What Is the Fick's Second Law Case Hardening Diffusion Calculator?
Fick's second law predicts how diffusion causes concentration to change across spatial coordinates over time.
For steel carburizing, it dictates how deeply carbon penetrates during furnace soak cycles.
How Does the Fick's Second Law Case Hardening Diffusion Calculator Work?
Calculates temperature-dependent diffusion coefficient D using the Arrhenius relationship.
Computes diffusion length 2*sqrt(D*t).
Evaluates the Gaussian error function erf(z) to find local carbon weight percentage at specified depth.
Fick's Second Law Case Hardening Diffusion Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Non-steady-state Fickian diffusion analytical solution for semi-infinite solid with constant surface boundary concentration.
How to Use the Fick's Second Law Case Hardening Diffusion Calculator
- Enter surface carbon potential and baseline steel core carbon content.
- Provide carburizing temperature in °C and cycle duration in hours.
- Specify the target depth in millimeters.
Step-by-Step Example Calculation
AISI 8620 Gear Tooth Carburizing
Input Values:
Understanding Your Result
Concentration at depth indicates exact carbon percentage at the specified distance beneath the surface.
Effective case depth is typically defined as the depth where carbon drops to 0.40 wt% (or 50 HRC hardness).
Factors That Affect the Result
- Temperature: Diffusion rates increase exponentially with temperature (Arrhenius), dramatically accelerating carburizing.
- Time: Case depth scales with square root of time (sqrt(t)); doubling depth requires quadrupling furnace cycle time.
When Should You Use This Calculator?
- Specifying furnace cycle times and recipe parameters in heat treatment shops.
- Designing surface-hardened pinions, shafts, gears, and bearing races.
Assumptions & Limitations
- Assumes 1D diffusion into semi-infinite planar geometry without edge/corner effects.
- Assumes diffusion coefficient D is independent of local carbon concentration.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard metallurgical diffusion model validated by ASTM surface hardening standards.