Mechanism-based estimations of the relationship between the critical distance and the grain size for quasi-brittle fracture

•A mechanism-based model for the critical distance L and grain size d relationships.•Non-local energy balance in the fracture process zone is the underlying mechanism.•L / d ratio is related to the Poisson’s ratio of the material. It is well known that the grain size has significant influence on the fracture of quasi-brittle materials. In order to give a quantitative description of this influence, many researchers have tried to find empirical relationships between the critical distance and the grain size, connecting a macroscopic parameter with the material microstructures. In this paper, a more rational model of this relationship is proposed based on the energy balance in the fracture process zone. This model naturally considers the size effect and can be implemented to both a nearly plain specimen and a specimen containing a long crack. It is not only helpful to explain the existing empirical estimations, but also reveals more underlying mechanisms of the quasi-brittle fracture.