Anisotropic gradient damage modelling of cleavage crack propagation in metallic polycrystals

An anisotropic gradient damage model specifically built to capture cleavage-like crack propagation in metallic polycrystalline aggregates is developed. This study extends the classical scalar characteristic length of gradient damage models to a tensorial characteristic length field. This second-order tensor, varying from grain to grain with the local crystallographic orientation, contains information related to the anisotropy of single-crystal fracture resistance, and thus provides a physically motivated parameter governing crack path selection. By appropriately tuning this tensorial field, damage evolution can be hindered in certain directions while being promoted along others, naturally reproducing cleavage fracture behaviour where cracks propagate along preferred crystallographic planes. The present model is built within the framework of the thermodynamics of irreversible processes using the approach of Frémond and Nedjar. To account for the damage evolution under multi-axial stress states, an anisotropic volumetric-deviatoric stiffness decomposition is used. The model is assessed through several loading cases, including a crack propagation simulation in a polycrystalline aggregate where the effect of a tensorial characteristic length field is investigated.