Experimental investigation of shock wave pressure induced by a ns laser pulse under varying confined regimes

Optics and Lasers in Engineering 126 (2020) 105913

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Experimental investigation of shock wave pressure induced by a ns laser pulse under varying confined regimes J. Radziejewska a, M. Strzelec b,∗, R. Ostrowski b, A. Sarzyński b a b

Warsaw University of Technology, Faculty of Production Engineering, Narbutta 85, 02-524 Warsaw, Poland Institute of Optoelectronics, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw 46, Poland

a r t i c l e Key words: Laser pulse Shock wave PVDF sensor VISAR

i n f o

a b s t r a c t The article presents a study of shock waves induced by a nanosecond laser pulse in samples in the form of steel plates. Its contents include a description of the measurement system, methods of calculations and some characteristics of the measuring instruments and materials used. The quoted formulas enabled the processing of recorded measurement signals. The influence of material used as a confining layer (glass, PMMA - Plexiglass, water) and substrate (PMMA, aluminium, steel) on the amplitude and shape of recorded pressure waves was studied. Pressure behind the shock wave measurements were conducted using piezoelectric polymer PVDF (polivinylidene fluoride) sensors. Verifications of PVDF results were conducted by 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. The strains (about 0.3%) and strain rates (about 3 × 105 1/sec) were evaluated. The obtained results will allow for a better selection of test conditions for studying material properties by using a shock wave induced by the laser pulse.

1. Introduction Shock waves have a great practical influence on all dynamic systems in a wide range, starting with cosmology - the creation and evolution of stars and planets [1] - to microbiology, materials engineering [2] or medicine [3]. They are usually generated by energy released in a medium, in the form of an explosion, an electrical discharge, high speed collisions or a strong, short laser pulse. Shock waves are a dominant process of energy scattering where the speed level of material transport is higher than the relevant speed of propagation of acoustic waves. The possibility of creating pressure load as a result of metal surface evaporation by a high-energy laser pulse was invented in 1963 [4], and it was verified for metals with uncovered surface in a direct regime [5], and subsequently for an area covered with a confining layer transparent for laser radiation (a confined regime) [6]. Further study quickly led to the creation of the shock waves with much higher amplitudes, causing compression stress exceeding the yield point of metals [7]. In the 1970s, studies on the influence of different materials of confining and absorption layers [8,9] on the measured or calculated profiles of generated pressures were carried out [10–12]. First information about the possibility of changing the microstructure of materials (aluminium) af-

fected by high stress waves appeared in 1972 [13]. The apparent success achieved in these early experiments quickly led to extensive research on the use of laser shock processing (LSP) as an alternative method to conventional shot peening and deep rolling [14]. As many articles and monographs have shown [15–16], the use of lasers to generate high-pressure shock waves creates many unique possibilities in materials engineering. Contrary to collision systems, a wider range of pressures, speed and deformation settings may be achieved as a result of changes in the shape or duration of a laser pulse. Laser systems also allow the use of simple diagnostic methods of in situ processes [17]. One of the simplest is the use of polyvinylidene (PVDF) sensors. The piezoelectric effect of Polyvinylidene Fluoride (PVDF) was first raised by Kawai in 1969 [18]. Early works have shown that highly reproducible piezoelectric film PVDF can be reliably used in a wide range of precise stress and stress-rate measurements, due to nanosecond resolution and one of the highest operating stress limits [19,20]. Ferroelectric polymers with well-defined and precisely known electrical properties are now routinely available from commercial sources [e.g. 21]. These polymers provide an unusual opportunity to study the structure and physical properties of materials subjected to shock loading induced by strong laser pulses. The behavior of PVDF sensors has been studied over a wide

Abbreviations: PMMA, Plexiglass; PVDF, polivinylidene; VISAR, Velocity Interferometer System for Any Reflector; LSP, Laser Shock Processing; LST, Laser Spallation Technique; LASAT, Laser Shock Adhesion Test; EB-PVD TBC, Electron Beam Physical Vapour Deposition Thermal Barrier Coating; CFRP, carbon fibre reinforced composite; DVI, Doppler Velocity Interferometer. ∗ Corresponding author. E-mail address: [email protected] (M. Strzelec). https://doi.org/10.1016/j.optlaseng.2019.105913 Received 8 June 2019; Received in revised form 9 September 2019; Accepted 20 October 2019 0143-8166/© 2019 Published by Elsevier Ltd.

J. Radziejewska, M. Strzelec and R. Ostrowski et al.

range of pressures using high-pressure shock loading and has yielded well-behaved, reproducible data up to 35 GPa in inert materials [22]. The use of more sophisticated, additional experimental VISAR determinations to analyze pressure loadings and elastic limits under shock conditions was shown to be a key point to improve simulations [23] or allowed, by a simple measurement of sample back free surface velocities to analyses shock wave propagation, and deduce the pressure versus time profiles Hugoniot conservation equations [24,25]. On the basis of laser shock waves, new diagnostic methods for the dynamic behaviour of a material and layer [26], as well as adhesion of thin films, could be developed [27]. Several practical techniques of measuring the adhesion of thin layers were described in literature. The most well-known method is the scratch test, as well as the peel, pull, blister and indentation tests. Laser Spallation Technique (LST) was first introduced by Vossen [28]. The technique was later called LASAT (LAser Shock Adhesion Test) [17,29]. Soon, a combination of the laser shock wave generation and measurement was developed, which is still very useful in scanning analyses of structures [30]. In the recent years, the interest in measuring techniques for laser shock waves has not diminished. A number of review articles on measurement methods for specific applications and layer materials, such as TiN [31], hydroxyapatite [32], thermal barrier coatings EB-PVD TBC (Electron Beam Physical Vapour Deposition Thermal Barrier Coating) with the use of shock wave propagation in two dimensions (LASAT 2D) [33], or carbon fibre reinforced composite (CFRP) [34], have been published. Also, surface shapes of the substrate and the configuration of samples have been analysed in detail [35,36]. As it can be seen, the area of studying of shock waves induced by intense laser pulses is not new and was widely exploited in the past. However, the simultaneous, time-resolved measurements with VISAR and PVDF are rather rarely the subject of scientific reports (see e.g. some different sources [37–39]. Moreover, simultaneous use of both techniques is frequently described in papers dealing with other than laser driven techniques of shock generation, e.g. for blast and shock in air [40] or mechanical impactors [41]. Apart from mutual verification of data (after some necessary recalculations), the use of the simultaneous PVDF stress analysis and VISAR velocity technique provide stress- and volume related measurements. It permits far better assessment of theoretical deformation models applied to rate-dependent problems study [16,42]. Taking this into account, both techniques have been in the past successfully applied to analysis of viscous compression behavior of highly explosive porous materials [43] or cavitation inception in a confined glycerol layer [44]. The paper presents the results of research on measuring the characteristics of laser-induced shock waves. The waves were induced in steel plates by a 1 J laser pulse using different inertial layers and various substrates. The main goals of the performed research were as follows: •

• •

development of simultaneous, qualitative reliable shock pressure measurement procedures using PVDF sensors and VISAR measurements of the velocity of surfaces reflecting shock waves; examination of the correctness and comparability of measurements; formulation of recommendations for improving the quality of the developed procedures.

