PSI - Issue 6

Yurii Meshcheryakov et al. / Procedia Structural Integrity 6 (2017) 146–153 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

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Fig.1. Time resolved profiles for the free surface velocity u fs , velocity variance D and strain rate ( ) d t dt  . Consider once more important relationship between dynamic variables which is proper for the shock front propagating in heterogeneous medium. Shock-wave experiments reveal correlation between velocity variance and strain rate. In Fig.1 the time-resolved free surface velocity profile ( ) fs u t , the time-resolved variance profile ( ) D t and time profile for strain rate ( ) d t dt  are plotted together. Two last profiles are seen to be synchronously changed along the steady velocity profile. Indeitzev et al. (2015) found that the following relationship can be written: ( ) d t D R dt   , (3) where R is the proportionality coefficient. Analogous relationship is known in turbulence where intensity of turbulent pulsations of particle velocity are proportional to mean particle acceleration [4]. We are using the dependencies (2) and (3) for the description of the shock-wave propagation in relaxing heterogeneous medium. For one-dimensional propagation of shock wave the balance equations for impulse and continuity of medium 0; t x u     0; x t u    (4) can be reduced to equation 0; tt xx     (5) Constitutive equation for relaxing medium can written in the form suggested by Taylor (1965): 2 t l t C F       , (6) where C l is the sound velocity. The relaxation function F= 2µ d( Δε р )/dt) is expressed through the plastic strain rate. We accept that relaxation of medium at the shock front is realized by means of motion of elementary carriers of deformation at the mesoscale and the relaxation function F can be defined through the velocity defect only. In the case of uniaxial straining, the plastic deformation and particle velocity are related as follows p l u C   . (7)