Question

Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt% at a position 4 mm into an iron–carbon alloy that initially contains 0.10 wt% C. The surface concentration is to be maintained at 0.90 wt% C, and the treatment is to be conducted at 1100°C. Use the diffusion data for γ-Fe in Table 5.2. please show equations used and calculations thank you for your help

Answer 1

We need to find out the carburizing time necessary to achieve the given carbon concentration. So, we need to use the following equation:

(C_s - C_x) / (C_s - C₀) = ERF( x / 2√Dt)

where, C_s -> Concentration of carbon at surface = 0.90

   C_x -> Concentration of carbon at distance x = 0.30 ; x in this case is 4 mm

C₀ -> Initial concentration of carbon = 0.10

ERF() = Error function at the given value

D = Diffusion of Carbon into steel

t = Time necessary to achieve given carbon concentration

Now,

(C_s - C_x) / (C_s - C₀) = (0.9 - 0.3) / (0.9 - 0.1)

= 0.6/0.8

= 0.75

ERF(z) = 0.75; using ERF table we can say that

z ~ 0.81; which means ( x / 2√Dt) = 0.81

Using the table of disffusion data

D = 5.35 * 10-11 m²/sec at 1373 K

Now solving the above equatio for t;

2√Dt = 0.81/0.004

= 0.00493 m^-1

√Dt = 0.0024 m^-1

Dt = 6.096 * 10^-6 m^-2

t = 113955.731 seconds

t = 31.65 hours