The main text describes a study on the influence of the material used for the confining layer (glass, PMMA, water) and the substrate (PMMA, aluminium, steel) on the amplitude and shape of a pressure wave, induced by a nanosecond laser pulse. Three series of experiments were carried out. In the first, basic series, pressure measurements were the only ones to be made using piezoelectric PVDF sensors. In the second series, only measurements of the velocity of the surface reflecting the shock waves were performed. In these measurements, a VISAR four-channel optical fibre interferometer was used. In the third series, an attempt was made to measure simultaneously both the shock wave pressure and the induced surface velocity after shock wave reflection. Particularly, the second chapter describes the configuration of the experimental setup

Optics and Lasers in Engineering 126 (2020) 105913

Fig. 1. Diagram of the experimental setup for testing the pressure behind the shock wave induced by a laser pulse with different confining and substrate layers. 1 – Nd:YAG laser; 2 – laser beam; 3 - confining layer (glass, PMMA or water); 4 – absorption layer (graphite moistened with paraffin oil); 5 – front of the shock wave; 6 – investigated sample (steel); 7 – PVDF sensor; 8 – substrate (steel, PMMA or aluminium); 9 – oscilloscope (laser pulse and PVDF signal acquisition); 10 – VISAR probing laser beam; 11 – VISAR; 12 – oscilloscope (VISAR signal acquisition). Items No. 10–12 were used only during VISAR velocity measurements.

and selected main characteristics of the measuring instruments and materials used. Included are also formulas that enable the processing of registered measurement signals. The third chapter contains the results of measurements and calculations, as well as their discussion. The use of various substrates allowed the demonstration of the disturbing effects of system configuration on the results obtained. The fourth, final chapter summarises the results and presents recommendations for future experiments. 2. Experimental method A diagram of the measurement system is shown in Fig. 1. A laser beam (2) falls through a transparent confining layer (3) onto an absorption layer (4), where it is absorbed and creates high pressure plasma, which in turn induces a shock wave. The confining layer (3) inhibits the expansion of plasma created by the laser beam. Plasma is thus created in a small volume, limited by the inertial layer on one side and the test sample on the other. Thanks to this, compared to the case of free expansion into the surrounding atmosphere, both the plasma pressure and its duration are increasing. Paraffin oil was introduced between all layers to avoid the creation of air gaps, which, due to very low wave impedance, might strongly reduce the amplitude of the transmitted wave. Vacuum grease or epoxy glue [17] can also be used instead of oil. The shock wave (5) propagates through the steel sample plate (6) and falls onto the PVDF sensor (7). The piezoelectric PVDF sensor (7) creates a charge proportional to the transient value of pressure inside it. The substrate (8) is pressed with the sensor in such a way that it does not lose contact with the tested sample during the experiment. The measurement of the current flowing through the sensor load circuit makes it possible to calculate the charge and then the pressure as a function of time. The temporal profile of the laser pulse was registered by a photo-diode with a rise time of 0.4 ns. The photodiode signal was also used for triggering both oscilloscopes (9 and 12) shown in Fig. 1. The first oscilloscope (9) is used to record the temporal shape of the laser pulse and the PVDF sensor signal. The rear surface of the sample moves after being loaded by the shockwave. The dependence of the velocity of this surface on time is the only source of information about processes occurring during shockwave propagation inside the sample material. The velocity of this surface can be measured using VISAR (11). The VISAR laser beam (10) falls through

J. Radziejewska, M. Strzelec and R. Ostrowski et al.

Optics and Lasers in Engineering 126 (2020) 105913

a transparent substrate layer (8) onto the moving rear surface of the sample and is reflected. Due to the Doppler effect, the reflected radiation wavelength changes, which allows calculating the velocity of the reflecting surface. The second oscilloscope (12) is used to record four signals generated by VISAR. The experiments were carried out with a Q-switched multimode Nd:YAG pulse laser (the authors’ own construction) with a wavelength of 1064 nm and an energy level from 1 to 1.2 J. The pulse duration was 8 - 12 ns and the spot diameter ranged from 2 to 3 mm. The energy density that hits the sample surface was thus changing within a range from 14.1 to 38.2 J/cm2 , while laser power density varied from 1.2 to 4.8 GW/cm2 , respectively. Samples with a diameter of 25 mm and thickness of 0.5, 0.8 or 1 mm were prepared from stainless steel 304. Both surfaces of samples were polished electrochemically. The shock wave, induced at the front surface of the sample, dissipates energy during propagation, thus the sensor placed on the back side of the sample registers a lower pressure than the one from the front side. The use of samples with different thickness allows estimating the pressure behind the shock wave on the front surface based on an attenuation process [45,46]. Pressure measurements were realised using type S_25CP PVDF sensors from Piezotech, France, with a sensing area of 1 × 1 mm, which was sufficiently small to consider a 2 mm diameter laser beam as a flat one. These are the only PVDF sensors that are supported by extensive shock calibration data. These data range from several kPa to over 25 GPa. At low pressures (< 1000 bars), the delivered electrical charge is linearly proportional to the applied stress. The sensibility of the sensor is constant and equals 15.7 pC/N [47]. For higher pressures, the sensibility cannot be considered as constant and calibration data have to be used in order to calculate the charge and pressure. In our case, the sensor was used in the so-called “current mode” [47] with a 50 Ω current viewing resistor. Charge density was calculated by integrating the recorded voltage of the PVDF sensor divided by the resistance R of the circuit and the area S of the piezoelectric active area: 𝑡

𝑉 (𝑡)𝑑𝑡 𝑅𝑆

Acquisition of the PVDF’s and VISAR’s waveforms was carried out using four-channel Tektronix type DPO7000 digital oscilloscopes with bandwidths up to 3.5 GHz and sampling rates up to 40 GS/s. Velocity measurements were performed using a four channel fiber DVI (Doppler Velocity Interferometer), also known as VISAR (Velocity Interferometer System for Any Reflector), from Martin, Froeschner & Associates, Livermore, USA [58]. The system operates at a wavelength of 1550.4 nm. The power output of the operating VISAR laser can reach up to 16 mW. Four InGaAs PIN photodiodes with a rise/fall time ≤ 35 ps convert optical signals of the interferometer into electrical signals registered by the oscilloscope (12 in Fig. 1). The VISAR determines the velocity of the moving surface by measuring the Doppler shift of laser light reflected or scattered from the surface. It is sensitive to wavelength and converts changes in the wavelength to changes in the intensity of four output signals. Velocities can be determined within a range from m/s up to km/s, and with a sub-nanosecond time resolution accuracy of ±1%. The observed surface does not need to be mirror polished. Moreover, changes in its reflectivity or in the background light have no effect on the derivation of velocity. The VISAR system was delivered with software, written in FORTRAN, that enables the processing of signals and calculation of the measured velocity. Generally, the calculations adopted a procedure described in the manual [56], with some changes. All software was converted to MATLAB. The signals were smoothed using a standard “smooth” function of MATLAB with a “moving average” option. The system is characterised by the so-called “fringe constant” [58]: ( ) 𝐾 𝑓 = 𝑐 𝜆0 ∕ 2 𝐿 𝑛 𝐷 , (4) where: c – speed of light; 𝜆0 == 1550.4 nm - wavelength of the VISAR’s laser; L = =1107 mm - length of delay fibre; n = =1.4441 - index of refraction of delay fibre; Kf = 145.5 m/s. The system was constructed in the so-called “push-pull” configuration, so it delivers four signals which are conjugated in pairs ± sin, ± cos. In an ideal case, the signals can be presented by the following equations:

