Temporal Evolution of Pressure Generated by a Nanosecond Laser Pulse Used for Assessment of Adhesive Strength of the Tungsten–Zirconium–Borides Coatings

The article presents theoretical and experimental study of shock waves induced by a nanosecond laser pulse. Generation of surface plasma pressure by ablation of the graphite absorption layer in water medium and shock wave formation were analyzed theoretically and experimentally. The amplitude and temporal variation of the shock wave pressure was determined basing on a proposed hydrodynamic model of nanosecond laser ablation and experimentally verified with use of a polyvinylidene fluoride (PVDF) piezoelectric-film sensor. The determined pressure wave was used for examination of adhesive strength of tungsten–zirconium–boride coatings on steel substrate. The magnetron sputtered (MS) W–Zr–B coatings show good adhesion to the steel substrate. The obtained experimental results prove the correctness of the proposed model as well as the suitability of the procedure for assessment of adhesive strength.


Introduction
The shock waves create many unique possibilities in materials testing. Generating pressure load as a result of applications of a high-energy laser pulse that caused metal surface evaporation was invented in the nineteen-sixties [1], and it was verified for metals with an uncovered surface in direct regime [2]. Such experiments required lasers with high pulse energy, which limited the application of this method in practice.
Application of inertial layer being transparent for the laser beam, confined regime, allows creating of the shock waves with high amplitudes, causing compression stress exceeding the yield point of metals [3,4]. The influence of different materials of inertial and absorption layers [5,6] on the profiles of generated pressures waves were studied extensively in the 1970s [7][8][9]. High stress waves induced by laser pulse give the possibility of changing the microstructure of materials [10]. This finding quickly led to extensive research onto the use of laser shock processing (LSP) as an alternative method for conventional shot peening and deep rolling [11].
High-pressure shock waves generated by laser pulse create many unique possibilities in testing of materials [12,13]. A broad range of pressures, speed, and deformation settings may be achieved as a result of changes in energy, shape, or duration of the laser pulse. On the basis of the laser shock waves, new diagnostic methods of dynamic behavior of material and layer [14], as well as adhesion of thin films could be developed [15]. Thin films are essential components of many microelectronic, optical, and micromechanical systems. During their manufacturing, a large amount of residual stresses is induced which influences their mechanical properties. In certain conditions, the residual stress may cause layer delamination from the substrate or its cracking. Several practical techniques of Surfaces of the samples were ground and polished using diamond suspensions Before deposition process surface roughness was measured on confocal microscope VK-X100 (Keyence, 2800 Mechelen, Belgium) according to [39]. Values of roughness parameters were as follow: Ra = 0.024 µm, R p = 0.07 µm, R z = 0.133, and R Sm = 141 µm.
The W 0.76 Zr 0.24 B 2.5 target [40] was mounted on the water-cooled 1-inch magnetron sputtering cathode (TORUS Magnetron Sputtering Cathode, Kurt J. Lesker, Jefferson Hills, PA, USA). Deposition parameters were chosen on the basis of [41] and were as follows: initial and working pressure values were 2 × 10 −5 mbar and 9 × 10 −3 mbar, respectively, the gas flow of argon was 19 mL/min, power supplied to the magnetron cathode was 50 W. Each film was deposited for 120 min on high speed steel HSS samples heated up to 520 • C and positioned 40 mm in front of the target.
In order to ensure surface purity of the target and provide stability of sputtering conditions, the target was sputtered for 5 min prior to each deposition.
After the deposition process, the surface quality and thickness of the film were checked on a confocal microscope. The thickness estimated by the step method was 2.33 ± 0.14 µm. An example of the measurement result is shown in the Figure 1a. Roughness of the surface after film deposition slightly changed. Values of roughness parameters were as follow: R a = 0.025 µm, R p = 0.09 µm, R z = 0.175, and R Sm = 160 µm. Higher values of picks amplitude R p and maximum roughness R z were due to the presence of single particles on the surface visible in Figure 1b. Nanoindentation analyses were performed at room temperature using Vantage (Micro Materials Limited, Wrexham, UK) with Berkovich-shaped dia denter calibrated before each measurement with Diamond Area Function. Ea ment has been repeated 12 times in the line with a distance of 50 µm from each minimize the effect of the substrate, the hardness and elastic modulus values w lated based on the average data obtained at depths of about 100 nm (indentati 10 mN). It was done to ensure the maximum indentation depth of 1/10 of th thickness and thus minimize substrate effect and measure hardness in the load ent region. Values of hardness and Young's modulus were as follows: H = 43.6 E = 415.6 ± 6.5 GPa.

