A two-scale model for subcritical damage propagation

The failure behaviour of quasi-brittle materials is often time-dependent. This dependence is due to physical processes taking place at the level of the micro-structure. For a rigorous modeling of the time-dependent behaviour of that kind of solids, a two-scale approach is well suited. This paper investigates time-dependent damage which microscopic origin is the subcritical micro-crack growth. We present a two-scale time-dependent damage model completely deduced from small-scale descriptions of subcritical micro-crack propagation, without any macroscopic assumptions. The passage from the micro-scale to the macro-scale is done through an asymptotic homogenization approach. At the micro-scale, the tensile failure due to the subcritical propagation of cracks is the dominant mechanism of creep observed at the macro-scale. We consider microstructures with cracks evolving in different subcritical regimes. We assume a complex propagation law that considers three characteristic regimes of subcritical crack growth, corresponding to different physical processes at the crack tip level. Numerical simulations of constant strain rate, relaxation and creep tests illustrate the ability of the developed model to reproduce different regimes of time-dependent damage response.