Fracture scaling of quasibrittle composites and thin films: new asymptotic matching approach
Professor Zdenek P. Bazant
McCormick School Professor and W.P. Murphy Professor of Civil Engineering and Materials Science, Northwestern University
Until about two decades ago, all observed the size effects on structural strength were automatically attributed to the randomness of material strength, as described by the classical Weibull theory. By now it has been established that, in quasibrittle materials characterized by a fracture process zone (FPZ) that is not negligible compared to structural dimensions, the mean size effect is energetic if large stable fracture can grow prior to maximum load, and energetic-statistical if it cannot. The size effect law must asymptotically approach three simple power laws, characterizing the scaling of plasticity, linear elastic fracture mechanics and Weibull theory. Of practical interest is the transitional range, for which a simple approximate scaling law can be derived by asymptotic matching. Presented is a new asymptotic matching method, the idea of which is to formulate the governing equation in such a way that, in each asymptotic case, all the dimensionless variables vanish except one. Applications of the scaling laws to structural design and identification of fracture properties deal with fiber-polymer composites (laminates and sandwich structures), and with particulate composites (concrete, rock, sea ice, foam, tough ceramics and snow slabs). Generalization to determine the entire probability distribution of size effect and characterize structural reliability is outlined, with a focus on failure loads of extremely small probability important for structural design. Finally, a similar asymptotic analysis of the size effects observed in thin metallic films on the micrometer scale is described, and it is shown that the gradient theory of metal plasticity needs to be generalized for the effect of a boundary layer epitaxially induced on the substrate side.
