Fiber Pull-Out: Interfacial Debonding & the Kelly-Tyson Model

Fiber & Interface

Fiber material

Embedded length L 200 μm

Interfacial shear strength τᵢ 30 MPa

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Pull force

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Displacement

0 μm

Peak force

0.00 N

Critical length L꜀

0 μm

How it works

This is the single-fiber pull-out test used to characterize a fiber-matrix interface. As the free end of the fiber is pulled, load enters the fiber only through interfacial shear stress τ over the embedded length L:

Debonding force:   F_d = τᵢ · π · d · L
Fiber break force: F_b = σ_fu · π · d² / 4
Critical length:   L꜀ = σ_fu · d / (4·τᵢ)

Three failure paths follow directly from comparing F_d to F_b:

L < L꜀ (pull-out): the interface debonds before the fiber can reach its breaking stress. A debond crack initiates at the loaded end and sweeps down the embedded length at roughly constant load F_d, then the fiber slides out under kinetic friction (τ_f ≈ 0.8τᵢ), so pull-out force falls linearly with the shrinking contact length: F = τ_f·π·d·(L − slip).
L > L꜀ (fracture): the shear-transferred load reaches the fiber's tensile strength before the interface fully debonds, so the fiber snaps in two instead of pulling out.
This is why short-fiber composites are engineered with L below L꜀ — a fiber that pulls out (rather than snaps) absorbs far more fracture energy, which is the main toughening mechanism in these materials.

Note: this single-ended-pull critical length is half the classic symmetric Kelly-Tyson value (L꜀,classic = σ_fu·d / 2τᵢ) used for a fiber loaded from both ends inside a bulk composite.

Controls: pick a fiber, set the embedded length and interfacial shear strength, then press Run — or drag the progress slider to scrub through the test by hand.

Matrix (fixed) Debonded / sliding zone

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