MY SIMULATOR

English Blacksmith: Case-Hardening Lab

Pack the iron in charcoal. Let the carbon creep in.

INTERACTIVE 3D

Virtual smithy with an illustrative model. Not forging or heat-treatment instructions; never heat metal without proper training and safety equipment.

Iron temperature

20°C

Bellows

Packing

Lab & science

Drag to orbit, wheel / pinch to zoom. Space = start / pause, Q = quench, R = reset. The clock is sped up: set how many simulated minutes pass per real second.

Presets

Clock speed

Quench in

Camera

Graphics (High on every device; Low = 1x pixel ratio, smaller shadows)

Live readout (model values)

Strip: surface on the left, centre of the stock on the right (3 mm). Darker = more carbon.

Missions

Mission 5: carbon diffuses with D = 8.4e-12 m2/s at 925 C. After 4 h, what is 2 sqrt(D t) in millimetres?

The science

What you see

A low-carbon iron horseshoe lies in a closed iron box packed with charcoal on a blown hearth. Above about 800 C the iron is austenite and can dissolve carbon, which creeps in from the surface. Quenched, the carbon-rich skin turns hard martensite while the low-carbon core stays tough. The strip shows where the carbon went.

Equations

Fire (bellows a = 0..1)   T_fire,eq = 200 + 950 a  (C);  dT_fire/dt = (T_eq - T_fire)/90 s
Piece, lumped heating     dT/dt = (T_fire - T)/tau ,   tau = 540 s  (exact exponential step)
Diffusivity (Arrhenius)   D = D0 exp(-Q/(R T)),  D0 = 2.3e-5 m2/s,  Q = 148 kJ/mol,  T in K
Fick's second law         dC/dt = D d2C/dx2 ,   C(0) = Cs when packed and T >= 800 C,  dC/dx = 0 at the centre
Closed form (constant D)  C(x,t) = Cs - (Cs - C0) erf( x / (2 sqrt(D t)) )
Case depth (C = 0.4 %)    x_c = 2 sqrt(D t) erf^-1((Cs - 0.4)/(Cs - C0))   (grows as sqrt(t))
Surface carbon            Cs = min(pack potential, A_cm(T)),  A_cm = 0.77 + 0.00319 (T - 727) wt%
Hardness (as quenched)    HRC_max = min(66, 20 + 46 sqrt(C)),  air/soft: 8 + 28 sqrt(C)
                          blended by the austenitised fraction f = (T - 727)/(800 - 727), clamped 0..1

Assumptions & honest simplifications

One-dimensional diffusion into a flat 6 mm stock; corners, the nail holes and the curved shoe geometry are not modelled. Below 727 C the model treats carbon as frozen.
The fire temperature, the heating time constant, the pack potential (1.0 / 0.7 wt%) and the hardness fits are illustrative round numbers, not measurements; the Arrhenius constants are typical textbook values for carbon in austenite [verify before real use].
No decarburisation, no carbide network, no tempering, no distortion, no real quench-cooling-rate model: hardness is a simple function of carbon and austenitising. The cracking flag is a rule of thumb.
Real packs use energisers and strict process control; this page is about the physics of diffusion, not about how to run a forge.

Independent numerical checks

Also in node: node check.js.

Sources

Fick's laws and the erf solution for carburising: standard materials-science texts (e.g. Callister, Materials Science and Engineering, diffusion chapter; Porter and Easterling, Phase Transformations in Metals and Alloys). Carbon-in-austenite D0 and Q: typical tabulated values. Fe-C solubility line A_cm and A1 = 727 C: the iron-carbon phase diagram. Hardness-vs-carbon relation is a simplified fit [verify against a handbook before any use].

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