Role of the quenched disorder in fracture front propagation

Abstract

The process of materials fracture is not yet understood across all levels. This thesis contains detailed description on a model of in-plane fracture along with results obtained using this model. The results from the model are in very good agreement with experimental observations, both with respect to the static scaling of the front (morphology) and a dynamic study of the underlying processes. This is quite remarkable, considering our model is quasistatic, meaning that the dynamics are time independent.

Using this model, I have found two scaling regimes which corresponds to the two different regimes found experimentally for in-plane fracture. This is the first model to successfully reproduce these two scaling regimes, allowing us to clearly state the important processes in this constrained form of fracture. Only the geometry is constrained, any material obeying the quite general assumptions in the model should contain the same processes and fracture in the same way.

The results indicate that a percolation process is controlling the fracture on small scales. At larger scales, the elastic material properties leads to a stress concentration which eventually constrains damage formation to the immediate area near the fracture front. In the large scale regime I have measured a roughness exponent of

large = 0.39 ± 0.04 .

In the small scale regime, I show data consistent with and present evidence based on several different analyses for a roughness exponent of small = 2/3.