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

34

3

where Г p is the kinetic coefficient. The kinetics of spinodal decomposition for qualitative different metastability of free energy is obtained from the self-similar solutions: in the range c * < < δ δ δ

1/2

1 2

1

4

1 2

χ      





  1 tanh , 





  V = Γ χC p  1/2

(4)

, ζ ζ = x Vt L = 

2 ,

p x Vt = p 

  





S

p

L

Δp C

S

1  c δ < δ

in the range

m



1       c t t 

x

      , p x t = φ t f ζ ζ = φ t =Φ L   , ,

(5)

.

0

c

Solution (4) describes the dynamics of a solitary wave, S L is the wave front length, V is the front wave velocity, p  is the jump in the metastability area, which depends on the load intensity. Solution (5) describes the blow-up dynamics of mesodefect growth t t c p   as the generation of blow-up dissipative structures on the set of spatial scales , 1, 2, ... H c L = iL i = . The parameter c L , determining the fundamental blow-up length, and c t , representing the blow-up time, have the meaning of spatial and temporal scales of the self-similar solution, ~ 5 m is the power exponent related to the corresponding term in Eq. (2). The function   ζ f was determined by Kurdyumov (1988) when solving the corresponding eigen-function problem. It describes the profile of density of the microshear, which can trigger the blow-up dynamics of the microshear density generation over the fundamental length c L . Subjection of the defect dynamics to self-similar solutions Eq. (4), (5) reflects the global symmetry changes in the condensed matter. As has been stated in the work by Naimark (2010), the existence of scales S L and c L , which is characteristic of the string field theory, represents in our case the extended one-dimension topological objects with qualitative different microshear dynamics and reflects the internal degrees of freedom in the corresponding  - range.

Nomenclature A , B , C , D

phenomenological parameters

self-diffusion coefficient

D sd

c d

velocity of sound in a condensed matter

thickness of tube

length of liquid elasticity

d el

index

i

nonequilibrium free energy profile of density of the microshear

F

f

kinetic coefficient

G

wavenumber

k

wavenumber of gap

k g k Н k * L C L Н L S M m m f

autosolitary wave spectrum characteristic parameter of tube

parameter, determining the fundamental blow-up length

spatial scale

length of wave front

operator

power exponent in Eq. 2

mass of the fragments is greater than some given