Abstract :
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 isshown that the size of the fracture process zone
increases with increasing porosity in accordance
with experimental observations [Haidar K, Pijaudier-
Cabot G, Dubé 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.
