https://doi.org/10.1007/s100510050037
Scaling behaviour in the fracture of fibrous materials
1
Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de
Minas Gerais, C.P. 702,
30123-970, Belo Horizonte, MG, Brazil
2
Departamento de Física, Universidade Federal de Ouro Preto, Campus do Morro do
Cruzeiro, 35400-000
Ouro Preto, MG, Brazil
Received:
24
June
1999
Published online: 19 October 2012
We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density ρ scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation.
PACS: 62.20.Mk – Fatigue, brittleness, fracture, and cracks / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
