Use defining equation for the carbon profile from the surface:

where

Cx,t	is the carbon concentration at a distance x (in m) from the surface at a time t (in seconds)
C0	is the carbon concentration of the bulk steel (typically a low C steel · 0.15 wt% C)
Cs	is the surface carbon concentration (typically 0.6 ® 0.8 wt% C use 0.7)
D	is the diffusion coefficient of carbon in steel (in cm2 s-1)

The diffusion coefficient depends on temperature according to D=D₀ exp(-Q/RT)

where

D0	is 0.15 cm2 s-1 in austenite
Q	is the activation energy of diffusion, 135 KJ mol-1 in austenite
R	is the gas constant, 8.314 J K-1 mol-1
T	is temperature in K

 

The case depth can be defined as the distance below the surface at which a carbon concentration of

(C_s+C₀)/2

is reached. Carburising is capable of producing a wide range of case depths and gives a high surface hardness whilst maintaining a high toughness central steel core. Distortion following quenching can be a problem and a lower carburising temperature can be used to try to minimise the problem. The degree of distortion will also be affected by the quenching medium selected (i.e. the severity of the quench). Alternatively if a high carburising temperature is required to give sufficient case depth in an economical time the component can be air cooled and then reheated to a lower temperature (for example 840°C) prior to quenching.