PSI - Issue 32

O.B. Naimark et al. / Procedia Structural Integrity 32 (2021) 144–151 Author name / Structural Integrity Procedia 00 (2019) 000–000

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spinodal decomposition, V is the front wave velocity, Δp is the jump in the metastability area, which depends on the load intensity. Solution (7) describes the blow-up dynamics of mesodefect growth → ∞ → t t c p for c p p ≥ as generation of blow-up dissipative structures on the set of spatial scales Ι ... 1,2 , L = iL , i = c H . The parameter c L is the fundamental blow-up length and c t is the blow-up time and have the meaning of spatial and temporal scales of self-similar solution [Naimark (2004)], ~ 5 m is the power exponent related to corresponding term in (5). The function ( ) ζ f is determined by Kurdyumov (1988) solving corresponding eigen-function problem and describes the microshear density profile that could trigger the blow-up dynamics of the microshear density generation over the fundamental length c L . Subjection of mesodefects dynamics to self-similar solutions (6), (7) reflects the global symmetry changes in the condensed matter. It was discussed by Naimark (2010) that the existence of scales S L and c L is characteristic for string field theory, represents in our case extended one dimension topological objects with qualitative different microshear dynamics and play the role of internal degrees Two types of experiments were conducted to study the dispersion properties in liquid and solid in the GMS conditions. The momentum transfer under quasi-hydrodynamic flow is considered as the motion of the microshears in the conservative (elastic) field under high strain rate loading produced by shock waves. The method of investigating viscosity of materials behind the Shock Wave Front (SWF), proposed first by Sakharov et al. (1964) and then by Barker (1968), is based on the usage of the Doppler interferometry (VISAR) technique. The Sakharov experiments revealed in the shocked liquid (water and mercury) a relaxation time s 5 1 ~ 10 − − > ε τ  in the pressure range KBar P 80 100 ≈ − differing by 6 orders from the molecular (diffusion) relaxation times estimated by the Einstein formula as s D sd D 11 6 ~ 10 2 − = ∆ τ , where ∆ is the distance between the particles, sd D is the self diffusion coefficient. It means that a liquid behaves in the indicated experiments effectively like a solid. Generation of the collective solitary and blow-up modes follows to the scenario of the energy absorption at the vicinity of critical points c δ , δ * localized on characteristic length S L and ... ) ( 1,2 Ι , L = iL i = c H for the characteristic times t L V S S = and c t consequently. These times can be identified with the effective relaxation time and have to estimate as s t S 5 ~ 10 − and s t c 7 6 10 ~ 10 − − − . The existence of characteristic lengths S L and H L as the parameters of the self-similar solutions (6) and (7) characterizes two slits of wave numbers S S k L 1 = and H H k L 1 = , where the system reveals GMS with new mechanisms of momentum transfer.The mechanism of GMS related to the wave number slit S S k L 1 = was studied experimentally by Bannikova et al. (2014) to analyze the power universality of plastic wave fronts in shock-loaded liquids to follow the conventional universality of steady plastic wave fronts in solids studied by Bayandin et. al. (2004). A copper wire was blown by high density electric current in a cylindrical chamber [8] to initiate a compression wave in distilled water. The mass velocity in the liquid at different distances from the wire was measured using the VISAR system with a fiber optic gauge. Thus, from wave profiles, it was possible to study the strain rate versus the pulse amplitude. Figure 1 shows several experimental velocity profiles. Figure 2a shows the strain rate at the compression wave front * ε  versus pulse amplitude o P in log-log coordinates. The power exponent was found by Bannikova et al. (2014), which is close to the power exponent for metals, suggesting the self-similarity of the wave profile. The observed regularities allowed the assumption that the water under these loading conditions behaves as a quasi-plastic non-Newtonian liquid. The GMS induced dispersion effects in solid can be illustrated by the experiments on the initiation of the so called Failure Waves studied by Rasorenov et al. (1991) and Bourne et al. (1998). The “failure wave” dynamics S L is the wave front length, of freedom in corresponding δ - range. 2. Materials and experimental conditions