(1)

[ ( )] 𝐶1 (𝑡) = 𝑃 (𝑡)𝑔1 (𝑡) 1 + cos 2𝜋𝑣(𝑡)∕𝐾𝑓 + Φ0 + 𝐵𝑔

(5)

The calibration curve was developed using the MATLAB nonlinear least squares method with data reads from the graphs in [46] (compare also [26,48–56]). The following formulas were used to calculate the pressure:

[ ( )] 𝐶2 (𝑡) = 𝑃 (𝑡)𝑔2 (𝑡) 1 − cos 2𝜋𝑣(𝑡)∕𝐾𝑓 + Φ0 + 𝐵𝑔

(6)

)] [ ( 𝑆1 (𝑡) = 𝑃 (𝑡)𝑔3 (𝑡) 1 + sin 2𝜋𝑣(𝑡)∕𝐾𝑓 + Φ0 + 𝜖 + 𝐵𝑔

(7)

𝑃 = 0.6369𝑄; 𝑄 ⩽ 0.157 𝑎𝑛𝑑 𝑄1 exp(0.67104Q1 ) 𝑃 = 0.1 + 0.6369 2 ; 𝑄 > 0.157

[ ( )] 𝑆2 (𝑡) = 𝑃 (𝑡)𝑔4 (𝑡) 1 − sin 2𝜋𝑣(𝑡)∕𝐾𝑓 + Φ0 + 𝜖 + 𝐵𝑔 ,

(8)

𝑄 (𝑡 ) = ∫ 0

(2)

1−0.013565Q1 +0.16857Q1

where: P – pressure [GPa], Q – charge density [μC/cm2 ], Q1 = Q – 0.157. In turn, the formula proposed by Hodges [53]: 𝑃 = 1.4813Q − 0.31836Q2 + 0.14131Q3 ,

(3)

slightly overestimates the low pressures for our data. Three different kinds of confining layers were applied: 2.6 mm thick glass, 10 mm thick Plexiglas (PMMA) and a 6 mm thick water layer. The substrate was made of steel and PMMA, 10 mm thick, as well as 4 mm thick aluminium. The absorption layer consisted of graphite moistened by paraffin oil with thickness in a range between 10 and 20 μm. Gaps between all layers were also filled with liquid paraffin to provide good physical contact which enabled effective penetration of the stress wave across the boundaries of a layer. The value of stress was calculated based on electric signals recorded from the PVDF sensor (Fig. 2a). The temporal resolution of the sensor in our case could reach several dozen nanoseconds. A detailed description of the calculation procedure was presented in previous studies [16,26,57]. The recommended measurement procedure and the pressure calculation method can be also found in the manufacturer’s brochure [47] or in a review paper [17].

where: P(t) – intensity of the Doppler shifted light entering the interferometer; gn – overall optical gain of channel n; Φ0 – initial signal phase; C1 , C2 , S1 , S2 –+cos, -cos, +sin, -sin, respectively, of signals recorded by the oscilloscope; e - inevitable phase misalignment; Bg – background noise. Light intensity P(t), gain gn and background Bg are usually unknown, so it is assumed that constant components, amplitudes and noises take on approximately the same values in four channels and 𝜀 ≈ 0. Subtracting one signal (in pairs of sin/cos) from the other eliminates background and constant components, then after dividing both differences we obtain: 𝑆 − 𝑆2 tan(Φ(𝑡)) = 1 (9) 𝐶1 − 𝐶2 The problem of phase ambiguity was solved in the following way. Let Φ1 , Φ2 mean phases of neighbouring samples and t1 , t2 their tangents, respectively. Then the tangent of phase difference can be expressed by the formula: ( ) 𝑡 − 𝑡1 tan(ΔΦ) = tan Φ2 − Φ1 = 2 (10) 1 + 𝑡2 𝑡1 and knowing Φ1 from earlier calculations, we can calculate Φ2 as: ( ) 𝑡 − 𝑡1 Φ2 = Φ1 + arctan 2 (11) 1 + 𝑡2 𝑡1

J. Radziejewska, M. Strzelec and R. Ostrowski et al.

Optics and Lasers in Engineering 126 (2020) 105913

Fig. 2. Examples of recorded waveforms: a) yellow - laser pulse profile (400 mV/div, input 50 Ω, 200 ns/div, 5 GS/s), cyan - signal of the pressure sensor (voltage vertical scale 200 mV/div, input 50 Ω, time horizontal scale 200 ns/div, 5 GS/s); b) four VISAR signals (500 mV/div, input 50 Ω, 200 ns/div, 5 GS/s).

Fig. 3. Sample laser pulse profiles at the highest energy of the laser pulse.

The measured velocity is calculated from the formula: ( ) 𝑣(𝑡) = 𝐾𝑓 Φ(𝑡) − Φ0 ∕2∕𝜋

(12)

Fig. 2 shows examples of registered signals. Fig. 2a shows a waveform signal from the PVDF sensor (cyan) and a laser intensity profile (yellow). Dozens of pulses corresponding to the shock wave reverberating between the front and back side of the sample (0.5 mm thick) may be observed. Fig. 2b shows four signals of the VISAR interferometer. Three examples of laser pulse profiles are shown in Fig. 3. It can be seen that temporal profiles are changing from shot to shot with a maximum change in energy of up to 5%. 3. Test results 3.1. Preliminary tests of the influence of absorption and confining layers and substrate on pressure Before the discussion of results, it is worth explaining the role of all layers (inertial, absorption and substrate) in forming the pressure registered by a PVDF sensor. The inertial layer (also known as confining), as it was mentioned earlier, inhibits the expansion of plasma created by laser radiation, causes a significant pressure increase (even four times in a water-confined regime) and elongates the pressure pulse duration (even three times) [59]. The absorption layer also plays a very important role. First of all, it increases the absorption of laser radiation. Secondly, it provides material for ablation processes, thanks to which the surface of the processed sample is not damaged by laser radiation. Thirdly, the

