Some Notes on Microcracking, Softening, Localization, and Size Effects

Fracture of concrete and other brittle disordered materials is a complex process involving microcracks (that can be arrested by the heterogeneous material structure) and macrocracks (that lead to failure of the structure/specimen). The process is basically the same for any type of loading as long as global failure is not ductile (for these materials: usually at high confinement). The focus in the article is on mode I cracking, showing similarities of the fracture process for other loading cases, in particular (multiaxial) compression. The fracture process in tension can be sub-divided in four stages: elastic, microcracking, macrocrack growth (localization), and bridging. Improvements in simulations over two decades are shown. The various fracture stages can be simulated using models that allow for local brittle mode I fracture and where the material structure has been included. At present simulations in 3D, with great amount of detail such as realistic particle distributions and particle shapes can be carried out routinely. One example is shown, focusing on size effects of fracture strength in 3-point bending. The results reveal that the microcrack population at peak-load is the fracture pattern to consider, and not the localized macrocrack at the end of the softening branch. The consequence is that size-effect must be expressed in terms of log(nominal stress) versus log(volume) diagrams, which makes the formulation more general.