Calculator Inputs
This tool assumes constant surface carbon, constant temperature, and one-dimensional diffusion inside steel.
Carbon Profile Graph
Formula Used
For simplified carburization, the page uses Fick’s second law with constant surface carbon and semi-infinite geometry.
C(x,t) = C₀ + (Cₛ − C₀) × erfc[x / (2√(Dt))]
D = D₀ × exp[−Q / (RT)]
x = 2√(Dt) × erfc⁻¹[(Cₓ − C₀) / (Cₛ − C₀)]
t = {x / [2 × erfc⁻¹((Cₓ − C₀) / (Cₛ − C₀))]}² / D
Symbols: C₀ is core carbon, Cₛ is surface carbon, Cₓ is carbon at depth, D is diffusivity, D₀ is pre-exponential diffusivity, Q is activation energy, R is the gas constant, and x is depth.
How to Use This Calculator
- Select the calculation mode that matches your task.
- Choose a diffusion preset or enter custom diffusivity values.
- Enter furnace temperature, carbon levels, and depth or time.
- Press calculate to show the result above the form.
- Review the graph to inspect the full carbon profile.
- Download the result summary as CSV or PDF.
- Compare runs by changing temperature, target carbon, or depth.
- Use shop data to refine D₀ and activation energy.
Example Data Table
| Run | Temperature °C | Time h | Surface wt% C | Core wt% C | Target wt% C | Depth mm |
|---|---|---|---|---|---|---|
| 1 | 900 | 6.0 | 1.00 | 0.20 | 0.40 | 0.55 |
| 2 | 920 | 7.5 | 1.05 | 0.20 | 0.40 | 0.68 |
| 3 | 930 | 8.0 | 1.10 | 0.20 | 0.40 | 0.77 |
| 4 | 950 | 10.0 | 1.20 | 0.25 | 0.45 | 0.95 |
| 5 | 980 | 12.0 | 1.15 | 0.20 | 0.40 | 1.18 |
FAQs
1. What does this calculator estimate?
It estimates effective case depth, required soak time, or carbon concentration at a selected depth using a simplified diffusion model.
2. Which physical model does it use?
It uses the constant-surface-concentration solution to Fick’s second law with an Arrhenius diffusivity term for temperature dependence.
3. Why do I need surface and core carbon?
Those values define the diffusion driving force. The target carbon must stay between them for valid case depth and soak time estimates.
4. Can I use custom diffusivity values?
Yes. Select the custom preset, then enter your own D₀ and activation energy values from plant trials, literature, or metallurgical data.
5. Does this replace furnace qualification work?
No. It is a planning tool. Actual results also depend on atmosphere control, alloy chemistry, grain size, and quench response.
6. Why is the graph useful?
The graph shows the carbon gradient through the case. It helps compare different temperatures, times, and target depths quickly.
7. Which units are supported?
The page accepts depth in millimeters, micrometers, or inches. Temperature is entered in degrees Celsius, and time is entered in hours.
8. When should I avoid this simplified model?
Avoid it when carbon potential changes strongly, geometry is thin, or alloy effects require concentration-dependent diffusion modeling.