absorbing layer can also act as an insulation layer, not allowing the sample to be heated by the high temperature plasma. Its role is particularly important in the process of laser shock processing (LSP), where the only factor influencing the sample should be the shockwave, and a temperature increase in the sample should be minimal. As a result, cold forming could be executed in the process of LSP. The use of a substrate allows the regulation of the amplitude, profile and duration of the shock wave registered by the sensor. The substrate also protects the PVDF sensor from perforation and damage by the tested shockwave. The substrate usually has acoustic impedance that differs from the sensor, which causes splitting of the falling wave into two waves: the reflected one and the transmitted one. The amplitude of the reflected wave can be significantly reduced when the substrate has acoustic impedance close to the impedance of the sensor material. In each case, a shock wave propagating in a multi-layer medium is divided at all boundaries of layers into two waves: the transmitted and the reflected one. In case of weak shock waves, linear approximation may be used, which means that energy distribution between the reflected and transmitted waves depends on the value of the ratio of acoustic impedances of the contacting media. Coefficients of transformation may be presented by equations [60,61]: 𝑇 =

𝜌 𝑐 2A 𝐴−1 ;𝑅 = ;𝐴 = 2 2, 𝐴+1 𝐴+1 𝜌1 𝑐 1

(13)

where: 𝜌2 c2 , 𝜌1 c1 – acoustic impedances of contacting media (product of the density 𝜌1 and the speed of sound ci ); A – ratio of acoustic impedances; T – relative amplitude of wave transmitted from medium 1 to medium 2; R – relative amplitude of wave reflected from material boundaries. It should be emphasised that the formula (13) applies only to media with initial pressure much lower than the pressure of the incident shockwave. The influence of system configuration on pressure profiles was tested for various substate and samples materials, and different plate thickness. Fig. 4 presents preliminary test results conducted to evaluate the influence of substrate material on pressure profiles. Based on these results the correctness of the numerical model of stress waves propagating in different configuration was verified. When the substrate (Teflon - Fig. 4a) has sufficiently large thickness and approximately the same acoustic impedance as the PVDF sensor material, then we directly get information about the shape of the wave reverberating between the front and back surfaces of the sample. There is only low distortion related to the interference of the incident wave with the low-amplitude wave reflected from the substrate (Fig. 4a). For convenience, in further part of this article, the wave induced directly by the laser pulse will be called the ballistic wave (see Fig. 4a). In contrast, when the sample, the sensor and the substrate (bronze) have different acoustic impedances, then reflected and transmitted

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Optics and Lasers in Engineering 126 (2020) 105913

Fig. 4. Influence of experimental configuration on pressure profiles at a pulse energy of nearly 100 mJ and a comparison of measured and calculated results. No inertial layer. (a) a 1 mm thick Al plate as the sample, a PVDF sensor, 10 mm thick Teflon as the substrate; (b) a 0.3 mm thick bronze plate as the sample, a PVDF sensor, 10 mm thick Al as the substrate.

Fig. 5. Comparison of stresses calculated in the centre of the sample (dashed line) and in the active layer of the PVDF sensor (solid line). Pulse energy about 100 mJ. No inertial layer was applied. (a) a 1 mm thick Al sample plate, a PVDF sensor, a 10 mm thick Teflon substrate; (b) a 0.3 mm thick bronze sample plate, a PVDF sensor, a 10 mm thick Al substrate.

waves of high amplitude are formed at each layer boundary. The interference of many reflected and transmitted waves with comparable amplitudes creates a very complicated pressure profile, as the one shown in Fig. 4b. In this case, the measured pressure reaches a maximum value at about 500 ns, and then gradually decreases, as the wave loses energy during propagation and deformation of the adjacent layers. The regularity of some measurements could be easily verified, but several results have raised doubts as to the origin of the shape of shock wave or to the amplitude dispersion. Therefore, computer simulations were performed to clarify these issues. A hydrodynamic code was developed to simulate the propagation of the shock waves in multilayer medium. Equations, in the form of one-dimensional hydrodynamic equations, were solved using explicit differential method. Computer code included three layers with following assumption and data: the first layer, an aluminum plate with a thickness of 1.0 mm was used; the second layer was a sensor with a thickness of 175 𝜇m, and as the substrate, 10 mm thick Teflon polymer was used, having properties slightly different than those of the PVDF piezoelectric sensor (Fig. 4a and 5a). In the second example Computer code also included three layers with following assumption and data: the first layer, an bronze plate with a thickness of 0.3 mm was used; the second layer was a sensor with a thickness of 175 𝜇m, and as the substrate, 10 mm thick aluminum plate was used, having properties far different than those of the PVDF piezoelectric sensor. Described above qualitative numerical modelling of stress waves propagating were applied to both situations shown in Figs. 4 and 5. “Qualitative” means that numerical modelling was done in a highly

simplified way. The absorption of laser radiation was not considered. Instead of laser radiation, the pressure profile registered in the experiment (the portion denoted as the ballistic wave in Fig. 4a) was applied to the front face of the sample. As a result of many attempts, an amplitude was found at which the pressure calculated in the sensor was approximately equal to the measured one. Despite these simplifications, within a range of 0–400 ns, in both situations there is good compliance between the measured and numerical results (Fig. 4). The same numerical calculations have also confirmed the limits of correctness of the formula (13). Fig. 5 shows plots of amplitudes of stresses occurring in the middle of the sample and in the active layer of the sensor. The amplitude ratio takes on values according to the formula (13). In any case, the amplitude of stresses in the interior of the sample is much higher than in the active sensor layer. However, due to the interference of many waves with comparable amplitudes Fig. 5b), it can be seen that the formula ((13) can only apply to the ballistic wave (say, up to 150 ns). In the subsequent time periods, the pressure indicated by the sensor continues to grow almost monotonically, while in the sample it is still oscillating. So, formula (13) is no longer applicable to this situation. Fig. 5 can also be interpreted in a different way. Let us assume that the substrate is a treated sample. Then, by appropriate selection of layers, a pressure profile (duration and amplitude) that acts on such a sample can be shaped. Now it is clear that if we want to measure the ballistic pressure profile only, we have to choose a substrate with impedance close to the

J. Radziejewska, M. Strzelec and R. Ostrowski et al.

Fig. 6. Pressure profiles obtained for a 0.49 mm thick steel plate using PMMA as a substrate and glass, water and PMMA as a confining layer. Laser pulse energy 1050 mJ, pulse duration 10 ns.

Optics and Lasers in Engineering 126 (2020) 105913

Fig. 7. Pressure profiles obtained in a 0.79 mm thick steel plate using PMMA as a substrate and glass, water and PMMA as a confining layer. Laser pulse energy 1050 mJ, pulse duration 10 ns.

impedance of the PVDF sensor. If, on the other hand, we want to profile the pressure acting on the substrate, then a system of many layers should be selected. In addition to the inertial and absorption layers, a system of several layers with different acoustic impedances can be additionally applied in order to effectively shape the pressure profile. This creates a lot of possibilities. The behaviour of the shock wave reflected from the sample/sensor contact is interesting. The amplitude of the wave reflected from a medium with low (or zero) acoustic impedance changes its sign, and in the case of a compressive ballistic wave becomes a tensile wave. For sufficiently high amplitude of the tensile wave, the phenomenon of spalling or material delamination may occur. This effect is one of the methods for testing the adhesion of thin layers.

