Universal Features of Dynamic Failure and Turbulence Phenomena Caused by the Critical Behavior of Nonlinear Systems

Abstract

Universal features of dynamic failure and turbulence phenomena are considered on the basis of results of research and analyses of published data. The absorbed energy density causing the failure is comparable to the energy parameter of the crystal lattice E, which is fractions of electronvolt per atom in the range of nonequilibrium states t ~ 3 × 10^–6–10^–10 s. Macrofailure, changing the body connectivity, arises when approaching the critical density of the failure center cascade, i.e., percolation cluster, through the cascade of bifurcations. Fully developed turbulence is a chaotic dynamics, which is related to the stochastic instability of the transition through a sequence of period-doubling bifurcations, through intermittency, etc. At present, a strict mathematically grounded theory of dynamic failure phenomena of condensed matters and turbulence theories are absent, which implies the application of scaling relations and phenomenological approaches for their description. On the basis of design-theoretical studies and analysis of published data, it has been shown that phenomena of dynamic metal failure and fully developed turbulence are analogous, meaning that these processes have close values of critical exponents and belong to one universality class.