Shock Wave Pressure
Experiments were carried out with Nd:YAG pulse laser (981E, Quante Cedex, France) with a wavelength of 1064 nm, a pulse duration of 10 ns, and en to 1 J. A spot diameter of 2.5 mm was used. The energy density that hit the samp was changing from 10 to 20 J/cm 2 , while the laser power density varied fr GW/cm 2 . The carbon layer was sprayed on irradiated surface of the sample to absorption. The average thickness, measured by confocal microscope, was abou Figure 2 shows a schematic of pressure measurement system. The set-up five elements: a layer of water (1), graphite film (2), steel sample plate (3), polyv fluoride (PVDF) piezoelectric-film sensor (4), and (S_25CP Piezotech, Lyon, Fr Teflon disc (5).
Water serves as a transparent confining medium, whereas graphite is an Teflon disc placed under the sensor is an energy absorber. Small amounts of par used to improve the mechanical contact between the successive elements. Nanoindentation analyses were performed at room temperature using NanoTest Vantage (Micro Materials Limited, Wrexham, UK) with Berkovich-shaped diamond indenter calibrated before each measurement with Diamond Area Function. Each experiment has been repeated 12 times in the line with a distance of 50 µm from each other. To minimize the effect of the substrate, the hardness and elastic modulus values were calculated based on the average data obtained at depths of about 100 nm (indentation load of 10 mN). It was done to ensure the maximum indentation depth of 1/10 of the coating thickness and thus minimize substrate effect and measure hardness in the load independent region. Values of hardness and Young's modulus were as follows: H = 43.6 ± 0.7 GPa, E = 415.6 ± 6.5 GPa.

Shock Wave Pressure
Experiments were carried out with Nd:YAG pulse laser (981E, Quantel, Le Ulis Cedex, France) with a wavelength of 1064 nm, a pulse duration of 10 ns, and energy of 0.5 to 1 J. A spot diameter of 2.5 mm was used. The energy density that hit the sample surface was changing from 10 to 20 J/cm 2 , while the laser power density varied from 1 to 2 GW/cm 2 . The carbon layer was sprayed on irradiated surface of the sample to facilitate absorption. The average thickness, measured by confocal microscope, was about 5 µm. Figure 2 shows a schematic of pressure measurement system. The set-up consists of five elements: a layer of water (1), graphite film (2), steel sample plate (3), polyvinylidene fluoride (PVDF) piezoelectric-film sensor (4), and (S_25CP Piezotech, Lyon, France) and Teflon disc (5). A PVDF sensor is placed on the back of the sample. However, registered pressures are lower than those occurring at the front surface of the sample. This phenomenon is caused by energy loses of the shock wave during propagation through the sample. In order to estimate pressure values of the shock wave at the front side of the sample, samples with different thicknesses were used. The estimation was made on the basis of an attenuation process [42,43].
Set-up characteristics and methods of calculations were presented in detail in previous studies [44][45][46]. The value of stress was calculated from registered signals from PVDF sensor. Results from PVDF sensor were compared with the measurements of velocity of back sample surface by VISAR (Velocity Interferometer System for Any Reflector). A qualitative compliance between the PVDF's pressure and VISAR's velocity rescaled to pressure was achieved [47].
The experimental set-up was modified to measure film adhesion to the substrate. In this case, there PVDF sensor was removed. Tested thin layer was on back side of steel plate and contact with atmosphere and the surface could deform freely.

