Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN: 9781111988609
Author: Charles Gilmore
Publisher: Cengage Learning
Question
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Chapter 5, Problem 5.17P

(a)

To determine

The phases present and the weight fraction of each phase after the procedure.

(a)

Expert Solution
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Answer to Problem 5.17P

The phases present is α+Fe3C and the weight fraction of α phase and Fe3C phase after the procedure is 0.96 and 0.04 respectively.

Explanation of Solution

Draw the phase diagram for Iron carbon alloy as shown below:

  Materials Science And Engineering Properties, Chapter 5, Problem 5.17P

Refer to Above figure; when 0.30%C carbon steel is heated to 1000°C the phase of alloy is γ solid region and when it cool down slowly the proeutectoid α phase tends to form to the temperature of 780°C . The remaining γphase converted to proeutectoid α phase by the temperature of 727°C .

At 600°C the phase of alloy is in α+Fe3C region. From above diagram the chemical composition of α phase is approximated as 0 wt% of C and chemical composition of Fe3C is 6.67 wt% of C .

Write the expression for weight fraction of α phase by lever rule.

  fα=C Fe3CC0C Fe3CCα   ........... (1)

Here, fα is weight fraction of α phase, C0 is the original composition of alloy, CFe3C is the composition of Fe3C and Cα is the composition of α phase.

Write the expression weight fraction for Fe3C phase by lever rule.

  fFe3C=1fα   ........... (2)

Here, fFe3C is the weight fraction for Fe3C phase.

Calculation:

Substitute 6.67 for CFe3C , 0.33 for C0 and 0 for Cα in equation (1).

  fα=6.670.336.670=0.96

Substitute 0.96 for fα in equation (2).

  f Fe3C=10.96=0.04

Thus, the phases present is α+Fe3C and the weight fraction of α phase and Fe3C phase after the procedure is 0.96 and 0.04 respectively.

(b)

To determine

The approximate weight fraction of alloy in proeutectoid α phase and the weight fraction of pearlite phase.

(b)

Expert Solution
Check Mark

Answer to Problem 5.17P

The approximate weight fraction of alloy in proeutectoid α phase is 0.63 and the weight fraction of pearlite phase is 0.37 .

Explanation of Solution

Refer to the phase diagram of iron-carbon alloy the chemical composition of α phase little above the temperature of 727°C is 0.02 wt% of C and the chemical composition of Fe3C phase is 0.77wt%of C .

Write the expression for weight fraction of αProeutectiod phase by lever rule.

  fαPro=CγC0CγCα   ........... (3)

Here, fαPro is weight fraction of αProeutectiod phase and Cγ is the composition of Pearlite phase.

Write the expression weight fraction for Pearlite phase by lever rule.

  fγ=1fαPro   ........... (4)

Here, fFe3C is the weight fraction for Pearlitephase.

Calculation:

Substitute 0.77 for Cγ , 0.30 for C0 and 0.02 for Cα in equation (3).

  fαPro=0.770.300.770.02=0.63

Substitute 0.63 for fαPro in equation (4).

  fγ=10.63=0.37

Thus, the approximate weight fraction of alloy in proeutectoid α phase is 0.63 and the weight fraction of pearlite phase is 0.37 .

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