Estimate hardened layer depth using temperature, diffusion, and time. Compare treatment assumptions confidently. Support stronger engineering decisions with faster case depth estimates.
The chart uses the simplified diffusion-based depth model across time.
| Component | Temperature (°C) | Time (h) | Simple Depth (mm) | Recommended Depth (mm) |
|---|---|---|---|---|
| Gear Pin | 880 | 2 | 0.65 | 0.71 |
| Cam Follower | 900 | 3.5 | 0.91 | 0.98 |
| Shaft Sleeve | 920 | 4 | 1.02 | 1.11 |
| Drive Collar | 940 | 5 | 1.18 | 1.3 |
1. Arrhenius diffusion coefficient
D = D₀ × exp(-Q / R T)
Where D is diffusion coefficient, D₀ is diffusion constant, Q is activation energy, R is the gas constant, and T is absolute temperature.
2. Simplified case depth estimate
x = k × √(D × t)
Where x is case depth, k is an empirical factor, D is diffusion coefficient, and t is time in seconds.
3. Carbon criterion depth estimate
x = 2 × z × √(D × t)
Here z is based on the chosen surface, core, and case criterion carbon levels. This improves the estimate when a composition threshold defines effective case depth.
4. Required time from target depth
t = (x / k)² / D
This inverse form estimates treatment time for a desired hardened depth.
It estimates case hardening depth or required treatment time using diffusion-based engineering formulas. It also shows diffusion coefficient, carbon-threshold depth, and a recommended value for practical comparison.
Effective case depth is the distance from the surface to the point where hardness or carbon concentration falls to a selected criterion. Shops often define it using a hardness threshold such as 50 HRC.
Temperature strongly changes diffusion rate. A small increase in temperature can significantly raise the diffusion coefficient, which increases estimated case depth and can reduce required treatment time.
The factor k is an empirical adjustment for the simplified depth model. It helps align the equation with process experience, alloy behavior, furnace conditions, and the depth definition used in your operation.
This tool is useful for engineering estimates, but real outcomes vary by alloy, atmosphere, quench practice, grain size, and prior microstructure. Validate results with your material data and shop trials.
D₀ is the pre-exponential diffusion constant used in the Arrhenius equation. Together with activation energy, it determines the diffusion coefficient at the selected treatment temperature.
The simple result uses a direct engineering depth model. The carbon-based result adds a concentration criterion. Showing both helps compare a quick estimate against a threshold-oriented estimate.
No. Treat it as a planning and comparison tool. Final production approval should rely on metallographic measurement, hardness traverse testing, process qualification, and applicable specifications.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.