Micromechanics of crack bridging stress-displacement and fracture energy in steel hooked-end fiber-reinforced cementitious composites

This paper presents a probabilistic micromechanical framework for analyzing crack bridging stress-displacement in short steel hooked-end fiber-reinforced cementitious composites, featuring the fiber length/diameter aspect ratios of 45 and 80, with varying fiber volume fractions and varying snubbing coefficients. The proposed formulation is constructed based on the randomly located, randomly oriented distribution of steel fibers. This random nature accounts for the dominant features of the composite failure mechanisms. The composite fracture energy dissipation may be obtained from the area under the tension-softening curve. The fracture energy dissipations contributed by the fiber interfacial debonding and fiber pullout of both the straight-part and the hooked-end element are systematically investigated. Further, the fiber bridging micromechanical mechanism and the bridging stress-displacement are accommodated. The fracture energy dissipation attributable to the hooked-end element is shown to be smaller than that of the straight element, but still remains significant. Comprehensive comparisons between the constant shear model predictions and experimental data manifest significant improvements when the hooked-end effects are incorporated into the composite fracture energy dissipation analyses. Based on the experimental data and micromechanical predictions, we recommend the range of the fiber volume fraction to be from 0.75% to 1%.