Failure of quasi-brittle materials modelled at the mesoscale: experimental and numerical analysis of the correlation during the damage process
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 progressively 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 effects, boundary effects and shielding effects. Meso-scale models capture the failure process at the scale of the heterogeneities with details that continuum based model cannot provide. Typical mesoscale models such as the one used in this contribution consider aggregate embedded in a mortar matrix and introduce also a special response of the interfacial transition zone between mortar and the aggregate. 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 [1]. 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 histograms of relative distance between locations at which damage grows within a given loading step are considered first. They are compared to the histograms of the relative distances between the locations of successive acoustic events in experiments. These numerical and experimental histograms are similar, which provides added confidence in the mesoscale approach. Then, Ripley functions [2] are used to characterise the correlation patterns in the course of failure. As expected, it is observed that the failure patterns deviates from random fields in the course of localisation of damage and from auto-correlated random fields resulting from the initial disorder in the material too. Patterns are then compared to those resulting from auto-correlated random fields in order to extract a correlation length involved in the localization of damage during failure. Finally, we compare the computations performed on the lattices with acoustic emission data on the same geometry. The analysis with Ripley functions reveals the same trend, with a good agreement on the evolution of the correlation length involved in the failure process.