Analysis for multi-linear stress-crack opening cohesive relationship: Application to macro-synthetic fiber reinforced concrete

An analytical formulation for flexure behaviour of concrete considering a multi-linear stress-crack separation (σ-w) relationship is developed using the cracked hinge model. An inversion procedure for obtaining the multi-linear cohesive stress response from the flexural load response of a beam is presented. The procedure is applied to obtain the σ-w relationship for macro-synthetic fiber reinforced concrete. An experimental investigation of the crack propagation in flexural response of macro-synthetic fiber reinforced concrete is presented using the digital image correlation technique. The post-cracking response of macro-synthetic fiber reinforced concrete during the initial softening and the subsequent load recovery is experimentally shown to be associated with a hinge-type behaviour and is produced by crack closing stresses contributed by fibers. From the optical measurements the hinge length is identified with a zone of length equal to twice the aggregate size. Using the measured hinge length, the multi-linear σ-w relationship for macro-synthetic fiber reinforced concrete obtained by matching the experimental and the analytical load responses exhibits a stress recovery following initial softening. The cohesive stress subsequently decreases following the recovery at large crack separation. The crack closing stresses contributed by the pullout of fibers produce stress recovery in the σ-w relationship and are primarily active after the formation of the hinge resulting in significant contribution to fracture energy at large crack openings. There is a good correlation in the fracture energy obtained from load response and the σ-w relationship at different values of crack opening displacements.