The objective of PhyCracks is to provide a statistical description of the basic processes occurring at the microstructure scale during the failure of materials (damage, plasticity…). This description will result in a model of crack propagation that ultimately will lead to predictive constitutive laws less phenomenological than the ones currently used by engineers. While existing theories allow to estimate quite precisely mechanical properties like Young modulus for instance, the failure properties are far more difficult to predict: Since the crack evolution is only sensitive to the very vicinity of the crack tip, it can be irrelevant to replace an heterogeneous material by an effective continuum medium to make predictions on toughness or life duration for instance. However, some theoretical concepts developed within the framework of out-of-equilibrium statistical physics were shown to be very promising. A crack is then described as an elastic line propagating within the microstructural obstacles of the materials. This approach was successfully applied to perfectly brittle failure. However, the understanding of crack propagation within the great majority of materials for which damage is involved is still lacking. PhyCracks will provide a description of the development of damage and cracks. At first, the damage spreading and the resulting crack propagation will be numerically and experimentally explored for model heterogeneous materials. The basic failure processes identified, they will then be implemented in a model of crack propagation using the same theoretical tools than used for brittle failure (elastic manifolds driven in random media), but adapted to quasi-brittle failure. This model will be used to decipher the fracture surfaces morphology (scaling properties of roughness, roughening development from an initial straight notch…), the jerky progression of crack fronts, and more generally will provide an equation of motion for cracks in quasi-brittle materials.