3.2. Influence of a confining layer and sample thickness on pressure The use of different confining layers caused changes in the registered amplitude of stress wave in the sensor. Fig. 6 presents examples of stress course for a system in which a 0.49 mm thick steel plate and a PMMA substrate were used. The maximum value of pressure reaches 150 MPa after about 1000 ns (time zero means the beginning of a laser pulse for glass as the inertial layer – see Fig. 3). The pressure value in the ballistic wave is slightly lower - about 135 MPa. The maximum pressure for a PMMA inertial layer reaches about 65 MPa, while for a water layer it reaches only 57 Mpa. Formulas (13) show that in the PVDF sensor (small impedance 𝜌2 == 1.8 g/cm3 ; c2 = 2.2 km/s) in contact with steel (high impedance 𝜌1 == 7.9 g/cm3 ; c1 = 5.9 km/s), the amplitude of shock wave decreases nearly 6.67 times in comparison with a steel sample. For a steel sample with thickness of 0.49 mm and glass as the confining layer, the sensor recorded a pressure value of the ballistic wave of about 135 MPa (see Fig. 6). Similar experiments were conducted for 0.79 mm and 0.98 mm thick steel test plates (Figs. 7 and 8). With thickness of the plate increased from 0.49 to 0.79 mm, peak pressure fell from 150 MPa down to 100 MPa. However, similarities in shapes of stress profiles (Fig. 68) are noticeable. The stress amplitude should vary proportionally to the square root of the reduced acoustic impedance of adjacent layers [59] (formulas in Chapter 3.5). As can be seen from Figs. 6–8, this relationship is fulfilled qualitatively. Acoustic impedance in the form of a product of the density 𝜌 and the speed of sound c and units [106 kg/(s•m2 )] equals 1.5 for water (𝜌 = 1000 kg/m3 , c == 1500 m/s), 3.47 for Plexiglas (1300, 2670), 3.92 for PVDF (1800, 2180), 2.97 for Teflon (2200, 1350), 13.8 for glass (2500, 5500)), 32.1 for bronze (9000, 3570) and 47.4 for steel 304 (7900, 6000). Values for bronze and steel are approximate due to many types of alloys. The higher acoustic

Fig. 8. Pressure profiles obtained in a 0.98 mm thick steel plate using PMMA as a substrate and glass, water and PMMA as a confining layer. Laser pulse energy 1050 mJ, pulse duration 10 ns.

impedance of the inertial layer corresponds to the higher maximal pressure registered by the PVDF sensor. An increase in the thickness of steel sample decreased the pressure value, while increasing the time of arrival of the stress wave to the sensor. This delay equals 112 ns for a 0.49 mm thick sample, 165 ns for a 0.79 mm thick sample and 199 ns for a 0.98 mm thick sample. These time delays should be reduced by about 30 ns, because the coaxial cable of the photodiode recording the laser radiation was about 6 m longer than the cable of the PVDF sensor. Taking this correction into account, the velocity of the shockwave in steel can be estimated as: 0.49 mm/82 ns @ 5.97 km/s; 0.79 mm/135 ns @ 5.85 km/s and 0.98 mm/169 ns @ 5.80 km/s. These velocities are approximately equal to the speed of sound in steel, as the studied shock wave should be considered weak in the sense that its amplitude (around 1 GPa) is much lower than the elasticity modulus of steel (around 200 GPa). It should also be emphasised that in all cases repeatability of several per cent of registered pressure profiles was observed. 3.3. Influence of substrate on pressure behind the shock wave Figs. 9-11 compare pressure profiles registered in PVDF sensors using steel as the substrate for varying thickness of steel samples. Similar experiments were performed for an aluminium substrate (thickness 4 mm) and a glass confining layer (thickness 2.6 mm). The sample was made of a 0.47 mm thick steel plate, covered with graphite. Measurement results are shown in Fig. 12. Charts in Figs. 9–12 contain oscillations with a period of 66 ns. They are connected to the stress wave reverberating inside the sensor (mainly

J. Radziejewska, M. Strzelec and R. Ostrowski et al.

Fig. 9. Pressure profiles measured for a 0.49 mm thick steel sample plate using steel as a substrate and glass, water and PMMA as a confining layer. Laser pulse energy 1050 mJ, pulse duration 10 ns.

Fig. 10. Pressure profiles measured for a 0.79 mm thick steel sample plate using steel as a substrate and glass, water and PMMA as a confining layer. Laser pulse energy 1050 mJ, pulse duration 10 ns.

Fig. 11. Pressure profiles measured for a 1.0 mm thick steel sample plate using steel as a substrate and glass, water and PMMA as a confining layer. Laser pulse energy 1050 mJ, pulse duration 10 ns.

polyester) with thickness of about 135 𝜇m. For the speed of sound of about 2.2 km/s, it corresponds to the stress oscillation period at a level of 60 ns. Fig. 12 shows a perfectly visible additional peak in signal from the pressure sensor indicated by the vertical dashed line. It is caused by the stress wave reflected from the back side of the aluminium plate. This phenomenon was not observed for other substrates because of their high thickness or rugged back sides. The value of time interval between the ballistic wave that hits the sensor and the wave reflected from the back side of the aluminium substrate is about 1330 ns. Considering sub-

Optics and Lasers in Engineering 126 (2020) 105913

Fig. 12. Pressure profile measured for a 0.47 mm thick steel plate using a 4 mm thick aluminium plate as a substrate and a 2.6 mm thick glass as a confining layer. The vertical dashed line indicates the location of the signal related to a wave reflected from the back surface of the substrate. Laser pulse energy 1050 mJ, pulse duration 10 ns.