Theoretical Model
The temporal variation of pressure that is induced on the surface of the sample and next generates a shock wave in it, can be theoretically modeled using the hydrodynamic model. The details of theoretical model were presented in [38]. During the first several microseconds after the beginning of the laser pulse the plasma is so dense, that it can be treated as continuum fluid and equations of gas dynamics can be applied for its description. The model which describes both the target heating, formation of the plasma and its expansion consists of equations of conservation of mass, momentum, energy, and the diffusion (species transport) equation. It is solved in axial symmetry with the use of the AN-SYS-Fluent software package. The laser beam is normal to the surface and the focal spot on the target is 4.52 mm 2 . It is assumed that the plumes expand to water at ambient condition. The laser is a Nd:YAG laser operating at its first harmonic wavelength of 1064 nm with a pulse energy of 0.452-1.356 J and 10-ns pulse duration. The laser beam is focused on graphite layer with the laser fluence of 10-30 J·cm −2 . For comparison for surface pressures the model of laser ablation in ambient argon is used, whose description was presented in [48]. Figure 3 presents the temporal variation of maximal surface pressure on the sample surface during the first 50 ns as calculated in the model. The results for Ar ambient are also presented for comparison to show the differences in values of maximum pressure ( Figure 4). In both cases, the shock wave creation is observed. For the target, which has been previously covered with a water layer, the plasma is confined and its expansion is Water serves as a transparent confining medium, whereas graphite is an absorber. Teflon disc placed under the sensor is an energy absorber. Small amounts of paraffin were used to improve the mechanical contact between the successive elements.

Theoretical Surface Pressure
A PVDF sensor is placed on the back of the sample. However, registered pressures are lower than those occurring at the front surface of the sample. This phenomenon is caused by energy loses of the shock wave during propagation through the sample. In order to estimate pressure values of the shock wave at the front side of the sample, samples with different thicknesses were used. The estimation was made on the basis of an attenuation process [42,43].
Set-up characteristics and methods of calculations were presented in detail in previous studies [44][45][46]. The value of stress was calculated from registered signals from PVDF sensor. Results from PVDF sensor were compared with the measurements of velocity of back sample surface by VISAR (Velocity Interferometer System for Any Reflector). A qualitative compliance between the PVDF's pressure and VISAR's velocity rescaled to pressure was achieved [47].
The experimental set-up was modified to measure film adhesion to the substrate. In this case, there PVDF sensor was removed. Tested thin layer was on back side of steel plate and contact with atmosphere and the surface could deform freely.

Theoretical Model
