Phase-field modelling of size effect on strength and structural brittleness

In elastic degrading models, cracks are considered in a continuous way, without any geometric representation of the region where the crack takes place, and the released energy used in crack growth is controlled by the energy fracture parameter. Phase-field models consider a diffuse and smooth crack that belongs to a certain region where a function that describes the crack density is prescribed. Some of these phase-field models do not use any material strength limit to detect the nucleation of the crack or to follow its path, on the contrary of elastic degrading approaches. This article presents a study of the size effect based on one of these models. Structural and material behaviours predictions, based on both the phase-field model and an elastic degrading model, are presented. Numerical simulations show the size effect on strength and structural brittleness of the Brazilian splitting tests and of beams under three-point bending.