Size Effect on Strength of Quasibrittle Structures with Reentrant Corners Symmetrically Loaded in Tension

The effect of V-notches (or reentrant corners) on fracture propagation has been analyzed for brittle materials, but not for quasibrittle materials such as concrete, marked by a large material characteristic length producing a strong size effect transitional between plasticity and linear elastic fracture mechanics. A simple size effect law for the nominal strength of quasibrittle structures with symmetrically loaded notches, incorporating the effect of notch angle, is derived by asymptotic matching of the following five limit cases: (1) Bažant’s size effect law for quasibrittle structures with large cracks for notch angle approaching zero; (2) absence of size effect for vanishing structure size; (3) absence of size effect for notch angle approaching $\pi$ ; (4) plasticity-based notch angle effect for vanishing size; and (5) the notch angle effect on crack initiation in brittle structures, which represents the large-size limit of quasibrittle structures. Accuracy for the brittle large-size limit, with notch angle effect only, is first verified by extensive finite-element analyses of bodies with various notch angles. Then a cohesive crack characterized by a softening stress-separation law is considered to emanate from the notch tip, and the same finite-element model is used to verify and calibrate the proposed law for size and angle effects in the transitional size range in which the body is not far larger than Irwin’s material characteristic length. Experimental verification of the notch angle effect is obtained by comparisons with Dunn et al.’s extensive tests of three-point-bend notched beams made of plexiglass (polymethyl methacrylate), and Seweryn’s tests of double-edge-notched tension specimens, one set made of plexiglass and another of aluminum alloy.