The temporal variation of pressure that is induced on the surface of the sample and next generates a shock wave in it, can be theoretically modeled using the hydrodynamic model. The details of theoretical model were presented in [38]. During the first several microseconds after the beginning of the laser pulse the plasma is so dense, that it can be treated as continuum fluid and equations of gas dynamics can be applied for its description. The model which describes both the target heating, formation of the plasma and its expansion consists of equations of conservation of mass, momentum, energy, and the diffusion (species transport) equation. It is solved in axial symmetry with the use of the ANSYS-Fluent software package. The laser beam is normal to the surface and the focal spot on the target is 4.52 mm 2 . It is assumed that the plumes expand to water at ambient condition. The laser is a Nd:YAG laser operating at its first harmonic wavelength of 1064 nm with a pulse energy of 0.452-1.356 J and 10-ns pulse duration. The laser beam is focused on graphite layer with the laser fluence of 10-30 J·cm −2 . For comparison for surface pressures the model of laser ablation in ambient argon is used, whose description was presented in [48].  Figure 3 presents the temporal variation of maximal surface pressure on the sample surface during the first 50 ns as calculated in the model. The results for Ar ambient are also presented for comparison to show the differences in values of maximum pressure (Figure 4). In both cases, the shock wave creation is observed. For the target, which has been previously covered with a water layer, the plasma is confined and its expansion is delayed [38]. Therefore, the induced pressure is an order of magnitude greater (as 200 to 2000 MPa) and the pressure pulse duration 2-3-times longer than in the ambient gas (argon) [48] at the same power density. As it is shown in Figure 4, for laser fluence increasing from 6.5 to 15 J/cm 2 the surface pressure increases almost linearly from 800 to 1900 MPa, respectively. It is due to growth of evaporation rate. After that, the absorption of a plasma plume is significant [38] what causes the surface pressure stabilization slightly below 2000 MPa. The second phenomena that can influence a growth of the plasma pressure is change of ablation regime. After reaching of critical parameters the phase explosion and fragmentation begin [49]. The maximum time duration of pressure above 1000 MPa is~42 ns for 20 J/cm 2 ( Figure 3). aterials 2021, 14, x FOR PEER REVIEW delayed [38]. Therefore, the induced pressure is an order of magnitude gre 2000 MPa) and the pressure pulse duration 2-3-times longer than in the am gon) [48] at the same power density. As it is shown in Figure 4, for laser fluen from 6.5 to 15 J/cm 2 the surface pressure increases almost linearly from 800 respectively. It is due to growth of evaporation rate. After that, the absorptio plume is significant [38] what causes the surface pressure stabilization slight MPa. The second phenomena that can influence a growth of the plasma pres of ablation regime. After reaching of critical parameters the phase explosion tation begin [49]. The maximum time duration of pressure above 1000 MP 20 J/cm 2 ( Figure 3).   aterials 2021, 14, x FOR PEER REVIEW delayed [38]. Therefore, the induced pressure is an order of magnitude gre 2000 MPa) and the pressure pulse duration 2-3-times longer than in the am gon) [48] at the same power density. As it is shown in Figure 4, for laser flue from 6.5 to 15 J/cm 2 the surface pressure increases almost linearly from 800 respectively. It is due to growth of evaporation rate. After that, the absorptio plume is significant [38] what causes the surface pressure stabilization sligh MPa. The second phenomena that can influence a growth of the plasma pres of ablation regime. After reaching of critical parameters the phase explosion tation begin [49]. The maximum time duration of pressure above 1000 MP 20 J/cm 2 (Figure 3).

