Shear-Lag Fiber Pull-Out: Stress & Shear Profiles (2D)

Fiber & Interface

Fiber material

Embedded length L 200 μm

Interfacial shear strength τᵢ 30 MPa

Pull-test progress 0%

Live Readout

Ready

Pull force

0.00 mN

Displacement

0 μm

Peak force

0.00 mN

Shear-lag length 1/n

0 μm

How it works

This is a 2D closed-form shear-lag (Cox/Kelly) model, solved directly from the equilibrium ODE for the bonded (still-adhered) part of the embedded fiber, instead of the flat constant-force approximation often used for a quick estimate:

Shear-lag parameter:  n = sqrt( 2·Gₘ / (E_f·r² ·ln(R/r)) )
Bonded stress:   σ_f(ξ) = σₐ · cosh(n(L_b−ξ)) / cosh(n·L_b)
Interface shear: τ(ξ)   = (r·n/2) · σₐ · sinh(n(L_b−ξ)) / cosh(n·L_b)

ξ runs from the debond front (0) to the still-bonded embedded tip (L_b = L − a, where a is the debonded length). Debonding advances once τ at the front reaches the interfacial strength τᵢ; that condition is solved for σₐ at every debond length a, so — unlike a flat plateau — the force needed to keep the front moving actually rises as the bonded region shrinks (a real stress-concentration effect near full debond). Once a = L the fiber slides under constant kinetic friction τ_f ≈ 0.8τᵢ. If σₐ ever reaches the fiber's tensile strength before full debond, the fiber fractures instead of pulling out.

The right-hand plot shows the live σ_f(x) and τ(x) profiles across the current embedded length — this is the actual mechanism the force-displacement curve is integrated from, not a separate illustration.

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.

Bonded interface Debonded / sliding