Interface crack propagation in porous and time-dependent materials analyzed with discrete models

A model describing the crack propagation at the interface between a rigid substratum and a beam is considered. The interface is modeled using a fiber bundle model (i.e. using a discrete set of elements having a random strength). The distribution of avalanches, defined as the distance over which the crack is propagated under a fixed force, is studied in order to capture the effect of ageing and time-dependent response of the interface. The avalanches depend not only on the statistical distribution of strength but more importantly on time (or displacement) correlations. Namely, local fiber breakage kinetics is related to a correlation length, which sets the size of the fracture process zone which occurs ahead of the crack due to progressive failure. First, a variation of porosity of the interface is considered. It corresponds for instance to diffusion controlled dissolution processes. Interpreting the results in Delaplace et al. [Delaplace A, Roux S, Pijaudier-Cabot G (2001) J Eng Mech 127:646–652], it is shown that the size of the fracture process zone increases with increasing porosity in accordance with experimental observations [Haidar K, Pijaudier-Cabot G, Dube J-F, Loukili A (2005) Mater Struct 38:201–210]. The creep–fracture interaction is analyzed in the second part of the paper. It is found based on a Maxwell model that the size of the process zone depends on the fracture propagating velocity and on the distribution of forces in the interface due to the interaction between the interface and the rest of the specimen. The observed decrease of the size of the process zone, in creep experiments, compared to the size of the process zone in a time-independent process, is justified by the proposed model for an interface that is less viscous than the rest of the material.