Experimental Measurement of Pressure
Unfortunately, it is not possible to measure pressure directly at the fr

Experimental Measurement of Pressure
Unfortunately, it is not possible to measure pressure directly at the front surface of the sample. The sensor is placed on its back side. Hence, the comparison of pressure calculated in the model with measurements is not straightforward. It demands taking into account all energy losses during wave propagation. Firstly, there are partial reflections of wave at every boundary between the media: water, steel, and the sensor. Secondly, wave propagation in any medium is accompanied by energy losses. In our case a steel plate has the biggest thickness then wave attenuation in it must be included. The thicker the plate, the more it weakens the wave after it passes. Both issues are discussed in more detail in the following text.
Results of pressure measurement by a PVDF sensor registered for different thicknesses of the steel samples allowed estimation of pressure level on the front surface of the steel plate. The laser pulse and a waveform of pressure calculated from the PVDF sensor signal are presented in Figure 5. A series of subsequent pulses corresponding to shock wave reflection from the test plate back and front sides can be observed. Their amplitude gradually decreases as a result of attenuation in the plate. signal are presented in Figure 5. A series of subsequent pulses corresponding to shock wave reflection from the test plate back and front sides can be observed. Their amplitude gradually decreases as a result of attenuation in the plate. The stress course for a system, with a steel plate that is 1-mm thick was used, is presented in Figure 5a. The maximum value of pressure at the first peak reaches 85 MPa. Time course of stress and amplitude are strongly modified by reflected stress waves. The velocity of sound inside steel plate estimated from experiment is about 5920 m/s. Propagation of shock wave in real medium is accompanied by energy losses. Moreover, in a layered medium, the wave is partially reflected at boundaries. For a weak shock wave, the linear approximation holds, i.e., coefficients of reflection and transmission are functions of the ratio of acoustic impedances A, and given by Equation (1)  (1) where: ρ2c2, ρ1c1-acoustic impedances of contacting media (product of the density ρi and The stress course for a system, with a steel plate that is 1-mm thick was used, is presented in Figure 5a. The maximum value of pressure at the first peak reaches 85 MPa. Time course of stress and amplitude are strongly modified by reflected stress waves. The velocity of sound inside steel plate estimated from experiment is about 5920 m/s. Propagation of shock wave in real medium is accompanied by energy losses. Moreover, in a layered medium, the wave is partially reflected at boundaries. For a weak shock wave, the linear approximation holds, i.e., coefficients of reflection and transmission are functions of the ratio of acoustic impedances A, and given by Equation (1) [50,51]: where: ρ 2 c 2 , ρ 1 c 1 -acoustic impedances of contacting media (product of the density ρ i and the speed of sound c i ); T-relative amplitude of wave transmitted from medium 1 to medium 2; R-relative amplitude of wave reflected from material boundaries. Calculations of acoustic impedances were performed using the following data: steel-47 × 10 6 kg/m 2 s, PVDF-3.8 × 10 6 kg/m 2 s, or paraffin oil-2 × 10 6 kg/m 2 s. The small impedance of the PVDF sensor in contact with the high impedance of the steel sample results in a five-fold decrease of pressure amplitude, i.e., pressure near the back side of the steel sample is five times the pressure measured by the sensor. In order to calculate pressure at the front of the sample, attenuation of the shock wave during propagation in steel has to be considered. Assuming an exponential damping formula after [42]: where: n-wave attenuation coefficient; x-distance from front surface; P-initial pressure on the front surface at x = 0. Estimation was made only for the first peak of the pressure registered by the sensor because amplitudes of subsequent peaks are distorted by reflected waves. In Figure 6, the dependence of pressure on the wave path in the steel (sample thickness) is presented. Points show values calculated from measurements, and the solid line is the fit of exponential formula from Equation (2)  where: n-wave attenuation coefficient; x-distance from front sure on the front surface at x = 0. Estimation was made only for the first peak of the pressure because amplitudes of subsequent peaks are distorted by reflected dependence of pressure on the wave path in the steel (sample Points show values calculated from measurements, and the solid l tial formula from Equation (2) using the attenuation coefficient n plitude of the shock wave at the front surface P = 900 MPa. Knowledge of the pressure value on the front side of steel pla pressure in confining medium. The pressure wave in water is m shows that in water with small impedance (ρ2 = 1 g/cm 3 ; c2 = 1500 with steel with high impedance (ρ1 = 7.9 g/cm 3 ; c1 = 5920 m/s), the wave is going to be two-times higher than inside the steel sampl wave in water near sample surface according to these calculatio Knowledge of the pressure value on the front side of steel plate allows for estimating pressure in confining medium. The pressure wave in water is much higher. Formula (1) shows that in water with small impedance (ρ 2 = 1 g/cm 3 ; c 2 = 1500 m/s) that has a contact with steel with high impedance (ρ 1 = 7.9 g/cm 3 ; c 1 = 5920 m/s), the amplitude of the shock wave is going to be two-times higher than inside the steel sample. The value of pressure wave in water near sample surface according to these calculations is equal about 1800 MPa for a 10-ns pulse with energy of 1 J. It should be noted that theoretical model of laser ablation was made for ideal conditions. Moreover, uncertainty in material properties and quality of contact between the sensor and the sample may affect the consistency of the results. However, the durations of first pressure peaks are comparable (~50 ns) that also confirms the compliance of the measurements with the theoretical model.
In Figure 3, the pressure registered at the back of 0.3-mm thick sample scaled according to the above procedure, alongside with theoretical pressure waveforms is presented. It was also necessary to shift it in time due to delays introduced by propagation in subsequent media. Unfortunately, such delays cannot be calculated with high accuracy due to lack of precise data concerning velocity of high amplitude wave. The experimental pressure waveform shows longer rise and fall times. It is due to dispersion in media in which the wave propagates, i.e., different propagation velocity for wave components.

