Flexural Crack Bridging Across Loading Stages in Hybrid Steel Fiber Mortar Prepared with a Magnetic Field: A Model of Orientation and Dispersion

Fiber scale, dosage, and preparation govern flexural crack bridging in mortar reinforced with steel fibers. Straight fine steel fibers (FSF, 16 mm) and common steel fibers (CSF, 30 mm) were evaluated by central point flexural testing of mortars containing a single fiber type and 1.60 vol.% hybrid mortars prepared through magnetic field treatment (A) and vibration (R). Corrected nominal stress, residual stress at common machine displacements, work partitioned by loading stage, digital image correlation (DIC), fracture surface observations, scanning electron microscopy (SEM), and a multiscale bridging model of orientation and dispersion were combined. Among the tested contents, performance with a single fiber type peaked at 0.80% FSF and 1.60% CSF. The A route increased peak stress by 15.3–45.3% in mixtures containing a single fiber type and 18.7–34.9% in hybrids, with larger gains in late stress and cumulative energy. The CSF:FSF = 2:1 A mixture reached a peak stress of 26.26 MPa and cumulative flexural energy of 17.06 N·m, exceeding baselines calculated using the rule of mixtures under matched preparation conditions by 40.2% and 60.9%, respectively. Responses at common displacements and qualitative image observations supported stronger early bridging by FSF and more persistent bridging by CSF at large crack openings. The model connects effective fiber populations, single-fiber forces, bridging traction, and sectional response to explain the contributions of the two fiber scales during loading. These results reveal complementarity between FSF and CSF across loading stages and interactions that vary with composition.