PSI - Issue 71

Oleg Plekhov et al. / Procedia Structural Integrity 71 (2025) 10–17

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=√ 2 + 3 ∙ ∙ .

where = 2∙ ∙ + , . 4. PDV system for measurement the intensity of mechanical impact

(9)

The applicability of R. Fabbro's one-dimensional plasma expansion model is one of the key issues in modeling the LSP process Fabbro et al. (1990). The constants used in equation (9) are empirical and require independent experimental evaluation. One of the ways for direct measurement of the pressure pulse is experiments with photonic Doppler velocimetry (PDV). PDV is hardware and software setup, which realize a Fourier analysis of a heterodyne laser interferometry. It was developed in Lawrence Livermore National Laboratory to measure velocities in dynamic experiments with high temporal resolution Strand et al. (2006). The basic mechanism of PDV is the investigation of interference patterns of two electromagnetic waves with a small difference in frequency. According to the relativistic Doppler effect, the frequency of electromagnetic waves reflected off a moving surface undergoes a change as = √ 1+ 1− , where V is the velocity of a moving surface and C – light speed. The interference of the reflected wave with the original source generates a beat signal with the value of frequency within the range of a few gigahertz. By analyzing the beat frequency and taking into account the condition ≪1 , a history of surface motion can be obtained. By considering both the forward and reverse course of the light beam, the velocity of the moving surface can be estimated as = 2 , where is the source wavelength and – the beat signal frequency. To calculate the signal frequency the Fourier transform analysis is typically employed. To quantify the pressure impulse, a PDV was assembled. The principal scheme of the PDV is presented in figure 2a, while the experimental setup – in figure 3b. The PDV includes the following components: laser with wavelength 1550 nm, oscilloscope with a bandwidth of 2 GHz, 4 analog channels, four InGaAs Photodetectors, acoustic-optical modulator (AOM). The apparatus enables the measurement of the velocity of a specimen (construction part) free surface with high precision, up to 2 m/s in range from 5 m/s to 1380 m/s.

a

b

a) b) Fig. 2: Schematic diagram of a (a) photonic Doppler velocimetry and (b) schematic diagram of experiment.

The velocity of the free surface of Ti-6Al-4V titanium alloy specimens was measured during laser pulse irradiation. The shape of the laser beam spot on the specimen surface is a circle with a diameter of 2 mm. The pulse duration is 10 ns. The measurements are carried out with the values of energies of 2, 3, 4, and 6 J, which corresponded to the energy power densities of 7, 10, 13, and 19 GW/cm 2 . Due to the technological features, the copper specimens have thicknesses of 0.5, 0.8, and 1.0 mm and the titanium specimens – 0.8, 1.0, and 1.4 mm. The laser is focused at the center of the front surface of the specimen. The PDV measures the velocity in the center of the back surface of the specimen. The water is used as a limiting layer on the front surface. The measurement results of the free surface velocity profiles are shown in Figure 3a. The pressure (figure 4b) can be calculated based on the results presented in figure 3a as follows: = 1 2 . (10) The pressure impulse profiles for copper specimens (Figs. 3a, 3b) reveal a distinct elastic precursor, indicating a nonlinear relationship between pressure amplitude and laser power density. Notably, at 19 GW/cm², the amplitude decreases compared to measurements at 10 GW/cm², suggesting inefficient energy transfer to the plasma at higher intensities. This inefficiency likely arises from energy absorption at the water-air interface rather than effective