Coating Adhesion Test
Tests were carried out for film W-Zr-B deposited on steel plates of thickness 0.3, 0.5, and 1 mm. Based on measurement results of the amplitude of pressure wave on the back side of the sample, the strength of adhesion was determined. The surface of samples after each test were observed and destruction of film was measured on the microscope. The tests show that in the case of the sample with 1-mm thickness there was no delamination. First, small deformation of the film after test was observed in the case of the 0.5-mm thickness plate. Measurable delamination was observed only for the sample with a thickness of 0.3 mm. In Figure 7, the surface of the film on the 0.3-mm sample after LASAT with 1 J is shown. The surface is flat and smooth, only a small local protuberance was observed probably in place of an imperfection of the film. terials 2021, 14, x FOR PEER REVIEW is shown. The surface is flat and smooth, only a small local protube probably in place of an imperfection of the film.
In the case of the 0.3-mm thick plate, delamination of the coating ure 8). The maximum delamination height (determined in a referen film) was 1.6 to 2.5 um and the diameter was about 0.2 mm. No pr served when a laser pulse energy of 0.7 and 0.5 J was used. Adhesio based on value of the maximum amplitude of compressive shock w Delamination is caused by tensile shock wave emerging due to reflec wave from the free surface. In case of the W-Zr-B film (ρ = 10.95 [40,52]) on steel substrate the ratio of acoustic impedances is about 0 tude of the wave transmitted from steel to the film is T = 0.78. In the c steel, the amplitude of pressure wave on steel/film boundary is abou mated amplitude of the tensile wave that caused coating delamina MPa.  In the case of the 0.3-mm thick plate, delamination of the coatings can be visible ( Figure 8). The maximum delamination height (determined in a reference to non-deformed film) was 1.6 to 2.5 um and the diameter was about 0.2 mm. No protuberance was observed when a laser pulse energy of 0.7 and 0.5 J was used. Adhesion can be estimated based on value of the maximum amplitude of compressive shock wave at the interface. Delamination is caused by tensile shock wave emerging due to reflection of compressive wave from the free surface. In case of the W-Zr-B film (ρ = 10.95 g/cm 3 , c = 6600 m/s [40,52]) on steel substrate the ratio of acoustic impedances is about 0.64. Relative amplitude of the wave transmitted from steel to the film is T = 0.78. In the case of 0.3-mm thick steel, the amplitude of pressure wave on steel/film boundary is about 700 MPa. The estimated amplitude of the tensile wave that caused coating delamination was about 320 MPa.

Conclusions
Theoretical and experimental studies of shock waves induced by a nanosecond laser pulse are presented. Generation of pressure induced by a nanosecond laser pulse ablation of absorption layer (graphite) in water medium and shock wave formation were analyzed theoretically and experimentally. The amplitude of the shock wave pressure was determined based on the proposed hydrodynamic model of nanosecond laser ablation and experimentally validated with the use of piezoelectric polymer PVDF sensors. The determined pressure wave was used for assessment of adhesive strength of magnetron sputtered, novel tungsten-zirconium-boride coatings on steel substrate. The main conclusions are as follows: 1. The amplitude of the shock wave estimated based on the proposed hydrodynamic model was validated experimentally. Both methods showed good agreement. The maximal pressure in water near the sample surface can reach 2 GPa. Time duration of the first pressure peak is about 50 ns; 2. Based on knowledge of shock wave pressure and acoustic impedance of tested materials, adhesive strength of coatings can be determined. The estimated amplitude of the tensile wave that caused W-Zr-B film delamination was about 320 MPa; 3. The described above method is simple and does not require advanced equipment.
The proposed method is less time-consuming than a traditional scratch test, which

Conclusions
Theoretical and experimental studies of shock waves induced by a nanosecond laser pulse are presented. Generation of pressure induced by a nanosecond laser pulse ablation of absorption layer (graphite) in water medium and shock wave formation were analyzed theoretically and experimentally. The amplitude of the shock wave pressure was determined based on the proposed hydrodynamic model of nanosecond laser ablation and experimentally validated with the use of piezoelectric polymer PVDF sensors. The determined pressure wave was used for assessment of adhesive strength of magnetron sputtered, novel tungsten-zirconium-boride coatings on steel substrate. The main conclusions are as follows: 1.
The amplitude of the shock wave estimated based on the proposed hydrodynamic model was validated experimentally. Both methods showed good agreement. The maximal pressure in water near the sample surface can reach 2 GPa. Time duration of the first pressure peak is about 50 ns;

2.
Based on knowledge of shock wave pressure and acoustic impedance of tested materials, adhesive strength of coatings can be determined. The estimated amplitude of the tensile wave that caused W-Zr-B film delamination was about 320 MPa; 3.
The described above method is simple and does not require advanced equipment. The proposed method is less time-consuming than a traditional scratch test, which additionally needs greater surface to measure. However, the thickness of the sample is a limiting factor in the measuring range.
The proposed method is not intended to replace a traditional scratch test, but to augment the material testing toolbox. It helps to perform assessment of adhesion in dynamic conditions. We are currently planning more extensive tests of coating adhesion, carried out in parallel with two methods: scratch test and laser pulse.