Fully-developed FPZ length in quasi-brittle materials

This paper studies the development of fracture processes in quasi-brittle materials. We propose to use the length of the fracture process zone (FPZ) once it is fully developed as a material parameter. This assumption allows us to build an analytical formulation that reproduces the mechanical behavior of any specimen as a cohesive crack advances. Extensive comparisons with experimental results lead us to define a new characteristic length that commensurates with the fully-developed FPZ and that together with the new analytical model, is used to provide a complete and consistent study on the fracture process. In particular, the size-effect deriving from our formulation coincides with the statistical size-effect law of BaA3/4ant for small and medium sizes, whereas it smoothly converges to size-independent results as size increases. The analytical cohesive formulation developed here is validated against experimental results on various types of normal and high-strength concretes as well as construction ceramics for several experimental set-ups and test scales. Because of its simplicity as compared with numerical models for fracture, this analytical formulation constitutes a powerful tool for studying fracture processes in a wide variety of mechanical configurations. Meanwhile, analytical expression for a fully-developed FPZ length is given for a general type of cohesive law.