In-Situ Distribution
Fiber orientation changes how the hook is mobilized
Not every fiber crosses a crack at 90 degrees. Mixing, pumping, concrete flow, formwork geometry, and casting direction create statistical fiber orientation distributions throughout the element.
An inclined hooked-end fiber does not pull out in the same way as an orthogonally aligned fiber. Research on deformed steel fibers confirms that embedded angle materially alters the pullout curve, inducing localized matrix spalling at the crack mouth before full hook engagement.
This orientation effect is particularly pronounced in thin slabs, tunnel linings, shotcrete layers, and narrow precast sections where boundary constraints force 2D planar alignment.
Embedment length changes available bond mechanisms
The hook is not the only source of resistance. The straight embedded portion carries interfacial shear and friction. Because fibers are randomly dispersed across the fracture plane, embedment lengths vary statistically.
The structural design response is not to assume every fiber achieves theoretical maximum pullout. It is to ensure a sufficient, well-distributed fiber count and qualify the finished composite through standardized flexural tests.