Carbon Nanotube Crack-Bridging in Nanoconcrete

Crack Loading

Crack opening displacement 60 nm

Nanotube Bridging

Areal CNT density 15 /µm²

Interfacial shear strength τ 20 MPa

CNT diameter 16 nm

Live Readouts

Bridging stress σ

0.0 MPa

Toughening energy G

0.0 J/m²

Fiber state at this COD

—

bonded (elastic) frictional pullout ruptured

How it works

Each carbon nanotube crossing a nanoscale crack in the cement matrix behaves like a shear-lag pullout fiber. As the crack opening displacement δ grows, a bridging tube slides a distance s = δ / cos θ along its own axis (θ = inclination to the crack normal):

Elastic (bonded) stage, s ≤ s_deb:
  F(s) = k·s,   F(s_deb) = F_bond = τ·π·d·L_e·e^(f·θ)

Frictional pullout stage, s > s_deb:
  L_e(s) = L_e0 − (s − s_deb)
  F(s)   = 0.7τ·π·d·L_e(s)·e^(f·θ)

Rupture criterion (checked at debonding):
  F_bond > F_rupture = σ_CNT·π·d²/4  →  tube snaps instead of sliding

τ is the CNT–cement interfacial shear strength, d the tube diameter, L_e the embedded length on the shorter side, e^(f·θ) a snubbing factor for inclined tubes (f ≈ 0.7), and σ_CNT ≈ 30 GPa a fixed single-wall tensile strength. Summing the axial force's opening-direction component over every tube per unit crack area gives the crack-bridging stress:

σ_bridge(δ) = Σᵢ F_i(δ)·cos θᵢ / A_crack
G(δ) = ∫₀^δ σ_bridge(δ') dδ'   (toughening energy)

Crack opening displacement — widens the crack; tubes stretch elastically, then debond and slide, then either rupture or fully pull out.
Areal CNT density — how many nanotubes cross a unit area of the crack face; more tubes raise bridging stress but each carries the same load.
Interfacial shear strength τ — bond quality between tube and cement paste; higher τ raises pullout capacity but also raises the odds of rupture instead of sliding.
CNT diameter — bigger tubes have more bonded surface (∝ d) but the rupture load grows faster (∝ d²), so thick tubes tend to pull out rather than snap.

This crack-bridging mechanism — not just stiffer bulk material — is why adding a small mass fraction of multiwall carbon nanotubes to cement paste ("nanoconcrete") measurably increases fracture toughness and delays crack growth in real structural tests.

drag to orbit · scroll to zoom

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.