the critical fiber length
A short fiber embedded in a matrix is gripped only along its sides. Load does not jump into the fiber at its cut ends; it builds up gradually along the length through shear at the interface, like a nail held in wood, where the more length is gripped, the more you can pull before it slips. If the fiber is too short, it pulls out before it ever gets stressed enough to break.
The critical length lc is the minimum length that lets the fiber reach its full breaking stress before the interface gives way. It is lc = (sigma_f times d) / (2 times tau_c), where sigma_f is the fiber strength, d its diameter, and tau_c the matrix-fiber shear (bond or matrix yield) strength. Example: sigma_f = 3500 MPa, d = 10 micrometres, tau_c = 25 MPa gives lc = (3500 times 10)/(2 times 25) = 700 micrometres, that is 0.7 mm. Fibers much longer than lc (say more than 15 times lc) behave almost like continuous fibers; shorter ones carry less and mostly pull out.
This sets whether short chopped fibers reinforce well or just fill space. Continuous fibers (length much greater than lc) use the fiber's strength fully; sub-critical fibers pull out, which interestingly can add toughness by absorbing energy even as it lowers strength. Interface strength tau_c directly tunes lc: a stronger bond means a shorter critical length and better strength, but too strong a bond can make the composite brittle.
Injection-moulded short-glass-fiber nylon gears use fibers a few millimetres long, comfortably above the sub-millimetre critical length, so each fiber carries real load rather than just sitting inert.
Below the critical length a fiber pulls out; above it, the fiber can break at full strength.
A stronger interface lowers the critical length and raises strength, but it also removes the energy-absorbing pull-out that gives toughness, so the best bond is a compromise, not the strongest possible.