Hydrogen Embrittlement of Steel (2D Cross-Section)

Steel Grade

Loading Conditions

Applied stress σ 300 MPa

Environmental H₂ 10 ppm

Temperature 300 K

Live Readouts

Crack length a

2.0 mm

Stress intensity K

11.9 MPa√m

H at crack tip

0 ppm

Threshold K_TH

28.0 MPa√m

Elapsed time

0.0 h

Status

Stable

How it works

Hydrogen-enhanced decohesion (HEDE): atomic hydrogen dissolved in steel diffuses down the hydrostatic stress gradient ahead of a crack tip, where lattice dilation traps it (Oriani equilibrium). Once trapped there in enough concentration, it weakens interatomic bonding and lowers the stress intensity needed to grow the crack — a component can fail at a fraction of its dry design stress. This 2D cross-section view shows the same crack-plane physics as the 3D lattice model, seen edge-on.

Trapped H at tip (relaxes toward equilibrium):
  C_eq = C0 · exp(σh·V_H / R·T)        Oriani/Sievert
  dC/dt = (C_eq − C_tip) / τ,  τ = r_p² / D(T)
  D(T)  = D0 · exp(−Q / R·T)            Arrhenius diffusion

Crack driving force:
  K = σ·√(π·a)                          stress intensity factor
  r_p = K² / (2π·σ_ys²)                 crack-tip plastic zone

Hydrogen lowers the growth threshold:
  K_TH(C_tip) = K_TH0 · exp(−γ·C_tip)   HEDE threshold drop
  da/dt = A·(K − K_TH)²  if K > K_TH, else 0
  Fracture also triggers outright if K ≥ K_IC (dry toughness)

Steel grade — high-strength steel has a higher yield stress (smaller plastic zone, so hydrogen concentrates faster) and a lower baseline toughness, making it far more embrittlement-prone than mild steel — exactly the trend seen in real pipeline and fastener failures.
Applied stress — raises both the crack-driving K and the hydrostatic stress that pulls hydrogen toward the tip.
Environmental H₂ — sets the background dissolved-hydrogen level (from gas exposure, cathodic charging, or corrosion) that the tip equilibrates toward.
Temperature — raises the diffusion coefficient (faster hydrogen delivery) but also lowers the Oriani stress-trapping enhancement, so embrittlement peaks near room temperature and fades toward the extremes.

This is why hydrogen pipelines, storage vessels, and refuelling infrastructure specify low-hydrogen-susceptibility steels and limit yield strength — a real constraint on how "cheap" H₂ transport hardware can be built.

⚠ CRACK PROPAGATED TO FAILURE

Iron lattice Hydrogen atoms Crack / notch

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