Size effect in blunt fracture: Concrete, rock, metal

ABSTRACT: The fracture front in concrete, as well as rock, is blunted by a zone of microcracking, and in ductile metals by a zone of yielding. This blunting causes deviations from the structural size effect known from linear elastic frac-ture mechanics (LEFM). The size effect is studied first for concrete or rock struc-tures, using dimensional analysis and illustrative examples. Fracture is consid-ered to be caused by propagation of a crack band that has a fixed width at its front relative to the aggregate size. The analysis rests on the hypothesis that the energy release caused by fracture depends on both the length and the area of the crack band. The size effect is shown to consist in a smooth transition from the strength criterion for small sizes to LEFM for large sizes, and the nom-inal stress (IN at failure is found to decline as (1 + 1../1.. 0)-112 in which 1..0 = constant and A = relative structure size. This function is verified by Walsh's test data. If reinforcement is present at the fracture front and behaves elasti-cally, the decline of (J N is of the same type but is shifted to larger sizes; how-ever, if the reinforcement yields, the decline of (J N stops. It is also noted that some known size effects which have been attributed to random strength vari-ations within the structure should be explained by fracture mechanics, which gives a very different extrapolation to large structures. Finally, exploiting the fact that in metals the size of the yielding zone at the fracture front is approx-imately constant, it is shown by dimensional analYSis that elastic-plastic fracture causes a similar size effect