Abstract
The roughness exponent is reported in numerical simulations with a three-dimensional elastic beam lattice. Two different types of disorder have been used to generate the breaking thresholds, i.e., distributions with a tail towards either strong or weak beams. Beyond the weak disorder regime a universal exponent of 0.59(1) is obtained. This is within the range 0.4-0.6 reported experimentally for small scale quasi-static fracture, as would be expected for media with a characteristic length scale.
Highlights
The modern academic interest in crack morphology can be traced back to Mandelbrot et al who introduced a mathematical framework for describing rough surfaces in terms of fractal geometry [1]
The result, ζ = 0.5 [20], is consistent with the range of exponents obtained with the random fuse model and agrees rather well with the scaling expected at length scales above those relevant to the fracture process zone
The roughness is obtained as the root-mean-square of the variance perpendicular to the fracture plane, i.e., Wx(L) =
Summary
Reviewed by: Stefano Zapperi, National Research Council, Italy Roberto Brighenti, University of Parma, Italy Elisabeth Bouchaud, Commissariat à l’énergie Atomique and Ecole Supérieure de Physique et de Chimie Industrielles, France. Physical properties are embedded on a regular three dimensional lattice as discrete stochastic elements which conform to the laws of linear elasticity. The stochastic nature enters via the introduction of random breaking thresholds on the individual elements Using this model, the exponent characterizing the scaling with system size of the crack roughness perpendicular to the fracture plane is reported. At stronger disorders a self-affine regime appears, for which we obtain exponents consistent with ζ 0.6 for both types of disorder. The latter result is in fair agreement with the experimental value reported for large length scales, ζ 0.50
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
