Size Effect in Fracture: Roughening of Crack Surfaces and Asymptotic Analysis

Recently the scaling laws describing the roughness development of fracture surfaces was proposed to be related to the macroscopic elastic energy released during crack propagation [Mor00]. On this basis, an energy-based asymptotic analysis allows to extend the link to the nominal strength of structures. We show that a Family-Vicsek scaling leads to the classical size effect of linear elastic fracture mechanics. On the contrary, in the case of an anomalous scaling, there is a smooth transition from the case of no size effect, for small structure sizes, to a power law size effect which appears weaker than the linear elastic fracture mechanics one, in the case of large sizes. This prediction is confirmed by fracture experiments on wood.Comment: 9 pages, 6 figures, accepted for publication in Physical Review

Size Effect in Fracture of Concrete Specimens and Structures: New Problems and Progress

Presented is a concise summary of recent Northwestern University studies of six new problems. First, the decrease of fracture energy during crack propagation through a boundary layer, documented by Hu and Wittmann, is shown to be captured by a cohesive crack model in which the softening tail slope depends on the distance from the boundary (which causes an apparent size effect on fracture energy and implies that the nonlocal damage model is more fundamental than the cohesive crack model). Second, an improved universal size effect law giving a smooth transition between failures at large cracks (or notches) and at crack initiation is presented. Third, a recent renewed proposal that the nominal strength variation as a function of notch depth be used for measuring fracture energy is critically examined. Fourth, numerical results and a formula describing the size effect of finite-angle notches are presented. Fifth, a new size effect law derivation from dimensional analysis coupled with asymptotic matching is given. Finally, an improved code-type formula for shear capacity of R.C. beams is proposed.

Damage-cluster distributions and size effect on strength in compressive failure

We investigate compressive failure of heterogeneous materials on the basis of a continuous progressive damage model. The model explicitely accounts for tensile and shear local damage and reproduces the main features of compressive failure of brittle materials like rocks or ice. We show that the size distribution of damage-clusters, as well as the evolution of an order parameter, the size of the largest damage-cluster, argue for a critical interpretation of fracture. The compressive failure strength follows a normal distribution with a very small size effect on the mean strength, in good agreement with experiments

Polygonization of carbon nanotubes

We use a multiscale procedure to derive a simple continuum model of multiwalled carbon nanotubes that takes into account both strong covalent bonds within graphene layers and weak bonds between atoms in different layers. The model predicts polygonization of crossections of large multiwalled nanotubes as a consequence of their curvature-induced turbostratic structure