Analytical Study of Fracture in Concrete Beams Using Blunt Crack Model

An analytical study of nonlinear fracture of beams using a blunt crack model is presented. The fracture is modeled by a blunt front smeared over an elastic layer around the midsection of the beam. Outside the elastic layer, the deformations are modeled by beam theory. From the knowledge of the uniaxial stress-strain relation including the postpeak softening portion, calculations are presented for the determination of moment-curvature and load-deflection relations. A generalized power law (with an exponent n) has been used for the postpeak stress-strain relation. It is shown that, for a linear postpeak relation (n = 1), the equations coincide with those described when using the fictitious crack model with a linear stress-displacement law in the softening portion. Results for both the blunt crack model and the fictitious crack model are compared for nonlinear softening relations. Calculations are given for the critical brittleness factor from the snapback considerations for the beam. A method of determining n and the elasticity coefficient of the central layer k from an experiment is outlined.