Smooth-to-rough transition in the fracture of fibrous materials

In this paper, a computational model in (2+1) dimensions which simulates the creep rupture of a fibrous material submitted to a constant uniaxial force F is analyzed. This force F produces in the bundle an initial displacement z0 which increases with time. In our model, the breakage of a fiber can provoke a cascade of breaking fibers which describes the propagation of a crack through the fiber bundle. In addition, the crack velocity is not constant, depending on the number of broken fibers in the bundle. Our goal here is to examine the fracture of this type of material as a function of the temperature t and of the initial displacement ratio δ0=z0/zc (zc is a critical displacement), as well as to investigate the effects of these parameters on the fracture roughness and on the roughness exponent ζ. Our results indicate that as δ0 approaches the critical initial displacement ratio δ0c the roughness W obey the following power law W∼(δ0c−δ0)β, where β≃0.33 is a critical exponent. These results can be understood in terms of a phase transition from a smooth phase to a rough one.