Modeling of fiber toughening in cementitious materials using an R-curve approach

This paper presents the theoretical formulation describing the role of fibers in enhancing the fracture toughness of quasi-brittle cement based materials. The formulation is based on the well known R-curve approach which correlates the increase of the apparent fracture toughness of a material with the existence of a pre-critical stable crack growth region.By assuming that the critical crack length in plain matrix is a function of an initial crack length a₀, a formulation for the R-curves has recently been derived and applied to predict the response of positive and negative geometry specimens of various sizes and materials. This approach is further applied to uniaxial tensile specimens containing various fiber types. Fiber reinforcement is modeled by means of applying closing pressure on crack surfaces resulting in closure of the crack faces and a decrease in the stress intensity factor at the tip of the propagating crack. Incorporation of these two factors in the energy balance equations for crack growth results in increases in both the slope and the plateau value of the R-curve representing matrix response. Enhancement in material response is shown to occur only if precritical crack growth exists, causing fibers to convert the stable cracking process into an increase in load carrying capacity of the material. Fracture response of fiber reinforced composites can be predicted up to the bend-over-point. The theoretical predictions are compared with the experimental results of cement-based composites containing unidirectional, continuous glass, steel or polypropylene fibers.