Question

Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt.% at a position of 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 C. Use the diffusion data for -Fe in Table 5.2

Answer 1

The carburizing time necessary to achieve a carbon concentration is 31.35 hours

How to find the Carburizing Time?

To determine the carburizing time necessary to achieve the given carbon concentration, we will use the equation:

(Cs - Cx)/(Cs - C0) = ERF(x/2√Dt)

where;

Cs is Concentration of carbon at surface = 0.90

Cx is Concentration of carbon at distance x = 0.30

Distance x = 4 mm = 0.004 m

C0 is 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 ,

Thus, plugging in the relevant values gives;

(Cs - Cx)/(Cs - C0) = (0.9 - 0.3)/(0.9 - 0.1)

= 0.6/0.8 = 0.75

now, ERF(z) = 0.75 and as such using ERF table, we can say that;

Z = 0.814. Thus;

(x/2√Dt) = 0.81

Using the table of diffusion data, we have;

At a temperature of  (1100°C) or 1373 K, we have;

D = 5.35 × 10⁻¹¹ m²/sec.

Calculating the carbonizing time by using the equation z = (x/2√Dt);

where;

t is carbonizing time

Thus;

0.814 = (0.004/(2 × √5.35 × 10⁻¹¹ × √t))

0.814 = 0.004 /(1.4628 × 10⁻⁵ × √t)

0.814 × 1.4628 × 10⁻⁵ × √t = 0.004

1.19072 × 10⁻⁵ × √t = 0.004  

√t = 0.004/(1.19072 × 10⁻⁵)

√t = 335.93

t = 112848.96 seconds

Converting to hours gives;

t = 112848.96/3600

t = 31.35 hours

Therefore, the carburizing time necessary to achieve a carbon concentration is 31.35 hours

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