strate plate thickness of 4 mm, the speed of sound may be estimated as 6.01 km/s. This confirms that the abovementioned peak comes from the back side of the aluminium plate. The maximum stress wave pressure of 350 MPa occurred after 400 ns. For such high amplitude, the dispersion virtually smoothens the pressure profile, and the amplitude of the oscillation caused by the reverberation of the wave inside the sample reaches relatively low values. The same smoothing effect is visible in Figs. 9–11. The value of pressure in the ballistic wave is close to the one with the substrate made of steel and PMMA. The maximum value (350 MPa in Fig. 12) is slightly lower compared to the steel substrate (400 MPa in Fig. 9). Also, a faster decline in its value may be observed. Attention should be paid to the maximum value of pressure, 350 MPa, that occurred in the sensor layer within a period of time from 500 up to 700 ns. It does not equal the maximum value of pressure wave inside the sample. The real maximum pressure inside the steel sample is higher and should be calculated by computer modelling (see Chapter 3.5). As a result of the interference of the stress waves generated during reflections at the boundaries of the layers, the maximum pressure recorded in the sensor increases. For the steel substrate and a 0.49 mm thick sample, the maximum pressure value of 400 MPa occurred after about 500 ns inside the PVDF sensor. For a 0.8 mm thick sample the achieved pressure was about 300 MPa, and for a 1 mm thick sample 260 MPa. An increase in plate thickness causes a delay in the moment of maximum stress value, from “after 500 ns” for a 0.49 mm thick sample to “after 1000 ns” for a 1 mm thick sample. Summarizing the results, it was confirmed that the stress amplitude in samples increases with the increase of acoustic impedance of the confining layers. The pressure value in the ballistic wave is approximately the same for all tested substrate materials and depends on the thickness of the sample. Low values of maximum pressure (400 MPa at PVDF sensor for glass confining layer an steel substrate) are connected with relatively low energy of experimental laser (1 J in 8–12 ns pulses, power density up to 4.8 GW/cm2 ). Higher pressures were reported in [24] for similar Nd:YAG laser (1.5 J, 10 ns, 8 GW/cm2 ), however generating green 0.532 nm radiation. As the authors called results in the range 2–5 GPa as “in-pressures” (inside sample), they should be compared to around 5 × 400 MPa ≈ 2 GPa (our recalculation of measurement place). French group [23,39,62] reported maximum pressures on the level of 10 GPa for short 0.6 ns pulse laser with highest output energy of 100 J. Lower than expected values of pressure are probably caused by problems with laser radiation delivery to the sample (optical breakdowns) which coused energy reduction or the increase of beam diameter. Comparison of many other cited results is difficult, mainly due to significant differences in test assembly constructions, laser power densities and pulse time durations.

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Fig. 13. VISAR interferometer signals recorded during deformation of a 1 mm thick steel plate, diameter 10 mm. Energy pulse 1200 mJ, 1.2 mm thick glass as the confining layer. (a) – recorded VISAR signals; (b) calculated velocity and displacement of the back surface of the sample.

3.4. Simultaneous measurement of pressure by a PVDF sensor and velocity by a VISAR interferometer In order to verify the resulting laser pulse pressure, an attempt was made to simultaneously measure the shock wave pressure profile (PVDF sensors) and velocity of the surface reflecting this shock wave (VISAR system). Fig. 13 presents measurement results for the velocity of the back surface of a 1 mm thick plate. Probing radiation falls directly onto the test surface, which in this case was not supported by a substrate layer. The front of the ballistic wave (Fig. 13b) appears at the time of 331 ns and the second pressure pulse at 677 ns. So, the speed of sound inside the steel plate can be estimated as 2 mm/346 ns @ 5.78 km/s, which with an approximation of 3% equals the speed of sound in the AISI 304 steel. This result indicates proper execution of the measurement. With a known speed of sound c (5.78 km/s) and density of steel 𝜌 (7.9 g/cm3 ), the pressure of the wave that accelerates the back side of the plate to a velocity of 29 m/s may be evaluated as follows [60,61]: 𝑃 = 𝜌𝑣𝑐∕2

(14)

This formula can be derived from the known Rankine-Hugoniot equations (see also [17], formulas 1–3), assuming that for a weak wave the velocity of the shock wave is equal to the speed of sound and taking into account the doubling of the speed of the particles upon reflection. Formula (14) gives a value of approximately 662 MPa. It should be noted that this estimate is related to pressure values inside the steel sample, much higher than values shown by the PVDF sensor. The transmission coefficient of the steel/PVDF interface (formula 13) should take on a value of about 0.15, which means that the sensor should measure a pressure of about 99.3 MPa. The received values of 97 Mpa (Fig. 7) and 94 MPa (Fig. 11) confirm good compatibility of both measurement methods (PVDF vs VISAR). A rough estimation of strain and strain rate can be received from formula (14). The strain can also be estimated from Hook’s law: 𝜖=

𝑃 𝑣 𝜌𝑣𝑐 𝑃 ;𝜖 = 𝑃 𝑉 𝐷𝐹 ; 𝜖𝑉 𝐼𝑆𝐴𝑅 = = 𝑉 𝐼𝑆𝐴𝑅 , 𝐸 𝑃 𝑉 𝐷𝐹 2𝐸 2c 0.15𝜌𝑐 2

(15)

where 𝐸 = 𝜌𝑐 2 – Young’s modulus, and the strain rates: 𝜖̇ 𝑃 𝑉 𝐷𝐹 =

𝑃̇ 𝑃 𝑉 𝐷𝐹 0.15𝜌𝑐 2

; 𝜖̇ 𝑉 𝐼𝑆𝐴𝑅 =

𝑣̇ 𝑉 𝐼𝑆𝐴𝑅 2c

where “dot” denotes a time derivative.

(16)

The subscripts PVDF, VISAR denote values taken from PVDF/VISAR measurements. The coefficient of 0.15 takes into account a decrease in the wave amplitude transmitted from steel into the PVDF material. Strains and strain rates calculated from the above formulas are plotted in Fig. 14. The maximum strain value for the ballistic wave ranges from 0.25% to 0.35%, while the strain rate changes from 2.5 × 105 to 3.5 × 105 1/s. These values show that even when using low laser pulse energy (about 1 J) it is possible to generate phenomena with a high strain rate. Therefore, laser-induced shock waves can be an alternative to other methods for inducing and investigating such phenomena at rates far exceeding 105 1/s, which is a value comparable to those obtained in impact experiments [63]. Figs. 15 and 16 show the results of interferometric measurement of velocity of the back side of a sample with thickness of 0.98 mm, recorded in full configuration shown in Fig. 1. 2.6 mm thick glass was used as a confining layer. This time it was necessary to use a substrate layer (10 mm thick PMMA transparent to VISAR radiation) to allow a simultaneous measurement of pressure and velocity. In addition, 7 μm thick aluminium foil was placed between the PVDF sensor and the substrate to protect the sensor against damage by VISAR radiation. The speed of sound, estimated from the time interval between successive pressure peaks, is about 5.78 km/s, which is typical of this grade of steel. The velocity of back sample surface determined based on the VISAR measurement is about 35 m/s. A comparison of pressure measured by the PVDF sensor and pressure calculated from the velocity profile plotted in Fig. 16 shows qualitative correlation between pressure and speed. High velocity peaks occur at the same moments at which pressure peaks appear. However, additional oscillation with a period of about 20 ns occurs in the profile of the measured speed. It may be assumed that it is a result of the reverberation of waves occurring between the PVDF sensor and the substrate (oil layer, aluminium foil and air gap). These oscillations are not visible in PVDF measurements, which means that the PVDF sensor load circuit has a long time constant. Agreement between the pressure determined from the particle velocity VISAR and pressure histories from PVDF is confirmed in several papers, but usually at lower pressure level [40], for fast events with the use of short pulse lasers and rather qualitatively [44]. Ito et al. [64] reported experiments with thin copper flyers, which could be launched from sapphire base with velocities up to 1 km/s using Nd:YAG laser with output energy 870 mJ (pulses 12 ns). The velocity value is proper for such lightweight samples. Calculated pressures at sample back surface (Hugoniot formula) were in the range 1–2 GPa, similar to our results. In certain publications authors compare only temporal shapes of PVDF and

