Correlations in the mesoscale modelling of fracture of quasi-brittle materials--extracting internal lengths
Résumé
The degradation of quasi-brittle materials encompasses micro-crack propagation, interaction and coalescence in order to form a macro-crack. These phenomena are located within the so-called Fracture Process Zone (FPZ). The shape and growth of the FPZ, and its interaction with boundaries lead to typical phenomena such as size, boundary and shielding effects. Meso-scale models capture the failure process at the scale of the heterogeneities. With the help of the 2D lattice model used in this paper, we were able to provide predictions of the experimental mechanical responses obtained from three-point bending tests on notched and un-notched concrete beams of different sizes. Both the maximum loads and the softening regime were recovered, and the energy dissipation within the FPZ was analysed. During the experiments, the damage events are recorded using emission acoustic techniques. The aim of this contribution is to provide a further insight in the description of failure with the help of statistical analyses of damage. The statistical analysis relies of the implementation of Ripleys functions which have been developed in order to exhibit patterns in image analyses. It is shown how an internal length, in the sense of non local models, may be extracted by comparing the computed Ripleys functions with analytical ones. Finally, the evolution of this extracted internal length upon failure is presented for both direct tension and three point bending specimens.