PSI - Issue 2_B

Yurii Meshcheryakov et al. / Procedia Structural Integrity 2 (2016) 477–484 Yu.I. Meshcheryakov, A,K. Divakov, N.I. Zhigacheva, G.V. Konovalov / Structural Integrity Procedia 00 (2016) 000–000

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pulse whereas the steps at the shock front are absent. This means that in amorphous brittle material such as fused quartz, the intermediate structural instability is not initiated so it may be concluded that the shock fracture of fused quartz happens within the specimen volume simultaneously Table 4. Results of shock tests of fused quartz . Sample h t , mm h imp , mm U imp , m/s U’ imp , m/s D max , m/s U inst , m/s W, m/s  t, ns 1 5.02 1.95 86.5 98.4 13.2 65.7 34.7 34 2 5.22 1.95 197.7 224.8 10.6 214.6 23.1 17 3. Discussion In the continuous mechanics, the shock front is considered as a particle velocity discontinuity. Herewith, it is supposed that all points of wave front have the identical particle velocities. Modern experimental researches show that in reality the shock wave propagation is characterized by two important peculiarities which cannot be taken into account for by the continuous mechanics: (а) propagation of shock front is the process which flows at the several scales; (b) motion of shock front is non-uniform in the velocity space. It supposes that together with the average particle velocity there is a particle velocity distribution. While for the structure-uniform material the sufficient characteristic of shock-wave process is space-temporal average velocity profile, in the case of structure non-uniform material, the additional dynamic characteristic should be introduced - the particle velocity dispersion (Meshcheryakov et.al., 2008). Development of mesomechanics shows that nucleation of meso-structures takes place not only under plastic deform ation but in non-linear region of elastic deformation as well. The modern theory of micro-deformation developed by Aero (2000) predicts instability of crystalline lattice subjected to deformations in non-linear elastic region, which results in meso-structure nucleation. If the deformation gradients is lower some critical value, the meso-structure can disappear after removing the external stress so in this stage the process remains to be reversible. In the case of shock loading the heterogeneous materials, a current momentum and energy exchange between scale levels of straining occurs. This exchange flows by means of changing the velocity variance. As a result, a defect (decrease) of particle velocity may appear at the next scale level. The analytical coupling between velocity defect and velocity variance has the following form (Meshcheryakov et.al., 2008): dD dt u D du dt    (1) The velocity defect Δ u is seen to be determined by the rate of change of the velocity variance dD/dt as compared to the rate of change of mean particle velocity du/dt . The local tension stress generated at the mesoscale-2 Let us determine the value of local displacement caused by the momentum exchange between mesoscale-1 and mesoscale-2 on example of the gabbro-diabase target loaded at the impact velocity of 117.5 m/s (Fig. 3). Pieces ОА at the velocity profile and A В at the velocity variance profile correspond to mean velocity of u = 74.5 m/s and velocity variance of D = 10.5 m/s, respectively. From Fig. 3 and expression (1) one obtains the velocity defect Δ u = 1.47 m/s. Local displacement Δ S 1 is determined by the duration of energy exchange process Δ t = 47 ns for which the velocity variance doesn’t equal zero, so that S 1 = Δ t ∙ Δ u ~ 0.1 ∙ 10 -4 cm. It is seen that the particle velocity pulsations at the mesoscale-1 lead to nucleation of localized displacements of the order of 100 nm. When pulsation process comes to the end, the local displacements at the mesoscale-1 are healed, so in this stage the process is reversible. Immediately after that, the horizontal step Δ t 2 = 40 ns appears on the velocity profile, which indicates on the displacement of structural element of mesoscale-2 and further relaxation of local stress. The value of local displacement at the mesoscale-2 equals Δ S 2 = 74.5 ∙ 10 2 ∙ 40 ∙ 10 -9 = 3 ∙ 10 -4 сm. 2 1 2 ms fs C u      . (2)