Scaling of quasi-brittle fracture : a boundary effect model

The common size effect on quasi-brittle fracture of concrete-like materials is analysed by a simple asymptotic analysis based on a boundary effect model originally proposed for a large plate with a small edge crack. The large plate analysis considers exclusively the interaction of the crack-tip fracture process zone with the specimen front face and its influence on the fracture conditions. The new asymptotic model considers both the specimen boundary and size, and thus extends the boundary effect model to the size effect study on finite-sized specimens. The new boundary effect model shows that the specimen size alone is not sufficient in determination of the size effect on quasi-brittle fracture behaviour, the specimen boundary conditions have to be considered as well. It is shown that even very large specimens that normally do not show any size effect can still experience quasi-brittle fracture if they contain very shallow or very deep cracks. The new boundary effect model uses the two well-defined fracture criteria, the tensile strength and fracture toughness, as its two asymptotic limits, which allows the determination of the two important material constants from the quasi-brittle fracture results. The size effect issue in concrete specimens without initial notches is also studied by the asymptotic model after assuming the natural pre-existing defects in concrete as very shallow notches. The geometrically similar specimen condition can be satisfied by those assumed shallow notched specimens.