Fiber Composite Stiffness & Failure Lab

Fiber Material

Load Direction

Fiber volume fraction 45%

Applied strain ε 0.00%

Effective modulus Ec

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Composite stress σc

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Fiber stress σf

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Matrix stress σm

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How it works

A fiber-reinforced composite behaves like two springs sharing a load — but which way they share it depends on whether the pull runs along the fibers or across them. Loading longitudinal to the fibers forces both phases to stretch by the same amount (iso-strain), so the stiff fiber grabs almost all the stress. Loading transverse to the fibers forces both phases to carry the same stress (iso-stress), so the soft matrix does nearly all the stretching — which is why composites are dramatically weaker across the fiber direction than along it.

Voigt (‖, iso-strain):  Ec = Vf·Ef + Vm·Em      σf = Ef·ε   σm = Em·ε
Reuss (⟂, iso-stress):  1/Ec = Vf/Ef + Vm/Em    εf = σ/Ef   εm = σ/Em
σc = Ec·ε   —   fails when either phase reaches its own ultimate strain

Fiber material — carbon is stiffest but most brittle (fails near 1.5% strain); glass is more compliant but stretches further before cracking; aramid sits between the two.
Load direction — toggling ‖/⟂ switches the model between Voigt (rule-of-mixtures upper bound) and Reuss (lower bound), the two textbook limits on composite stiffness.
Fiber volume fraction Vf — more fiber raises longitudinal stiffness almost linearly, but has a much smaller effect transverse, since the compliant matrix still governs the load path.
Applied strain — ramps the pull; the bar cracks red at whichever phase — fiber or matrix — hits its ultimate strain first, exactly as first-ply-failure theory predicts.

Real-world relevance: this fiber/matrix load-sharing asymmetry is why aircraft wing skins and bike frames are laid up with fibers running along the main stress path, and why cross-ply or woven layups exist — a single ply is strong in one direction and weak 90° from it.

Elastic

Matrix (epoxy) Fiber — low stress Fiber — near failure

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