
Figure 2. A) Sequence of experimental runs leading to the formation of a nano-crack.The number indicates the number N of experimental runs performed in the same position.Here, after 20 experimental runs, the crack becomes visible through the expansion of small bubbles formed on the crack.In the successive runs, that is, from N = 21 to N = 25, the nano-crack grows vertically.The photographs are taken at 15 ns after the laser bubble generation.The last frame corresponds to the same position without the elliptical laser-induced bubble after 25 runs.Although present, the nano-crack is not visible.The size of the individual frames is 200 μm × 200 μm.B) Probability of glass damage ϕ as a function of the number of repetitions N. The continuous line is a fit to the cumulative distribution function of the normal distribution.The expectation value is E(N) = 17.92 and the standard deviation is s = 5.73.

Figure 3 .
Figure 3. A) Generation of a vertical nano-crack of 150 μm length.In each frame, the vertical nano-crack is observed in the center of the elliptical laser bubble.The sample is moved upward in steps of 5 μm using a motorized stage.On the right, two marks in the glass with a distance of 150 μm are labeled.The nano-crack grows downward.In the bottom row, a second fixed mark in the glass is labeled.B) visualization of the finished 150 μm long crack using a smaller circular laser pulse shape.The emitted Rayleigh wave causes tension in the liquid, inducing cavitation bubbles, which make the path of the crack visible.C) SEM photograph of the crack (SEI, 5 kV, x50000).

Figure 4 .
Figure 4. Nano-cracks on the sides of a triangle (left) and a square (right).The laser is focused in the center of each shape, the emitted Rayleigh wave inducing bubbles on the cracks which make them visible.The images are the superposition of several photographs.

Figure 5 .
Figure 5. Carving process.A) Above, the elliptical configuration to induce a crack on the solid surface.Below, the geometry used to circumferentially propagate the crack.The laser bubble in water is shown in blue, while the propagation of the wave front is shown in shades of red.B) Circumferential crack propagation progression.The number of shots is indicated in each frame on the top left.After 45 shots, the circle-like crack is fully closed.C) Conchoidal structure before its detachment.The small conchoidal marks are enclosed by the propagated crack and a blurry line (bottom) on the opposite side of the glass.D) Topography of the conchoidal structure (seen from the bottom).E) Profiles of the conchoidal structure, along x = 0 (top) and along y = 0 (bottom).
, measured using areal confocal profilometry.It shows the glass now from the bottom with the depth color-coded with z = 0 being the top and z = −160 μm the bottom of the plate.Around the circular through hole of about 100 μm (white), a larger region of spallation is present.In Figure 5E a profile through the structure is shown, along x = 0 (top), and along y = 0 (bottom).

Figure 6 .
Figure 6.Maximum radial stresses on the glass over the full simulated time (200 ns).

Figure 7 .
Figure 7. Close-up of conchoidal marks in the glass.Hackle lines can be seen perpendicularly to the conchoidal marks.