Issue 20

H. Jasarevic et alii, Frattura ed Integrità Strutturale, 20 (2012) 32-35; DOI: 10.3221/IGF-ESIS.20.04 32 Case studies in numerical simulation of crack trajectories in brittle materials H. Jasarevic Faculty of Civil Engineering, University of Sarajevo, Sarajevo (Bosnia and Herzegovina) haris.jasarevic@gf.unsa.ba S. Gagula Faculty of Engineering and Natural Sciences, International University of Sarajevo, Sarajevo (Bosnia and Herzegovina) sadina@ius.edu.ba A BSTRACT . Statistical Fracture Mechanics, formalism of few natural ideas is applied to simulation of crack trajectories in brittle material. The “diffusion approximation” of the crack diffusion model represents crack trajectories as a one-dimensional Wiener process with advantage of well-developed mathematical formalism and simplicity of creating computer generated realizations (fractal dimension d = 1.5 ). However, the most of reported d values are in the range 1.1-1.3 . As a result, fractional integration of Wiener processes is applied for lowering d and to generate computer simulated trajectories. Case studies on numerical simulation of experimentally observed crack trajectories in sandstone (discs tested in indirect tensile strength test) and concrete (compact tension specimens tested in the quasi-static splitting tensile test) are presented here. K EYWORDS . Statistical Fracture Mechanics; Brittle materials; Crack trajectories; Fractal dimension; Sandstone; Concrete. I NTRODUCTION pproach to describe the physics of fracture for cases when failure of single element does not equal to failure of whole body was proposed first by Chudnovsky [1]. It evolved afterwards in crack diffusion model [2] and Statistical Fracture Mechanics (SFM) [3, 4], which both describe crack propagation in brittle materials. SFM formalizes following natural ideas [4]: i) crack advance consists of a sequence local fail ures in front of a crack tip, ii) the local failures are random events due to fluctuations of local strength of the material, iii) the crack trajectory is random, i.e. crack can follow any path from a set Ω of all admissible crack paths. For each of those paths conditional probability of failure along that path exists. The probability of crack advancing from point A to point B is an average of those conditional probabilities over all admissible crack paths leading from A to B. S IMULATION PROCEDURE he “diffusion approximation” of the crack diffusion model (see Chudnovsky and Gorelik, 1994), represents crack trajectories as a one-dimensional Wiener process (Brownian motion) w(t) . This approach has advantage due to well-developed mathematical formalism and simplicity of creating computer generated realizations with known fractal dimension d = 1.5 . However, often it cannot be directly applied to simulate actually observed fracture profiles, A T