The outer surface of a steel alloy is to be hardened by increasing its carbon co

Question

The outer surface of a steel alloy is to be hardened by increasing its carbon content. The carbon is to be supplied from an external carbon-rich atmosphere, which is maintained at an elevated temperature. A diffusion heat treatment at 841°C for 13 min increases the carbon concentration to 0.77 wt% at a position 1.6 mm below the surface. Estimate the diffusion time required at 620°C to achieve this same concentration also at a 1.6 mm position. Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. The preexponential and activation energy values for the diffusion of carbon in the iron are 6.5 × 10-7 m2/s and 70.8 kJ/mol, respectively.

Explanation / Answer

Calculate diffusion coefficient at 841 ° C (1114 K)

D1 = D0 exp (-Qd/RT)

= 6.5 × 10^-7 m2/s × exp (-70.8*1000/8.314*1114)

= 3.113 x 10^-10 m2/s

Calculate diffusion coefficient at 620 ° C (893 K)

D2 = D0 exp (-Qd/RT)

= 6.5 × 10^-7 m2/s × exp (-70.8*1000/8.314*893)

= 4.693 x 10^-11 m2/s

Time required in diffusion process is inversely proportional to the diffusion coefficient

D1 x t1 = D2 x t2

t2 = D1 x t1 / D2

= (3.113 x 10^-10 m2/s x 13 min) / (4.693 x 10^-11 m2/s)

= 86.23 min

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