Statistical Size Effect in Quasi-Brittle Structures: I. Is Weibull Theory Applicable?

The classical applications of Weibull statistical theory of size effect in quasi-brittle structures such as reinforced concrete structures, rock masses, ice plates, or tough ceramic parts are being reexamined in light of recent results. After a brief review of the statistical weakest-link model, distinctions between structures that fail by initiation of macroscopic crack growth (metal structures) and structures that exhibit large macroscopic crack growth prior to failure (quasi-brittle structures) are pointed out. It is shown that the classical Weibull-type approach ignores the stress redistributions and energy release due to stable large fracture growth prior to failure, which causes a strong deterministic size effect. Further, it is shown that, according to this classical theory, every structure is equivalent to a uniaxially loaded bar of variable cross section, which means that the mechanics of the failure process are ignored. Discrepancies with certain recent test data on the size effect are also pointed out. Modification of the Weibull approach that can eliminate these shortcomings is left for a subsequent paper.