Chapter 5, Problem 5.60P

Interpretation Introduction

Interpretation:

The carbon content at 0.01 cm, 0.05 cm and 0.10 cm length surface after 1 hour needs to be calculated, if a carburizing process is formed on a 0.10 % C steel with 1.0 % C at 980⁰Cand if the iron is FCC.

Concept introduction:

Fick's second law equation based on boundary condition is given by the following relation:

$\frac{Cs-Cx}{Cs-Co}=erf(\frac{x}{2\sqrt{Dt}})$

Here,

Cs = constant concentration of diffusion atom

Cx = diffusion concentration atom at location x

Co = initial concentration of diffusion atom

T = time

D = diffusion coefficient

Also, diffusion coefficient according to Arrhenius type equation is given as follows:

$D=Do\exp (\frac{-Q}{RT})$

Here,

D = diffusion coefficient

Do = constant

Q = activation energy

R = gas constant

T = absolute temperature