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Optics and Lasers in Engineering 126 (2020) 105913

Fig. 14. Strains and strain rates estimated from formulas (15,16) for ballistic waves and a glass confining layer. str0.5/rat0.5 - strain and strain rate for a 0.5 mm (rounded off) thick sample (Fig. 9) from PVDF measurements; str1.0/rat1.0 strain and strain rate for a 1.0 mm thick (rounded off) sample (Fig. 11) from PVDF measurements; strVIS/ratVIS strain and strain rate for a 1.0 mm thick sample (Fig. 13b) from VISAR measurements. VISAR curves were translated into a time coordinate.

Fig. 15. Signals from a VISAR interferometer during deformation of a steel plate with thickness of 0.98 mm and a diameter of 25 mm and velocity and displacement of back sample surface. Pulse energy 1200 mJ, 2.6 mm thick glass as a confining layer, 10 mm thick PMMA as a substrate layer: (a) – recorded VISAR signals; (b) calculated velocity and displacement of back sample surface.

resulting in the deviation of Hugoniot pressure data [64]. It is particularly important in the range of lower target velocities. This problem has been also found during our VISAR experiments and solved through the precise adjustment of laser beam at the central region of sample and multiple repeating of measurements. 3.5. Pressure inside the steel sample

Fig. 16. Comparison of a pressure profile measured by a PVDF sensor (solid line) with pressure calculated from a VISAR velocity measurement using formula (14) (dotted line).

VISAR characteristics [37,65]. Since the accuracy of the surface velocity measured by the VISAR is strongly dependent on the change of reflected ray strength from the free surface of the material, noticeable decrease of ray strength during the flight frequently leads to error in measurement,

On the basis of pressure value registered in the PVDF sensor and known acoustic impedance of the medium, it is possible to estimate the pressure of the stress wave on front sample surface. It was assumed that the value of pressure inside the steel plate near the back side is 6.67 times higher than the pressure inside the sensor. Calculation of pressure on the front surface of the sample was made with consideration of wave attenuation in the material, using the formula proposed in [45]: 𝜎𝑃 = 𝐴 ⋅ exp(−𝑛𝑥)

(17)

where: n – wave attenuation coefficient; x – distance from front surface; A – a constant (pressure at the front face of sample). Parameters A and n, for all cases plotted in Fig. 17, were determined by the nonlinear least square method using the MATLAB Curve Fitting Toolbox. Results produced for varying thickness of samples allowed estimating the value of pressure on the front surface of the steel plate. Cal-

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Optics and Lasers in Engineering 126 (2020) 105913

Fig. 17. Pressure changes as a function of distance from the front surface (sample thickness) set on the basis of measurements made by PVDF sensors: a) steel substrate; b) PMMA substrate. The points mark the results of PVDF measurements for different confining layers, while the lines are graphs of the approximation of formula (15). Table 1 Pressure estimation based on PVDF sensor and VISAR system measurements, and calculated using relations (13) and (16) for a 1 mm thick steel sample.

Substrate

Inertial layer

Pressure in the PVDF sensor [MPa]

PMMA

Glass PMMA Water Glass PMMA Water

95.5 65.9 46.7 92 66.3 53.3

Steel

Pressure on the back side of the plate acc. to formula (13) [MPa]

Pressure on the front side of the plate acc. to formula (17) [MPa] (A/n parameters)

Pressure on the front side of the plate acc. to formula (18) [MPa]

637 439 311 613 442 355

1236/0.736 593/0.311 466/0.325 1424/0.878 679/0.483 603/0.584

1274 701 470

culations were made for the pressure value of the ballistic wave. Fig. 17a presents a function describing the relationship between changes in pressure in steel for different inertial layers and distances from the surface. In this case, steel was used as a substrate. Fig. 17b shows values of pressure for the PMMA substrate. The pressure value of a wave generated by a laser pulse with the confining layer at the front side of a sample may also be estimated based on the density of laser power and acoustic impedance. The formula proposed in [55,59] for a water/steel interface is as follows: √ 𝑃𝑤𝑎𝑡𝑒𝑟 = 1.02 𝐼0 , (18) where: P – pressure [GPa]; I0 ≈ 0.217GW/cm2 – absorbed laser power density [GW/cm2 ]. For other inertial layers, the definition of reduced acoustic impedance was used [59]: √( ) 1∕𝑍 = 1∕𝑍𝑐𝑜𝑛𝑓 𝑖𝑛𝑖𝑛𝑔 + 1∕𝑍𝑠𝑎𝑚𝑝𝑙𝑒 ; 𝛽 = 𝑍𝑟𝑒𝑑 𝑢𝑐𝑒𝑑 𝑖𝑛𝑒𝑟𝑡 ∕𝑍𝑟𝑒𝑑 𝑢𝑐𝑒𝑑 𝑤𝑎𝑡𝑒𝑟 , (19) and pressure was calculated from the formula [59]: √( ) 𝑃𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 = 𝛽 ∗ 𝑃𝑤𝑎𝑡𝑒𝑟 ; 𝛽 = 𝑍𝑟𝑒𝑑 𝑢𝑐𝑒𝑑 𝑖𝑛𝑒𝑟𝑡 ∕𝑍𝑟𝑒𝑑 𝑢𝑐𝑒𝑑 𝑤𝑎𝑡𝑒𝑟

(20)

where 𝛽 ≈ 1.5, 2.7 for PMMA/steel and GLASS/steel interfaces, respectively. Table 1 summarizes the results of pressure measurement using PVDF sensor for a 1 mm steel plate, pressure on the back and front surfaces of the sample calculated using formula (17), and pressure on the front surface calculated based on formula (18–20). The pressure values specified inside the steel sample using different methods are comparable. Changes are proportional to the acoustic

impedance of the inertial layer, regardless of the base material. In the case of glass, it is over two times higher than when using water as an inertial layer. Formula 20 gives good correlations with experimental results when the ballistic wave is considered. The increase in pressure is a result of the effect of superposition of the individual stress waves, which are separately reflected from the surface of the sample, the steel substrate and two layers with different impedance (oil, sensor). The timing of maximum stress depends on the thickness of the sample and is observed after 500–1000 ns. Its duration is about 500 ns. 4. Conclusions The measurements of pressures behind the shock waves, including the amplitude and temporal characteristics, and using piezoelectric PVDF transducers, have shown high reproducibility. The results produced for different laser shots varied only within a range of several percent. The presented experiments confirmed a known fact that for fixed energy of a laser pulse, the maximum pressure of a shock wave is proportional to the square root of acoustic impedance of the confining layer. The maximum value of shock wave amplitude has been recorded for a glass confining layer, while significantly lower but comparable values were measured for water and PMMA confining layers. An increase in the amplitude of maximum pressure behind the shock wave can also be attained by the appropriate selection of substrate material. All above mentioned experimental conditions allow a fine adjustment of the amplitude, profile and duration of pressure peaks that have influence on

