Disorder and FractureJ.C. Charmet, E. Guyon, Stéphane Roux Fracture, and particularly brittle fracture, is a good example of an instability. For a homogeneous solid, subjected to a uniform stress field, a crack may appear anywhere in the structure once the threshold stress is reached. However, once a crack has been nucleated in some place, further damage in the solid will in most cases propagate from the initial crack, and not somewhere else in the solid. In this sense fracture is an unstable process. This property makes the process extremely sensitive to any heterogeneity present in the medium, which selects the location of the first crack nucleated. In particular, fracture appears to be very sensitive to disorder, which can favor or impede local cracks. Therefore, in most realistic cases, a good description of fracture mechanics should include the effect of disorder. Recently this need has motivated work in this direction starting from the usual description of fracture mechanics. Parallel with this first trend, statistical physics underwent a very important development in the description of disordered systems. In particular, let us mention the emergence of some "new" concepts (such as fractals, scaling laws, finite size effects, and so on) in this field. However, many models considered were rather simple and well adapted to theoretical or numerical introduction into a complex body of problems. An example of this can be found in percolation theory. This area is now rather well understood and accurately described. |
Contents
| 2 | |
Introduction to Multifractality | 17 |
Statistical Theory of Fragmentation | 31 |
DiffusionLimited Aggregation Model | 49 |
Fluid Flow Experiments | 63 |
Statistical Fracture Models | 117 |
Scaling in Fracture | 149 |
Rheology and Fracture | 165 |
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adhesion aftershocks aggregates Aifantis analysis behavior bond breaking boundary conditions breakup brittle characteristic cluster colloidal concrete constant corresponds crack growth crack propagation crack tip cracking patterns critical exponents curve deformation dependence described diffusion dislocation Disorder and Fracture displacement distribution dynamics earthquakes effects elastic elastomer equilibrium experimental exponent Figure finite flow fluctuations fluid force fractal dimension fracture mechanics fragmentation function geometry glycerol gradient H.J. Herrmann homogeneous increase instability interface lattice layer Lett linear loading macroscopic Måløy material Mech microcracks multifractal nonlinear obtained packing parameter particles percolation percolation threshold Phys physical plane plane strain plastic polymers porosity porous power law problem properties quenched disorder random rate equations regime rupture seismicity self-similar shear bands shear stress simulations smectites solid solution spheres stress structure tension threshold velocity viscoelastic viscous fingering void width zone