Discrete element modeling of brittle crack roughness in three dimensions - Skjetne, Bjørn; Helle, Torbjørn; Hansen, Alex (Frontiers in Physics, 2014)
Crack morphology obtained in the fracture of materials with a disordered micro-structure is studied using numerical simulations. Physical properties are embedded on a regular three dimensional lattice as discrete stochastic elements which conform to the laws of linear elasticity. In this model, also known as the beam lattice, these elements are analogous to beams in that relative displacements between neighbouring nodes induce axial, bending and shearing forces, as in a real elastic solid. 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. Two different types of disorder have been used to generate the thresholds, i.e., distributions with a tail towards strong elements or with a tail towards weak elements. At weak disorders the self-affine regime seems to lie beyond the system sizes presently included. At stronger disorders a self-affine regime appears, for which we obtain exponents consistent with 0.6 for both types of disorder. The latter result is in fair agreement with the experimental value reported for large length scales, 0.50.