PSI - Issue 40

I.A. Bannikova et al. / Procedia Structural Integrity 40 (2022) 32–39 I. A. Bannikova at al. / Structural Integrity Procedia 00 (2022) 000 – 000

36

5

application of the Doppler interferometry (VISAR) technique. The Sakharov experiments revealed in the liquid under shock wave loading (water and mercury) the relaxation time 5 1 ~10     s, which differs by 6 orders from the molecular (diffusion) time estimated by the Einstein formula as 2 11 / 6 ~10 D sd = τ D   s, where ∆ is the distance between the particles, sd D is the self-diffusion coefficient. It means that in the above experiments the effective liquid behavior is similar to that of a solid. The generation of collective solitary and blow-up modes follows the scenario of the energy absorption in the vicinity of critical points * , с   localized within the characteristic length S L and   , 1, 2,... c H L = iL i= and corresponding times S S t = L V and c t , respectively. These times can be identified with the effective relaxation time and have been estimated in Naimark (2004) as 5 ~ 10 S t s and 6 7 ~10 10 c t    s. The lengths S L and С L characterize two gapped states with wave numbers 1 g S k L  and 1 Н Н k L  , at which the system exhibits GMS with new mechanisms of momentum transfer. The mechanism of GMS with the wave number gap 1 g S k L  was studied experimentally by Bannikova et al. (2014) to analyze the power universality of plastic wave fronts and cavitation (spall fracture) in liquids under shock wave loading. In the center of the chamber, a compression wave in the liquid was produced by the electric explosion of a copper wire (EEW) as a result of a short-pulse discharge of the capacitor system. The velocity of the free surface of the liquid at different distances from the EEW was recorded using the VISAR system with a fiber optic gauge. Based on the time-series velocity records (Fig. 1, a), the stress dependence of the strain rate (Fig. 1, b) at the shock wave front and the strain rate S  dependence of the spall strength S P (Fig. 1, c, d) were determined by Bannikova et al. (2014), Bannikova et al. (2017). Fig. 1, a, b shows the experimental velocity profiles in distilled water and the power exponent dependence of the strain rate  on the pulse amplitude, 0 P . It was found that the power exponent is close to the exponent for metals, which is indicative of the fourth- power self-similarity of the plastic wave front (Bannikova et al. (2014)).

a

b

10

ε̇ = 5E-06P 0 R ² = 0.84

3.15

1

ε̇ , 10 6 1/s

0,1

1

10

100

1000

P 0 , МPа

c

d

60

100

40

Ps = 0.04 ε̇ S + 37.63

10

P S , МPа

P S = 21.31 ε̇ S R ² = 0.73

0.39

20

Ps, PMa

0

1

0

5

10

15

0,1

1

10

ε̇ S , 10

4 1/s

ε̇ S , 10

4 1/s

Fig. 1. (a) particle velocity profiles in distilled water: 1 – 8 mm; 2 – 11 mm; 3 – 14 mm; 4 – 25 mm; (b) strain rate versus pulse amplitude in distillated water, log-log axes; (c) spall strength versus strain rate in water by Bannikova et al. (2014), log-log axes; (d) spall strength versus strain rate in silicon oil (×) and transformer oil (∆) by Bannikova et al. (2017).