If the structure fails at fracture initiation from a smooth surface, and if the geometry is positive and the structure size tends to infinity, the Weibull-type size effect must be exactly followed, even if the material is quasibrittle. A nonlocal…
If the structure fails at fracture initiation from a smooth surface, and if the geometry is positive and the structure size tends to infinity, the Weibull-type size effect must be exactly followed, even if the material is quasibrittle. A nonlocal generalization of Weibull theory that satisfies this condition is presented. It predicts the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture. The probability of failW:e at a material point is assume~ to. be a power function of the average strain in the neighborhood of that pomt. The recent nonlocal generahzat1on of Weibull theory is reviewed and shown to exhibit the correct large-size properties. The size effect on the modulus of rupture (bending strength) and its statistics are analyzed and comparisons with extensive test data are presented.