J. Radziejewska, M. Strzelec and R. Ostrowski et al.

the material behaviour of a sample. It proves proper selection of conditions for studying material properties under a high stress rate, such as the delamination of thin films and micro-forming processes, and the hardening of material by a stress wave induced by the laser pulse. This is consistent with actual and future work of our team. Moreover, experience gained during the implementation of the presented work has already been used to investigate the adhesion of thin films [16,26,57]. The impact of system configuration on the produced results has been demonstrated. A measurement of the actual profile of the pressure induced by a laser pulse is possible, provided that a substrate with acoustic impedance close to that of the sensor material is used. The attempt which was made to simultaneously measure the profile of shock wave pressure and the velocity of surface reflecting this wave using the VISAR system demonstrated the complex nature of this experiment. It was mainly due to rather low values of measured velocities, which in principle fall near the lower limit of the measuring range of the VISAR system used. However, it has been demonstrated that rescaling of the velocity measurements with the pressures behind the shock waves using formula (14) resulted in a high consistency of several percent. The velocity measured by VISAR contains two components: the velocity of the rear side of a sample and velocities connected to the reverberation of the shock wave inside and between layers adjacent to the PVDF transducer. In this case, qualitative consistency of results can be seen (Fig. 15). Measurement procedures for PVDF sensors were significantly improved,which is expressed by the repeatability of results from shot to shot amounting to several percent. However, in future experiments, the acquisition of PVDF signals should be improved in order to receive a better time resolution. Measurements should be performed with the use of differential measuring probes. In the case of the VISAR system, more attention should be paid to more advanced methods of VISAR data processing [60]. Funding This work was supported by the National Science Centre in Poland [grant number 2013/09/B/ST8/03468]. A part of the experiment was realised under project No DOB-1–6/1/PS/2014, funded by the National Centre for Research and Development in Poland, entitled “Laser Systems of Directed Energy Weapons, Laser Systems of Non-Lethal Weapons”. Declarations of Competing Interest none. References [1] Thomas K, Hornemann U, Sauer M, Schneider E. Shock waves – Phenomenology, experimental, and numerical simulation. Meteorit Planet Sci 2005;40:1283–98. https://doi.org/10.1111/j.1945-5100.2005.tb00401.x. [2] Niehoff HS, Vollertsen F. Laser induced shock waves in hardening and forming technologies. J Technol Plast 2005;30:37–51. https://pdfs. semanticscholar.org/540d/fa4c5a6f6df9541eef471b9a5d7dd747c41b.pdf. [3] Takayama K, Ohtani K. Applications of shock wave research to medicine. WIT Trans Model Sim 2005;41:653–61. https://www.witpress.com/ elibrary/wit-transactions-on-modelling-and-simulation/41/15261. [4] Askaryon GA, Moroz EM. Pressure on evaporation of matter in a radiation beam. JETP Lett 1963;16:1638–44. http://adsabs.harvard.edu/abs/1963JETP..16.1638A. [5] Gregg DW, Thomas SJ. Momentum transfer produced by focused laser giant pulses. J Appl Phys 1966;37:2787–9. doi:10.1063/1.1782123. [6] Anderholm NC. Laser generated stress waves. Appl Phys Lett 1970;16:113–15. doi:10.1063/1.1653116. [7] Skeen CH, York CM. Laser-Induced "blow-off"; phenomenon. Appl Phys Lett 1968;12:369–71. doi:10.1063/1.1651859. [8] O’Keefe JO, Skeen CH, York CM. Laser induced deformation modes in thin metal targets. J Appl Phys 1973;44:4622–6. doi:10.1063/1.1662012. [9] Yang LC. Stress waves generated in thin metallic films by a Q-switched ruby laser. J Appl Phys 1974;45:2601–8. doi:10.1063/1.1663636. [10] Fairand BP, Clauer AH, Jung RG, Wilcox BA. Quantitative assessment of laser‐induced stress waves generated at confined surfaces. Appl Phys Lett 1974;25:430–3. doi:10.1063/1.1655536.

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Joanna Radziejewska. Scientific degrees: 1985 - Msc in Materials Science & Engineering at Warsaw University of Technology, 1999 - DSc in Materials Science&Engineering, 2013 - DSc (Postdoctoral degree, habilitation) in Mechanics &Mechanical Engineering, Warsaw University of Technology. Employment: Institute of Fundamental Technological Research Polish Academy of Sciences, Warsaw, 1986–1999 - Assistant at Laboratory of Surface Layer, Department of Mechanic Material, 2000–2008 - Assistant Professor at Laboratory of Surface Layer, 2009 - Assistant Professor at Laboratory of Technological Applications of Lasers, Department of Strength of Materials, From 2014 Warsaw Technical University, Professor at Faculty of Production Engineering, Department of Manufacturing Techniques.

M. Strzelec received M.Sc. degree in 1974 from Warsaw Technical University and the Ph.D. in 1988 from Military University of Technology (MUT) in the field of quantum electronics. In 1976 he joined Institute of Quantum Electronics MUT, from 1988 Institute of Optoelectronics MUT. He participated in several international projects. From 1999 he was a member of NATO Team of Experts for CB Defence. In the years 2001– 2006 he coordinated Pollasnet – Polish Laser Network. Dr Strzelec is a specialist in the field of laser physics and technology. His recent works focus on laser applications in micromachining.

Roman Ostrowski received the M.Sc. degree in optoelectronics in 1987 from Military University of Technology (MUT) in Warsaw and then he studied laser resonators in the Institute of Plasma Physics and Laser Microfusion. In 1992 he joined the Institute of Optoelectronics (IOE) at MUT, where he investigated eye-safe lasers (PhD in 2003) and laser-matter interaction. From 1999 he was involved in many R&D projects connected with utilization of lasers in conservation of cultural heritage. His recent works focus on laser micromachining and laser cleaning of art works. From 2016 he is a head of Laser Applications Group at IOE MUT.

Dr. Eng. Antoni Sarzyński received M.Sc. degree in 1973, in the field of quantum and solid-state electronics from Military University of Technology (MUT), and Ph.D. in 1992 from Warsaw University of Technology in the field of physics. During the years 1973–1992 he was a scientist at the Institute of Plasma Physics and Laser Microfusion. From 1992 to 2018 he worked at the Institute of Optoelectronics MUT. Dr Sarzyński is an author or coauthor of several dozens of scientific papers in the field of plasma and laser physics, laser induced shock waves, and laser processing of materials for medical applications.