PSI - Issue 6

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

147

2

of high hydrostatic pressure and local heating can lead to further increase of temperature in the regions of high intensity of plastic flow (for example, in regions dislocation accumulations). This in turn, must lead to local decrease of viscosity, and further, to decrease of shock front duration. In this region, the temperature begins to grow much faster since the thermo-conductivity mechanism has not time to remove the energy from region of local heating, which results in further decrease of viscosity. This model was used for explaining the shock-induced shear bands nucleation in 6061- Т6 aluminum alloy discovered by Asay and Chhabildas (1981). In the present work, a n alternative mechanism of shock-induced structural heterogenization is suggested. The theoretical model is based, firstly, on the uniaxial shock tests of two kinds of aluminum alloys, and secondly, on new kind of constitutive equation which takes into account the multi-scale mesoscopic mechanism of stress relaxation. Comparison of experiment and theory allows to conclude that possible reason for shock-induced structural instability may be the resonance interaction between oscillations of plastic flow and shock-induced structural element of mesostructure which dimensions coincide with the space period of oscillations for each kind of aluminum alloy under investigation. 2. Multiscale mechanism of stress relaxation in shock-deformed material In heterogeneous medium, as shown by Meshcheryakov et al. (2008), the shock front is a totality of local regions which move with different velocities. In this situation, the motion of wave front can be considered as a superposition of two modes: M1 (mode one) - averaged motion of approximately plane front and M2 (mode two) - fluctuative motions of separate regions of medium (mesoparticles) due to action of random stress fields. In common case of stochastic motion of mesoparticles in random stress fields, the velocity distribution of mesoparticles is non-equilibrium. Such a kind of distribution can be quantitatively characterized by the statistic moments of the particle velocity distribution function. The zero statistical moment is the density of medium ρ(r,t ), the first moment is the mathematical expectation or mean particle velocity, the second moment is the particle velocity dispersion, the third moment is asymmetry of velocity distribution function:



  

( , , ) vf x v t dv

;



2 ( ) ( , , ) D v u f x v t dv      ; 2

;

(1)

 

u x t

( , )

( , ) r t

( , , ) f r v t dv







Let max u is the particle velocity which corresponds to maximum of distribution function and D is a particle velocity variance (square root of the particle velocity dispersion) . The difference max ( ) u u t u    calls the velocity defect. In the shock-wave processes, the velocity defect and velocity variance are shown by Meshcheryakov et. al (2008) to be not independent: 2

D

1 2



(2)

u   

u

