Size effect in shallow and deep notched quasi-brittle structures

The nominal strength of a quasi-brittle structure is known to vary with its size. If the structure undergoes large stable crack growth prior to failure or if it contains a large pre-existing crack, then the failure load is known to approach the asymptotic limit of linear elastic fracture mechanics (LEFM) for large structures from below. In this paper, the size effect is studied on a particular structural geometry containing a crack which can be relatively shallow or deep. The study is conducted within the framework of the fictitious crack model for the fracture of quasi-brittle materials. By allowing for the redistribution of the stresses in the fracture process zone (FPZ), the essential result of the size effect is confirmed. However, it is shown that this result can only be obtained from tests on specimens whose size exceeds a certain minimum value depending on the material, so that at failure the fully developed FPZ is contained wholly within the test specimen. Moreover, the minimum size of the test specimen is shown to increase as the depth of the pre-crack is reduced, thus requiring specimens of very large sizes to obtain valid results from tests on specimens with very shallow pre-cracks.