Flory-like statistics of fracture in the fiber bundle model as obtained via Kolmogorov dispersion for turbulence: A conjecture.

Abstract

It has long been conjectured that (rapid) fracture propagation dynamics in materials and turbulent motion of fluids are two manifestations of the same physical process. The universality class of turbulence (Kolmogorov dispersion, in particular) is conjectured to be identifiable with the Flory statistics for linear polymers (self-avoiding walks on lattices). These help us to relate fracture statistics to those of linear polymers (Flory statistics). The statistics of fracture in the fiber bundle model (FBM) are now well studied and many exact results are now available for the equal-load-sharing (ELS) scheme. Yet, the correlation length exponent in this model was missing and we show here how the correspondence between fracture statistics and the Flory mapping of Kolmogorov statistics for turbulence helps us to make a conjecture about the value of the correlation length exponent for fracture in the ELS limit of FBM and, also, about the upper critical dimension. In addition, the fracture avalanche size exponent values at lower dimensions (as estimated from such mapping to Flory statistics) also compare well with the observations.