Size effect in blunt fracture: Concrete, rock, metal

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 fracture mechanics (LEFM). The size effect is studied first for concrete or rock structures, using dimensional analysis and illustrative examples. Fracture is considered 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 nominal stress σ_N at failure is found to decline as (1 + λ/λ₀)^−1/2 in which λ₀ = constant and λ = relative structure size. This function is verified by Walsh's test data. If reinforcement is present at the fracture front and behaves elastically, the decline of σ_N is of the same type but is shifted to larger sizes; however, if the reinforcement yields, the decline of σ_N stops. It is also noted that some known size effects which have been attributed to random strength variations 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 approximately constant, it is shown by dimensional analysis that elastic-plastic fracture causes a similar size effect.