Hydrodynamic descriptions for surface roughness in fracture front propagation

Abstract

Fracture is ubiquitous in a crystalline material. Inspired by the observed phenomenological similarities between the spatial profile of a fractured surface and velocities in hydrodynamic turbulence, we set up a hydrodynamic description for the dynamics of fracture surface propagation mode I or opening fracture front. We consider several related continuum hydrodynamic models and use them to extract the similarities between the profile of a fractured surface and velocities in hydrodynamic turbulence. We conclude that a fractured surface should be generically self-similar with an underlying multifractal behaviour. This article is part of the theme issue ‘Statistical physics of fracture and earthquakes’.

Rigidity-Controlled Crossover: From Spinodal to Critical Failure

“…Here we extend this analogy showing that if rigidity is interpreted as "time", and strain as "space", the brittle-to-ductile transition and the associated critical behavior can be viewed as a "finite time" Burgers turbulence [47]. Given that our model is essentially a mean-field version of the Burridge-Knopoff model [39], the developed analogy reinforces a conceptual link between earthquakes (fracture) and turbulence [48]. Consider a discrete system with dimensionless energy:…”

Statistical physics of fracture and earthquakes

“…Next, the equation of motion of the velocity field of a fracture front through a disordered solid is considered in analogy with the velocity field for turbulence in an incompressible fluid [29]. A generic equation of motion containing all terms permitted under the symmetry constraints of the system was written and the scaling features of the roughness profiles are derived.…”

Cooperative Dynamics in the Fiber Bundle Model

“…Among other attempts to relate fracture and in particular FBM dynamics with different universality classes, a relatively less explored route is that of the hydrodynamics of turbulence. The analogy between the velocity fluctuation in turbulence and surface roughness due to fracture have been explored before [47]. However, given that FBM is able to provide a reasonably consistent picture for fracture dynamics, its association with hydrodynamics of fracture is a crucial question.…”