Case studies in numerical simulation of crack trajectories in brittle materials

H Jasarevic,S Gagula

doi:10.3221/igf-esis.20.04

Abstract

Statistical Fracture Mechanics, formalism of few natural ideas is applied to simulation of cracktrajectories in brittle material. The “diffusion approximation” of the crack diffusion model represents cracktrajectories as a one-dimensional Wiener process with advantage of well-developed mathematical formalismand simplicity of creating computer generated realizations (fractal dimension d = 1.5). However, the most ofreported d values are in the range 1.1-1.3. As a result, fractional integration of Wiener processes is applied forlowering d and to generate computer simulated trajectories. Case studies on numerical simulation ofexperimentally observed crack trajectories in sandstone (discs tested in indirect tensile strength test) andconcrete (compact tension specimens tested in the quasi-static splitting tensile test) are presented here.

Highlights

A 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]
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
The “diffusion approximation” of the crack diffusion model cannot be applied to crack trajectories experimentally observed in sandstone and concrete, since their fractal dimension is less 1.5

Summary

INTRODUCTION

A 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]. 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

SIMULATION PROCEDURE

CONCLUSION